%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV844-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:27:31 PM UTC 2026
% Result : Unsatisfiable 1.77s 2.73s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1043)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_fold__image__insert_0,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X1),X2,X1,X3),X4),c_Set_Oinsert(X5,X6,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(X2,X5)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X1),X2,X1,X3),X4),X6))
| hBOOL(c_in(X5,X6,X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ c_Finite__Set_Ofinite(X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__image__insert_0) ).
cnf(cls_fold__image__def_0,axiom,
c_Finite__Set_Ofold__image(X1,X2,X3,X4) = c_Finite__Set_Ofold(c_COMBB(X1,X2,X3,tc_fun(X3,X3),X4),X4,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__image__def_0) ).
cnf(cls_comm__monoid__add_Ofold__image__insert_0,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,X1,X3),X4),c_Set_Oinsert(X5,X6,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X2,X5)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,X1,X3),X4),X6))
| hBOOL(c_in(X5,X6,X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__image__insert_0) ).
cnf(cls_ab__semigroup__mult_Ofold__image__insert_0,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3,X4),X5),c_Set_Oinsert(X6,X7,X4)) = hAPP(hAPP(X1,hAPP(X2,X6)),hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3,X4),X5),X7))
| hBOOL(c_in(X6,X7,X4))
| ~ c_Finite__Set_Ofinite(X7,X4)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__image__insert_0) ).
cnf(cls_fold__image__empty_0,axiom,
hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3,X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__image__empty_0) ).
cnf(cls_escape_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X4,X3)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X3),c_COMBK(hAPP(X4,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X4,X3)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_1) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P_H,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_conseq_2,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X2,X4,X3,X5,X6)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_2) ).
cnf(cls_hoare__derivs_Ointros_I6_J_2,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X4,X3,X5,X6)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
cnf(cls_conjecture_3,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P_H,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_card__Diff2__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1)),c_Finite__Set_Ocard(X2,X1)))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff2__less_0) ).
cnf(cls_hoare__derivs_Ointros_I6_J_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X4,X3,X7,X5)))
| ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X2,X4,X3)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X3),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
cnf(cls_conseq_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X2,X4,X3,X7,X5)))
| ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X2,X4,X3)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X3),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_1) ).
cnf(cls_fold__graph__permute__diff_0,axiom,
( c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,c_Set_Oinsert(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X4),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1),X5,X1,X1)
| hBOOL(c_in(X3,X4,X1))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ hBOOL(c_in(X2,X4,X1))
| ~ c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X3,X4,X5,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__permute__diff_0) ).
cnf(cls_comm__monoid__add_Ofold__graph__permute__diff_0,axiom,
( c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,c_Set_Oinsert(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X4),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1),X5,X1,X1)
| hBOOL(c_in(X3,X4,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(c_in(X2,X4,X1))
| ~ c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X3,X4,X5,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__permute__diff_0) ).
cnf(cls_ab__semigroup__mult_Ofold__graph__permute__diff_0,axiom,
( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X4,tc_bool)),X5),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)),X4),X6,X4,X4)
| hBOOL(c_in(X3,X5,X4))
| ~ hBOOL(c_in(X2,X5,X4))
| ~ c_Finite__Set_Ofold__graph(X1,X3,X5,X6,X4,X4)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__permute__diff_0) ).
cnf(cls_less__add__iff1_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
cnf(cls_le__add__iff1_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
cnf(cls_fold__graph_H_Ointros_I2_J_0,axiom,
( c_Nitpick_Ofold__graph_H(X1,X2,X3,hAPP(hAPP(X1,X4),X5),X6,X7)
| ~ c_Nitpick_Ofold__graph_H(X1,X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X6,tc_bool)),X3),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6)),X5,X6,X7)
| ~ hBOOL(c_in(X4,X3,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).
cnf(cls_Diff1__fold__graph_0,axiom,
( c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X5),X6,X7)
| ~ hBOOL(c_in(X4,X3,X6))
| ~ c_Finite__Set_Ofold__graph(X1,X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X6,tc_bool)),X3),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6)),X5,X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
cnf(cls_fold__graph__insert__swap_0,axiom,
( c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,c_Set_Oinsert(X3,X4,X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5),X1,X1)
| hBOOL(c_in(X3,X4,X1))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X3,X4,X5,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__insert__swap_0) ).
cnf(cls_comm__monoid__add_Ofold__graph__insert__swap_0,axiom,
( c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,c_Set_Oinsert(X3,X4,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X5),X1,X1)
| hBOOL(c_in(X3,X4,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X3,X4,X5,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__insert__swap_0) ).
cnf(cls_ab__semigroup__mult_Ofold__graph__insert__swap_0,axiom,
( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,X4,X5),hAPP(hAPP(X1,X2),X6),X5,X5)
| hBOOL(c_in(X3,X4,X5))
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X6,X5,X5)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__insert__swap_0) ).
cnf(cls_fold__graph_OinsertI_0,axiom,
( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,X4,X5),hAPP(hAPP(X1,X3),X6),X5,X7)
| hBOOL(c_in(X3,X4,X5))
| ~ c_Finite__Set_Ofold__graph(X1,X2,X4,X6,X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
cnf(cls_image__diff__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,X5,X4,X1))),c_Set_Oimage(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X4,tc_bool)),X3),X5),X4,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
cnf(cls_less__add__iff1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
cnf(cls_le__add__iff1_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
cnf(cls_setsum__left__distrib_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetsum(X2,X3,X4,X1)),X5) = c_Finite__Set_Osetsum(hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X4),X4,X1,X1),X5),X3,X4,X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
cnf(cls_image__Int__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5),X3,X1)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X4,X3,X1)),c_Set_Oimage(X2,X5,X3,X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
cnf(cls_less__add__iff2_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
cnf(cls_le__add__iff2_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
cnf(cls_empty__fold__graphE_0,axiom,
( X1 = X2
| ~ c_Finite__Set_Ofold__graph(X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X1,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
cnf(cls_fold__graph__imp__finite_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofold__graph(X3,X4,X1,X5,X2,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
cnf(cls_less__add__iff2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
cnf(cls_le__add__iff2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
cnf(cls_setsum__subtractf_0,axiom,
( c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),c_Finite__Set_Osetsum(X2,X5,X3,X1)),c_Finite__Set_Osetsum(X4,X5,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__subtractf_0) ).
cnf(cls_setsum__addf_0,axiom,
( c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,X5,X3,X1)),c_Finite__Set_Osetsum(X4,X5,X3,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__addf_0) ).
cnf(cls_Un__Int__crazy_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
cnf(cls_card__bij__eq_0,axiom,
( c_Finite__Set_Ocard(X1,X2) = c_Finite__Set_Ocard(X3,X4)
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_Set_Oimage(X5,X3,X4,X2)),X1))
| ~ c_Fun_Oinj__on(X5,X3,X4,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X6,X1,X2,X4)),X3))
| ~ c_Fun_Oinj__on(X6,X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).
cnf(cls_setsum__Un_0,axiom,
( c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)),c_Finite__Set_Osetsum(X2,X5,X3,X1))),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5),X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un_0) ).
cnf(cls_fun__upd__twist_0,axiom,
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X7,X4,X5) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X6,X7,X4,X5),X2,X3,X4,X5)
| X2 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
cnf(cls_inj__on__insert_1,axiom,
( ~ hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X3,X5),X5))
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X4,X3),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
cnf(cls_inj__on__Un_3,axiom,
( c_Fun_Oinj__on(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),X5),X3,X1)),c_Set_Oimage(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X5),X4),X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Fun_Oinj__on(X2,X5,X3,X1)
| ~ c_Fun_Oinj__on(X2,X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
cnf(cls_conseq12_2,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq12__1(X2,X5,X4,X6)),v_sko__Hoare__Mirabelle__Xconseq12__3(X2,X5,X4,X6)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_2) ).
cnf(cls_finite__range__imageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X1,X2,X3,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4),X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).
cnf(cls_psubset__insert__iff_9,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).
cnf(cls_image__vimage__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,c_Set_Ovimage(X2,X3,X4,X1),X4,X1)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
cnf(cls_card__Diff1__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1)),c_Finite__Set_Ocard(X2,X1)))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__less_0) ).
cnf(cls_psubset__insert__iff_8,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).
cnf(cls_fold__graph_H_Ointros_I1_J_0,axiom,
c_Nitpick_Ofold__graph_H(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
cnf(cls_fold__graph_OemptyI_0,axiom,
c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
cnf(cls_inj__image__Compl__subset_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4),X3,X1)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X4,X3,X1))))
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__Compl__subset_0) ).
cnf(cls_psubset__insert__iff_5,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
cnf(cls_card__Diff1__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1)),c_Finite__Set_Ocard(X2,X1)))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__le_0) ).
cnf(cls_inj__image__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X5,X2,X1,X4)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ c_Fun_Oinj__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
cnf(cls_subset__insert__iff_4,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
cnf(cls_psubset__insert__iff_4,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
cnf(cls_subset__insert__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
cnf(cls_diff__single__insert_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
cnf(cls_conseq12_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq12__1(X2,X5,X4,X6)),v_sko__Hoare__Mirabelle__Xconseq12__2(X2,X5,X4,X6)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_0) ).
cnf(cls_setsum__Un__Int_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1)),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5),X3,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)),c_Finite__Set_Osetsum(X2,X5,X3,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__Int_0) ).
cnf(cls_fun__upd__upd_0,axiom,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2,X6,X4,X5) = c_Fun_Ofun__upd(X1,X2,X6,X4,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
cnf(cls_fun__upd__image_0,axiom,
( c_Set_Oimage(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5) = c_Set_Oinsert(X3,c_Set_Oimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X4,tc_bool)),X6),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)),X4,X5),X5)
| ~ hBOOL(c_in(X2,X6,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
cnf(cls_vimage__subsetI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Ovimage(X2,X3,X1,X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),c_Set_Oimage(X2,X5,X1,X4)))
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
cnf(cls_inj__on__insert_2,axiom,
( c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X4,tc_bool)),X3),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)),X4,X5),X5))
| ~ c_Fun_Oinj__on(X1,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
cnf(cls_the__inv__into__into_0,axiom,
( hBOOL(c_in(hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5),X6,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X6))
| ~ hBOOL(c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__into_0) ).
cnf(cls_conseq12_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xconseq12__3(X2,X7,X4,X5)))
| ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xconseq12__2(X2,X7,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X3),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_1) ).
cnf(cls_range__ex1__eq_2,axiom,
( hBOOL(c_in(hAPP(X1,X4),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3))
| hAPP(X1,X4) = hAPP(X1,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(hAPP(X1,X4),X1,X4,X3,X2))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_2) ).
cnf(cls_card__inj__on__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X4)))
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X5,X1,X2,X4)),X3))
| ~ c_Fun_Oinj__on(X5,X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__inj__on__le_0) ).
cnf(cls_card__image__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4)),c_Finite__Set_Ocard(X2,X3)))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image__le_0) ).
cnf(cls_endo__inj__surj_0,axiom,
( c_Set_Oimage(X1,X2,X3,X3) = X2
| ~ c_Fun_Oinj__on(X1,X2,X3,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oimage(X1,X2,X3,X3)),X2))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
cnf(cls_inj__on__Un_2,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),X5),X3,X1)),c_Set_Oimage(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X5),X4),X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Fun_Oinj__on(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
cnf(cls_psubset__insert__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4))
| hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
cnf(cls_inj__image__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X5))
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
cnf(cls_inj__on__fun__updI_0,axiom,
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5)
| hBOOL(c_in(X3,c_Set_Oimage(X1,X6,X4,X5),X5))
| ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
cnf(cls_subset__insert__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
cnf(cls_image__subset__iff_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),X3,X4))
| ~ hBOOL(c_in(X2,X5,X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X1,X5,X6,X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
cnf(cls_range__ex1__eq_3,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3),X3))
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(hAPP(X1,X2),X1,X2,X3,X4) != X2
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_3) ).
cnf(cls_conseq_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X2,X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_0) ).
cnf(cls_hoare__derivs_Ointros_I6_J_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X2,X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
cnf(cls_escape_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_0) ).
cnf(cls_image__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
cnf(cls_vimage__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Ovimage(X2,X3,X1,X4)),c_Set_Ovimage(X2,X5,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
cnf(cls_subset__image__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X5,X2,X1,X4)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
cnf(cls_min__max_Odistrib__inf__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
cnf(cls_distrib__inf__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
cnf(cls_range__composition_0,axiom,
c_Set_Oimage(c_COMBB(X1,X2,X3,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4) = c_Set_Oimage(X1,c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X3),X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__composition_0) ).
cnf(cls_Comp_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),c_Com_Ocom_OSemi(X4,X5)),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X7),X5),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),X4),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comp_0) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X1)),hAPP(v_c0,X1)),hAPP(v_Q,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X1)),hAPP(v_c0,X1)),hAPP(v_Q_H,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_inj__on__image__Int_0,axiom,
( c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X6))
| ~ c_Fun_Oinj__on(X1,X6,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
cnf(cls_inj__on__image__set__diff_0,axiom,
( c_Set_Oimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X6))
| ~ c_Fun_Oinj__on(X1,X6,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
cnf(cls_image__image_0,axiom,
c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
cnf(cls_setsum__right__distrib_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,X5),X4,X5,X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
cnf(cls_setsum__negf_0,axiom,
( c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),X4,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
cnf(cls_f__the__inv__into__f_0,axiom,
( hAPP(X1,hAPP(c_Fun_Othe__inv__into(X2,X1,X3,X4),X5)) = X5
| ~ hBOOL(c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__the__inv__into__f_0) ).
cnf(cls_Diff__subset__conv_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
cnf(cls_vimage__singleton__eq_0,axiom,
( hAPP(X1,X2) = X3
| ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
cnf(cls_range__ex1__eq_0,axiom,
( X1 = hAPP(X2,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X1,X2,X3,X4))
| ~ hBOOL(c_in(X1,c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3),X3))
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_0) ).
cnf(cls_fun__upd__image_1,axiom,
( c_Set_Oimage(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5) = c_Set_Oimage(X1,X6,X4,X5)
| hBOOL(c_in(X2,X6,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
cnf(cls_Un__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
cnf(cls_Int__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
cnf(cls_Diff__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X5),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
cnf(cls_range__ex1__eq_1,axiom,
( X2 = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(X1,X2),X1,X4,X3)
| ~ hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_1) ).
cnf(cls_lower__semilattice_Ofold__inf__le__inf_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Finite__Set_Ofold(X2,X3,X3),X4),X5)),hAPP(hAPP(X2,X6),X4)))
| ~ hBOOL(c_in(X6,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Lattices_Olower__semilattice(X1,X7,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold__inf__le__inf_0) ).
cnf(cls_vimage__insert_0,axiom,
c_Set_Ovimage(X1,c_Set_Oinsert(X2,X3,X4),X5,X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4)),c_Set_Ovimage(X1,X3,X5,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
cnf(cls_inj__transfer_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(c_in(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(X1,X3,X4,X5),c_Set_Oimage(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5),X5))
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__transfer_0) ).
cnf(cls_Diff__subset__conv_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
cnf(cls_min__max_Odistrib__sup__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
cnf(cls_distrib__sup__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
cnf(cls_fold__inf__le__inf_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(c_in(X4,X3,X1))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__le__inf_0) ).
cnf(cls_eq__add__iff2_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X2)),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
cnf(cls_eq__add__iff1_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4))
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
cnf(cls_image__Int_0,axiom,
( c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
cnf(cls_image__set__diff_0,axiom,
( c_Set_Oimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
cnf(cls_setsum__diff_0,axiom,
( c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),X5),X3,X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)),c_Finite__Set_Osetsum(X2,X5,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X4))
| ~ c_Finite__Set_Ofinite(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff_0) ).
cnf(cls_Un__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
cnf(cls_Un__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
cnf(cls_setsum__diff__nat_0,axiom,
( c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2,tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Osetsum(X1,X3,X2,tc_nat)),c_Finite__Set_Osetsum(X1,X4,X2,tc_nat))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X4),X3))
| ~ c_Finite__Set_Ofinite(X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff__nat_0) ).
cnf(cls_ATP__Linkup_OCOMBS__def_0,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
cnf(cls_setsum__diff1_H_0,axiom,
( c_Finite__Set_Osetsum(X2,X3,X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X2,X5)),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X4,tc_bool)),X3),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)),X4,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(c_in(X5,X3,X4))
| ~ c_Finite__Set_Ofinite(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_H_0) ).
cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_COMBS__def__raw_0,axiom,
hAPP(c_COMBS(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def__raw_0) ).
cnf(cls_fun__upd__other_0,axiom,
( hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| X6 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
cnf(cls_fun__upd__apply_1,axiom,
( hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| X6 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
cnf(cls_COMBB__def__raw_0,axiom,
hAPP(c_COMBB(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(v_P,hAPP(v_Q,v_R)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def__raw_0) ).
cnf(cls_fun__upd__apply_0,axiom,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
cnf(cls_fun__upd__same_0,axiom,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
cnf(cls_inj__image__mem__iff_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
cnf(cls_setsum__Un__disjoint_0,axiom,
( c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X5,X3,X2,X1)),c_Finite__Set_Osetsum(X5,X4,X2,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__disjoint_0) ).
cnf(cls_Un__subset__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
cnf(cls_Un__least_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
cnf(cls_finite__surj__inj_0,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oimage(X1,X2,X3,X3)))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
cnf(cls_setsum__diff1__ring_0,axiom,
( c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X3,X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)),hAPP(X2,X5))
| ~ class_Ring__and__Field_Oring(X1)
| ~ hBOOL(c_in(X5,X4,X3))
| ~ c_Finite__Set_Ofinite(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).
cnf(cls_setsum__diff1_0,axiom,
( c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X3,X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)),hAPP(X2,X5))
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ hBOOL(c_in(X5,X4,X3))
| ~ c_Finite__Set_Ofinite(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).
cnf(cls_conseq2_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X4,X5)),v_sko__Hoare__Mirabelle__Xconseq2__2(X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_1) ).
cnf(cls_conseq1_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X2,X5)),v_sko__Hoare__Mirabelle__Xconseq1__2(X2,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_1) ).
cnf(cls_setsum__diff1__nat_0,axiom,
( c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),X2,tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Osetsum(X1,X3,X2,tc_nat)),hAPP(X1,X4))
| ~ hBOOL(c_in(X4,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_0) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
cnf(cls_vimage__Un_0,axiom,
c_Set_Ovimage(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X5,X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X2)),c_Set_Ovimage(X1,X4,X5,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
cnf(cls_vimage__Int_0,axiom,
c_Set_Ovimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X5,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X2)),c_Set_Ovimage(X1,X4,X5,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
cnf(cls_vimage__Diff_0,axiom,
c_Set_Ovimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X5,X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X2)),c_Set_Ovimage(X1,X4,X5,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
cnf(cls_vimage__singleton__eq_1,axiom,
hBOOL(c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
cnf(cls_Un__Int__assoc__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X2))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
cnf(cls_conseq1_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X2,X5)),v_sko__Hoare__Mirabelle__Xconseq1__2(X2,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_0) ).
cnf(cls_conseq2_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X4,X5)),v_sko__Hoare__Mirabelle__Xconseq2__2(X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_0) ).
cnf(cls_finite__surj_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_Set_Oimage(X3,X4,X5,X2)))
| ~ c_Finite__Set_Ofinite(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_Compl__subset__Compl__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
cnf(cls_fun__upd__idem__iff_0,axiom,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
cnf(cls_eq__add__iff1_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4) = X6
| ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
cnf(cls_eq__add__iff2_0,axiom,
( X4 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)
| ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
cnf(cls_vimageD_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),X3,X4))
| ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
cnf(cls_vimageE_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),X3,X4))
| ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).
cnf(cls_atLeastatMost__psubset__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).
cnf(cls_combine__common__factor_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
cnf(cls_sup__le__fold__sup_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(c_in(X2,X4,X1))
| ~ c_Finite__Set_Ofinite(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__le__fold__sup_0) ).
cnf(cls_Diff__insert2_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
cnf(cls_inj__image__mem__iff_1,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
cnf(cls_Int__subset__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
cnf(cls_Int__greatest_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
cnf(cls_atLeastatMost__psubset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).
cnf(cls_atLeastatMost__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
cnf(cls_atLeastatMost__psubset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).
cnf(cls_atLeastatMost__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
cnf(cls_Diff__Int2_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
cnf(cls_Un__Int__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
cnf(cls_Int__Un__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
cnf(cls_Diff__Int__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
cnf(cls_Un__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
cnf(cls_atLeastLessThan__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X2,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X5,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).
cnf(cls_atLeastLessThan__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X5,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).
cnf(cls_vimage__code_0,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
cnf(cls_card__Suc__Diff1_0,axiom,
( c_Suc(c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1)) = c_Finite__Set_Ocard(X2,X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__Diff1_0) ).
cnf(cls_Int__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
cnf(cls_Int__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
cnf(cls_the__inv__into__onto_0,axiom,
( c_Set_Oimage(c_Fun_Othe__inv__into(X1,X2,X3,X4),c_Set_Oimage(X2,X1,X3,X4),X4,X3) = X1
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__onto_0) ).
cnf(cls_inj__on__the__inv__into_0,axiom,
( c_Fun_Oinj__on(c_Fun_Othe__inv__into(X1,X2,X3,X4),c_Set_Oimage(X2,X1,X3,X4),X4,X3)
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__the__inv__into_0) ).
cnf(cls_inj__on__Un__image__eq__iff_0,axiom,
( X2 = X5
| c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
cnf(cls_atLeastatMost__psubset__iff_6,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).
cnf(cls_atLeastatMost__psubset__iff_5,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).
cnf(cls_Un__Int__assoc__eq_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
cnf(cls_card__insert_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X3))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert_0) ).
cnf(cls_atLeastatMost__psubset__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).
cnf(cls_psubset__insert__iff_7,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
cnf(cls_Compl__anti__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
cnf(cls_Compl__subset__Compl__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
cnf(cls_image__vimage__eq_0,axiom,
c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
cnf(cls_card__Diff__subset__Int_0,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Ocard(X2,X1)),c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1))
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__subset__Int_0) ).
cnf(cls_Int__lower1_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
cnf(cls_Int__lower2_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
cnf(cls_Diff__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
cnf(cls_Un__Int__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
cnf(cls_Int__Un__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
cnf(cls_Diff__Int__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
cnf(cls_Diff__Un_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
cnf(cls_Diff__Int_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
cnf(cls_insert__subset_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X4,X2,X1)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
cnf(cls_less__diff__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
cnf(cls_le__diff__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
cnf(cls_insert__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),c_Set_Oinsert(X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
cnf(cls_rangeI_0,axiom,
hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
cnf(cls_vimageI_0,axiom,
( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
| ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
cnf(cls_vimageI2_0,axiom,
( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
| ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
cnf(cls_vimage__eq_1,axiom,
( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
| ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
cnf(cls_mult__less__cancel__right__disj_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
cnf(cls_insert__subset_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(c_in(X2,X4,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
cnf(cls_Nitpick_OEx1__def_2,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
cnf(cls_setsum__diff1_1,axiom,
( c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X3,X1) = c_Finite__Set_Osetsum(X2,X4,X3,X1)
| hBOOL(c_in(X5,X4,X3))
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ c_Finite__Set_Ofinite(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).
cnf(cls_double__diff_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4)) = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
cnf(cls_imageI_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
cnf(cls_image__eqI_0,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
cnf(cls_image__iff_2,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
cnf(cls_rev__image__eqI_0,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
cnf(cls_lower__semilattice_Ofold__inf__insert_0,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X2),X3),c_Set_Oinsert(X4,X5,X2)) = hAPP(hAPP(X1,X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X2),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X2)
| ~ c_Lattices_Olower__semilattice(X6,X7,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold__inf__insert_0) ).
cnf(cls_setsum__diff1__nat_1,axiom,
( c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),X2,tc_nat) = c_Finite__Set_Osetsum(X1,X3,X2,tc_nat)
| hBOOL(c_in(X4,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
cnf(cls_psubset__insert__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X2,X1))
| hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
cnf(cls_UnE_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
cnf(cls_atLeastatMost__subset__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
cnf(cls_max__lattice_0,axiom,
( c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__lattice_0) ).
cnf(cls_dual__semilattice_0,axiom,
( c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__semilattice_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_psubset__insert__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
cnf(cls_subset__singletonD_0,axiom,
( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
cnf(cls_inj__image__eq__iff_0,axiom,
( X2 = X5
| c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
cnf(cls_DiffE_1,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
cnf(cls_add__less__cancel__right_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
cnf(cls_add__less__cancel__left_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
cnf(cls_add__le__cancel__right_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
cnf(cls_add__le__cancel__left_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
cnf(cls_insert__subset_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
cnf(cls_fold1__antimono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1),X3)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__antimono_0) ).
cnf(cls_fun__upd__idem__iff_1,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
cnf(cls_fun__upd__triv_0,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
cnf(cls_fun__upd__idem_0,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
cnf(cls_inj__vimage__image__eq_0,axiom,
( c_Set_Ovimage(X1,c_Set_Oimage(X1,X2,X3,X4),X3,X4) = X2
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
cnf(cls_atLeastatMost__psubset__iff_4,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).
cnf(cls_finite__imageD_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,X1,X2,X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
cnf(cls_psubset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
cnf(cls_subset__psubset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
cnf(cls_psubset__subset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
cnf(cls_subset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
cnf(cls_subset__insert_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
cnf(cls_subset__insert__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
cnf(cls_IntE_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
cnf(cls_IntE_1,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
cnf(cls_DiffE_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
cnf(cls_psubset__insert__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X2,X1))
| hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
cnf(cls_Diff__insert_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X4)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
cnf(cls_card__psubset_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X2,X1)),c_Finite__Set_Ocard(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__psubset_0) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
cnf(cls_vimage__code_1,axiom,
( hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
| ~ hBOOL(hAPP(X2,hAPP(X1,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
cnf(cls_Un__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
cnf(cls_Int__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
cnf(cls_Int__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
cnf(cls_psubset__insert__iff_6,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
cnf(cls_less__fun__def_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,X1)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,X1)),X4),X3))
| ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,X1)),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
cnf(cls_the__inv__f__f_0,axiom,
( hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),hAPP(X2,X4)) = X4
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__f__f_0) ).
cnf(cls_finite__Diff__insert_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
cnf(cls_the__inv__into__f__f_0,axiom,
( hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5
| ~ hBOOL(c_in(X5,X1,X3))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__f_0) ).
cnf(cls_the__inv__into__f__eq_0,axiom,
( hAPP(c_Fun_Othe__inv__into(X2,X1,X3,X4),hAPP(X1,X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(c_in(X5,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__eq_0) ).
cnf(cls_subset__inj__on_0,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X5))
| ~ c_Fun_Oinj__on(X1,X5,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
cnf(cls_setsum__insert_0,axiom,
( c_Finite__Set_Osetsum(X2,c_Set_Oinsert(X3,X4,X5),X5,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X2,X3)),c_Finite__Set_Osetsum(X2,X4,X5,X1))
| hBOOL(c_in(X3,X4,X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__insert_0) ).
cnf(cls_eq__card__imp__inj__on_0,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).
cnf(cls_inj__on__Un_0,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
cnf(cls_inj__on__Un_1,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X5),X2),X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
cnf(cls_less__diff__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
cnf(cls_le__diff__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
cnf(cls_fold1__Un_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__Un_0) ).
cnf(cls_comm__monoid__add_Ofold1__Un_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__Un_0) ).
cnf(cls_lower__semilattice_Obelow__fold1__iff_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X3,X4,X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),hAPP(c_Finite__Set_Ofold1(X6,X5),X4)))
| ~ c_Finite__Set_Ofinite(X4,X5)
| ~ c_Lattices_Olower__semilattice(X1,X7,X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Obelow__fold1__iff_0) ).
cnf(cls_subset__insert_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
cnf(cls_subset__insert__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_Max__eqI_1,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X2,X3,X1)),X3))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__eqI_1) ).
cnf(cls_add__strict__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
cnf(cls_add__le__less__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
cnf(cls_add__less__le__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
cnf(cls_add__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
cnf(cls_atLeastatMost__subset__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
cnf(cls_disjoint__eq__subset__Compl_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).
cnf(cls_IntI_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
| ~ hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
cnf(cls_Int__iff_2,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
| ~ hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
cnf(cls_min__less__iff__disj_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
cnf(cls_min__le__iff__disj_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
cnf(cls_COMBC__def__raw_0,axiom,
hAPP(hAPP(c_COMBC(v_P,t_a,t_b,t_c),v_Q),v_R) = hAPP(hAPP(v_P,v_R),v_Q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def__raw_0) ).
cnf(cls_fold__sup__insert_0,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_Finite__Set_Ofinite(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__sup__insert_0) ).
cnf(cls_fold__inf__insert_0,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_Finite__Set_Ofinite(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__insert_0) ).
cnf(cls_sup1E_0,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
cnf(cls_finite__vimageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Ovimage(X1,X2,X3,X4),X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).
cnf(cls_Un__Diff__Int_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
cnf(cls_insert__image_0,axiom,
( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
| ~ hBOOL(c_in(X2,X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
cnf(cls_less__fun__def_1,axiom,
( ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,X1)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,X1)),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
cnf(cls_ab__semigroup__mult_Ofold1__Un_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(c_Finite__Set_Ofold1(X4,X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(X4,hAPP(c_Finite__Set_Ofold1(X4,X1),X2)),hAPP(c_Finite__Set_Ofold1(X4,X1),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_OrderedGroup_Oab__semigroup__mult(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__Un_0) ).
cnf(cls_finite__Diff__insert_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
cnf(cls_lower__semilattice_Ofold1__belowI_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X2,X3),X4)),X5))
| ~ hBOOL(c_in(X5,X4,X3))
| ~ c_Finite__Set_Ofinite(X4,X3)
| ~ c_Lattices_Olower__semilattice(X1,X6,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold1__belowI_0) ).
cnf(cls_le__add__right__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
cnf(cls_inf1E_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
cnf(cls_inf1E_1,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
cnf(cls_DiffI_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2))
| hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
cnf(cls_Diff__iff_2,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2))
| hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
cnf(cls_subset__Compl__self__eq_1,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
cnf(cls_subset__insertI2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
cnf(cls_insert__Diff_0,axiom,
( c_Set_Oinsert(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),X2) = X3
| ~ hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
cnf(cls_vimage__Compl_0,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
cnf(cls_Nitpick_OEx1__def_3,axiom,
( X1 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
cnf(cls_inj__on__iff__eq__card_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff__eq__card_0) ).
cnf(cls_diff__less__mono2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
cnf(cls_diff__less__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
cnf(cls_image__insert_0,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
cnf(cls_max__less__iff__conj_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
cnf(cls_max__less__iff__conj_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
cnf(cls_le__supE_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
cnf(cls_le__sup__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
cnf(cls_le__supE_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
cnf(cls_le__sup__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
cnf(cls_min__max_Ole__supE_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
cnf(cls_min__max_Ole__sup__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
cnf(cls_min__max_Ole__supE_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
cnf(cls_min__max_Ole__sup__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
cnf(cls_inj__on__diff_0,axiom,
( c_Fun_Oinj__on(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Fun_Oinj__on(X1,X3,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
cnf(cls_fold1__strict__below__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1),X2)),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__strict__below__iff_2) ).
cnf(cls_fold1__below__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1),X2)),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__below__iff_2) ).
cnf(cls_set__eq__subset_2,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
cnf(cls_equalityI_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
cnf(cls_lower__semilattice_Ole__infI1_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X3),X5))
| ~ c_Lattices_Olower__semilattice(X1,X6,X2,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI1_0) ).
cnf(cls_lower__semilattice_Ole__infI2_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Lattices_Olower__semilattice(X1,X6,X2,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI2_0) ).
cnf(cls_lower__semilattice_Oless__infI1_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X3),X5))
| ~ c_Lattices_Olower__semilattice(X6,X1,X2,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oless__infI1_0) ).
cnf(cls_lower__semilattice_Oless__infI2_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Lattices_Olower__semilattice(X6,X1,X2,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oless__infI2_0) ).
cnf(cls_card__image_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).
cnf(cls_card__Diff__subset_0,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Ocard(X2,X1)),c_Finite__Set_Ocard(X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__subset_0) ).
cnf(cls_ivl__disj__un_I5_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I5_J_0) ).
cnf(cls_add__less__cancel__left_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
cnf(cls_add__strict__left__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
cnf(cls_add__less__cancel__right_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(cls_add__strict__right__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
cnf(cls_add__le__cancel__left_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
cnf(cls_add__left__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
cnf(cls_add__le__cancel__right_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
cnf(cls_add__right__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
cnf(cls_subset__Compl__self__eq_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
cnf(cls_lower__semilattice_Oinf__greatest_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X4))
| ~ c_Lattices_Olower__semilattice(X1,X6,X3,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__greatest_0) ).
cnf(cls_lower__semilattice_Ole__inf__iff_2,axiom,
( hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X4))
| ~ c_Lattices_Olower__semilattice(X1,X6,X3,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_2) ).
cnf(cls_lower__semilattice_Ole__infI_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X4))
| ~ c_Lattices_Olower__semilattice(X1,X6,X3,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI_0) ).
cnf(cls_Diff__partition_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X2)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
cnf(cls_Compl__Un_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
cnf(cls_Compl__Int_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).
cnf(cls_card__seteq_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(X2,X3)),c_Finite__Set_Ocard(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).
cnf(cls_Int__insert__left_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = c_Set_Oinsert(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),X1)
| ~ hBOOL(c_in(X2,X4,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
cnf(cls_card__Diff__singleton__if_1,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1) = c_Finite__Set_Ocard(X2,X1)
| hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).
cnf(cls_ivl__disj__un_I20_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I20_J_0) ).
cnf(cls_ivl__disj__un_I22_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I22_J_0) ).
cnf(cls_ivl__disj__un_I21_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).
cnf(cls_ivl__disj__un_I17_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
cnf(cls_Un__upper1_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
cnf(cls_Un__upper2_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
cnf(cls_max__less__iff__conj_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
cnf(cls_min__max_Ole__sup__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
cnf(cls_min__max_Osup__least_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
cnf(cls_min__max_Ole__supI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
cnf(cls_le__supI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
cnf(cls_sup__least_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
cnf(cls_le__sup__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
cnf(cls_Un__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
cnf(cls_Int__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
cnf(cls_Un__Diff__cancel2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
cnf(cls_Diff__idemp_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X3) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
cnf(cls_UnCI_1,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2))
| ~ hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
cnf(cls_UnCI_0,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2))
| ~ hBOOL(c_in(X1,X4,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
cnf(cls_Max__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).
cnf(cls_Min__antimono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
cnf(cls_lower__semilattice_Ole__infE_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X4,X3),X5)))
| ~ c_Lattices_Olower__semilattice(X1,X6,X4,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infE_0) ).
cnf(cls_lower__semilattice_Ole__inf__iff_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X4,X3),X5)))
| ~ c_Lattices_Olower__semilattice(X1,X6,X4,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_0) ).
cnf(cls_lower__semilattice_Ole__infE_1,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X4,X5),X3)))
| ~ c_Lattices_Olower__semilattice(X1,X6,X4,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infE_1) ).
cnf(cls_lower__semilattice_Ole__inf__iff_1,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X4,X5),X3)))
| ~ c_Lattices_Olower__semilattice(X1,X6,X4,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_1) ).
cnf(cls_singletonE_0,axiom,
( X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
cnf(cls_doubleton__eq__iff_0,axiom,
( X1 = X5
| X1 = X4
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
cnf(cls_doubleton__eq__iff_1,axiom,
( X2 = X4
| X1 = X4
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
cnf(cls_doubleton__eq__iff_2,axiom,
( X1 = X5
| X2 = X5
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
cnf(cls_doubleton__eq__iff_3,axiom,
( X2 = X4
| X2 = X5
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
cnf(cls_strict__below__fold1__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1),X4)))
| ~ c_Finite__Set_Ofinite(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__below__fold1__iff_0) ).
cnf(cls_below__fold1__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X1),X4)))
| ~ c_Finite__Set_Ofinite(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).
cnf(cls_disjoint__eq__subset__Compl_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
cnf(cls_insert__Diff__single_0,axiom,
c_Set_Oinsert(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),X2) = c_Set_Oinsert(X1,X3,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
cnf(cls_less__fun__def_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,X1)),X3),X4))
| ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,X1)),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
cnf(cls_insert__Diff__if_1,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = c_Set_Oinsert(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4),X1)
| hBOOL(c_in(X2,X4,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
cnf(cls_fold1__Un2_0,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__Un2_0) ).
cnf(cls_inj__on__insert_0,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
cnf(cls_insert__inter__insert_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),c_Set_Oinsert(X2,X4,X1)) = c_Set_Oinsert(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
cnf(cls_ivl__disj__un_I6_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).
cnf(cls_inj__onD_0,axiom,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ c_Fun_Oinj__on(X1,X4,X5,X6)
| ~ hBOOL(c_in(X3,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).
cnf(cls_inj__on__def_0,axiom,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ hBOOL(c_in(X3,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
cnf(cls_inj__on__iff_0,axiom,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ hBOOL(c_in(X3,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
cnf(cls_inj__on__contraD_0,axiom,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ hBOOL(c_in(X3,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
cnf(cls_diff__le__mono2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
cnf(cls_diff__le__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
cnf(cls_lower__semilattice_Oinf__le1_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X3))
| ~ c_Lattices_Olower__semilattice(X1,X5,X2,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__le1_0) ).
cnf(cls_lower__semilattice_Oinf__le2_0,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X4))
| ~ c_Lattices_Olower__semilattice(X1,X5,X2,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__le2_0) ).
cnf(cls_hoare__derivs_OSkip_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),c_Com_Ocom_OSKIP),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
cnf(cls_hoare__derivs_Oinsert_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
cnf(cls_Int__insert__right_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = c_Set_Oinsert(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),X1)
| ~ hBOOL(c_in(X3,X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
cnf(cls_le__funD_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(X2,X3)),hAPP(X4,X3)))
| ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X5,X1)),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
cnf(cls_Compl__Diff__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).
cnf(cls_subset__iff__psubset__eq_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
cnf(cls_psubset__eq_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
cnf(cls_psubset__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
cnf(cls_psubsetD_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).
cnf(cls_set__mp_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
cnf(cls_subsetD_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
cnf(cls_set__rev__mp_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2))
| ~ hBOOL(c_in(X1,X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
cnf(cls_subset__iff_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
cnf(cls_Int__greaterThanAtMost_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X1)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greaterThanAtMost_0) ).
cnf(cls_Int__atLeastAtMost_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__atLeastAtMost_0) ).
cnf(cls_Int__atLeastLessThan_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__atLeastLessThan_0) ).
cnf(cls_Min__eqI_1,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X2,X3,X1)))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__eqI_1) ).
cnf(cls_psubset__card__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__card__mono_0) ).
cnf(cls_card__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__mono_0) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
cnf(cls_ab__semigroup__idem__mult_Ofold1__Un2_0,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)) = hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__Un2_0) ).
cnf(cls_fold1__belowI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).
cnf(cls_less__max__iff__disj_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
cnf(cls_le__max__iff__disj_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
cnf(cls_lower__semilattice_Oinf__assoc_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
| ~ c_Lattices_Olower__semilattice(X5,X6,X1,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__assoc_0) ).
cnf(cls_card__insert__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2)))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_0) ).
cnf(cls_Un__insert__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = c_Set_Oinsert(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
cnf(cls_ivl__diff_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)) = c_SetInterval_Oord__class_OatLeastLessThan(X4,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).
cnf(cls_less__infI1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
cnf(cls_less__infI2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
cnf(cls_min__less__iff__disj_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
cnf(cls_min__max_Oless__infI1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
cnf(cls_min__less__iff__disj_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
cnf(cls_min__max_Oless__infI2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
cnf(cls_le__infI1_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
cnf(cls_le__infI2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
cnf(cls_min__le__iff__disj_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
cnf(cls_min__max_Ole__infI1_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
cnf(cls_min__le__iff__disj_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
cnf(cls_min__max_Ole__infI2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = X3
| hBOOL(c_in(X2,X3,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
cnf(cls_insert__Diff1_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4)
| ~ hBOOL(c_in(X2,X4,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
cnf(cls_minus__less__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
cnf(cls_minus__less__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
cnf(cls_minus__le__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
cnf(cls_minus__le__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
cnf(cls_Nat_Odiff__diff__eq_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
cnf(cls_min__less__iff__conj_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
cnf(cls_le__infI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
cnf(cls_le__inf__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
cnf(cls_inf__greatest_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
cnf(cls_min__max_Oinf__greatest_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).
cnf(cls_min__max_Ole__inf__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
cnf(cls_min__max_Ole__infI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
cnf(cls_sup1CI_1,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
cnf(cls_sup1CI_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
cnf(cls_subset__empty_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
cnf(cls_neg__less__iff__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
cnf(cls_neg__le__iff__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
cnf(cls_image__constant_0,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(c_in(X5,X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
cnf(cls_lower__semilattice_Oinf__left__commute_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
| ~ c_Lattices_Olower__semilattice(X5,X6,X1,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__left__commute_0) ).
cnf(cls_insertE_0,axiom,
( hBOOL(c_in(X1,X2,X3))
| X1 = X4
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
cnf(cls_min__max_Osup__inf__distrib2_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
cnf(cls_sup__inf__distrib2_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
cnf(cls_inf__sup__distrib2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
cnf(cls_max__diff__distrib__left_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
cnf(cls_min__diff__distrib__left_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
cnf(cls_max__add__distrib__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
cnf(cls_add__sup__distrib__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
cnf(cls_add__inf__distrib__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
cnf(cls_min__add__distrib__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
cnf(cls_min__max_Oinf__sup__distrib2_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
cnf(cls_insert__is__Un_0,axiom,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_not__psubset__empty_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
cnf(cls_Int__insert__left_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)
| hBOOL(c_in(X2,X4,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
cnf(cls_less__imp__diff__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
cnf(cls_min__less__iff__conj_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
cnf(cls_min__less__iff__conj_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
cnf(cls_le__inf__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
cnf(cls_le__infE_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
cnf(cls_le__inf__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
cnf(cls_le__infE_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
cnf(cls_min__max_Ole__inf__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
cnf(cls_min__max_Ole__infE_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
cnf(cls_min__max_Ole__inf__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
cnf(cls_min__max_Ole__infE_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
cnf(cls_Inf__binary_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
cnf(cls_subset__empty_1,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
cnf(cls_Un__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
cnf(cls_Un__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
cnf(cls_Int__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
cnf(cls_Int__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
cnf(cls_derivs__insertD_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).
cnf(cls_Un__insert__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = c_Set_Oinsert(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
cnf(cls_Min__Un_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__Un_0) ).
cnf(cls_Max__Un_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__Un_0) ).
cnf(cls_fold1__eq__fold_0,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X1),X1,X1),X2),X3)
| hBOOL(c_in(X2,X3,X1))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__eq__fold_0) ).
cnf(cls_comm__monoid__add_Ofold1__eq__fold_0,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X1),X1,X1),X2),X3)
| hBOOL(c_in(X2,X3,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__eq__fold_0) ).
cnf(cls_card__Suc__eq_5,axiom,
( hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).
cnf(cls_Un__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
cnf(cls_Un__Diff__cancel_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X2)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
cnf(cls_Int__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
cnf(cls_lower__semilattice_Ole__iff__inf_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(X4,X2),X3))
| ~ c_Lattices_Olower__semilattice(X4,X5,X1,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__iff__inf_0) ).
cnf(cls_lower__semilattice_Oinf__absorb2_0,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(X4,X3),X2))
| ~ c_Lattices_Olower__semilattice(X4,X5,X1,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__absorb2_0) ).
cnf(cls_ab__semigroup__mult_Ofold1__eq__fold_0,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,X4,X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X2),X3),X4)
| hBOOL(c_in(X3,X4,X2))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__eq__fold_0) ).
cnf(cls_vimage__const_0,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).
cnf(cls_Min__eqI_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2) = X3
| hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X2,X3,X1),X2,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__eqI_0) ).
cnf(cls_Max__eqI_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2) = X3
| hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X2,X3,X1),X2,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__eqI_0) ).
cnf(cls_lower__semilattice_Oinf__left__idem_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X2),X3)) = hAPP(hAPP(X1,X2),X3)
| ~ c_Lattices_Olower__semilattice(X4,X5,X1,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__left__idem_0) ).
cnf(cls_lower__semilattice_Ole__iff__inf_1,axiom,
( hBOOL(hAPP(hAPP(X4,X2),X3))
| hAPP(hAPP(X1,X2),X3) != X2
| ~ c_Lattices_Olower__semilattice(X4,X5,X1,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__iff__inf_1) ).
cnf(cls_predicate1D_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
cnf(cls_rev__predicate1D_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X1))
| ~ hBOOL(hAPP(X4,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
cnf(cls_doubleton__eq__iff_4,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
cnf(cls_finite__imageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
cnf(cls_inf__le1_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
cnf(cls_inf__le2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
cnf(cls_min__max_Oinf__le1_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
cnf(cls_min__max_Oinf__le2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
cnf(cls_min__max_Osup__inf__distrib1_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
cnf(cls_add__sup__distrib__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
cnf(cls_add__inf__distrib__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
cnf(cls_min__max_Oinf__sup__distrib1_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_injD_0,axiom,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
cnf(cls_subset__Un__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
cnf(cls_neg__less__iff__less_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
cnf(cls_le__imp__neg__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
cnf(cls_finite__Diff2_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
cnf(cls_Suc__diff__diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(X1)),X2)),c_Suc(X3)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
cnf(cls_Int__insert__right_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)
| hBOOL(c_in(X3,X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
cnf(cls_subset__insertI_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X2,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
cnf(cls_insertCI_0,axiom,
( hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
cnf(cls_insert__iff_2,axiom,
( hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
cnf(cls_ivl__disj__int_I14_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I14_J_0) ).
cnf(cls_ivl__disj__int_I16_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I16_J_0) ).
cnf(cls_ivl__disj__int_I15_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I15_J_0) ).
cnf(cls_ivl__disj__int_I11_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).
cnf(cls_empty__subsetI_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(cls_finite__subset_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
cnf(cls_rev__finite__subset_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
cnf(cls_vimage__const_1,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X4,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
cnf(cls_image__constant__conv_1,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
cnf(cls_less__max__iff__disj_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
cnf(cls_min__max_Oless__supI1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
cnf(cls_less__max__iff__disj_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
cnf(cls_min__max_Oless__supI2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
cnf(cls_less__supI1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
cnf(cls_less__supI2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
cnf(cls_min__max_Ole__supI1_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
cnf(cls_le__max__iff__disj_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
cnf(cls_min__max_Ole__supI2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
cnf(cls_le__max__iff__disj_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
cnf(cls_le__supI1_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
cnf(cls_le__supI2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
cnf(cls_finite__Un_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
cnf(cls_finite__Un_1,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
cnf(cls_fold1__insert_0,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3))
| hBOOL(c_in(X2,X3,X1))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__insert_0) ).
cnf(cls_comm__monoid__add_Ofold1__insert_0,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3))
| hBOOL(c_in(X2,X3,X1))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__insert_0) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X2))
| hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_less__minus__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
cnf(cls_less__minus__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
cnf(cls_le__minus__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
cnf(cls_le__minus__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
cnf(cls_lower__semilattice_Oinf__commute_0,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_Lattices_Olower__semilattice(X4,X5,X1,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__commute_0) ).
cnf(cls_fold1__eq__fold__idem_0,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X1),X1,X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__eq__fold__idem_0) ).
cnf(cls_diff__less__Suc_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),c_Suc(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
cnf(cls_Min__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).
cnf(cls_empty__is__image_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X2,X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
cnf(cls_image__is__empty_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
cnf(cls_Diff__disjoint_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
cnf(cls_psubset__eq_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
cnf(cls_diff__le__self_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
cnf(cls_diff__commute_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
cnf(cls_ab__semigroup__mult_Ofold1__insert_0,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,X4,X2)) = hAPP(hAPP(X1,X3),hAPP(c_Finite__Set_Ofold1(X1,X2),X4))
| hBOOL(c_in(X3,X4,X2))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__insert_0) ).
cnf(cls_order__less__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
cnf(cls_order__le__less__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
cnf(cls_order__less__le__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
cnf(cls_xt1_I10_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_xt1_I8_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
cnf(cls_order__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
cnf(cls_xt1_I6_J_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_less__eqI_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
cnf(cls_less__eqI_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
cnf(cls_le__eqI_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X5),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
cnf(cls_le__eqI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X5),X4))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
cnf(cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,X4,X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X2),X3),X4)
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0) ).
cnf(cls_eq__diff__iff_0,axiom,
( X1 = X3
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
cnf(cls_image__constant__conv_0,axiom,
c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
cnf(cls_lower__semilattice_Oinf__idem_0,axiom,
( hAPP(hAPP(X1,X2),X2) = X2
| ~ c_Lattices_Olower__semilattice(X3,X4,X1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__idem_0) ).
cnf(cls_Compl__partition2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).
cnf(cls_Compl__disjoint2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
cnf(cls_sup__fun__eq_0,axiom,
( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
cnf(cls_inf__fun__eq_0,axiom,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
cnf(cls_fun__diff__def_0,axiom,
( hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_HOL_Ominus(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
cnf(cls_min__max_Osup__assoc_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
cnf(cls_sup__assoc_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
cnf(cls_inf__assoc_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_min__max_Oinf__assoc_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_add__eq__inf__sup_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).
cnf(cls_Diff__Compl_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).
cnf(cls_Diff__eq_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
cnf(cls_insert__code_0,axiom,
( hBOOL(hAPP(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
cnf(cls_less__trans__Suc_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
cnf(cls_Diff__triv_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3) = X2
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
cnf(cls_sup__eq__neg__inf_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).
cnf(cls_inf__eq__neg__sup_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).
cnf(cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Lattices_Olower__semilattice(X3,X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0) ).
cnf(cls_insert__ident_0,axiom,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,X2,X3))
| X2 = X4
| c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
cnf(cls_subset__UNIV_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
cnf(cls_Inf__lower_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Complete__Lattice_OInf__class_OInf(X2,X1)),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(c_in(X3,X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
cnf(cls_le__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
cnf(cls_less__le__not__le_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
cnf(cls_Max__ge_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X2,X3,X1))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).
cnf(cls_inf__Inf__fold__inf_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1)) = hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Inf__fold__inf_0) ).
cnf(cls_bex__empty_0,axiom,
( ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
cnf(cls_add__cancel__21_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_fold1__insert__idem_0,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__insert__idem_0) ).
cnf(cls_ball__empty_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
cnf(cls_triple_Oinject_0,axiom,
( X2 = X5
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X6),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
cnf(cls_triple_Oinject_1,axiom,
( X3 = X6
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X6),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
cnf(cls_triple_Oinject_2,axiom,
( X4 = X7
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X6),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
cnf(cls_finite__Un_2,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
cnf(cls_finite__UnI_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
cnf(cls_finite__Diff2_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_order__antisym_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
cnf(cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,X4,X2)) = hAPP(hAPP(X1,X3),hAPP(c_Finite__Set_Ofold1(X1,X2),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
cnf(cls_empty__iff_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
cnf(cls_singleton__inject_0,axiom,
( X1 = X3
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
cnf(cls_ab__semigroup__mult_Omult__ac_I1_J_0,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__ac_I1_J_0) ).
cnf(cls_not__less__eq__eq_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X2)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
cnf(cls_Inf__fold__inf_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(X2,X1) = hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1),c_Orderings_Otop__class_Otop(X1)),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__fold__inf_0) ).
cnf(cls_card__insert__if_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Finite__Set_Ocard(X2,X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).
cnf(cls_derivs__insertD_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X4,X2,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).
cnf(cls_Un__empty_2,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
cnf(cls_image__empty_0,axiom,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
cnf(cls_vimage__UNIV_0,axiom,
c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
cnf(cls_vimage__empty_0,axiom,
c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
cnf(cls_empty__is__image_1,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
cnf(cls_insertCI_1,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
cnf(cls_insertI1_0,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
cnf(cls_finite__Int_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
cnf(cls_finite__Int_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
cnf(cls_finite__Diff_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
cnf(cls_le__less__Suc__eq_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
cnf(cls_le__maxI1_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
cnf(cls_le__maxI2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
cnf(cls_sup__ge1_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
cnf(cls_sup__ge2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
cnf(cls_not__less__eq_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),c_Suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
cnf(cls_min__max_Osup__left__commute_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
cnf(cls_sup__left__commute_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
cnf(cls_inf__left__commute_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_add__cancel__21_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_min__max_Oinf__left__commute_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
cnf(cls_finite__compl_0,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_0) ).
cnf(cls_add__minus__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
cnf(cls_Compl__eq__Diff__UNIV_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Diff__UNIV_0) ).
cnf(cls_fold__empty_0,axiom,
hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__empty_0) ).
cnf(cls_greaterThanAtMost__empty__iff2_0,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_0) ).
cnf(cls_atLeastatMost__empty__iff2_0,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
cnf(cls_atLeastLessThan__empty__iff2_0,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
cnf(cls_greaterThanAtMost__empty__iff_0,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_0) ).
cnf(cls_atLeastatMost__empty__iff_0,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
cnf(cls_atLeastLessThan__empty__iff_0,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).
cnf(cls_Suc__diff__le_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
cnf(cls_Suc__less__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
cnf(cls_Suc__le__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),c_Suc(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
cnf(cls_Compl__partition_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).
cnf(cls_Compl__disjoint_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
cnf(cls_inj__on__empty_0,axiom,
c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
cnf(cls_le__antisym_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
cnf(cls_Un__empty_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
cnf(cls_Un__empty_1,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
cnf(cls_neg__sup__eq__inf_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).
cnf(cls_compl__sup_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).
cnf(cls_neg__inf__eq__sup_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).
cnf(cls_compl__inf_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).
cnf(cls_minus__add__distrib_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
cnf(cls_minus__add_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
cnf(cls_insert__code_2,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
cnf(cls_subset__refl_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
cnf(cls_equalityE_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
cnf(cls_Un__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
cnf(cls_Int__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
cnf(cls_diff__diff__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
cnf(cls_card__insert__if_1,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
| hBOOL(c_in(X1,X2,X3))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_1) ).
cnf(cls_order__neq__le__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
cnf(cls_order__le__neq__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
cnf(cls_order__less__le_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
cnf(cls_order__le__less_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
cnf(cls_xt1_I12_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
cnf(cls_order__less__imp__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
cnf(cls_order__le__less_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
cnf(cls_Suc__lessD_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
cnf(cls_Suc__le__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
cnf(cls_less__eq__Suc__le_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
cnf(cls_Suc__leD_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
cnf(cls_Suc__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
cnf(cls_less__Suc__eq__0__disj_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
cnf(cls_Suc__le__mono_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
cnf(cls_Min__insert_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__insert_0) ).
cnf(cls_Max__insert_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__insert_0) ).
cnf(cls_Un__UNIV__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
cnf(cls_Int__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
cnf(cls_empty__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
cnf(cls_nat__less__cases_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
cnf(cls_add__cancel__end_0,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X4)
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
cnf(cls_Suc__lessI_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2))
| c_Suc(X1) = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
cnf(cls_finite__compl_1,axiom,
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X1)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_1) ).
cnf(cls_le__SucE_0,axiom,
( X1 = c_Suc(X2)
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),c_Suc(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
cnf(cls_Suc__leI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
cnf(cls_less__eq__Suc__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
cnf(cls_add__diff__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_not__less__less__Suc__eq_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
cnf(cls_less__SucE_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
cnf(cls_less__antisym_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),c_Suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
cnf(cls_ab__semigroup__mult_Ononempty__iff_2,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ononempty__iff_2) ).
cnf(cls_less__Suc__eq__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
cnf(cls_ab__semigroup__mult_Omult__left__commute_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__left__commute_0) ).
cnf(cls_card__eq__UNIV__imp__eq__UNIV_0,axiom,
( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
cnf(cls_minus__mult__left_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
cnf(cls_greaterThanAtMost__empty_0,axiom,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty_0) ).
cnf(cls_atLeastatMost__empty_0,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).
cnf(cls_atLeastLessThan__empty_0,axiom,
( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
cnf(cls_le__less__Suc__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
cnf(cls_less__SucI_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
cnf(cls_less__Suc__eq__le_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
cnf(cls_le__SucI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
cnf(cls_fold1__singleton_0,axiom,
hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
cnf(cls_Un__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
cnf(cls_Int__UNIV__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
cnf(cls_Min__in_0,axiom,
( hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2),X2,X1))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).
cnf(cls_Max__in_0,axiom,
( hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2),X2,X1))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).
cnf(cls_le__neq__implies__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
cnf(cls_le__eq__less__or__eq_0,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
cnf(cls_nat__less__le_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_nat__less__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
cnf(cls_termination__basic__simps_I5_J_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
cnf(cls_minus__add__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
cnf(cls_add__cancel__end_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
cnf(cls_Min__singleton_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
cnf(cls_Max__singleton_0,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
cnf(cls_Inf__singleton_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
cnf(cls_insert__absorb_0,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_min__max_Osup__absorb1_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
cnf(cls_min__max_Ole__iff__sup_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
cnf(cls_sup__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
cnf(cls_le__iff__sup_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
cnf(cls_le__iff__inf_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(cls_inf__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
cnf(cls_min__max_Ole__iff__inf_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
cnf(cls_min__max_Oinf__absorb2_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
cnf(cls_cut_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).
cnf(cls_square__eq__iff_1,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
cnf(cls_minus__mult__minus_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
cnf(cls_minus__mult__commute_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
cnf(cls_linorder__less__linear_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
cnf(cls_linorder__neqE_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
cnf(cls_Un__UNIV__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
cnf(cls_Int__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
cnf(cls_Diff__UNIV_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
cnf(cls_linorder__not__less_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
cnf(cls_linorder__not__le_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
cnf(cls_not__leE_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
cnf(cls_linorder__linear_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
cnf(cls_minus__mult__right_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
cnf(cls_min__max_Osup__left__idem_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
cnf(cls_sup__left__idem_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
cnf(cls_inf__left__idem_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
cnf(cls_mult__left__idem_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
cnf(cls_min__max_Oinf__left__idem_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
cnf(cls_not__less__eq__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_Compl__eq__Compl__iff_0,axiom,
( X2 = X3
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
cnf(cls_Inf__insert_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,X3,X1),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
cnf(cls_compl__unique_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__unique_0) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_finite__insert_0,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
cnf(cls_not__less__less__Suc__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
cnf(cls_not__less__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
cnf(cls_min__max_Ole__iff__sup_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
cnf(cls_le__iff__sup_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
cnf(cls_le__iff__inf_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
cnf(cls_min__max_Ole__iff__inf_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_Int__UNIV__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
cnf(cls_Diff__empty_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_greaterThanAtMost__empty__iff2_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_1) ).
cnf(cls_atLeastatMost__empty__iff2_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
cnf(cls_atLeastLessThan__empty__iff2_1,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).
cnf(cls_greaterThanAtMost__empty__iff_1,axiom,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_1) ).
cnf(cls_atLeastatMost__empty__iff_1,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
cnf(cls_atLeastLessThan__empty__iff_1,axiom,
( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).
cnf(cls_square__eq__iff_0,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
cnf(cls_fun__Compl__def_0,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
cnf(cls_nat__neq__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
cnf(cls_nat__le__linear_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
cnf(cls_Suc__n__not__le__n_0,axiom,
~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
cnf(cls_minus__diff__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X2)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_ab__semigroup__idem__mult_Omult__left__idem_0,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X2),X3)) = hAPP(hAPP(X1,X2),X3)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__left__idem_0) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_eq__eqI_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_add__right__cancel_0,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_eq__eqI_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_add__left__cancel_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_Diff__cancel_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_atLeastAtMost__singleton_0,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
cnf(cls_min__max_Osup__inf__absorb_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
cnf(cls_sup__inf__absorb_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
cnf(cls_inf__sup__absorb_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_min__max_Oinf__sup__absorb_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ hBOOL(c_in(v_x,v_F,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_bot__empty__eq_0,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
cnf(cls_diff__minus__eq__add_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
cnf(cls_diff__eq_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
cnf(cls_ab__diff__minus_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
cnf(cls_diff__def_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).
cnf(cls_diff__minus_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
cnf(cls_class__ring_Osub__add_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
cnf(cls_less__not__refl_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
cnf(cls_nat__less__le_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
cnf(cls_Compl__UNIV__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
cnf(cls_Compl__empty__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
cnf(cls_Un__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
cnf(cls_Int__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
cnf(cls_finite__insert_1,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
cnf(cls_compl__sup__top_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
cnf(cls_compl__inf__bot_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
cnf(cls_bot__least_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
cnf(cls_le__Suc__eq_2,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),c_Suc(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
cnf(cls_empty_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_insert__not__empty_0,axiom,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
cnf(cls_top__greatest_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_order__eq__refl_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
cnf(cls_order__eq__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_min__max_Osup__commute_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
cnf(cls_sup__commute_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_inf__commute_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_min__max_Oinf__commute_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
cnf(cls_diff__Suc__Suc_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(X1)),c_Suc(X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
cnf(cls_COMBK__def__raw_0,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def__raw_0) ).
cnf(cls_less__Suc__eq_2,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
cnf(cls_lessI_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_ab__semigroup__mult_Omult__commute_0,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__commute_0) ).
cnf(cls_sup__compl__top_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
cnf(cls_inf__compl__bot_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
cnf(cls_inf__eq__top__eq1_0,axiom,
( X2 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
cnf(cls_inf__eq__top__eq2_0,axiom,
( X3 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( X3 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
cnf(cls_eq__imp__le_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
cnf(cls_le__refl_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
cnf(cls_Inf__UNIV_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
cnf(cls_Inf__empty_0,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
cnf(cls_sup__top__left_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(cls_inf__bot__left_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
cnf(cls_top__fun__eq_0,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
cnf(cls_bot__fun__eq_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
cnf(cls_finite__UNIV_0,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
cnf(cls_neg__equal__iff__equal_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
cnf(cls_sup__bot__left_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
cnf(cls_inf__top__left_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
cnf(cls_sup__top__right_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
cnf(cls_inf__bot__right_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
cnf(cls_sup__bot__right_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
cnf(cls_inf__top__right_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
cnf(cls_minus__equation__iff_1,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
cnf(cls_minus__minus_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
cnf(cls_double__compl_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_equation__minus__iff_1,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_equation__minus__iff_0,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
cnf(cls_ab__semigroup__idem__mult_Omult__idem_0,axiom,
( hAPP(hAPP(X1,X2),X2) = X2
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__idem_0) ).
cnf(cls_min__max_Osup__idem_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
cnf(cls_sup__idem_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(cls_inf__idem_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
cnf(cls_mult__idem_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
cnf(cls_min__max_Oinf__idem_0,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
cnf(cls_com_Osimps_I3_J_0,axiom,
( X1 = X3
| c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSemi(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
cnf(cls_com_Osimps_I3_J_1,axiom,
( X2 = X4
| c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSemi(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
cnf(clsarity_fun__Finite__Set_Ofinite_Ofinite,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
cnf(cls_compl__top__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
cnf(cls_compl__bot__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
cnf(clsarity_fun__Orderings_Otop,axiom,
( class_Orderings_Otop(tc_fun(X1,X2))
| ~ class_Orderings_Otop(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
cnf(clsarity_fun__Orderings_Obot,axiom,
( class_Orderings_Obot(tc_fun(X1,X2))
| ~ class_Orderings_Obot(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
cnf(clsarity_fun__HOL_Ominus,axiom,
( class_HOL_Ominus(tc_fun(X1,X2))
| ~ class_HOL_Ominus(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
cnf(clsarity_fun__HOL_Ouminus,axiom,
( class_HOL_Ouminus(tc_fun(X1,X2))
| ~ class_HOL_Ouminus(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).
cnf(clsarity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
cnf(clsarity_fun__Lattices_Odistrib__lattice,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Odistrib__lattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
| ~ class_Lattices_Oboolean__algebra(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
cnf(clsarity_fun__HOL_Oord,axiom,
( class_HOL_Oord(tc_fun(X1,X2))
| ~ class_HOL_Oord(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Obounded__lattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
cnf(clsarity_fun__Lattices_Olattice,axiom,
( class_Lattices_Olattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
cnf(cls_linorder__class_OMin__def__raw_0,axiom,
( c_Finite__Set_Olinorder__class_OMin(X1) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__class_OMin__def__raw_0) ).
cnf(cls_Max__def__raw_0,axiom,
( c_Finite__Set_Olinorder__class_OMax(X1) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__def__raw_0) ).
cnf(cls_ab__semigroup__idem__mult__max_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__max_0) ).
cnf(cls_ab__semigroup__idem__mult__sup_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__sup_0) ).
cnf(cls_ab__semigroup__idem__mult__inf_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__inf_0) ).
cnf(cls_ab__semigroup__idem__mult__min_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__min_0) ).
cnf(cls_com_Osimps_I13_J_0,axiom,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
cnf(cls_com_Osimps_I12_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
cnf(cls_sup__max_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1) = c_Orderings_Oord__class_Omax(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__max_0) ).
cnf(cls_inf__min_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1) = c_Orderings_Oord__class_Omin(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__min_0) ).
cnf(cls_finite_0,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
cnf(cls_nat_Oinject_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
cnf(cls_Suc__inject_0,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Finite__Set_Ofinite(v_F,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(X1) != X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(cls_n__not__Suc__n_0,axiom,
X1 != c_Suc(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
cnf(clsarity_nat__HOL_Ominus,axiom,
class_HOL_Ominus(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
cnf(clsarity_bool__HOL_Ominus,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
cnf(clsarity_bool__HOL_Ouminus,axiom,
class_HOL_Ouminus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(i_0_1042,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X1),X2,X1,X3),X4),c_Set_Oinsert(X5,X6,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(X2,X5)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(X1),X2,X1,X3),X4),X6))
| hBOOL(c_in(X5,X6,X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ c_Finite__Set_Ofinite(X6,X3) ),
cls_fold__image__insert_0 ).
cnf(i_0_1043,axiom,
c_Finite__Set_Ofold__image(X1,X2,X3,X4) = c_Finite__Set_Ofold(c_COMBB(X1,X2,X3,tc_fun(X3,X3),X4),X4,X3),
cls_fold__image__def_0 ).
cnf(i_0_1044,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,X1,X3),X4),c_Set_Oinsert(X5,X6,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X2,X5)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(X1),X2,X1,X3),X4),X6))
| hBOOL(c_in(X5,X6,X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X6,X3) ),
cls_comm__monoid__add_Ofold__image__insert_0 ).
cnf(i_0_1045,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3,X4),X5),c_Set_Oinsert(X6,X7,X4)) = hAPP(hAPP(X1,hAPP(X2,X6)),hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3,X4),X5),X7))
| hBOOL(c_in(X6,X7,X4))
| ~ c_Finite__Set_Ofinite(X7,X4)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3) ),
cls_ab__semigroup__mult_Ofold__image__insert_0 ).
cnf(i_0_1046,axiom,
hAPP(hAPP(c_Finite__Set_Ofold__image(X1,X2,X3,X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))) = X5,
cls_fold__image__empty_0 ).
cnf(i_0_1047,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X4,X3)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),X3),c_COMBK(hAPP(X4,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X4,X3)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_escape_1,
[final] ).
cnf(i_0_1048,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P_H,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
cls_conjecture_6,
[final] ).
cnf(i_0_1049,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X2,X4,X3,X5,X6)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_conseq_2,
[final] ).
cnf(i_0_1050,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X4,X3,X5,X6)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_hoare__derivs_Ointros_I6_J_2,
[final] ).
cnf(i_0_1051,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P_H,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
cls_conjecture_3,
[final] ).
cnf(i_0_1052,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X3),X3,X1),X4),c_Set_Oinsert(X5,X6,X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(X2,X5)),hAPP(hAPP(c_Finite__Set_Ofold(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X3),X3,X1),X4),X6))
| hBOOL(c_in(X5,X6,X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ c_Finite__Set_Ofinite(X6,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1042,c_0_1043]),c_0_1043]),
[final] ).
cnf(i_0_1053,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(c_COMBB(c_HOL_Oplus__class_Oplus(X1),X2,X1,tc_fun(X1,X1),X3),X3,X1),X4),c_Set_Oinsert(X5,X6,X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X2,X5)),hAPP(hAPP(c_Finite__Set_Ofold(c_COMBB(c_HOL_Oplus__class_Oplus(X1),X2,X1,tc_fun(X1,X1),X3),X3,X1),X4),X6))
| hBOOL(c_in(X5,X6,X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X6,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1044,c_0_1043]),c_0_1043]),
[final] ).
cnf(i_0_1054,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(c_COMBB(X1,X2,X3,tc_fun(X3,X3),X4),X4,X3),X5),c_Set_Oinsert(X6,X7,X4)) = hAPP(hAPP(X1,hAPP(X2,X6)),hAPP(hAPP(c_Finite__Set_Ofold(c_COMBB(X1,X2,X3,tc_fun(X3,X3),X4),X4,X3),X5),X7))
| hBOOL(c_in(X6,X7,X4))
| ~ c_Finite__Set_Ofinite(X7,X4)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1045,c_0_1043]),c_0_1043]),
[final] ).
cnf(i_0_1055,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1)),c_Finite__Set_Ocard(X2,X1)))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_card__Diff2__less_0,
[final] ).
cnf(i_0_1056,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X4,X3,X7,X5)))
| ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X2,X4,X3)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X3),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_hoare__derivs_Ointros_I6_J_1,
[final] ).
cnf(i_0_1057,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X1,X2,X4,X3,X7,X5)))
| ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X2,X4,X3)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X3),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_conseq_1,
[final] ).
cnf(i_0_1058,axiom,
( c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,c_Set_Oinsert(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X4),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1),X5,X1,X1)
| hBOOL(c_in(X3,X4,X1))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ hBOOL(c_in(X2,X4,X1))
| ~ c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X3,X4,X5,X1,X1) ),
cls_fold__graph__permute__diff_0,
[final] ).
cnf(i_0_1059,axiom,
( c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,c_Set_Oinsert(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X4),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1),X5,X1,X1)
| hBOOL(c_in(X3,X4,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(c_in(X2,X4,X1))
| ~ c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X3,X4,X5,X1,X1) ),
cls_comm__monoid__add_Ofold__graph__permute__diff_0,
[final] ).
cnf(i_0_1060,axiom,
( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X4,tc_bool)),X5),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)),X4),X6,X4,X4)
| hBOOL(c_in(X3,X5,X4))
| ~ hBOOL(c_in(X2,X5,X4))
| ~ c_Finite__Set_Ofold__graph(X1,X3,X5,X6,X4,X4)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
cls_ab__semigroup__mult_Ofold__graph__permute__diff_0,
[final] ).
cnf(i_0_1061,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6)) ),
cls_less__add__iff1_1,
[final] ).
cnf(i_0_1062,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4)),X6)) ),
cls_le__add__iff1_1,
[final] ).
cnf(i_0_1063,axiom,
( c_Nitpick_Ofold__graph_H(X1,X2,X3,hAPP(hAPP(X1,X4),X5),X6,X7)
| ~ c_Nitpick_Ofold__graph_H(X1,X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X6,tc_bool)),X3),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6)),X5,X6,X7)
| ~ hBOOL(c_in(X4,X3,X6)) ),
cls_fold__graph_H_Ointros_I2_J_0,
[final] ).
cnf(i_0_1064,axiom,
( c_Finite__Set_Ofold__graph(X1,X2,X3,hAPP(hAPP(X1,X4),X5),X6,X7)
| ~ hBOOL(c_in(X4,X3,X6))
| ~ c_Finite__Set_Ofold__graph(X1,X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X6,tc_bool)),X3),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool)),X6)),X5,X6,X7) ),
cls_Diff1__fold__graph_0,
[final] ).
cnf(i_0_1065,axiom,
( c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X2,c_Set_Oinsert(X3,X4,X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5),X1,X1)
| hBOOL(c_in(X3,X4,X1))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(X1),X3,X4,X5,X1,X1) ),
cls_fold__graph__insert__swap_0,
[final] ).
cnf(i_0_1066,axiom,
( c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X2,c_Set_Oinsert(X3,X4,X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X5),X1,X1)
| hBOOL(c_in(X3,X4,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(X1),X3,X4,X5,X1,X1) ),
cls_comm__monoid__add_Ofold__graph__insert__swap_0,
[final] ).
cnf(i_0_1067,axiom,
( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,X4,X5),hAPP(hAPP(X1,X2),X6),X5,X5)
| hBOOL(c_in(X3,X4,X5))
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X6,X5,X5)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
cls_ab__semigroup__mult_Ofold__graph__insert__swap_0,
[final] ).
cnf(i_0_1068,axiom,
( c_Finite__Set_Ofold__graph(X1,X2,c_Set_Oinsert(X3,X4,X5),hAPP(hAPP(X1,X3),X6),X5,X7)
| hBOOL(c_in(X3,X4,X5))
| ~ c_Finite__Set_Ofold__graph(X1,X2,X4,X6,X5,X7) ),
cls_fold__graph_OinsertI_0,
[final] ).
cnf(i_0_1069,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,X5,X4,X1))),c_Set_Oimage(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X4,tc_bool)),X3),X5),X4,X1))),
cls_image__diff__subset_0,
[final] ).
cnf(i_0_1070,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
cls_less__add__iff1_0,
[final] ).
cnf(i_0_1071,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X4)),X5)),X6))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),X6))) ),
cls_le__add__iff1_0,
[final] ).
cnf(i_0_1072,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetsum(X2,X3,X4,X1)),X5) = c_Finite__Set_Osetsum(hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X4),X4,X1,X1),X5),X3,X4,X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
cls_setsum__left__distrib_0,
[final] ).
cnf(i_0_1073,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5),X3,X1)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X4,X3,X1)),c_Set_Oimage(X2,X5,X3,X1)))),
cls_image__Int__subset_0,
[final] ).
cnf(i_0_1074,plain,
hAPP(hAPP(c_Finite__Set_Ofold(c_COMBB(X1,X2,X3,tc_fun(X3,X3),X4),X4,X3),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))) = X5,
inference(rw,[status(thm)],[i_0_1046,c_0_1043]),
[final] ).
cnf(i_0_1075,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))) ),
cls_less__add__iff2_1,
[final] ).
cnf(i_0_1076,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6))) ),
cls_le__add__iff2_1,
[final] ).
cnf(i_0_1077,axiom,
( X1 = X2
| ~ c_Finite__Set_Ofold__graph(X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X1,X4,X5) ),
cls_empty__fold__graphE_0,
[final] ).
cnf(i_0_1078,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofold__graph(X3,X4,X1,X5,X2,X6) ),
cls_fold__graph__imp__finite_0,
[final] ).
cnf(i_0_1079,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
cls_less__add__iff2_0,
[final] ).
cnf(i_0_1080,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4)),X5)),X6)))
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)),X6))) ),
cls_le__add__iff2_0,
[final] ).
cnf(i_0_1081,axiom,
( c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),c_Finite__Set_Osetsum(X2,X5,X3,X1)),c_Finite__Set_Osetsum(X4,X5,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_setsum__subtractf_0,
[final] ).
cnf(i_0_1082,axiom,
( c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,X5,X3,X1)),c_Finite__Set_Osetsum(X4,X5,X3,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_setsum__addf_0,
[final] ).
cnf(i_0_1083,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X2)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)),
cls_Un__Int__crazy_0,
[final] ).
cnf(i_0_1084,axiom,
( c_Finite__Set_Ocard(X1,X2) = c_Finite__Set_Ocard(X3,X4)
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),c_Set_Oimage(X5,X3,X4,X2)),X1))
| ~ c_Fun_Oinj__on(X5,X3,X4,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X6,X1,X2,X4)),X3))
| ~ c_Fun_Oinj__on(X6,X1,X2,X4) ),
cls_card__bij__eq_0,
[final] ).
cnf(i_0_1085,axiom,
( c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)),c_Finite__Set_Osetsum(X2,X5,X3,X1))),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5),X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X4,X3) ),
cls_setsum__Un_0,
[final] ).
cnf(i_0_1086,axiom,
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X7,X4,X5) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X6,X7,X4,X5),X2,X3,X4,X5)
| X2 = X6 ),
cls_fun__upd__twist_0,
[final] ).
cnf(i_0_1087,axiom,
( ~ hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X3,X5),X5))
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X4,X3),X3,X5) ),
cls_inj__on__insert_1,
[final] ).
cnf(i_0_1088,axiom,
( c_Fun_Oinj__on(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),X5),X3,X1)),c_Set_Oimage(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X5),X4),X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Fun_Oinj__on(X2,X5,X3,X1)
| ~ c_Fun_Oinj__on(X2,X4,X3,X1) ),
cls_inj__on__Un_3,
[final] ).
cnf(i_0_1089,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq12__1(X2,X5,X4,X6)),v_sko__Hoare__Mirabelle__Xconseq12__3(X2,X5,X4,X6)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_conseq12_2,
[final] ).
cnf(i_0_1090,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(X1,X2,X3,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4),X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X3),X3) ),
cls_finite__range__imageI_0,
[final] ).
cnf(i_0_1091,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_psubset__insert__iff_9,
[final] ).
cnf(i_0_1092,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,c_Set_Ovimage(X2,X3,X4,X1),X4,X1)),X3)),
cls_image__vimage__subset_0,
[final] ).
cnf(i_0_1093,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1)),c_Finite__Set_Ocard(X2,X1)))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_card__Diff1__less_0,
[final] ).
cnf(i_0_1094,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_psubset__insert__iff_8,
[final] ).
cnf(i_0_1095,axiom,
c_Nitpick_Ofold__graph_H(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
cls_fold__graph_H_Ointros_I1_J_0,
[final] ).
cnf(i_0_1096,axiom,
c_Finite__Set_Ofold__graph(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X2,X3,X4),
cls_fold__graph_OemptyI_0,
[final] ).
cnf(i_0_1097,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X4),X3,X1)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X4,X3,X1))))
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X1) ),
cls_inj__image__Compl__subset_0,
[final] ).
cnf(i_0_1098,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4)) ),
cls_psubset__insert__iff_5,
[final] ).
cnf(i_0_1099,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1)),c_Finite__Set_Ocard(X2,X1)))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_card__Diff1__le_0,
[final] ).
cnf(i_0_1100,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X5,X2,X1,X4)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ c_Fun_Oinj__on(X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X4) ),
cls_inj__image__subset__iff_0,
[final] ).
cnf(i_0_1101,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4)) ),
cls_subset__insert__iff_4,
[final] ).
cnf(i_0_1102,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4)) ),
cls_psubset__insert__iff_4,
[final] ).
cnf(i_0_1103,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4)) ),
cls_subset__insert__iff_3,
[final] ).
cnf(i_0_1104,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4)) ),
cls_diff__single__insert_0,
[final] ).
cnf(i_0_1105,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq12__1(X2,X5,X4,X6)),v_sko__Hoare__Mirabelle__Xconseq12__2(X2,X5,X4,X6)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_conseq12_0,
[final] ).
cnf(i_0_1106,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1)),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X5),X3,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)),c_Finite__Set_Osetsum(X2,X5,X3,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Finite__Set_Ofinite(X4,X3) ),
cls_setsum__Un__Int_0,
[final] ).
cnf(i_0_1107,axiom,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2,X6,X4,X5) = c_Fun_Ofun__upd(X1,X2,X6,X4,X5),
cls_fun__upd__upd_0,
[final] ).
cnf(i_0_1108,axiom,
( c_Set_Oimage(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5) = c_Set_Oinsert(X3,c_Set_Oimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X4,tc_bool)),X6),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)),X4,X5),X5)
| ~ hBOOL(c_in(X2,X6,X4)) ),
cls_fun__upd__image_0,
[final] ).
cnf(i_0_1109,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Ovimage(X2,X3,X1,X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),c_Set_Oimage(X2,X5,X1,X4)))
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X4) ),
cls_vimage__subsetI_0,
[final] ).
cnf(i_0_1110,axiom,
( c_Fun_Oinj__on(X1,c_Set_Oinsert(X2,X3,X4),X4,X5)
| hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X4,tc_bool)),X3),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)),X4,X5),X5))
| ~ c_Fun_Oinj__on(X1,X3,X4,X5) ),
cls_inj__on__insert_2,
[final] ).
cnf(i_0_1111,axiom,
( hBOOL(c_in(hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),X5),X6,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X6))
| ~ hBOOL(c_in(X5,c_Set_Oimage(X2,X1,X3,X4),X4))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
cls_the__inv__into__into_0,
[final] ).
cnf(i_0_1112,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,X6),v_sko__Hoare__Mirabelle__Xconseq12__3(X2,X7,X4,X5)))
| ~ hBOOL(hAPP(hAPP(X7,X6),v_sko__Hoare__Mirabelle__Xconseq12__2(X2,X7,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X7),X3),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_conseq12_1,
[final] ).
cnf(i_0_1113,axiom,
( hBOOL(c_in(hAPP(X1,X4),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3),X3))
| hAPP(X1,X4) = hAPP(X1,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(hAPP(X1,X4),X1,X4,X3,X2))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X3) ),
cls_range__ex1__eq_2,
[final] ).
cnf(i_0_1114,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X4)))
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X5,X1,X2,X4)),X3))
| ~ c_Fun_Oinj__on(X5,X1,X2,X4) ),
cls_card__inj__on__le_0,
[final] ).
cnf(i_0_1115,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4)),c_Finite__Set_Ocard(X2,X3)))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_card__image__le_0,
[final] ).
cnf(i_0_1116,axiom,
( c_Set_Oimage(X1,X2,X3,X3) = X2
| ~ c_Fun_Oinj__on(X1,X2,X3,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oimage(X1,X2,X3,X3)),X2))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_endo__inj__surj_0,
[final] ).
cnf(i_0_1117,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),X5),X3,X1)),c_Set_Oimage(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X5),X4),X3,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Fun_Oinj__on(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X5),X3,X1) ),
cls_inj__on__Un_2,
[final] ).
cnf(i_0_1118,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4))
| hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
cls_psubset__insert__iff_1,
[final] ).
cnf(i_0_1119,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X5))
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X1) ),
cls_inj__image__subset__iff_1,
[final] ).
cnf(i_0_1120,axiom,
( c_Fun_Oinj__on(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5)
| hBOOL(c_in(X3,c_Set_Oimage(X1,X6,X4,X5),X5))
| ~ c_Fun_Oinj__on(X1,X6,X4,X5) ),
cls_inj__on__fun__updI_0,
[final] ).
cnf(i_0_1121,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4))
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1))) ),
cls_subset__insert__iff_0,
[final] ).
cnf(i_0_1122,axiom,
( hBOOL(c_in(hAPP(X1,X2),X3,X4))
| ~ hBOOL(c_in(X2,X5,X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X1,X5,X6,X4)),X3)) ),
cls_image__subset__iff_0,
[final] ).
cnf(i_0_1123,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3),X3))
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(hAPP(X1,X2),X1,X2,X3,X4) != X2
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3) ),
cls_range__ex1__eq_3,
[final] ).
cnf(i_0_1124,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X1,X2,X4,X3))) ),
cls_conseq_0,
[final] ).
cnf(i_0_1125,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X2,X4,X3))) ),
cls_hoare__derivs_Ointros_I6_J_0,
[final] ).
cnf(i_0_1126,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xescape__1(X1,X2,X4,X3)),v_sko__Hoare__Mirabelle__Xescape__2(X1,X2,X4,X3))) ),
cls_escape_0,
[final] ).
cnf(i_0_1127,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oimage(X2,X3,X4,X1)),c_Set_Oimage(X2,X5,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X5)) ),
cls_image__mono_0,
[final] ).
cnf(i_0_1128,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Ovimage(X2,X3,X1,X4)),c_Set_Ovimage(X2,X5,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X5)) ),
cls_vimage__mono_0,
[final] ).
cnf(i_0_1129,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),c_Set_Oimage(X5,X2,X1,X4)),c_Set_Oimage(X5,X3,X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
cls_subset__image__iff_2,
[final] ).
cnf(i_0_1130,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Odistrib__inf__le_0,
[final] ).
cnf(i_0_1131,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))))
| ~ class_Lattices_Olattice(X1) ),
cls_distrib__inf__le_0,
[final] ).
cnf(i_0_1132,axiom,
c_Set_Oimage(c_COMBB(X1,X2,X3,X4,X5),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X4) = c_Set_Oimage(X1,c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X5,X3),X3,X4),
cls_range__composition_0,
[final] ).
cnf(i_0_1133,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),c_Com_Ocom_OSemi(X4,X5)),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X7),X5),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),X4),X7),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2) ),
cls_Comp_0,
[final] ).
cnf(i_0_1134,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X1)),hAPP(v_c0,X1)),hAPP(v_Q,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X1)),hAPP(v_c0,X1)),hAPP(v_Q_H,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
cls_conjecture_5,
[final] ).
cnf(i_0_1135,axiom,
( c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X6))
| ~ c_Fun_Oinj__on(X1,X6,X2,X5) ),
cls_inj__on__image__Int_0,
[final] ).
cnf(i_0_1136,axiom,
( c_Set_Oimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X3),X6))
| ~ c_Fun_Oinj__on(X1,X6,X2,X5) ),
cls_inj__on__image__set__diff_0,
[final] ).
cnf(i_0_1137,axiom,
c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6),
cls_image__image_0,
[final] ).
cnf(i_0_1138,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,X5),X4,X5,X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
cls_setsum__right__distrib_0,
[final] ).
cnf(i_0_1139,axiom,
( c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),X4,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_setsum__negf_0,
[final] ).
cnf(i_0_1140,axiom,
( hAPP(X1,hAPP(c_Fun_Othe__inv__into(X2,X1,X3,X4),X5)) = X5
| ~ hBOOL(c_in(X5,c_Set_Oimage(X1,X2,X3,X4),X4))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
cls_f__the__inv__into__f_0,
[final] ).
cnf(i_0_1141,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X4)) ),
cls_Diff__subset__conv_0,
[final] ).
cnf(i_0_1142,axiom,
( hAPP(X1,X2) = X3
| ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4),X5)) ),
cls_vimage__singleton__eq_0,
[final] ).
cnf(i_0_1143,axiom,
( X1 = hAPP(X2,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X1,X2,X3,X4))
| ~ hBOOL(c_in(X1,c_Set_Oimage(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3),X3))
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X3) ),
cls_range__ex1__eq_0,
[final] ).
cnf(i_0_1144,axiom,
( c_Set_Oimage(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6,X4,X5) = c_Set_Oimage(X1,X6,X4,X5)
| hBOOL(c_in(X2,X6,X4)) ),
cls_fun__upd__image_1,
[final] ).
cnf(i_0_1145,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_Un__mono_0,
[final] ).
cnf(i_0_1146,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_Int__mono_0,
[final] ).
cnf(i_0_1147,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X5),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_Diff__mono_0,
[final] ).
cnf(i_0_1148,axiom,
( X2 = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(X1,X2),X1,X4,X3)
| ~ hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
cls_range__ex1__eq_1,
[final] ).
cnf(i_0_1149,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Finite__Set_Ofold(X2,X3,X3),X4),X5)),hAPP(hAPP(X2,X6),X4)))
| ~ hBOOL(c_in(X6,X5,X3))
| ~ c_Finite__Set_Ofinite(X5,X3)
| ~ c_Lattices_Olower__semilattice(X1,X7,X2,X3) ),
cls_lower__semilattice_Ofold__inf__le__inf_0,
[final] ).
cnf(i_0_1150,axiom,
c_Set_Ovimage(X1,c_Set_Oinsert(X2,X3,X4),X5,X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4),X5,X4)),c_Set_Ovimage(X1,X3,X5,X4)),
cls_vimage__insert_0,
[final] ).
cnf(i_0_1151,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(c_in(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(X1,X3,X4,X5),c_Set_Oimage(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5),X5))
| ~ c_Fun_Oinj__on(X3,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
cls_inj__transfer_0,
[final] ).
cnf(i_0_1152,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))) ),
cls_Diff__subset__conv_1,
[final] ).
cnf(i_0_1153,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Odistrib__sup__le_0,
[final] ).
cnf(i_0_1154,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))))
| ~ class_Lattices_Olattice(X1) ),
cls_distrib__sup__le_0,
[final] ).
cnf(i_0_1155,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X2)))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(c_in(X4,X3,X1))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_fold__inf__le__inf_0,
[final] ).
cnf(i_0_1156,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X2)),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_eq__add__iff2_1,
[final] ).
cnf(i_0_1157,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4))
| ~ class_Ring__and__Field_Oring(X1) ),
cls_eq__add__iff1_1,
[final] ).
cnf(i_0_1158,axiom,
( c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X5) ),
cls_image__Int_0,
[final] ).
cnf(i_0_1159,axiom,
( c_Set_Oimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2,X5) ),
cls_image__set__diff_0,
[final] ).
cnf(i_0_1160,axiom,
( c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),X5),X3,X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)),c_Finite__Set_Osetsum(X2,X5,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X5),X4))
| ~ c_Finite__Set_Ofinite(X4,X3) ),
cls_setsum__diff_0,
[final] ).
cnf(i_0_1161,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),X3)) ),
cls_Un__subset__iff_0,
[final] ).
cnf(i_0_1162,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X4),X2)),X3)) ),
cls_Un__subset__iff_1,
[final] ).
cnf(i_0_1163,axiom,
( c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2,tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Osetsum(X1,X3,X2,tc_nat)),c_Finite__Set_Osetsum(X1,X4,X2,tc_nat))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X4),X3))
| ~ c_Finite__Set_Ofinite(X4,X2) ),
cls_setsum__diff__nat_0,
[final] ).
cnf(i_0_1164,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),hAPP(X2,X6)),
cls_ATP__Linkup_OCOMBS__def_0,
[final] ).
cnf(i_0_1165,axiom,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),hAPP(X2,X6)),
cls_COMBS__def_0,
[final] ).
cnf(i_0_1166,axiom,
( c_Finite__Set_Osetsum(X2,X3,X4,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X2,X5)),c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X4,tc_bool)),X3),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),X4)),X4,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ hBOOL(c_in(X5,X3,X4))
| ~ c_Finite__Set_Ofinite(X3,X4) ),
cls_setsum__diff1_H_0,
[final] ).
cnf(i_0_1167,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_ATP__Linkup_OCOMBB__def_0,
[final] ).
cnf(i_0_1168,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0,
[final] ).
cnf(i_0_1169,axiom,
hAPP(c_COMBS(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)),
cls_COMBS__def__raw_0,
[final] ).
cnf(i_0_1170,axiom,
( hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| X6 = X2 ),
cls_fun__upd__other_0,
[final] ).
cnf(i_0_1171,axiom,
( hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X6) = hAPP(X1,X6)
| X6 = X2 ),
cls_fun__upd__apply_1,
[final] ).
cnf(i_0_1172,axiom,
hAPP(c_COMBB(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(v_P,hAPP(v_Q,v_R)),
cls_COMBB__def__raw_0,
[final] ).
cnf(i_0_1173,axiom,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
cls_fun__upd__apply_0,
[final] ).
cnf(i_0_1174,axiom,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
cls_fun__upd__same_0,
[final] ).
cnf(i_0_1175,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ c_Fun_Oinj__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X5) ),
cls_inj__image__mem__iff_0,
[final] ).
cnf(i_0_1176,axiom,
( c_Finite__Set_Osetsum(X5,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_Finite__Set_Osetsum(X5,X3,X2,X1)),c_Finite__Set_Osetsum(X5,X4,X2,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
cls_setsum__Un__disjoint_0,
[final] ).
cnf(i_0_1177,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_Un__subset__iff_2,
[final] ).
cnf(i_0_1178,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_Un__least_0,
[final] ).
cnf(i_0_1179,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),c_Set_Oimage(X1,X2,X3,X3)))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_finite__surj__inj_0,
[final] ).
cnf(i_0_1180,axiom,
( c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X3,X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)),hAPP(X2,X5))
| ~ class_Ring__and__Field_Oring(X1)
| ~ hBOOL(c_in(X5,X4,X3))
| ~ c_Finite__Set_Ofinite(X4,X3) ),
cls_setsum__diff1__ring_0,
[final] ).
cnf(i_0_1181,axiom,
( c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X3,X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1)),hAPP(X2,X5))
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ hBOOL(c_in(X5,X4,X3))
| ~ c_Finite__Set_Ofinite(X4,X3) ),
cls_setsum__diff1_0,
[final] ).
cnf(i_0_1182,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xconseq2__1(X4,X5)),v_sko__Hoare__Mirabelle__Xconseq2__2(X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_conseq2_1,
[final] ).
cnf(i_0_1183,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq1__1(X2,X5)),v_sko__Hoare__Mirabelle__Xconseq1__2(X2,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_conseq1_1,
[final] ).
cnf(i_0_1184,axiom,
( c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),X2,tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Osetsum(X1,X3,X2,tc_nat)),hAPP(X1,X4))
| ~ hBOOL(c_in(X4,X3,X2)) ),
cls_setsum__diff1__nat_0,
[final] ).
cnf(i_0_1185,axiom,
c_Set_Oimage(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2,X5) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Set_Oimage(X1,X3,X2,X5)),c_Set_Oimage(X1,X4,X2,X5)),
cls_image__Un_0,
[final] ).
cnf(i_0_1186,axiom,
c_Set_Ovimage(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X5,X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X2)),c_Set_Ovimage(X1,X4,X5,X2)),
cls_vimage__Un_0,
[final] ).
cnf(i_0_1187,axiom,
c_Set_Ovimage(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X5,X2) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X2)),c_Set_Ovimage(X1,X4,X5,X2)),
cls_vimage__Int_0,
[final] ).
cnf(i_0_1188,axiom,
c_Set_Ovimage(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X5,X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X5,tc_bool)),c_Set_Ovimage(X1,X3,X5,X2)),c_Set_Ovimage(X1,X4,X5,X2)),
cls_vimage__Diff_0,
[final] ).
cnf(i_0_1189,axiom,
hBOOL(c_in(X1,c_Set_Ovimage(X2,c_Set_Oinsert(hAPP(X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X4,X3),X4)),
cls_vimage__singleton__eq_1,
[final] ).
cnf(i_0_1190,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X2))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) ),
cls_Un__Int__assoc__eq_0,
[final] ).
cnf(i_0_1191,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X2,v_sko__Hoare__Mirabelle__Xconseq1__1(X2,X5)),v_sko__Hoare__Mirabelle__Xconseq1__2(X2,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X5),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_conseq1_0,
[final] ).
cnf(i_0_1192,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X4),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X5,v_sko__Hoare__Mirabelle__Xconseq2__1(X4,X5)),v_sko__Hoare__Mirabelle__Xconseq2__2(X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),X2),X3),X5),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
cls_conseq2_0,
[final] ).
cnf(i_0_1193,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_Set_Oimage(X3,X4,X5,X2)))
| ~ c_Finite__Set_Ofinite(X4,X5) ),
cls_finite__surj_0,
[final] ).
cnf(i_0_1194,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
cls_conjecture_4,
[final] ).
cnf(i_0_1195,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2))) ),
cls_Compl__subset__Compl__iff_0,
[final] ).
cnf(i_0_1196,axiom,
( hAPP(X1,X2) = X3
| c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X1 ),
cls_fun__upd__idem__iff_0,
[final] ).
cnf(i_0_1197,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X5)),X3)),X4) = X6
| ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6) ),
cls_eq__add__iff1_0,
[final] ).
cnf(i_0_1198,axiom,
( X4 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X5),X2)),X3)),X6)
| ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X3)),X6) ),
cls_eq__add__iff2_0,
[final] ).
cnf(i_0_1199,axiom,
( hBOOL(c_in(hAPP(X1,X2),X3,X4))
| ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
cls_vimageD_0,
[final] ).
cnf(i_0_1200,axiom,
( hBOOL(c_in(hAPP(X1,X2),X3,X4))
| ~ hBOOL(c_in(X2,c_Set_Ovimage(X1,X3,X5,X4),X5)) ),
cls_vimageE_0,
[final] ).
cnf(i_0_1201,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X3,X1))) ),
cls_atLeastatMost__psubset__iff_2,
[final] ).
cnf(i_0_1202,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
cls_combine__common__factor_0,
[final] ).
cnf(i_0_1203,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(c_in(X2,X4,X1))
| ~ c_Finite__Set_Ofinite(X4,X1) ),
cls_sup__le__fold__sup_0,
[final] ).
cnf(i_0_1204,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1))),X4),
cls_Diff__insert2_0,
[final] ).
cnf(i_0_1205,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4))
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
cls_inj__image__mem__iff_1,
[final] ).
cnf(i_0_1206,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
cls_Int__subset__iff_2,
[final] ).
cnf(i_0_1207,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
cls_Int__greatest_0,
[final] ).
cnf(i_0_1208,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1))) ),
cls_atLeastatMost__psubset__iff_0,
[final] ).
cnf(i_0_1209,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X5,X1))) ),
cls_atLeastatMost__subset__iff_0,
[final] ).
cnf(i_0_1210,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X3,X1))) ),
cls_atLeastatMost__psubset__iff_1,
[final] ).
cnf(i_0_1211,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X2,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X5,X3,X1))) ),
cls_atLeastatMost__subset__iff_1,
[final] ).
cnf(i_0_1212,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4),
cls_Diff__Int2_0,
[final] ).
cnf(i_0_1213,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
cls_Un__Int__distrib2_0,
[final] ).
cnf(i_0_1214,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
cls_Int__Un__distrib2_0,
[final] ).
cnf(i_0_1215,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
cls_Diff__Int__distrib2_0,
[final] ).
cnf(i_0_1216,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X4)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4)),
cls_Un__Diff_0,
[final] ).
cnf(i_0_1217,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X2,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X5,X3,X1))) ),
cls_atLeastLessThan__subset__iff_1,
[final] ).
cnf(i_0_1218,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X5,X1))) ),
cls_atLeastLessThan__subset__iff_0,
[final] ).
cnf(i_0_1219,axiom,
( hBOOL(hAPP(X1,hAPP(X2,X3)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X2,X1,X4,X5),X3)) ),
cls_vimage__code_0,
[final] ).
cnf(i_0_1220,axiom,
( c_Suc(c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1)) = c_Finite__Set_Ocard(X2,X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_card__Suc__Diff1_0,
[final] ).
cnf(i_0_1221,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4))) ),
cls_Int__subset__iff_0,
[final] ).
cnf(i_0_1222,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3))) ),
cls_Int__subset__iff_1,
[final] ).
cnf(i_0_1223,axiom,
( c_Set_Oimage(c_Fun_Othe__inv__into(X1,X2,X3,X4),c_Set_Oimage(X2,X1,X3,X4),X4,X3) = X1
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
cls_the__inv__into__onto_0,
[final] ).
cnf(i_0_1224,axiom,
( c_Fun_Oinj__on(c_Fun_Othe__inv__into(X1,X2,X3,X4),c_Set_Oimage(X2,X1,X3,X4),X4,X3)
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
cls_inj__on__the__inv__into_0,
[final] ).
cnf(i_0_1225,axiom,
( X2 = X5
| c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),X3,X4) ),
cls_inj__on__Un__image__eq__iff_0,
[final] ).
cnf(i_0_1226,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2)) ),
cls_atLeastatMost__psubset__iff_6,
[final] ).
cnf(i_0_1227,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2)) ),
cls_atLeastatMost__psubset__iff_5,
[final] ).
cnf(i_0_1228,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X2)) ),
cls_Un__Int__assoc__eq_1,
[final] ).
cnf(i_0_1229,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X2),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X3))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_card__insert_0,
[final] ).
cnf(i_0_1230,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1))) ),
cls_atLeastatMost__psubset__iff_3,
[final] ).
cnf(i_0_1231,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_psubset__insert__iff_7,
[final] ).
cnf(i_0_1232,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
cls_Compl__anti__mono_0,
[final] ).
cnf(i_0_1233,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
cls_Compl__subset__Compl__iff_1,
[final] ).
cnf(i_0_1234,axiom,
c_Set_Oimage(X1,c_Set_Ovimage(X1,X2,X3,X4),X3,X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X4,tc_bool)),X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4)),
cls_image__vimage__eq_0,
[final] ).
cnf(i_0_1235,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Ocard(X2,X1)),c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1))
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1) ),
cls_card__Diff__subset__Int_0,
[final] ).
cnf(i_0_1236,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X2)),
cls_Int__lower1_0,
[final] ).
cnf(i_0_1237,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X3)),
cls_Int__lower2_0,
[final] ).
cnf(i_0_1238,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X2)),
cls_Diff__subset_0,
[final] ).
cnf(i_0_1239,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
cls_Un__Int__distrib_0,
[final] ).
cnf(i_0_1240,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
cls_Int__Un__distrib_0,
[final] ).
cnf(i_0_1241,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
cls_Diff__Int__distrib_0,
[final] ).
cnf(i_0_1242,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X4)),
cls_Diff__Un_0,
[final] ).
cnf(i_0_1243,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X4)),
cls_Diff__Int_0,
[final] ).
cnf(i_0_1244,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X4,X2,X1)),X3)) ),
cls_insert__subset_1,
[final] ).
cnf(i_0_1245,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X1)) ),
cls_less__diff__iff_0,
[final] ).
cnf(i_0_1246,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X1)) ),
cls_le__diff__iff_0,
[final] ).
cnf(i_0_1247,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),c_Set_Oinsert(X2,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4)) ),
cls_insert__mono_0,
[final] ).
cnf(i_0_1248,axiom,
hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4),X4)),
cls_rangeI_0,
[final] ).
cnf(i_0_1249,axiom,
( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
| ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
cls_vimageI_0,
[final] ).
cnf(i_0_1250,axiom,
( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
| ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
cls_vimageI2_0,
[final] ).
cnf(i_0_1251,axiom,
( hBOOL(c_in(X1,c_Set_Ovimage(X2,X3,X4,X5),X4))
| ~ hBOOL(c_in(hAPP(X2,X1),X3,X5)) ),
cls_vimage__eq_1,
[final] ).
cnf(i_0_1252,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))) ),
cls_mult__less__cancel__right__disj_3,
[final] ).
cnf(i_0_1253,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X2))) ),
cls_mult__less__cancel__left__disj_3,
[final] ).
cnf(i_0_1254,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X4))
| ~ hBOOL(c_in(X2,X4,X1)) ),
cls_insert__subset_2,
[final] ).
cnf(i_0_1255,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2))),
cls_Nitpick_OEx1__def_2,
[final] ).
cnf(i_0_1256,axiom,
( c_Finite__Set_Osetsum(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X3,X1) = c_Finite__Set_Osetsum(X2,X4,X3,X1)
| hBOOL(c_in(X5,X4,X3))
| ~ class_OrderedGroup_Oab__group__add(X1)
| ~ c_Finite__Set_Ofinite(X4,X3) ),
cls_setsum__diff1_1,
[final] ).
cnf(i_0_1257,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4)) = X4
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X2)) ),
cls_double__diff_0,
[final] ).
cnf(i_0_1258,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
cls_imageI_0,
[final] ).
cnf(i_0_1259,axiom,
( hBOOL(c_in(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5))
| ~ hBOOL(c_in(X2,X3,X4)) ),
cls_image__eqI_0,
[final] ).
cnf(i_0_1260,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
cls_image__iff_2,
[final] ).
cnf(i_0_1261,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
cls_rev__image__eqI_0,
[final] ).
cnf(i_0_1262,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X2),X3),c_Set_Oinsert(X4,X5,X2)) = hAPP(hAPP(X1,X4),hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X2),X3),X5))
| ~ c_Finite__Set_Ofinite(X5,X2)
| ~ c_Lattices_Olower__semilattice(X6,X7,X1,X2) ),
cls_lower__semilattice_Ofold__inf__insert_0,
[final] ).
cnf(i_0_1263,axiom,
( c_Finite__Set_Osetsum(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),c_Set_Oinsert(X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),X2,tc_nat) = c_Finite__Set_Osetsum(X1,X3,X2,tc_nat)
| hBOOL(c_in(X4,X3,X2)) ),
cls_setsum__diff1__nat_1,
[final] ).
cnf(i_0_1264,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X2,X1))
| hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1))) ),
cls_psubset__insert__iff_2,
[final] ).
cnf(i_0_1265,axiom,
( hBOOL(c_in(X1,X2,X3))
| hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X4),X2),X3)) ),
cls_UnE_0,
[final] ).
cnf(i_0_1266,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X2)) ),
cls_atLeastatMost__subset__iff_3,
[final] ).
cnf(i_0_1267,axiom,
( c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_max__lattice_0,
[final] ).
cnf(i_0_1268,axiom,
( c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(X1),X1,X1,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(X1),X1,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_dual__semilattice_0,
[final] ).
cnf(i_0_1269,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
cls_conjecture_2,
[final] ).
cnf(i_0_1270,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(c_in(X4,X3,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1))) ),
cls_psubset__insert__iff_0,
[final] ).
cnf(i_0_1271,axiom,
( X1 = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3))) ),
cls_subset__singletonD_0,
[final] ).
cnf(i_0_1272,axiom,
( X2 = X5
| c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X5,X3,X4)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
cls_inj__image__eq__iff_0,
[final] ).
cnf(i_0_1273,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X4),X2),X3)) ),
cls_DiffE_1,
[final] ).
cnf(i_0_1274,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))) ),
cls_add__less__cancel__right_0,
[final] ).
cnf(i_0_1275,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3))) ),
cls_add__less__cancel__left_0,
[final] ).
cnf(i_0_1276,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))) ),
cls_add__le__cancel__right_0,
[final] ).
cnf(i_0_1277,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3))) ),
cls_add__le__cancel__left_0,
[final] ).
cnf(i_0_1278,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,X4,X3)),X2)) ),
cls_insert__subset_0,
[final] ).
cnf(i_0_1279,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1),X3)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
cls_fold1__antimono_0,
[final] ).
cnf(i_0_1280,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
cls_fun__upd__idem__iff_1,
[final] ).
cnf(i_0_1281,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
cls_fun__upd__triv_0,
[final] ).
cnf(i_0_1282,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
cls_fun__upd__idem_0,
[final] ).
cnf(i_0_1283,axiom,
( c_Set_Ovimage(X1,c_Set_Oimage(X1,X2,X3,X4),X3,X4) = X2
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
cls_inj__vimage__image__eq_0,
[final] ).
cnf(i_0_1284,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X5)) ),
cls_atLeastatMost__psubset__iff_4,
[final] ).
cnf(i_0_1285,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X3,X1,X2,X4)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(X3,X1,X2,X4),X4) ),
cls_finite__imageD_0,
[final] ).
cnf(i_0_1286,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_psubset__trans_0,
[final] ).
cnf(i_0_1287,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_subset__psubset__trans_0,
[final] ).
cnf(i_0_1288,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_psubset__subset__trans_0,
[final] ).
cnf(i_0_1289,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_subset__trans_0,
[final] ).
cnf(i_0_1290,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1))) ),
cls_subset__insert_0,
[final] ).
cnf(i_0_1291,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(c_in(X4,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1))) ),
cls_subset__insert__iff_1,
[final] ).
cnf(i_0_1292,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
cls_IntE_0,
[final] ).
cnf(i_0_1293,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2),X3)) ),
cls_IntE_1,
[final] ).
cnf(i_0_1294,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X3,tc_bool)),X2),X4),X3)) ),
cls_DiffE_0,
[final] ).
cnf(i_0_1295,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X2,X1))
| hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_psubset__insert__iff_3,
[final] ).
cnf(i_0_1296,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X4)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),
cls_Diff__insert_0,
[final] ).
cnf(i_0_1297,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X2,X1)),c_Finite__Set_Ocard(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_card__psubset_0,
[final] ).
cnf(i_0_1298,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
cls_class__ringb_Onoteq__reduce_0,
[final] ).
cnf(i_0_1299,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
cls_class__ringb_Oadd__mul__solve_0,
[final] ).
cnf(i_0_1300,axiom,
( hBOOL(hAPP(c_Set_Ovimage(X1,X2,X3,X4),X5))
| ~ hBOOL(hAPP(X2,hAPP(X1,X5))) ),
cls_vimage__code_1,
[final] ).
cnf(i_0_1301,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)),
cls_Un__assoc_0,
[final] ).
cnf(i_0_1302,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)),
cls_Int__assoc_0,
[final] ).
cnf(i_0_1303,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4)),
cls_Int__Diff_0,
[final] ).
cnf(i_0_1304,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_psubset__insert__iff_6,
[final] ).
cnf(i_0_1305,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,X1)),X3),X4))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,X1)),X4),X3))
| ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,X1)),X3),X4)) ),
cls_less__fun__def_2,
[final] ).
cnf(i_0_1306,axiom,
( hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,X1,X3),hAPP(X2,X4)) = X4
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1,X3) ),
cls_the__inv__f__f_0,
[final] ).
cnf(i_0_1307,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X4,X3,X1)),X1) ),
cls_finite__Diff__insert_0,
[final] ).
cnf(i_0_1308,axiom,
( hAPP(c_Fun_Othe__inv__into(X1,X2,X3,X4),hAPP(X2,X5)) = X5
| ~ hBOOL(c_in(X5,X1,X3))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
cls_the__inv__into__f__f_0,
[final] ).
cnf(i_0_1309,axiom,
( hAPP(c_Fun_Othe__inv__into(X2,X1,X3,X4),hAPP(X1,X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(c_in(X5,X2,X3)) ),
cls_the__inv__into__f__eq_0,
[final] ).
cnf(i_0_1310,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X5))
| ~ c_Fun_Oinj__on(X1,X5,X3,X4) ),
cls_subset__inj__on_0,
[final] ).
cnf(i_0_1311,axiom,
( c_Finite__Set_Osetsum(X2,c_Set_Oinsert(X3,X4,X5),X5,X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(X2,X3)),c_Finite__Set_Osetsum(X2,X4,X5,X1))
| hBOOL(c_in(X3,X4,X5))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X4,X5) ),
cls_setsum__insert_0,
[final] ).
cnf(i_0_1312,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) != c_Finite__Set_Ocard(X2,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_eq__card__imp__inj__on_0,
[final] ).
cnf(i_0_1313,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X2),X5),X3,X4) ),
cls_inj__on__Un_0,
[final] ).
cnf(i_0_1314,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X5),X2),X3,X4) ),
cls_inj__on__Un_1,
[final] ).
cnf(i_0_1315,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
cls_less__diff__iff_1,
[final] ).
cnf(i_0_1316,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
cls_le__diff__iff_1,
[final] ).
cnf(i_0_1317,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_fold1__Un_0,
[final] ).
cnf(i_0_1318,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_comm__monoid__add_Ofold1__Un_0,
[final] ).
cnf(i_0_1319,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(c_in(X3,X4,X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),hAPP(c_Finite__Set_Ofold1(X6,X5),X4)))
| ~ c_Finite__Set_Ofinite(X4,X5)
| ~ c_Lattices_Olower__semilattice(X1,X7,X6,X5) ),
cls_lower__semilattice_Obelow__fold1__iff_0,
[final] ).
cnf(i_0_1320,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_subset__insert_1,
[final] ).
cnf(i_0_1321,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_subset__insert__iff_2,
[final] ).
cnf(i_0_1322,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_ATP__Linkup_OCOMBC__def_0,
[final] ).
cnf(i_0_1323,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0,
[final] ).
cnf(i_0_1324,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X2,X3,X1)),X3))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Max__eqI_1,
[final] ).
cnf(i_0_1325,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_add__strict__mono_0,
[final] ).
cnf(i_0_1326,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_add__le__less__mono_0,
[final] ).
cnf(i_0_1327,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_add__less__le__mono_0,
[final] ).
cnf(i_0_1328,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_add__mono_0,
[final] ).
cnf(i_0_1329,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
cls_atLeastatMost__subset__iff_2,
[final] ).
cnf(i_0_1330,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
cls_disjoint__eq__subset__Compl_1,
[final] ).
cnf(i_0_1331,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
| ~ hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,X3,X2)) ),
cls_IntI_0,
[final] ).
cnf(i_0_1332,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X3),X4),X2))
| ~ hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,X3,X2)) ),
cls_Int__iff_2,
[final] ).
cnf(i_0_1333,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3)) ),
cls_min__less__iff__disj_0,
[final] ).
cnf(i_0_1334,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X2)),X3)) ),
cls_min__le__iff__disj_0,
[final] ).
cnf(i_0_1335,axiom,
hAPP(hAPP(c_COMBC(v_P,t_a,t_b,t_c),v_Q),v_R) = hAPP(hAPP(v_P,v_R),v_Q),
cls_COMBC__def__raw_0,
[final] ).
cnf(i_0_1336,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(X1),X1,X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_Finite__Set_Ofinite(X4,X1) ),
cls_fold__sup__insert_0,
[final] ).
cnf(i_0_1337,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_Finite__Set_Ofinite(X4,X1) ),
cls_fold__inf__insert_0,
[final] ).
cnf(i_0_1338,axiom,
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X4,tc_bool)),X3),X1),X2)) ),
cls_sup1E_0,
[final] ).
cnf(i_0_1339,axiom,
( c_Finite__Set_Ofinite(c_Set_Ovimage(X1,X2,X3,X4),X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X4) ),
cls_finite__vimageI_0,
[final] ).
cnf(i_0_1340,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = X2,
cls_Un__Diff__Int_0,
[final] ).
cnf(i_0_1341,axiom,
( c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5) = c_Set_Oimage(X1,X3,X4,X5)
| ~ hBOOL(c_in(X2,X3,X4)) ),
cls_insert__image_0,
[final] ).
cnf(i_0_1342,axiom,
( ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,X1)),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,X1)),X4),X3)) ),
cls_less__fun__def_1,
[final] ).
cnf(i_0_1343,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(c_Finite__Set_Ofold1(X4,X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(X4,hAPP(c_Finite__Set_Ofold1(X4,X1),X2)),hAPP(c_Finite__Set_Ofold1(X4,X1),X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_OrderedGroup_Oab__semigroup__mult(X4,X1) ),
cls_ab__semigroup__mult_Ofold1__Un_0,
[final] ).
cnf(i_0_1344,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X4),X1) ),
cls_finite__Diff__insert_1,
[final] ).
cnf(i_0_1345,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X2,X3),X4)),X5))
| ~ hBOOL(c_in(X5,X4,X3))
| ~ c_Finite__Set_Ofinite(X4,X3)
| ~ c_Lattices_Olower__semilattice(X1,X6,X2,X3) ),
cls_lower__semilattice_Ofold1__belowI_0,
[final] ).
cnf(i_0_1346,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))) ),
cls_le__add__right__mono_0,
[final] ).
cnf(i_0_1347,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),X4),X2)) ),
cls_inf1E_0,
[final] ).
cnf(i_0_1348,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X1),X2)) ),
cls_inf1E_1,
[final] ).
cnf(i_0_1349,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2))
| hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,X3,X2)) ),
cls_DiffI_0,
[final] ).
cnf(i_0_1350,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2))
| hBOOL(c_in(X1,X4,X2))
| ~ hBOOL(c_in(X1,X3,X2)) ),
cls_Diff__iff_2,
[final] ).
cnf(i_0_1351,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))))),
cls_subset__Compl__self__eq_1,
[final] ).
cnf(i_0_1352,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X4)) ),
cls_subset__insertI2_0,
[final] ).
cnf(i_0_1353,axiom,
( c_Set_Oinsert(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),X2) = X3
| ~ hBOOL(c_in(X1,X3,X2)) ),
cls_insert__Diff_0,
[final] ).
cnf(i_0_1354,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
cls_vimage__Compl_0,
[final] ).
cnf(i_0_1355,axiom,
( X1 = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X1)) ),
cls_Nitpick_OEx1__def_3,
[final] ).
cnf(i_0_1356,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_inj__on__iff__eq__card_0,
[final] ).
cnf(i_0_1357,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X2)) ),
cls_diff__less__mono2_0,
[final] ).
cnf(i_0_1358,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X3)) ),
cls_diff__less__mono_0,
[final] ).
cnf(i_0_1359,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I15_J_0,
[final] ).
cnf(i_0_1360,axiom,
c_Set_Oimage(X1,c_Set_Oinsert(X2,X3,X4),X4,X5) = c_Set_Oinsert(hAPP(X1,X2),c_Set_Oimage(X1,X3,X4,X5),X5),
cls_image__insert_0,
[final] ).
cnf(i_0_1361,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)) ),
cls_max__less__iff__conj_0,
[final] ).
cnf(i_0_1362,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3)) ),
cls_max__less__iff__conj_1,
[final] ).
cnf(i_0_1363,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3)) ),
cls_le__supE_0,
[final] ).
cnf(i_0_1364,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3)) ),
cls_le__sup__iff_0,
[final] ).
cnf(i_0_1365,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2)),X3)) ),
cls_le__supE_1,
[final] ).
cnf(i_0_1366,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2)),X3)) ),
cls_le__sup__iff_1,
[final] ).
cnf(i_0_1367,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)) ),
cls_min__max_Ole__supE_0,
[final] ).
cnf(i_0_1368,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3)) ),
cls_min__max_Ole__sup__iff_0,
[final] ).
cnf(i_0_1369,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3)) ),
cls_min__max_Ole__supE_1,
[final] ).
cnf(i_0_1370,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3)) ),
cls_min__max_Ole__sup__iff_1,
[final] ).
cnf(i_0_1371,axiom,
( c_Fun_Oinj__on(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),X4),X2,X5)
| ~ c_Fun_Oinj__on(X1,X3,X2,X5) ),
cls_inj__on__diff_0,
[final] ).
cnf(i_0_1372,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1),X2)),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_fold1__strict__below__iff_2,
[final] ).
cnf(i_0_1373,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1),X2)),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(c_in(X4,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_fold1__below__iff_2,
[final] ).
cnf(i_0_1374,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
cls_set__eq__subset_2,
[final] ).
cnf(i_0_1375,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
cls_equalityI_0,
[final] ).
cnf(i_0_1376,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X3),X5))
| ~ c_Lattices_Olower__semilattice(X1,X6,X2,X7) ),
cls_lower__semilattice_Ole__infI1_0,
[final] ).
cnf(i_0_1377,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Lattices_Olower__semilattice(X1,X6,X2,X7) ),
cls_lower__semilattice_Ole__infI2_0,
[final] ).
cnf(i_0_1378,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X3),X5))
| ~ c_Lattices_Olower__semilattice(X6,X1,X2,X7) ),
cls_lower__semilattice_Oless__infI1_0,
[final] ).
cnf(i_0_1379,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X5))
| ~ hBOOL(hAPP(hAPP(X1,X4),X5))
| ~ c_Lattices_Olower__semilattice(X6,X1,X2,X7) ),
cls_lower__semilattice_Oless__infI2_0,
[final] ).
cnf(i_0_1380,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(X1,X2,X3,X4),X4) = c_Finite__Set_Ocard(X2,X3)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
cls_card__image_0,
[final] ).
cnf(i_0_1381,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Ocard(X2,X1)),c_Finite__Set_Ocard(X3,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_card__Diff__subset_0,
[final] ).
cnf(i_0_1382,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_ivl__disj__un_I5_J_0,
[final] ).
cnf(i_0_1383,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_add__less__cancel__left_1,
[final] ).
cnf(i_0_1384,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_add__strict__left__mono_0,
[final] ).
cnf(i_0_1385,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_add__less__cancel__right_1,
[final] ).
cnf(i_0_1386,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_add__strict__right__mono_0,
[final] ).
cnf(i_0_1387,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
cls_add__le__cancel__left_1,
[final] ).
cnf(i_0_1388,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
cls_add__left__mono_0,
[final] ).
cnf(i_0_1389,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_add__le__cancel__right_1,
[final] ).
cnf(i_0_1390,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_add__right__mono_0,
[final] ).
cnf(i_0_1391,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X1))) ),
cls_subset__Compl__self__eq_0,
[final] ).
cnf(i_0_1392,axiom,
( hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X4))
| ~ c_Lattices_Olower__semilattice(X1,X6,X3,X7) ),
cls_lower__semilattice_Oinf__greatest_0,
[final] ).
cnf(i_0_1393,axiom,
( hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X4))
| ~ c_Lattices_Olower__semilattice(X1,X6,X3,X7) ),
cls_lower__semilattice_Ole__inf__iff_2,
[final] ).
cnf(i_0_1394,axiom,
( hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X3,X4),X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X5))
| ~ hBOOL(hAPP(hAPP(X1,X2),X4))
| ~ c_Lattices_Olower__semilattice(X1,X6,X3,X7) ),
cls_lower__semilattice_Ole__infI_0,
[final] ).
cnf(i_0_1395,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X2)) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
cls_Diff__partition_0,
[final] ).
cnf(i_0_1396,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)),
cls_Compl__Un_0,
[final] ).
cnf(i_0_1397,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)),
cls_Compl__Int_0,
[final] ).
cnf(i_0_1398,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(X2,X3)),c_Finite__Set_Ocard(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_card__seteq_0,
[final] ).
cnf(i_0_1399,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = c_Set_Oinsert(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),X1)
| ~ hBOOL(c_in(X2,X4,X1)) ),
cls_Int__insert__left_0,
[final] ).
cnf(i_0_1400,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),X1) = c_Finite__Set_Ocard(X2,X1)
| hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_card__Diff__singleton__if_1,
[final] ).
cnf(i_0_1401,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_ivl__disj__un_I20_J_0,
[final] ).
cnf(i_0_1402,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_ivl__disj__un_I22_J_0,
[final] ).
cnf(i_0_1403,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_ivl__disj__un_I21_J_0,
[final] ).
cnf(i_0_1404,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_ivl__disj__un_I17_J_0,
[final] ).
cnf(i_0_1405,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3))),
cls_Un__upper1_0,
[final] ).
cnf(i_0_1406,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2))),
cls_Un__upper2_0,
[final] ).
cnf(i_0_1407,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_max__less__iff__conj_2,
[final] ).
cnf(i_0_1408,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_min__max_Ole__sup__iff_2,
[final] ).
cnf(i_0_1409,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_min__max_Osup__least_0,
[final] ).
cnf(i_0_1410,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_min__max_Ole__supI_0,
[final] ).
cnf(i_0_1411,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_le__supI_0,
[final] ).
cnf(i_0_1412,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_sup__least_0,
[final] ).
cnf(i_0_1413,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_le__sup__iff_2,
[final] ).
cnf(i_0_1414,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4)),
cls_Un__left__commute_0,
[final] ).
cnf(i_0_1415,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)),
cls_Int__left__commute_0,
[final] ).
cnf(i_0_1416,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
cls_Un__Diff__cancel2_0,
[final] ).
cnf(i_0_1417,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)),X3) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),
cls_Diff__idemp_0,
[final] ).
cnf(i_0_1418,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2))
| ~ hBOOL(c_in(X1,X3,X2)) ),
cls_UnCI_1,
[final] ).
cnf(i_0_1419,axiom,
( hBOOL(c_in(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4),X2))
| ~ hBOOL(c_in(X1,X4,X2)) ),
cls_UnCI_0,
[final] ).
cnf(i_0_1420,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
cls_Max__mono_0,
[final] ).
cnf(i_0_1421,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
cls_Min__antimono_0,
[final] ).
cnf(i_0_1422,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X4,X3),X5)))
| ~ c_Lattices_Olower__semilattice(X1,X6,X4,X7) ),
cls_lower__semilattice_Ole__infE_0,
[final] ).
cnf(i_0_1423,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X4,X3),X5)))
| ~ c_Lattices_Olower__semilattice(X1,X6,X4,X7) ),
cls_lower__semilattice_Ole__inf__iff_0,
[final] ).
cnf(i_0_1424,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X4,X5),X3)))
| ~ c_Lattices_Olower__semilattice(X1,X6,X4,X7) ),
cls_lower__semilattice_Ole__infE_1,
[final] ).
cnf(i_0_1425,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X2),hAPP(hAPP(X4,X5),X3)))
| ~ c_Lattices_Olower__semilattice(X1,X6,X4,X7) ),
cls_lower__semilattice_Ole__inf__iff_1,
[final] ).
cnf(i_0_1426,axiom,
( X1 = X2
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3)) ),
cls_singletonE_0,
[final] ).
cnf(i_0_1427,axiom,
( X1 = X5
| X1 = X4
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
cls_doubleton__eq__iff_0,
[final] ).
cnf(i_0_1428,axiom,
( X2 = X4
| X1 = X4
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
cls_doubleton__eq__iff_1,
[final] ).
cnf(i_0_1429,axiom,
( X1 = X5
| X2 = X5
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
cls_doubleton__eq__iff_2,
[final] ).
cnf(i_0_1430,axiom,
( X2 = X4
| X2 = X5
| c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) != c_Set_Oinsert(X4,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) ),
cls_doubleton__eq__iff_3,
[final] ).
cnf(i_0_1431,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1),X4)))
| ~ c_Finite__Set_Ofinite(X4,X1) ),
cls_strict__below__fold1__iff_0,
[final] ).
cnf(i_0_1432,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(c_in(X3,X4,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X1),X4)))
| ~ c_Finite__Set_Ofinite(X4,X1) ),
cls_below__fold1__iff_0,
[final] ).
cnf(i_0_1433,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
cls_disjoint__eq__subset__Compl_0,
[final] ).
cnf(i_0_1434,axiom,
c_Set_Oinsert(X1,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X3),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),X2) = c_Set_Oinsert(X1,X3,X2),
cls_insert__Diff__single_0,
[final] ).
cnf(i_0_1435,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,X1)),X3),X4))
| ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,X1)),X3),X4)) ),
cls_less__fun__def_0,
[final] ).
cnf(i_0_1436,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = c_Set_Oinsert(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4),X1)
| hBOOL(c_in(X2,X4,X1)) ),
cls_insert__Diff__if_1,
[final] ).
cnf(i_0_1437,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X2)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_fold1__Un2_0,
[final] ).
cnf(i_0_1438,axiom,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Fun_Oinj__on(X1,c_Set_Oinsert(X5,X2,X3),X3,X4) ),
cls_inj__on__insert_0,
[final] ).
cnf(i_0_1439,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),c_Set_Oinsert(X2,X4,X1)) = c_Set_Oinsert(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4),X1),
cls_insert__inter__insert_0,
[final] ).
cnf(i_0_1440,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_ivl__disj__un_I6_J_0,
[final] ).
cnf(i_0_1441,axiom,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ c_Fun_Oinj__on(X1,X4,X5,X6)
| ~ hBOOL(c_in(X3,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5)) ),
cls_inj__onD_0,
[final] ).
cnf(i_0_1442,axiom,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ hBOOL(c_in(X3,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
cls_inj__on__def_0,
[final] ).
cnf(i_0_1443,axiom,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ hBOOL(c_in(X3,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
cls_inj__on__iff_0,
[final] ).
cnf(i_0_1444,axiom,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ hBOOL(c_in(X3,X4,X5))
| ~ hBOOL(c_in(X2,X4,X5))
| ~ c_Fun_Oinj__on(X1,X4,X5,X6) ),
cls_inj__on__contraD_0,
[final] ).
cnf(i_0_1445,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X2)) ),
cls_diff__le__mono2_0,
[final] ).
cnf(i_0_1446,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X3)) ),
cls_diff__le__mono_0,
[final] ).
cnf(i_0_1447,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X3))
| ~ c_Lattices_Olower__semilattice(X1,X5,X2,X6) ),
cls_lower__semilattice_Oinf__le1_0,
[final] ).
cnf(i_0_1448,axiom,
( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(X2,X3),X4)),X4))
| ~ c_Lattices_Olower__semilattice(X1,X5,X2,X6) ),
cls_lower__semilattice_Oinf__le2_0,
[final] ).
cnf(i_0_1449,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X2),X3),c_Com_Ocom_OSKIP),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),tc_Hoare__Mirabelle_Otriple(X2)),X2),
cls_hoare__derivs_OSkip_0,
[final] ).
cnf(i_0_1450,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X3,tc_Hoare__Mirabelle_Otriple(X4)),X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_bool)),tc_Hoare__Mirabelle_Otriple(X4)),X4) ),
cls_hoare__derivs_Oinsert_0,
[final] ).
cnf(i_0_1451,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = c_Set_Oinsert(X3,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4),X1)
| ~ hBOOL(c_in(X3,X2,X1)) ),
cls_Int__insert__right_0,
[final] ).
cnf(i_0_1452,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(X2,X3)),hAPP(X4,X3)))
| ~ class_HOL_Oord(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X5,X1)),X2),X4)) ),
cls_le__funD_0,
[final] ).
cnf(i_0_1453,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),X3)) ),
cls_ComplD_0,
[final] ).
cnf(i_0_1454,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),X3),
cls_Compl__Diff__eq_0,
[final] ).
cnf(i_0_1455,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X1),X2)) ),
cls_subset__iff__psubset__eq_0,
[final] ).
cnf(i_0_1456,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
cls_psubset__eq_2,
[final] ).
cnf(i_0_1457,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X3)) ),
cls_psubset__eq_0,
[final] ).
cnf(i_0_1458,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X3,tc_bool)),X4),X2)) ),
cls_psubsetD_0,
[final] ).
cnf(i_0_1459,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
cls_set__mp_0,
[final] ).
cnf(i_0_1460,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
cls_subsetD_0,
[final] ).
cnf(i_0_1461,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2))
| ~ hBOOL(c_in(X1,X4,X3)) ),
cls_set__rev__mp_0,
[final] ).
cnf(i_0_1462,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X2)) ),
cls_subset__iff_0,
[final] ).
cnf(i_0_1463,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__mul__solve_1,
[final] ).
cnf(i_0_1464,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Onoteq__reduce_1,
[final] ).
cnf(i_0_1465,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X4,X5,X1)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_Int__greaterThanAtMost_0,
[final] ).
cnf(i_0_1466,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X1)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_Int__atLeastAtMost_0,
[final] ).
cnf(i_0_1467,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X4,X5,X1)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X5),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_Int__atLeastLessThan_0,
[final] ).
cnf(i_0_1468,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X2,X3,X1)))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Min__eqI_1,
[final] ).
cnf(i_0_1469,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
cls_psubset__card__mono_0,
[final] ).
cnf(i_0_1470,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
cls_card__mono_0,
[final] ).
cnf(i_0_1471,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I13_J_0,
[final] ).
cnf(i_0_1472,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I20_J_0,
[final] ).
cnf(i_0_1473,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I14_J_0,
[final] ).
cnf(i_0_1474,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X4)) = hAPP(hAPP(X1,hAPP(c_Finite__Set_Ofold1(X1,X2),X3)),hAPP(c_Finite__Set_Ofold1(X1,X2),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
cls_ab__semigroup__idem__mult_Ofold1__Un2_0,
[final] ).
cnf(i_0_1475,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(X1),X1),X2)),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_fold1__belowI_0,
[final] ).
cnf(i_0_1476,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))) ),
cls_less__max__iff__disj_0,
[final] ).
cnf(i_0_1477,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X3))) ),
cls_le__max__iff__disj_0,
[final] ).
cnf(i_0_1478,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
| ~ c_Lattices_Olower__semilattice(X5,X6,X1,X7) ),
cls_lower__semilattice_Oinf__assoc_0,
[final] ).
cnf(i_0_1479,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X1,X2),X2)))
| ~ c_Finite__Set_Ofinite(X1,X2) ),
cls_card__insert__le_0,
[final] ).
cnf(i_0_1480,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = c_Set_Oinsert(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X4),X1),
cls_Un__insert__left_0,
[final] ).
cnf(i_0_1481,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_inf1I_0,
[final] ).
cnf(i_0_1482,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X4,X1)) = c_SetInterval_Oord__class_OatLeastLessThan(X4,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_ivl__diff_0,
[final] ).
cnf(i_0_1483,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_less__infI1_0,
[final] ).
cnf(i_0_1484,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_less__infI2_0,
[final] ).
cnf(i_0_1485,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_min__less__iff__disj_1,
[final] ).
cnf(i_0_1486,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_min__max_Oless__infI1_0,
[final] ).
cnf(i_0_1487,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_min__less__iff__disj_2,
[final] ).
cnf(i_0_1488,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X4)) ),
cls_min__max_Oless__infI2_0,
[final] ).
cnf(i_0_1489,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_le__infI1_0,
[final] ).
cnf(i_0_1490,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
cls_le__infI2_0,
[final] ).
cnf(i_0_1491,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_min__le__iff__disj_1,
[final] ).
cnf(i_0_1492,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_min__max_Ole__infI1_0,
[final] ).
cnf(i_0_1493,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
cls_min__le__iff__disj_2,
[final] ).
cnf(i_0_1494,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X4)) ),
cls_min__max_Ole__infI2_0,
[final] ).
cnf(i_0_1495,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = X3
| hBOOL(c_in(X2,X3,X1)) ),
cls_Diff__insert__absorb_0,
[final] ).
cnf(i_0_1496,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X4)
| ~ hBOOL(c_in(X2,X4,X1)) ),
cls_insert__Diff1_0,
[final] ).
cnf(i_0_1497,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
cls_minus__less__iff_1,
[final] ).
cnf(i_0_1498,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
cls_minus__less__iff_0,
[final] ).
cnf(i_0_1499,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
cls_minus__le__iff_1,
[final] ).
cnf(i_0_1500,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),X2)) ),
cls_minus__le__iff_0,
[final] ).
cnf(i_0_1501,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
cls_Nat_Odiff__diff__eq_0,
[final] ).
cnf(i_0_1502,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_min__less__iff__conj_2,
[final] ).
cnf(i_0_1503,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_le__infI_0,
[final] ).
cnf(i_0_1504,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_le__inf__iff_2,
[final] ).
cnf(i_0_1505,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_inf__greatest_0,
[final] ).
cnf(i_0_1506,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_min__max_Oinf__greatest_0,
[final] ).
cnf(i_0_1507,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_min__max_Ole__inf__iff_2,
[final] ).
cnf(i_0_1508,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_min__max_Ole__infI_0,
[final] ).
cnf(i_0_1509,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_sup1CI_1,
[final] ).
cnf(i_0_1510,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
cls_sup1CI_0,
[final] ).
cnf(i_0_1511,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))) ),
cls_subset__empty_0,
[final] ).
cnf(i_0_1512,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_neg__less__iff__less_0,
[final] ).
cnf(i_0_1513,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_neg__le__iff__le_0,
[final] ).
cnf(i_0_1514,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| ~ hBOOL(c_in(X5,X4,X3)) ),
cls_image__constant_0,
[final] ).
cnf(i_0_1515,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
| ~ c_Lattices_Olower__semilattice(X5,X6,X1,X7) ),
cls_lower__semilattice_Oinf__left__commute_0,
[final] ).
cnf(i_0_1516,axiom,
( hBOOL(c_in(X1,X2,X3))
| X1 = X4
| ~ hBOOL(c_in(X1,c_Set_Oinsert(X4,X2,X3),X3)) ),
cls_insertE_0,
[final] ).
cnf(i_0_1517,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I1_J_0,
[final] ).
cnf(i_0_1518,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__inf__distrib2_0,
[final] ).
cnf(i_0_1519,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_sup__inf__distrib2_0,
[final] ).
cnf(i_0_1520,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_inf__sup__distrib2_0,
[final] ).
cnf(i_0_1521,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
cls_max__diff__distrib__left_0,
[final] ).
cnf(i_0_1522,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) ),
cls_min__diff__distrib__left_0,
[final] ).
cnf(i_0_1523,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
cls_comm__semiring__class_Odistrib_0,
[final] ).
cnf(i_0_1524,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I8_J_0,
[final] ).
cnf(i_0_1525,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
cls_max__add__distrib__left_0,
[final] ).
cnf(i_0_1526,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
cls_add__sup__distrib__right_0,
[final] ).
cnf(i_0_1527,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,
[final] ).
cnf(i_0_1528,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
cls_add__inf__distrib__right_0,
[final] ).
cnf(i_0_1529,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,
[final] ).
cnf(i_0_1530,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
cls_min__add__distrib__left_0,
[final] ).
cnf(i_0_1531,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__sup__distrib2_0,
[final] ).
cnf(i_0_1532,axiom,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)),X2),
cls_insert__is__Un_0,
[final] ).
cnf(i_0_1533,axiom,
( ~ hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X4),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_disjoint__iff__not__equal_0,
[final] ).
cnf(i_0_1534,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
cls_not__psubset__empty_0,
[final] ).
cnf(i_0_1535,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Set_Oinsert(X2,X3,X1)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)
| hBOOL(c_in(X2,X4,X1)) ),
cls_Int__insert__left_1,
[final] ).
cnf(i_0_1536,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X3)) ),
cls_less__imp__diff__less_0,
[final] ).
cnf(i_0_1537,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))) ),
cls_min__less__iff__conj_0,
[final] ).
cnf(i_0_1538,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))) ),
cls_min__less__iff__conj_1,
[final] ).
cnf(i_0_1539,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))) ),
cls_le__inf__iff_0,
[final] ).
cnf(i_0_1540,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))) ),
cls_le__infE_0,
[final] ).
cnf(i_0_1541,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3))) ),
cls_le__inf__iff_1,
[final] ).
cnf(i_0_1542,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3))) ),
cls_le__infE_1,
[final] ).
cnf(i_0_1543,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))) ),
cls_min__max_Ole__inf__iff_0,
[final] ).
cnf(i_0_1544,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))) ),
cls_min__max_Ole__infE_0,
[final] ).
cnf(i_0_1545,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))) ),
cls_min__max_Ole__inf__iff_1,
[final] ).
cnf(i_0_1546,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3))) ),
cls_min__max_Ole__infE_1,
[final] ).
cnf(i_0_1547,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
cls_Inf__binary_0,
[final] ).
cnf(i_0_1548,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
cls_subset__empty_1,
[final] ).
cnf(i_0_1549,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
cls_Un__absorb2_0,
[final] ).
cnf(i_0_1550,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
cls_Un__absorb1_0,
[final] ).
cnf(i_0_1551,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3)) ),
cls_Int__absorb2_0,
[final] ).
cnf(i_0_1552,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X3),X2)) ),
cls_Int__absorb1_0,
[final] ).
cnf(i_0_1553,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)),tc_Hoare__Mirabelle_Otriple(X3)),X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X2,X4,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
cls_derivs__insertD_0,
[final] ).
cnf(i_0_1554,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = c_Set_Oinsert(X3,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X4),X1),
cls_Un__insert__right_0,
[final] ).
cnf(i_0_1555,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Min__Un_0,
[final] ).
cnf(i_0_1556,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2)),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Max__Un_0,
[final] ).
cnf(i_0_1557,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X1),X1,X1),X2),X3)
| hBOOL(c_in(X2,X3,X1))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_fold1__eq__fold_0,
[final] ).
cnf(i_0_1558,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(X1),X1,X1),X2),X3)
| hBOOL(c_in(X2,X3,X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_comm__monoid__add_Ofold1__eq__fold_0,
[final] ).
cnf(i_0_1559,axiom,
( hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2))
| c_Finite__Set_Ocard(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
cls_card__Suc__eq_5,
[final] ).
cnf(i_0_1560,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
cls_Un__left__absorb_0,
[final] ).
cnf(i_0_1561,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X2)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
cls_Un__Diff__cancel_0,
[final] ).
cnf(i_0_1562,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
cls_Int__left__absorb_0,
[final] ).
cnf(i_0_1563,axiom,
( hAPP(hAPP(X1,X2),X3) = X2
| ~ hBOOL(hAPP(hAPP(X4,X2),X3))
| ~ c_Lattices_Olower__semilattice(X4,X5,X1,X6) ),
cls_lower__semilattice_Ole__iff__inf_0,
[final] ).
cnf(i_0_1564,axiom,
( hAPP(hAPP(X1,X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(X4,X3),X2))
| ~ c_Lattices_Olower__semilattice(X4,X5,X1,X6) ),
cls_lower__semilattice_Oinf__absorb2_0,
[final] ).
cnf(i_0_1565,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,X4,X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X2),X3),X4)
| hBOOL(c_in(X3,X4,X2))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
cls_ab__semigroup__mult_Ofold1__eq__fold_0,
[final] ).
cnf(i_0_1566,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X2)) ),
cls_vimage__const_0,
[final] ).
cnf(i_0_1567,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2) = X3
| hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(X2,X3,X1),X2,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Min__eqI_0,
[final] ).
cnf(i_0_1568,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2) = X3
| hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(X2,X3,X1),X2,X1))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Max__eqI_0,
[final] ).
cnf(i_0_1569,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X2),X3)) = hAPP(hAPP(X1,X2),X3)
| ~ c_Lattices_Olower__semilattice(X4,X5,X1,X6) ),
cls_lower__semilattice_Oinf__left__idem_0,
[final] ).
cnf(i_0_1570,axiom,
( hBOOL(hAPP(hAPP(X4,X2),X3))
| hAPP(hAPP(X1,X2),X3) != X2
| ~ c_Lattices_Olower__semilattice(X4,X5,X1,X6) ),
cls_lower__semilattice_Ole__iff__inf_1,
[final] ).
cnf(i_0_1571,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X4,tc_bool)),X3),X1)) ),
cls_predicate1D_0,
[final] ).
cnf(i_0_1572,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X3,tc_bool)),X4),X1))
| ~ hBOOL(hAPP(X4,X2)) ),
cls_rev__predicate1D_0,
[final] ).
cnf(i_0_1573,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)),
cls_singleton__iff_1,
[final] ).
cnf(i_0_1574,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),X3),
cls_doubleton__eq__iff_4,
[final] ).
cnf(i_0_1575,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(X1,X2,X3,X4),X4)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_finite__imageI_0,
[final] ).
cnf(i_0_1576,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__le1_0,
[final] ).
cnf(i_0_1577,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I1_J_0,
[final] ).
cnf(i_0_1578,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__le2_0,
[final] ).
cnf(i_0_1579,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X3))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I2_J_0,
[final] ).
cnf(i_0_1580,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__le1_0,
[final] ).
cnf(i_0_1581,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X3))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__le2_0,
[final] ).
cnf(i_0_1582,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__inf__distrib1_0,
[final] ).
cnf(i_0_1583,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_sup__inf__distrib1_0,
[final] ).
cnf(i_0_1584,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_inf__sup__distrib1_0,
[final] ).
cnf(i_0_1585,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__d_0,
[final] ).
cnf(i_0_1586,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1) ),
cls_add__sup__distrib__left_0,
[final] ).
cnf(i_0_1587,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,
[final] ).
cnf(i_0_1588,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1) ),
cls_add__inf__distrib__left_0,
[final] ).
cnf(i_0_1589,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,
[final] ).
cnf(i_0_1590,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__sup__distrib1_0,
[final] ).
cnf(i_0_1591,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I16_J_0,
[final] ).
cnf(i_0_1592,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I23_J_0,
[final] ).
cnf(i_0_1593,axiom,
( X2 = X3
| hAPP(X1,X2) != hAPP(X1,X3)
| ~ c_Fun_Oinj__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),X4,X5) ),
cls_injD_0,
[final] ).
cnf(i_0_1594,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X3))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != X3 ),
cls_subset__Un__eq_1,
[final] ).
cnf(i_0_1595,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_neg__less__iff__less_1,
[final] ).
cnf(i_0_1596,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_le__imp__neg__le_0,
[final] ).
cnf(i_0_1597,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X2,tc_bool)),X1),X3),X2)
| ~ c_Finite__Set_Ofinite(X3,X2) ),
cls_finite__Diff2_0,
[final] ).
cnf(i_0_1598,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(X1)),X2)),c_Suc(X3)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X3),
cls_Suc__diff__diff_0,
[final] ).
cnf(i_0_1599,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X4,X1)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X4)
| hBOOL(c_in(X3,X2,X1)) ),
cls_Int__insert__right_1,
[final] ).
cnf(i_0_1600,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Set_Oinsert(X3,X2,X1))),
cls_subset__insertI_0,
[final] ).
cnf(i_0_1601,axiom,
( hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
cls_insertCI_0,
[final] ).
cnf(i_0_1602,axiom,
( hBOOL(c_in(X1,c_Set_Oinsert(X2,X3,X4),X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
cls_insert__iff_2,
[final] ).
cnf(i_0_1603,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
cls_ivl__disj__int_I14_J_0,
[final] ).
cnf(i_0_1604,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)),c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
cls_ivl__disj__int_I16_J_0,
[final] ).
cnf(i_0_1605,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
cls_ivl__disj__int_I15_J_0,
[final] ).
cnf(i_0_1606,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)),c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1) ),
cls_ivl__disj__int_I11_J_0,
[final] ).
cnf(i_0_1607,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2)),
cls_empty__subsetI_0,
[final] ).
cnf(i_0_1608,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3)) ),
cls_finite__subset_0,
[final] ).
cnf(i_0_1609,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X2,tc_bool)),X1),X3))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
cls_rev__finite__subset_0,
[final] ).
cnf(i_0_1610,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(c_in(X1,X4,X2)) ),
cls_vimage__const_1,
[final] ).
cnf(i_0_1611,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_image__constant__conv_1,
[final] ).
cnf(i_0_1612,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_less__max__iff__disj_1,
[final] ).
cnf(i_0_1613,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_min__max_Oless__supI1_0,
[final] ).
cnf(i_0_1614,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_less__max__iff__disj_2,
[final] ).
cnf(i_0_1615,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_min__max_Oless__supI2_0,
[final] ).
cnf(i_0_1616,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_less__supI1_0,
[final] ).
cnf(i_0_1617,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_less__supI2_0,
[final] ).
cnf(i_0_1618,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_min__max_Ole__supI1_0,
[final] ).
cnf(i_0_1619,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_le__max__iff__disj_1,
[final] ).
cnf(i_0_1620,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_min__max_Ole__supI2_0,
[final] ).
cnf(i_0_1621,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_le__max__iff__disj_2,
[final] ).
cnf(i_0_1622,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_le__supI1_0,
[final] ).
cnf(i_0_1623,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_le__supI2_0,
[final] ).
cnf(i_0_1624,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X1),X3),X2) ),
cls_finite__Un_0,
[final] ).
cnf(i_0_1625,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),X3),X1),X2) ),
cls_finite__Un_1,
[final] ).
cnf(i_0_1626,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3))
| hBOOL(c_in(X2,X3,X1))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_fold1__insert_0,
[final] ).
cnf(i_0_1627,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(X1),X1),X3))
| hBOOL(c_in(X2,X3,X1))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_comm__monoid__add_Ofold1__insert_0,
[final] ).
cnf(i_0_1628,axiom,
( hBOOL(c_in(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X2))
| hBOOL(c_in(X1,X3,X2)) ),
cls_ComplI_0,
[final] ).
cnf(i_0_1629,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_less__minus__iff_1,
[final] ).
cnf(i_0_1630,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_less__minus__iff_0,
[final] ).
cnf(i_0_1631,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_le__minus__iff_1,
[final] ).
cnf(i_0_1632,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))) ),
cls_le__minus__iff_0,
[final] ).
cnf(i_0_1633,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_Lattices_Olower__semilattice(X4,X5,X1,X6) ),
cls_lower__semilattice_Oinf__commute_0,
[final] ).
cnf(i_0_1634,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(X1),X1,X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_fold1__eq__fold__idem_0,
[final] ).
cnf(i_0_1635,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),c_Suc(X1))),
cls_diff__less__Suc_0,
[final] ).
cnf(i_0_1636,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2)),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X3,X2,X1))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Min__le_0,
[final] ).
cnf(i_0_1637,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X2,X3,X4,X1) ),
cls_empty__is__image_0,
[final] ).
cnf(i_0_1638,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)) ),
cls_image__is__empty_0,
[final] ).
cnf(i_0_1639,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X3),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Diff__disjoint_0,
[final] ).
cnf(i_0_1640,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X1,tc_bool)),X2),X2)),
cls_psubset__eq_1,
[final] ).
cnf(i_0_1641,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X1)),
cls_diff__le__self_0,
[final] ).
cnf(i_0_1642,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X3)),X2),
cls_diff__commute_0,
[final] ).
cnf(i_0_1643,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,X4,X2)) = hAPP(hAPP(X1,X3),hAPP(c_Finite__Set_Ofold1(X1,X2),X4))
| hBOOL(c_in(X3,X4,X2))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X2) ),
cls_ab__semigroup__mult_Ofold1__insert_0,
[final] ).
cnf(i_0_1644,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_order__less__trans_0,
[final] ).
cnf(i_0_1645,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_order__le__less__trans_0,
[final] ).
cnf(i_0_1646,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4)) ),
cls_order__less__le__trans_0,
[final] ).
cnf(i_0_1647,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
cls_xt1_I10_J_0,
[final] ).
cnf(i_0_1648,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
cls_xt1_I7_J_0,
[final] ).
cnf(i_0_1649,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3)) ),
cls_xt1_I8_J_0,
[final] ).
cnf(i_0_1650,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4)) ),
cls_order__trans_0,
[final] ).
cnf(i_0_1651,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X4),X3)) ),
cls_xt1_I6_J_0,
[final] ).
cnf(i_0_1652,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5)) ),
cls_less__eqI_1,
[final] ).
cnf(i_0_1653,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X5))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_less__eqI_0,
[final] ).
cnf(i_0_1654,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X5),X4)) ),
cls_le__eqI_1,
[final] ).
cnf(i_0_1655,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X5),X4))
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_le__eqI_0,
[final] ).
cnf(i_0_1656,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,X4,X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X2),X3),X4)
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0,
[final] ).
cnf(i_0_1657,axiom,
( X1 = X3
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X2)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
cls_eq__diff__iff_0,
[final] ).
cnf(i_0_1658,axiom,
c_Set_Oimage(c_COMBK(X1,X2,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_image__constant__conv_0,
[final] ).
cnf(i_0_1659,axiom,
( hAPP(hAPP(X1,X2),X2) = X2
| ~ c_Lattices_Olower__semilattice(X3,X4,X1,X5) ),
cls_lower__semilattice_Oinf__idem_0,
[final] ).
cnf(i_0_1660,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__partition2_0,
[final] ).
cnf(i_0_1661,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Compl__disjoint2_0,
[final] ).
cnf(i_0_1662,axiom,
( hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
cls_sup__fun__eq_0,
[final] ).
cnf(i_0_1663,axiom,
( hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__fun__eq_0,
[final] ).
cnf(i_0_1664,axiom,
( hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(t_a,X1)),X2),X3),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(X2,v_x)),hAPP(X3,v_x))
| ~ class_HOL_Ominus(X1) ),
cls_fun__diff__def_0,
[final] ).
cnf(i_0_1665,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__assoc_0,
[final] ).
cnf(i_0_1666,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__assoc_0,
[final] ).
cnf(i_0_1667,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I6_J_0,
[final] ).
cnf(i_0_1668,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__assoc_0,
[final] ).
cnf(i_0_1669,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I2_J_0,
[final] ).
cnf(i_0_1670,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,
[final] ).
cnf(i_0_1671,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I17_J_0,
[final] ).
cnf(i_0_1672,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
[final] ).
cnf(i_0_1673,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I21_J_0,
[final] ).
cnf(i_0_1674,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__assoc_0,
[final] ).
cnf(i_0_1675,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__assoc_0,
[final] ).
cnf(i_0_1676,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__a_0,
[final] ).
cnf(i_0_1677,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I18_J_0,
[final] ).
cnf(i_0_1678,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I25_J_0,
[final] ).
cnf(i_0_1679,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__a_0,
[final] ).
cnf(i_0_1680,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_add__eq__inf__sup_0,
[final] ).
cnf(i_0_1681,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),
cls_Diff__Compl_0,
[final] ).
cnf(i_0_1682,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)),
cls_Diff__eq_0,
[final] ).
cnf(i_0_1683,axiom,
( hBOOL(hAPP(X1,X2))
| X3 = X2
| ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2)) ),
cls_insert__code_0,
[final] ).
cnf(i_0_1684,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X3)) ),
cls_less__trans__Suc_0,
[final] ).
cnf(i_0_1685,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3) = X2
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
cls_Diff__triv_0,
[final] ).
cnf(i_0_1686,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_sup__eq__neg__inf_0,
[final] ).
cnf(i_0_1687,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_inf__eq__neg__sup_0,
[final] ).
cnf(i_0_1688,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2)
| ~ c_Lattices_Olower__semilattice(X3,X4,X1,X2) ),
cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0,
[final] ).
cnf(i_0_1689,axiom,
( hBOOL(c_in(X1,X4,X3))
| hBOOL(c_in(X1,X2,X3))
| X2 = X4
| c_Set_Oinsert(X1,X2,X3) != c_Set_Oinsert(X1,X4,X3) ),
cls_insert__ident_0,
[final] ).
cnf(i_0_1690,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
cls_subset__UNIV_0,
[final] ).
cnf(i_0_1691,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Complete__Lattice_OInf__class_OInf(X2,X1)),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(c_in(X3,X2,X1)) ),
cls_Inf__lower_0,
[final] ).
cnf(i_0_1692,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X3)) ),
cls_le__trans_0,
[final] ).
cnf(i_0_1693,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_less__le__not__le_2,
[final] ).
cnf(i_0_1694,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3)))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(c_in(X2,X3,X1))
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_Max__ge_0,
[final] ).
cnf(i_0_1695,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1)) = hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1),X2),X3)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_inf__Inf__fold__inf_0,
[final] ).
cnf(i_0_1696,axiom,
( ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
cls_bex__empty_0,
[final] ).
cnf(i_0_1697,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
cls_add__cancel__21_0,
[final] ).
cnf(i_0_1698,axiom,
( hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(X1),X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_fold1__insert__idem_0,
[final] ).
cnf(i_0_1699,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3)) ),
cls_ball__empty_0,
[final] ).
cnf(i_0_1700,axiom,
( X2 = X5
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X6),X7) ),
cls_triple_Oinject_0,
[final] ).
cnf(i_0_1701,axiom,
( X3 = X6
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X6),X7) ),
cls_triple_Oinject_1,
[final] ).
cnf(i_0_1702,axiom,
( X4 = X7
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X2),X3),X4) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(X1),X5),X6),X7) ),
cls_triple_Oinject_2,
[final] ).
cnf(i_0_1703,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_finite__Un_2,
[final] ).
cnf(i_0_1704,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X3,X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_finite__UnI_0,
[final] ).
cnf(i_0_1705,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X2,X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_finite__Diff2_1,
[final] ).
cnf(i_0_1706,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_order__antisym__conv_0,
[final] ).
cnf(i_0_1707,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_order__antisym_0,
[final] ).
cnf(i_0_1708,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_order__eq__iff_2,
[final] ).
cnf(i_0_1709,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_order__less__asym_H_0,
[final] ).
cnf(i_0_1710,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_order__less__asym_0,
[final] ).
cnf(i_0_1711,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_less__le__not__le_1,
[final] ).
cnf(i_0_1712,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_xt1_I9_J_0,
[final] ).
cnf(i_0_1713,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_not__less__iff__gr__or__eq_1,
[final] ).
cnf(i_0_1714,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
cls_linorder__antisym__conv2_1,
[final] ).
cnf(i_0_1715,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_linorder__not__le_1,
[final] ).
cnf(i_0_1716,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_linorder__not__less_1,
[final] ).
cnf(i_0_1717,axiom,
( hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,X4,X2)) = hAPP(hAPP(X1,X3),hAPP(c_Finite__Set_Ofold1(X1,X2),X4))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_Finite__Set_Ofinite(X4,X2)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X2) ),
cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0,
[final] ).
cnf(i_0_1718,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
cls_emptyE_0,
[final] ).
cnf(i_0_1719,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
cls_empty__iff_0,
[final] ).
cnf(i_0_1720,axiom,
~ hBOOL(c_in(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
cls_ex__in__conv_0,
[final] ).
cnf(i_0_1721,axiom,
( X1 = X3
| c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) != c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2) ),
cls_singleton__inject_0,
[final] ).
cnf(i_0_1722,axiom,
( hAPP(hAPP(X1,hAPP(hAPP(X1,X2),X3)),X4) = hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
cls_ab__semigroup__mult_Omult__ac_I1_J_0,
[final] ).
cnf(i_0_1723,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X2)),X1)) ),
cls_not__less__eq__eq_1,
[final] ).
cnf(i_0_1724,axiom,
( c_Complete__Lattice_OInf__class_OInf(X2,X1) = hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(X1),X1,X1),c_Orderings_Otop__class_Otop(X1)),X2)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Inf__fold__inf_0,
[final] ).
cnf(i_0_1725,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Finite__Set_Ocard(X2,X3)
| ~ hBOOL(c_in(X1,X2,X3))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_card__insert__if_0,
[final] ).
cnf(i_0_1726,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Set_Oinsert(X4,X2,tc_Hoare__Mirabelle_Otriple(X3)),X3) ),
cls_derivs__insertD_1,
[final] ).
cnf(i_0_1727,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Un__empty_2,
[final] ).
cnf(i_0_1728,axiom,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
cls_image__empty_0,
[final] ).
cnf(i_0_1729,axiom,
c_Set_Ovimage(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),
cls_vimage__UNIV_0,
[final] ).
cnf(i_0_1730,axiom,
c_Set_Ovimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
cls_vimage__empty_0,
[final] ).
cnf(i_0_1731,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,X1),
cls_empty__is__image_1,
[final] ).
cnf(i_0_1732,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
cls_insertCI_1,
[final] ).
cnf(i_0_1733,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
cls_insertI1_0,
[final] ).
cnf(i_0_1734,axiom,
hBOOL(c_in(X1,c_Set_Oinsert(X1,X2,X3),X3)),
cls_insert__iff_1,
[final] ).
cnf(i_0_1735,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
cls_insert__commute_0,
[final] ).
cnf(i_0_1736,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_finite__Int_0,
[final] ).
cnf(i_0_1737,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_finite__Int_1,
[final] ).
cnf(i_0_1738,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X3),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_finite__Diff_0,
[final] ).
cnf(i_0_1739,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
cls_le__less__Suc__eq_0,
[final] ).
cnf(i_0_1740,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)))
| ~ class_Orderings_Olinorder(X1) ),
cls_le__maxI1_0,
[final] ).
cnf(i_0_1741,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)))
| ~ class_Orderings_Olinorder(X1) ),
cls_le__maxI2_0,
[final] ).
cnf(i_0_1742,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__ge1_0,
[final] ).
cnf(i_0_1743,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I3_J_0,
[final] ).
cnf(i_0_1744,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__ge2_0,
[final] ).
cnf(i_0_1745,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I4_J_0,
[final] ).
cnf(i_0_1746,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),c_Suc(X1))) ),
cls_not__less__eq_1,
[final] ).
cnf(i_0_1747,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__left__commute_0,
[final] ).
cnf(i_0_1748,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__left__commute_0,
[final] ).
cnf(i_0_1749,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I7_J_0,
[final] ).
cnf(i_0_1750,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__left__commute_0,
[final] ).
cnf(i_0_1751,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I3_J_0,
[final] ).
cnf(i_0_1752,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I19_J_0,
[final] ).
cnf(i_0_1753,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__21_1,
[final] ).
cnf(i_0_1754,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I22_J_0,
[final] ).
cnf(i_0_1755,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__left__commute_0,
[final] ).
cnf(i_0_1756,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X4))
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__left__commute_0,
[final] ).
cnf(i_0_1757,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_finite__compl_0,
[final] ).
cnf(i_0_1758,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__minus__cancel_0,
[final] ).
cnf(i_0_1759,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),X2),
cls_Compl__eq__Diff__UNIV_0,
[final] ).
cnf(i_0_1760,axiom,
hAPP(hAPP(c_Finite__Set_Ofold(X1,X2,X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) = X4,
cls_fold__empty_0,
[final] ).
cnf(i_0_1761,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_greaterThanAtMost__empty__iff2_0,
[final] ).
cnf(i_0_1762,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_atLeastatMost__empty__iff2_0,
[final] ).
cnf(i_0_1763,axiom,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_atLeastLessThan__empty__iff2_0,
[final] ).
cnf(i_0_1764,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_greaterThanAtMost__empty__iff_0,
[final] ).
cnf(i_0_1765,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_atLeastatMost__empty__iff_0,
[final] ).
cnf(i_0_1766,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_atLeastLessThan__empty__iff_0,
[final] ).
cnf(i_0_1767,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(X1)),X2) = c_Suc(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
cls_Suc__diff__le_0,
[final] ).
cnf(i_0_1768,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2))) ),
cls_Suc__less__eq_0,
[final] ).
cnf(i_0_1769,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),c_Suc(X2))) ),
cls_Suc__le__mono_0,
[final] ).
cnf(i_0_1770,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__partition_0,
[final] ).
cnf(i_0_1771,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Compl__disjoint_0,
[final] ).
cnf(i_0_1772,axiom,
c_Fun_Oinj__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2,X3),
cls_inj__on__empty_0,
[final] ).
cnf(i_0_1773,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
cls_le__antisym_0,
[final] ).
cnf(i_0_1774,axiom,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
cls_Un__empty_0,
[final] ).
cnf(i_0_1775,axiom,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
cls_Un__empty_1,
[final] ).
cnf(i_0_1776,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_neg__sup__eq__inf_0,
[final] ).
cnf(i_0_1777,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup_0,
[final] ).
cnf(i_0_1778,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_neg__inf__eq__sup_0,
[final] ).
cnf(i_0_1779,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf_0,
[final] ).
cnf(i_0_1780,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__add__distrib_0,
[final] ).
cnf(i_0_1781,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add_0,
[final] ).
cnf(i_0_1782,axiom,
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_insert__code_2,
[final] ).
cnf(i_0_1783,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X2)),
cls_subset__refl_0,
[final] ).
cnf(i_0_1784,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X1,tc_bool)),X2),X2)),
cls_equalityE_0,
[final] ).
cnf(i_0_1785,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X3),X2),
cls_Un__commute_0,
[final] ).
cnf(i_0_1786,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X2),
cls_Int__commute_0,
[final] ).
cnf(i_0_1787,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
cls_diff__diff__cancel_0,
[final] ).
cnf(i_0_1788,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
| hBOOL(c_in(X1,X2,X3))
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_card__insert__if_1,
[final] ).
cnf(i_0_1789,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_order__neq__le__trans_0,
[final] ).
cnf(i_0_1790,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_order__le__neq__trans_0,
[final] ).
cnf(i_0_1791,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_order__less__le_2,
[final] ).
cnf(i_0_1792,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_order__le__less_0,
[final] ).
cnf(i_0_1793,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_xt1_I12_J_0,
[final] ).
cnf(i_0_1794,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_xt1_I11_J_0,
[final] ).
cnf(i_0_1795,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_linorder__antisym__conv2_0,
[final] ).
cnf(i_0_1796,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_linorder__antisym__conv1_0,
[final] ).
cnf(i_0_1797,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_order__less__imp__le_0,
[final] ).
cnf(i_0_1798,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_order__le__less_1,
[final] ).
cnf(i_0_1799,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2)) ),
cls_Suc__lessD_0,
[final] ).
cnf(i_0_1800,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2)) ),
cls_Suc__le__eq_0,
[final] ).
cnf(i_0_1801,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2)) ),
cls_less__eq__Suc__le_1,
[final] ).
cnf(i_0_1802,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2)) ),
cls_Suc__leD_0,
[final] ).
cnf(i_0_1803,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
cls_Suc__mono_0,
[final] ).
cnf(i_0_1804,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
cls_less__Suc__eq__0__disj_3,
[final] ).
cnf(i_0_1805,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
cls_Suc__le__mono_1,
[final] ).
cnf(i_0_1806,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_Min__insert_0,
[final] ).
cnf(i_0_1807,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),c_Set_Oinsert(X2,X3,X1)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X3))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X3,X1) ),
cls_Max__insert_0,
[final] ).
cnf(i_0_1808,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Un__UNIV__left_0,
[final] ).
cnf(i_0_1809,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Int__empty__left_0,
[final] ).
cnf(i_0_1810,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_empty__Diff_0,
[final] ).
cnf(i_0_1811,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X3))
| X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X2)) ),
cls_nat__less__cases_0,
[final] ).
cnf(i_0_1812,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X4)
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != X3 ),
cls_add__cancel__end_0,
[final] ).
cnf(i_0_1813,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(X1)),X2))
| c_Suc(X1) = X2
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
cls_Suc__lessI_0,
[final] ).
cnf(i_0_1814,axiom,
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X1)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_finite__compl_1,
[final] ).
cnf(i_0_1815,axiom,
( X1 = c_Suc(X2)
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),c_Suc(X2))) ),
cls_le__SucE_0,
[final] ).
cnf(i_0_1816,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
cls_Suc__leI_0,
[final] ).
cnf(i_0_1817,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
cls_less__eq__Suc__le_0,
[final] ).
cnf(i_0_1818,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__diff__cancel_0,
[final] ).
cnf(i_0_1819,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)),X3) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__add__cancel_0,
[final] ).
cnf(i_0_1820,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
cls_not__less__less__Suc__eq_0,
[final] ).
cnf(i_0_1821,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
cls_less__SucE_0,
[final] ).
cnf(i_0_1822,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),c_Suc(X1))) ),
cls_less__antisym_0,
[final] ).
cnf(i_0_1823,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(X4,X5) ),
cls_ab__semigroup__mult_Ononempty__iff_2,
[final] ).
cnf(i_0_1824,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2))) ),
cls_less__Suc__eq__le_0,
[final] ).
cnf(i_0_1825,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X3),X4)) = hAPP(hAPP(X1,X3),hAPP(hAPP(X1,X2),X4))
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X5) ),
cls_ab__semigroup__mult_Omult__left__commute_0,
[final] ).
cnf(i_0_1826,axiom,
( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))
| c_Finite__Set_Ocard(X1,X2) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2) ),
cls_card__eq__UNIV__imp__eq__UNIV_0,
[final] ).
cnf(i_0_1827,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__left_0,
[final] ).
cnf(i_0_1828,axiom,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_greaterThanAtMost__empty_0,
[final] ).
cnf(i_0_1829,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_atLeastatMost__empty_0,
[final] ).
cnf(i_0_1830,axiom,
( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_atLeastLessThan__empty_0,
[final] ).
cnf(i_0_1831,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X1)) ),
cls_le__less__Suc__eq_1,
[final] ).
cnf(i_0_1832,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
cls_less__SucI_0,
[final] ).
cnf(i_0_1833,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
cls_less__Suc__eq__le_1,
[final] ).
cnf(i_0_1834,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),c_Suc(X2)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
cls_le__SucI_0,
[final] ).
cnf(i_0_1835,axiom,
hAPP(c_Finite__Set_Ofold1(X1,X2),c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) = X3,
cls_fold1__singleton_0,
[final] ).
cnf(i_0_1836,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = X2,
cls_Un__empty__left_0,
[final] ).
cnf(i_0_1837,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))),X2) = X2,
cls_Int__UNIV__left_0,
[final] ).
cnf(i_0_1838,axiom,
( hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(X1),X2),X2,X1))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Min__in_0,
[final] ).
cnf(i_0_1839,axiom,
( hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(X1),X2),X2,X1))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Olinorder(X1)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
cls_Max__in_0,
[final] ).
cnf(i_0_1840,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
cls_le__neq__implies__less_0,
[final] ).
cnf(i_0_1841,axiom,
( X1 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
cls_le__eq__less__or__eq_0,
[final] ).
cnf(i_0_1842,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2)) ),
cls_nat__less__le_2,
[final] ).
cnf(i_0_1843,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
cls_insert__code_1,
[final] ).
cnf(i_0_1844,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
cls_nat__less__le_0,
[final] ).
cnf(i_0_1845,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2)) ),
cls_termination__basic__simps_I5_J_0,
[final] ).
cnf(i_0_1846,axiom,
( hBOOL(c_in(X1,X2,X3))
| c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_comm__monoid__add_Ononempty__iff_2,
[final] ).
cnf(i_0_1847,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add__cancel_0,
[final] ).
cnf(i_0_1848,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__end_1,
[final] ).
cnf(i_0_1849,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMin(X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_Min__singleton_0,
[final] ).
cnf(i_0_1850,axiom,
( hAPP(c_Finite__Set_Olinorder__class_OMax(X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_Max__singleton_0,
[final] ).
cnf(i_0_1851,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
cls_Inf__singleton_0,
[final] ).
cnf(i_0_1852,axiom,
( c_Set_Oinsert(X1,X2,X3) = X2
| ~ hBOOL(c_in(X1,X2,X3)) ),
cls_insert__absorb_0,
[final] ).
cnf(i_0_1853,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_min__max_Osup__absorb1_0,
[final] ).
cnf(i_0_1854,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_min__max_Ole__iff__sup_0,
[final] ).
cnf(i_0_1855,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_sup__absorb1_0,
[final] ).
cnf(i_0_1856,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_le__iff__sup_0,
[final] ).
cnf(i_0_1857,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_le__iff__inf_0,
[final] ).
cnf(i_0_1858,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_inf__absorb2_0,
[final] ).
cnf(i_0_1859,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_min__max_Ole__iff__inf_0,
[final] ).
cnf(i_0_1860,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = X3
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_min__max_Oinf__absorb2_0,
[final] ).
cnf(i_0_1861,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X4,X2,X3) ),
cls_cut_0,
[final] ).
cnf(i_0_1862,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_square__eq__iff_1,
[final] ).
cnf(i_0_1863,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__minus_0,
[final] ).
cnf(i_0_1864,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__commute_0,
[final] ).
cnf(i_0_1865,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_linorder__neqE__ordered__idom_0,
[final] ).
cnf(i_0_1866,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv3_0,
[final] ).
cnf(i_0_1867,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X3 = X2
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__less__linear_0,
[final] ).
cnf(i_0_1868,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__neqE_0,
[final] ).
cnf(i_0_1869,axiom,
( X2 = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
cls_not__less__iff__gr__or__eq_0,
[final] ).
cnf(i_0_1870,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Un__UNIV__right_0,
[final] ).
cnf(i_0_1871,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Int__empty__right_0,
[final] ).
cnf(i_0_1872,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Diff__UNIV_0,
[final] ).
cnf(i_0_1873,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv1_1,
[final] ).
cnf(i_0_1874,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__less_0,
[final] ).
cnf(i_0_1875,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__le_0,
[final] ).
cnf(i_0_1876,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_not__leE_0,
[final] ).
cnf(i_0_1877,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0,
[final] ).
cnf(i_0_1878,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__right_0,
[final] ).
cnf(i_0_1879,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,X2,X3),
cls_insert__absorb2_0,
[final] ).
cnf(i_0_1880,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
cls_UNIV__I_0,
[final] ).
cnf(i_0_1881,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__left__idem_0,
[final] ).
cnf(i_0_1882,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__left__idem_0,
[final] ).
cnf(i_0_1883,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I8_J_0,
[final] ).
cnf(i_0_1884,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__left__idem_0,
[final] ).
cnf(i_0_1885,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I4_J_0,
[final] ).
cnf(i_0_1886,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__left__idem_0,
[final] ).
cnf(i_0_1887,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__left__idem_0,
[final] ).
cnf(i_0_1888,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
cls_not__less__eq__eq_0,
[final] ).
cnf(i_0_1889,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0,
[final] ).
cnf(i_0_1890,axiom,
( X2 = X3
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3) ),
cls_Compl__eq__Compl__iff_0,
[final] ).
cnf(i_0_1891,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X2,X3,X1),X1) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Complete__Lattice_OInf__class_OInf(X3,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
cls_Inf__insert_0,
[final] ).
cnf(i_0_1892,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
cls_compl__unique_0,
[final] ).
cnf(i_0_1893,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(c_in(X2,X1,X3)) ),
cls_mem__def_0,
[final] ).
cnf(i_0_1894,axiom,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X3,X1,X2),X2) ),
cls_finite__insert_0,
[final] ).
cnf(i_0_1895,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1))) ),
cls_not__less__less__Suc__eq_1,
[final] ).
cnf(i_0_1896,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X2)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1)) ),
cls_not__less__eq_0,
[final] ).
cnf(i_0_1897,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) != X3 ),
cls_min__max_Ole__iff__sup_1,
[final] ).
cnf(i_0_1898,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != X3 ),
cls_le__iff__sup_1,
[final] ).
cnf(i_0_1899,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
cls_le__iff__inf_1,
[final] ).
cnf(i_0_1900,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) != X2 ),
cls_min__max_Ole__iff__inf_1,
[final] ).
cnf(i_0_1901,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
cls_Un__empty__right_0,
[final] ).
cnf(i_0_1902,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = X2,
cls_Int__UNIV__right_0,
[final] ).
cnf(i_0_1903,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
cls_Diff__empty_0,
[final] ).
cnf(i_0_1904,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0,
[final] ).
cnf(i_0_1905,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
cls_greaterThanAtMost__empty__iff2_1,
[final] ).
cnf(i_0_1906,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
cls_atLeastatMost__empty__iff2_1,
[final] ).
cnf(i_0_1907,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
cls_atLeastLessThan__empty__iff2_1,
[final] ).
cnf(i_0_1908,axiom,
( c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
cls_greaterThanAtMost__empty__iff_1,
[final] ).
cnf(i_0_1909,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
cls_atLeastatMost__empty__iff_1,
[final] ).
cnf(i_0_1910,axiom,
( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
cls_atLeastLessThan__empty__iff_1,
[final] ).
cnf(i_0_1911,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3) ),
cls_square__eq__iff_0,
[final] ).
cnf(i_0_1912,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
cls_fun__Compl__def_0,
[final] ).
cnf(i_0_1913,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X2 = X1 ),
cls_linorder__neqE__nat_0,
[final] ).
cnf(i_0_1914,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X2 = X1 ),
cls_nat__neq__iff_0,
[final] ).
cnf(i_0_1915,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
cls_nat__le__linear_0,
[final] ).
cnf(i_0_1916,axiom,
~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X1)),
cls_Suc__n__not__le__n_0,
[final] ).
cnf(i_0_1917,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X2)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__diff__eq_0,
[final] ).
cnf(i_0_1918,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_class__ringb_Oadd__cancel_0,
[final] ).
cnf(i_0_1919,axiom,
( hAPP(hAPP(X1,X2),hAPP(hAPP(X1,X2),X3)) = hAPP(hAPP(X1,X2),X3)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X4) ),
cls_ab__semigroup__idem__mult_Omult__left__idem_0,
[final] ).
cnf(i_0_1920,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
cls_order__less__irrefl_0,
[final] ).
cnf(i_0_1921,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
cls_order__less__le_1,
[final] ).
cnf(i_0_1922,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X2)) ),
cls_linorder__neq__iff_1,
[final] ).
cnf(i_0_1923,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X4),X4) ),
cls_eq__eqI_1,
[final] ).
cnf(i_0_1924,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
cls_add__right__cancel_0,
[final] ).
cnf(i_0_1925,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X4) ),
cls_eq__eqI_0,
[final] ).
cnf(i_0_1926,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_add__left__cancel_0,
[final] ).
cnf(i_0_1927,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_add__imp__eq_0,
[final] ).
cnf(i_0_1928,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X1,tc_bool)),X2),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Diff__cancel_0,
[final] ).
cnf(i_0_1929,axiom,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal(X3),X1),X2)) ),
cls_ATP__Linkup_Ofequal__imp__equal_0,
[final] ).
cnf(i_0_1930,axiom,
( c_SetInterval_Oord__class_OatLeastAtMost(X2,X2,X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
| ~ class_Orderings_Oorder(X1) ),
cls_atLeastAtMost__singleton_0,
[final] ).
cnf(i_0_1931,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__inf__absorb_0,
[final] ).
cnf(i_0_1932,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_sup__inf__absorb_0,
[final] ).
cnf(i_0_1933,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__absorb_0,
[final] ).
cnf(i_0_1934,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__sup__absorb_0,
[final] ).
cnf(i_0_1935,negated_conjecture,
~ hBOOL(c_in(v_x,v_F,t_a)),
cls_conjecture_1,
[final] ).
cnf(i_0_1936,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
cls_mem__def_1,
[final] ).
cnf(i_0_1937,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a),
cls_bot__empty__eq_0,
[final] ).
cnf(i_0_1938,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__minus__eq__add_0,
[final] ).
cnf(i_0_1939,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_diff__eq_0,
[final] ).
cnf(i_0_1940,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_ab__diff__minus_0,
[final] ).
cnf(i_0_1941,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_diff__def_0,
[final] ).
cnf(i_0_1942,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__minus_0,
[final] ).
cnf(i_0_1943,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ring_Osub__add_0,
[final] ).
cnf(i_0_1944,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
cls_less__not__refl_0,
[final] ).
cnf(i_0_1945,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
cls_nat__less__le_1,
[final] ).
cnf(i_0_1946,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Compl__UNIV__eq_0,
[final] ).
cnf(i_0_1947,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__empty__eq_0,
[final] ).
cnf(i_0_1948,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X2) = X2,
cls_Un__absorb_0,
[final] ).
cnf(i_0_1949,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
cls_Int__absorb_0,
[final] ).
cnf(i_0_1950,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X2,X3),X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_finite__insert_1,
[final] ).
cnf(i_0_1951,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup__top_0,
[final] ).
cnf(i_0_1952,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf__bot_0,
[final] ).
cnf(i_0_1953,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0,
[final] ).
cnf(i_0_1954,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0,
[final] ).
cnf(i_0_1955,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),c_Suc(X1))),
cls_le__Suc__eq_2,
[final] ).
cnf(i_0_1956,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_bool)),X2),
cls_empty_0,
[final] ).
cnf(i_0_1957,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
cls_empty__not__insert_0,
[final] ).
cnf(i_0_1958,axiom,
c_Set_Oinsert(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
cls_insert__not__empty_0,
[final] ).
cnf(i_0_1959,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
cls_top__greatest_0,
[final] ).
cnf(i_0_1960,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0,
[final] ).
cnf(i_0_1961,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
cls_order__eq__refl_0,
[final] ).
cnf(i_0_1962,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X2))
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0,
[final] ).
cnf(i_0_1963,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__commute_0,
[final] ).
cnf(i_0_1964,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__commute_0,
[final] ).
cnf(i_0_1965,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I5_J_0,
[final] ).
cnf(i_0_1966,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__commute_0,
[final] ).
cnf(i_0_1967,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I1_J_0,
[final] ).
cnf(i_0_1968,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I7_J_0,
[final] ).
cnf(i_0_1969,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__c_0,
[final] ).
cnf(i_0_1970,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I24_J_0,
[final] ).
cnf(i_0_1971,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__c_0,
[final] ).
cnf(i_0_1972,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__commute_0,
[final] ).
cnf(i_0_1973,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X2)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__commute_0,
[final] ).
cnf(i_0_1974,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(X1)),c_Suc(X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),
cls_diff__Suc__Suc_0,
[final] ).
cnf(i_0_1975,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P,
cls_COMBK__def__raw_0,
[final] ).
cnf(i_0_1976,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1))),
cls_less__Suc__eq_2,
[final] ).
cnf(i_0_1977,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Suc(X1))),
cls_lessI_0,
[final] ).
cnf(i_0_1978,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0,
[final] ).
cnf(i_0_1979,axiom,
( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,X3),X2)
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X4) ),
cls_ab__semigroup__mult_Omult__commute_0,
[final] ).
cnf(i_0_1980,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_sup__compl__top_0,
[final] ).
cnf(i_0_1981,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_inf__compl__bot_0,
[final] ).
cnf(i_0_1982,axiom,
( X2 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1) ),
cls_inf__eq__top__eq1_0,
[final] ).
cnf(i_0_1983,axiom,
( X2 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
cls_sup__eq__bot__eq1_0,
[final] ).
cnf(i_0_1984,axiom,
( X3 = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != c_Orderings_Otop__class_Otop(X1) ),
cls_inf__eq__top__eq2_0,
[final] ).
cnf(i_0_1985,axiom,
( X3 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
cls_sup__eq__bot__eq2_0,
[final] ).
cnf(i_0_1986,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X1)),
cls_eq__imp__le_0,
[final] ).
cnf(i_0_1987,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X1)),
cls_le__refl_0,
[final] ).
cnf(i_0_1988,axiom,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_UNIV__not__empty_0,
[final] ).
cnf(i_0_1989,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
cls_Inf__UNIV_0,
[final] ).
cnf(i_0_1990,axiom,
( c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
cls_Inf__empty_0,
[final] ).
cnf(i_0_1991,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__left_0,
[final] ).
cnf(i_0_1992,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__bot__left_0,
[final] ).
cnf(i_0_1993,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__fun__eq_0,
[final] ).
cnf(i_0_1994,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__fun__eq_0,
[final] ).
cnf(i_0_1995,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
cls_finite__UNIV_0,
[final] ).
cnf(i_0_1996,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
cls_neg__equal__iff__equal_0,
[final] ).
cnf(i_0_1997,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
cls_compl__eq__compl__iff_0,
[final] ).
cnf(i_0_1998,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__left_0,
[final] ).
cnf(i_0_1999,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__top__left_0,
[final] ).
cnf(i_0_2000,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__right_0,
[final] ).
cnf(i_0_2001,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__bot__right_0,
[final] ).
cnf(i_0_2002,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__right_0,
[final] ).
cnf(i_0_2003,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__top__right_0,
[final] ).
cnf(i_0_2004,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__equation__iff_1,
[final] ).
cnf(i_0_2005,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__minus_0,
[final] ).
cnf(i_0_2006,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0,
[final] ).
cnf(i_0_2007,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_1,
[final] ).
cnf(i_0_2008,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_0,
[final] ).
cnf(i_0_2009,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
cls_finite_OemptyI_0,
[final] ).
cnf(i_0_2010,axiom,
( hAPP(hAPP(X1,X2),X2) = X2
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X3) ),
cls_ab__semigroup__idem__mult_Omult__idem_0,
[final] ).
cnf(i_0_2011,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Osup__idem_0,
[final] ).
cnf(i_0_2012,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__idem_0,
[final] ).
cnf(i_0_2013,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__idem_0,
[final] ).
cnf(i_0_2014,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__idem_0,
[final] ).
cnf(i_0_2015,axiom,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__idem_0,
[final] ).
cnf(i_0_2016,axiom,
( X1 = X3
| c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSemi(X3,X4) ),
cls_com_Osimps_I3_J_0,
[final] ).
cnf(i_0_2017,axiom,
( X2 = X4
| c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSemi(X3,X4) ),
cls_com_Osimps_I3_J_1,
[final] ).
cnf(i_0_2018,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(X1,X2))
| ~ class_Finite__Set_Ofinite_Ofinite(X2)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
clsarity_fun__Finite__Set_Ofinite_Ofinite,
[final] ).
cnf(i_0_2019,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__top__eq_0,
[final] ).
cnf(i_0_2020,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__bot__eq_0,
[final] ).
cnf(i_0_2021,axiom,
( class_Orderings_Otop(tc_fun(X1,X2))
| ~ class_Orderings_Otop(X2) ),
clsarity_fun__Orderings_Otop,
[final] ).
cnf(i_0_2022,axiom,
( class_Orderings_Obot(tc_fun(X1,X2))
| ~ class_Orderings_Obot(X2) ),
clsarity_fun__Orderings_Obot,
[final] ).
cnf(i_0_2023,axiom,
( class_HOL_Ominus(tc_fun(X1,X2))
| ~ class_HOL_Ominus(X2) ),
clsarity_fun__HOL_Ominus,
[final] ).
cnf(i_0_2024,axiom,
( class_HOL_Ouminus(tc_fun(X1,X2))
| ~ class_HOL_Ouminus(X2) ),
clsarity_fun__HOL_Ouminus,
[final] ).
cnf(i_0_2025,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X1,X2))
| ~ class_Complete__Lattice_Ocomplete__lattice(X2) ),
clsarity_fun__Complete__Lattice_Ocomplete__lattice,
[final] ).
cnf(i_0_2026,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Odistrib__lattice(X2) ),
clsarity_fun__Lattices_Odistrib__lattice,
[final] ).
cnf(i_0_2027,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
| ~ class_Lattices_Oboolean__algebra(X2) ),
clsarity_fun__Lattices_Oboolean__algebra,
[final] ).
cnf(i_0_2028,axiom,
( class_HOL_Oord(tc_fun(X1,X2))
| ~ class_HOL_Oord(X2) ),
clsarity_fun__HOL_Oord,
[final] ).
cnf(i_0_2029,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
clsarity_fun__Orderings_Opreorder,
[final] ).
cnf(i_0_2030,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
clsarity_fun__Orderings_Oorder,
[final] ).
cnf(i_0_2031,axiom,
( class_Lattices_Obounded__lattice(tc_fun(X1,X2))
| ~ class_Lattices_Obounded__lattice(X2) ),
clsarity_fun__Lattices_Obounded__lattice,
[final] ).
cnf(i_0_2032,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Oupper__semilattice,
[final] ).
cnf(i_0_2033,axiom,
( class_Lattices_Olower__semilattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Olower__semilattice,
[final] ).
cnf(i_0_2034,axiom,
( class_Lattices_Olattice(tc_fun(X1,X2))
| ~ class_Lattices_Olattice(X2) ),
clsarity_fun__Lattices_Olattice,
[final] ).
cnf(i_0_2035,axiom,
( c_Finite__Set_Olinorder__class_OMin(X1) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__class_OMin__def__raw_0,
[final] ).
cnf(i_0_2036,axiom,
( c_Finite__Set_Olinorder__class_OMax(X1) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_Max__def__raw_0,
[final] ).
cnf(i_0_2037,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_ab__semigroup__idem__mult__max_0,
[final] ).
cnf(i_0_2038,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X1),X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_ab__semigroup__idem__mult__sup_0,
[final] ).
cnf(i_0_2039,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X1),X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_ab__semigroup__idem__mult__inf_0,
[final] ).
cnf(i_0_2040,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X1),X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_ab__semigroup__idem__mult__min_0,
[final] ).
cnf(i_0_2041,axiom,
c_Com_Ocom_OSemi(X1,X2) != c_Com_Ocom_OSKIP,
cls_com_Osimps_I13_J_0,
[final] ).
cnf(i_0_2042,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X2),
cls_com_Osimps_I12_J_0,
[final] ).
cnf(i_0_2043,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(X1) = c_Orderings_Oord__class_Omax(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__max_0,
[final] ).
cnf(i_0_2044,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(X1) = c_Orderings_Oord__class_Omin(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__min_0,
[final] ).
cnf(i_0_2045,axiom,
( c_Finite__Set_Ofinite(X2,X1)
| ~ class_Finite__Set_Ofinite_Ofinite(X1) ),
cls_finite_0,
[final] ).
cnf(i_0_2046,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
cls_nat_Oinject_0,
[final] ).
cnf(i_0_2047,axiom,
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
cls_Suc__inject_0,
[final] ).
cnf(i_0_2048,negated_conjecture,
c_Finite__Set_Ofinite(v_F,t_a),
cls_conjecture_0,
[final] ).
cnf(i_0_2049,axiom,
c_Suc(X1) != X1,
cls_Suc__n__not__n_0,
[final] ).
cnf(i_0_2050,axiom,
X1 != c_Suc(X1),
cls_n__not__Suc__n_0,
[final] ).
cnf(i_0_2051,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop,
[final] ).
cnf(i_0_2052,axiom,
class_Orderings_Obot(tc_nat),
clsarity_nat__Orderings_Obot,
[final] ).
cnf(i_0_2053,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot,
[final] ).
cnf(i_0_2054,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
clsarity_bool__Finite__Set_Ofinite_Ofinite,
[final] ).
cnf(i_0_2055,axiom,
class_HOL_Ominus(tc_nat),
clsarity_nat__HOL_Ominus,
[final] ).
cnf(i_0_2056,axiom,
class_HOL_Ominus(tc_bool),
clsarity_bool__HOL_Ominus,
[final] ).
cnf(i_0_2057,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_2058,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_2059,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_2060,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_2061,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_2062,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_2063,axiom,
class_HOL_Ouminus(tc_bool),
clsarity_bool__HOL_Ouminus,
[final] ).
cnf(i_0_2064,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_2065,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_2066,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
clsarity_bool__Complete__Lattice_Ocomplete__lattice,
[final] ).
cnf(i_0_2067,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
clsarity_nat__Lattices_Odistrib__lattice,
[final] ).
cnf(i_0_2068,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
clsarity_bool__Lattices_Odistrib__lattice,
[final] ).
cnf(i_0_2069,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_2070,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_2071,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra,
[final] ).
cnf(i_0_2072,axiom,
class_HOL_Oord(tc_nat),
clsarity_nat__HOL_Oord,
[final] ).
cnf(i_0_2073,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord,
[final] ).
cnf(i_0_2074,axiom,
class_Orderings_Opreorder(tc_nat),
clsarity_nat__Orderings_Opreorder,
[final] ).
cnf(i_0_2075,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder,
[final] ).
cnf(i_0_2076,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat__Orderings_Oorder,
[final] ).
cnf(i_0_2077,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder,
[final] ).
cnf(i_0_2078,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_2079,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice,
[final] ).
cnf(i_0_2080,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
clsarity_nat__Lattices_Oupper__semilattice,
[final] ).
cnf(i_0_2081,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice,
[final] ).
cnf(i_0_2082,axiom,
class_Lattices_Olower__semilattice(tc_nat),
clsarity_nat__Lattices_Olower__semilattice,
[final] ).
cnf(i_0_2083,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice,
[final] ).
cnf(i_0_2084,axiom,
class_Lattices_Olattice(tc_nat),
clsarity_nat__Lattices_Olattice,
[final] ).
cnf(i_0_2085,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice,
[final] ).
cnf(i_0_2086,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_2087,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder,
[final] ).
cnf(i_0_2088,axiom,
X1 = X1 ).
cnf(i_0_2089,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_2090,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_2091,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_2092,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_2093,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_2094,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_2095,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_2096,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_2097,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_2098,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_2099,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_2100,axiom,
( X1 != X2
| c_in(X1,X3,X4) = c_in(X2,X3,X4) ) ).
cnf(i_0_2101,axiom,
( X1 != X2
| c_in(X3,X1,X4) = c_in(X3,X2,X4) ) ).
cnf(i_0_2102,axiom,
( X1 != X2
| c_in(X3,X4,X1) = c_in(X3,X4,X2) ) ).
cnf(i_0_2103,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_2104,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_2105,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X1,X3,X4,X5) = c_Finite__Set_Osetsum(X2,X3,X4,X5) ) ).
cnf(i_0_2106,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X1,X4,X5) = c_Finite__Set_Osetsum(X3,X2,X4,X5) ) ).
cnf(i_0_2107,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X1,X5) = c_Finite__Set_Osetsum(X3,X4,X2,X5) ) ).
cnf(i_0_2108,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X5,X1) = c_Finite__Set_Osetsum(X3,X4,X5,X2) ) ).
cnf(i_0_2109,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X1) = c_Lattices_Olower__semilattice__class_Oinf(X2) ) ).
cnf(i_0_2110,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X1) = c_Lattices_Oupper__semilattice__class_Osup(X2) ) ).
cnf(i_0_2111,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).
cnf(i_0_2112,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).
cnf(i_0_2113,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).
cnf(i_0_2114,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).
cnf(i_0_2115,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).
cnf(i_0_2116,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_2117,axiom,
( X1 != X2
| c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).
cnf(i_0_2118,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).
cnf(i_0_2119,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).
cnf(i_0_2120,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).
cnf(i_0_2121,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_2122,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X1,X3,X4,X5,X6) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X2,X3,X4,X5,X6) ) ).
cnf(i_0_2123,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X1,X4,X5,X6) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X2,X4,X5,X6) ) ).
cnf(i_0_2124,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X1,X5,X6) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X2,X5,X6) ) ).
cnf(i_0_2125,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X5,X1,X6) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X5,X2,X6) ) ).
cnf(i_0_2126,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X5,X6,X1) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X5,X6,X2) ) ).
cnf(i_0_2127,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).
cnf(i_0_2128,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).
cnf(i_0_2129,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).
cnf(i_0_2130,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).
cnf(i_0_2131,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X1,X3,X4,X5) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X2,X3,X4,X5) ) ).
cnf(i_0_2132,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X1,X4,X5) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X2,X4,X5) ) ).
cnf(i_0_2133,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X4,X1,X5) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X4,X2,X5) ) ).
cnf(i_0_2134,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X4,X5,X1) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X4,X5,X2) ) ).
cnf(i_0_2135,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).
cnf(i_0_2136,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).
cnf(i_0_2137,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).
cnf(i_0_2138,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_2139,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_2140,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_2141,axiom,
( X1 != X2
| c_Suc(X1) = c_Suc(X2) ) ).
cnf(i_0_2142,axiom,
( X1 != X2
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X1,X3) = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X2,X3) ) ).
cnf(i_0_2143,axiom,
( X1 != X2
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X3,X1) = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X3,X2) ) ).
cnf(i_0_2144,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).
cnf(i_0_2145,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).
cnf(i_0_2146,axiom,
( X1 != X2
| c_Finite__Set_Olinorder__class_OMax(X1) = c_Finite__Set_Olinorder__class_OMax(X2) ) ).
cnf(i_0_2147,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).
cnf(i_0_2148,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).
cnf(i_0_2149,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).
cnf(i_0_2150,axiom,
( X1 != X2
| c_Finite__Set_Olinorder__class_OMin(X1) = c_Finite__Set_Olinorder__class_OMin(X2) ) ).
cnf(i_0_2151,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).
cnf(i_0_2152,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).
cnf(i_0_2153,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).
cnf(i_0_2154,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).
cnf(i_0_2155,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).
cnf(i_0_2156,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_2157,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_2158,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_2159,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_2160,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_2161,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_2162,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2163,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_2164,axiom,
( X1 != X2
| ~ c_Lattices_Olower__semilattice(X1,X3,X4,X5)
| c_Lattices_Olower__semilattice(X2,X3,X4,X5) ) ).
cnf(i_0_2165,axiom,
( X1 != X2
| ~ c_Lattices_Olower__semilattice(X3,X1,X4,X5)
| c_Lattices_Olower__semilattice(X3,X2,X4,X5) ) ).
cnf(i_0_2166,axiom,
( X1 != X2
| ~ c_Lattices_Olower__semilattice(X3,X4,X1,X5)
| c_Lattices_Olower__semilattice(X3,X4,X2,X5) ) ).
cnf(i_0_2167,axiom,
( X1 != X2
| ~ c_Lattices_Olower__semilattice(X3,X4,X5,X1)
| c_Lattices_Olower__semilattice(X3,X4,X5,X2) ) ).
cnf(i_0_2168,axiom,
( X1 != X2
| ~ class_Lattices_Olower__semilattice(X1)
| class_Lattices_Olower__semilattice(X2) ) ).
cnf(i_0_2169,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_2170,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2171,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_2172,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_2173,axiom,
( X1 != X2
| ~ class_Lattices_Oupper__semilattice(X1)
| class_Lattices_Oupper__semilattice(X2) ) ).
cnf(i_0_2174,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_2175,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_2176,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_2177,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_2178,axiom,
( X1 != X2
| ~ class_HOL_Oord(X1)
| class_HOL_Oord(X2) ) ).
cnf(i_0_2179,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_2180,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_2181,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_2182,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_2183,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_2184,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_2185,axiom,
( X1 != X2
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X3)
| c_OrderedGroup_Oab__semigroup__idem__mult(X2,X3) ) ).
cnf(i_0_2186,axiom,
( X1 != X2
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X3,X1)
| c_OrderedGroup_Oab__semigroup__idem__mult(X3,X2) ) ).
cnf(i_0_2187,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_2188,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_2189,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1)
| class_OrderedGroup_Olordered__ab__group__add__join(X2) ) ).
cnf(i_0_2190,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_2191,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
| class_OrderedGroup_Olordered__ab__group__add__meet(X2) ) ).
cnf(i_0_2192,axiom,
( X1 != X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(X2) ) ).
cnf(i_0_2193,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_2194,axiom,
( X1 != X2
| ~ class_HOL_Ominus(X1)
| class_HOL_Ominus(X2) ) ).
cnf(i_0_2195,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_2196,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_2197,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_2198,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_2199,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_2200,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_2201,axiom,
( X1 != X2
| ~ class_HOL_Ouminus(X1)
| class_HOL_Ouminus(X2) ) ).
cnf(i_0_2202,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_2203,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_2204,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_2205,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_2206,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_2207,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_2208,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(X2) ) ).
cnf(i_0_2209,axiom,
( X1 != X2
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3)
| c_OrderedGroup_Oab__semigroup__mult(X2,X3) ) ).
cnf(i_0_2210,axiom,
( X1 != X2
| ~ c_OrderedGroup_Oab__semigroup__mult(X3,X1)
| c_OrderedGroup_Oab__semigroup__mult(X3,X2) ) ).
cnf(i_0_2211,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X6,X7)
| c_Finite__Set_Ofold__graph(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_2212,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X3,X1,X4,X5,X6,X7)
| c_Finite__Set_Ofold__graph(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_2213,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X3,X4,X1,X5,X6,X7)
| c_Finite__Set_Ofold__graph(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_2214,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X1,X6,X7)
| c_Finite__Set_Ofold__graph(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_2215,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X1,X7)
| c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_2216,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7,X1)
| c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_2217,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_2218,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_2219,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X1,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_2220,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X1,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_2221,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X1,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_2222,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X1,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_2223,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X1)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_2088_001,axiom,
X1 = X1 ).
cnf(i_0_2089_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_2090_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_2091_004,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_2092_005,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_2093_006,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_2094_007,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_2095_008,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_2096_009,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_2097_010,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_2098_011,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_2099_012,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_2100_013,axiom,
( X1 != X2
| c_in(X1,X3,X4) = c_in(X2,X3,X4) ) ).
cnf(i_0_2101_014,axiom,
( X1 != X2
| c_in(X3,X1,X4) = c_in(X3,X2,X4) ) ).
cnf(i_0_2102_015,axiom,
( X1 != X2
| c_in(X3,X4,X1) = c_in(X3,X4,X2) ) ).
cnf(i_0_2103_016,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_2104_017,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_2105_018,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X1,X3,X4,X5) = c_Finite__Set_Osetsum(X2,X3,X4,X5) ) ).
cnf(i_0_2106_019,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X1,X4,X5) = c_Finite__Set_Osetsum(X3,X2,X4,X5) ) ).
cnf(i_0_2107_020,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X1,X5) = c_Finite__Set_Osetsum(X3,X4,X2,X5) ) ).
cnf(i_0_2108_021,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X5,X1) = c_Finite__Set_Osetsum(X3,X4,X5,X2) ) ).
cnf(i_0_2109_022,axiom,
( X1 != X2
| c_Lattices_Olower__semilattice__class_Oinf(X1) = c_Lattices_Olower__semilattice__class_Oinf(X2) ) ).
cnf(i_0_2110_023,axiom,
( X1 != X2
| c_Lattices_Oupper__semilattice__class_Osup(X1) = c_Lattices_Oupper__semilattice__class_Osup(X2) ) ).
cnf(i_0_2111_024,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).
cnf(i_0_2112_025,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).
cnf(i_0_2113_026,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).
cnf(i_0_2114_027,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).
cnf(i_0_2115_028,axiom,
( X1 != X2
| c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).
cnf(i_0_2116_029,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_2117_030,axiom,
( X1 != X2
| c_Set_Ovimage(X1,X3,X4,X5) = c_Set_Ovimage(X2,X3,X4,X5) ) ).
cnf(i_0_2118_031,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X1,X4,X5) = c_Set_Ovimage(X3,X2,X4,X5) ) ).
cnf(i_0_2119_032,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X4,X1,X5) = c_Set_Ovimage(X3,X4,X2,X5) ) ).
cnf(i_0_2120_033,axiom,
( X1 != X2
| c_Set_Ovimage(X3,X4,X5,X1) = c_Set_Ovimage(X3,X4,X5,X2) ) ).
cnf(i_0_2121_034,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_2122_035,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X1,X3,X4,X5,X6) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X2,X3,X4,X5,X6) ) ).
cnf(i_0_2123_036,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X1,X4,X5,X6) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X2,X4,X5,X6) ) ).
cnf(i_0_2124_037,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X1,X5,X6) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X2,X5,X6) ) ).
cnf(i_0_2125_038,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X5,X1,X6) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X5,X2,X6) ) ).
cnf(i_0_2126_039,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X5,X6,X1) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(X3,X4,X5,X6,X2) ) ).
cnf(i_0_2127_040,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).
cnf(i_0_2128_041,axiom,
( X1 != X2
| c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).
cnf(i_0_2129_042,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X1,X3) = c_Com_Ocom_OSemi(X2,X3) ) ).
cnf(i_0_2130_043,axiom,
( X1 != X2
| c_Com_Ocom_OSemi(X3,X1) = c_Com_Ocom_OSemi(X3,X2) ) ).
cnf(i_0_2131_044,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X1,X3,X4,X5) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X2,X3,X4,X5) ) ).
cnf(i_0_2132_045,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X1,X4,X5) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X2,X4,X5) ) ).
cnf(i_0_2133_046,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X4,X1,X5) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X4,X2,X5) ) ).
cnf(i_0_2134_047,axiom,
( X1 != X2
| c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X4,X5,X1) = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(X3,X4,X5,X2) ) ).
cnf(i_0_2135_048,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).
cnf(i_0_2136_049,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).
cnf(i_0_2137_050,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).
cnf(i_0_2138_051,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_2139_052,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_2140_053,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_2141_054,axiom,
( X1 != X2
| c_Suc(X1) = c_Suc(X2) ) ).
cnf(i_0_2142_055,axiom,
( X1 != X2
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X1,X3) = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X2,X3) ) ).
cnf(i_0_2143_056,axiom,
( X1 != X2
| c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X3,X1) = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(X3,X2) ) ).
cnf(i_0_2144_057,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).
cnf(i_0_2145_058,axiom,
( X1 != X2
| c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).
cnf(i_0_2146_059,axiom,
( X1 != X2
| c_Finite__Set_Olinorder__class_OMax(X1) = c_Finite__Set_Olinorder__class_OMax(X2) ) ).
cnf(i_0_2147_060,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).
cnf(i_0_2148_061,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).
cnf(i_0_2149_062,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).
cnf(i_0_2150_063,axiom,
( X1 != X2
| c_Finite__Set_Olinorder__class_OMin(X1) = c_Finite__Set_Olinorder__class_OMin(X2) ) ).
cnf(i_0_2151_064,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).
cnf(i_0_2152_065,axiom,
( X1 != X2
| c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).
cnf(i_0_2153_066,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X3,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X3,X4) ) ).
cnf(i_0_2154_067,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X1,X4)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X4) ) ).
cnf(i_0_2155_068,axiom,
( X1 != X2
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X1)
| c_Hoare__Mirabelle_Ohoare__derivs(X3,X4,X2) ) ).
cnf(i_0_2156_069,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_2157_070,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_2158_071,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_2159_072,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_2160_073,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_2161_074,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_2162_075,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_2163_076,axiom,
( X1 != X2
| ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(X2) ) ).
cnf(i_0_2164_077,axiom,
( X1 != X2
| ~ c_Lattices_Olower__semilattice(X1,X3,X4,X5)
| c_Lattices_Olower__semilattice(X2,X3,X4,X5) ) ).
cnf(i_0_2165_078,axiom,
( X1 != X2
| ~ c_Lattices_Olower__semilattice(X3,X1,X4,X5)
| c_Lattices_Olower__semilattice(X3,X2,X4,X5) ) ).
cnf(i_0_2166_079,axiom,
( X1 != X2
| ~ c_Lattices_Olower__semilattice(X3,X4,X1,X5)
| c_Lattices_Olower__semilattice(X3,X4,X2,X5) ) ).
cnf(i_0_2167_080,axiom,
( X1 != X2
| ~ c_Lattices_Olower__semilattice(X3,X4,X5,X1)
| c_Lattices_Olower__semilattice(X3,X4,X5,X2) ) ).
cnf(i_0_2168_081,axiom,
( X1 != X2
| ~ class_Lattices_Olower__semilattice(X1)
| class_Lattices_Olower__semilattice(X2) ) ).
cnf(i_0_2169_082,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_2170_083,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_2171_084,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_2172_085,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_2173_086,axiom,
( X1 != X2
| ~ class_Lattices_Oupper__semilattice(X1)
| class_Lattices_Oupper__semilattice(X2) ) ).
cnf(i_0_2174_087,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_2175_088,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_2176_089,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_2177_090,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_2178_091,axiom,
( X1 != X2
| ~ class_HOL_Oord(X1)
| class_HOL_Oord(X2) ) ).
cnf(i_0_2179_092,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_2180_093,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_2181_094,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_2182_095,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_2183_096,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_2184_097,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_2185_098,axiom,
( X1 != X2
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X1,X3)
| c_OrderedGroup_Oab__semigroup__idem__mult(X2,X3) ) ).
cnf(i_0_2186_099,axiom,
( X1 != X2
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(X3,X1)
| c_OrderedGroup_Oab__semigroup__idem__mult(X3,X2) ) ).
cnf(i_0_2187_100,axiom,
( X1 != X2
| ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(X2) ) ).
cnf(i_0_2188_101,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_2189_102,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__join(X1)
| class_OrderedGroup_Olordered__ab__group__add__join(X2) ) ).
cnf(i_0_2190_103,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_2191_104,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__meet(X1)
| class_OrderedGroup_Olordered__ab__group__add__meet(X2) ) ).
cnf(i_0_2192_105,axiom,
( X1 != X2
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| class_Complete__Lattice_Ocomplete__lattice(X2) ) ).
cnf(i_0_2193_106,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_2194_107,axiom,
( X1 != X2
| ~ class_HOL_Ominus(X1)
| class_HOL_Ominus(X2) ) ).
cnf(i_0_2195_108,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_2196_109,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_2197_110,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_2198_111,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_2199_112,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_2200_113,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_2201_114,axiom,
( X1 != X2
| ~ class_HOL_Ouminus(X1)
| class_HOL_Ouminus(X2) ) ).
cnf(i_0_2202_115,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_2203_116,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_2204_117,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_2205_118,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_2206_119,axiom,
( X1 != X2
| ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(X2) ) ).
cnf(i_0_2207_120,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_2208_121,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite_Ofinite(X1)
| class_Finite__Set_Ofinite_Ofinite(X2) ) ).
cnf(i_0_2209_122,axiom,
( X1 != X2
| ~ c_OrderedGroup_Oab__semigroup__mult(X1,X3)
| c_OrderedGroup_Oab__semigroup__mult(X2,X3) ) ).
cnf(i_0_2210_123,axiom,
( X1 != X2
| ~ c_OrderedGroup_Oab__semigroup__mult(X3,X1)
| c_OrderedGroup_Oab__semigroup__mult(X3,X2) ) ).
cnf(i_0_2211_124,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X1,X3,X4,X5,X6,X7)
| c_Finite__Set_Ofold__graph(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_2212_125,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X3,X1,X4,X5,X6,X7)
| c_Finite__Set_Ofold__graph(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_2213_126,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X3,X4,X1,X5,X6,X7)
| c_Finite__Set_Ofold__graph(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_2214_127,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X1,X6,X7)
| c_Finite__Set_Ofold__graph(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_2215_128,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X1,X7)
| c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_2216_129,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7,X1)
| c_Finite__Set_Ofold__graph(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_2217_130,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_2218_131,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X1,X3,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_2219_132,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X1,X4,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_2220_133,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X1,X5,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_2221_134,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X1,X6,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_2222_135,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X1,X7)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_2223_136,axiom,
( X1 != X2
| ~ c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X1)
| c_Nitpick_Ofold__graph_H(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_2224,plain,
( ~ class_Ring__and__Field_Oring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X2),X2)),X3)),X4) = X4 ),
inference(equality_inference,[],[1197]) ).
cnf(i_0_2225,plain,
( ~ class_Ring__and__Field_Oring(X1)
| X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X1),X3),X3)),X4)),X2) ),
inference(equality_inference,[],[1198]) ).
cnf(i_0_2226,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),X1),X1),X3,X4) ),
inference(equality_inference,[],[1225]) ).
cnf(i_0_2227,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
inference(equality_inference,[],[1272]) ).
cnf(i_0_2228,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = X4
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[1299]) ).
cnf(i_0_2229,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1427]) ).
cnf(i_0_2230,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1428]) ).
cnf(i_0_2231,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[1429]) ).
cnf(i_0_2232,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[1430]) ).
cnf(i_0_2233,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,X5)
| ~ hBOOL(c_in(X1,X3,X4))
| ~ hBOOL(c_in(X1,X3,X4)) ),
inference(equality_inference,[],[1444]) ).
cnf(i_0_2234,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3,X4) ),
inference(equality_inference,[],[1593]) ).
cnf(i_0_2235,plain,
( X1 = X1
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
inference(equality_inference,[],[1657]) ).
cnf(i_0_2236,plain,
( X1 = X1
| hBOOL(c_in(X2,X1,X3))
| hBOOL(c_in(X2,X1,X3)) ),
inference(equality_inference,[],[1689]) ).
cnf(i_0_2237,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
inference(equality_inference,[],[1697]) ).
cnf(i_0_2238,plain,
X1 = X1,
inference(equality_inference,[],[1700]) ).
cnf(i_0_2239,plain,
X1 = X1,
inference(equality_inference,[],[1701]) ).
cnf(i_0_2240,plain,
X1 = X1,
inference(equality_inference,[],[1702]) ).
cnf(i_0_2241,plain,
X1 = X1,
inference(equality_inference,[],[1721]) ).
cnf(i_0_2242,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ),
inference(equality_inference,[],[1826]) ).
cnf(i_0_2243,plain,
X1 = X1,
inference(equality_inference,[],[1890]) ).
cnf(i_0_2244,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oidom(X2)
| X1 = hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1) ),
inference(equality_inference,[],[1911]) ).
cnf(i_0_2245,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[1918]) ).
cnf(i_0_2246,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[1923]) ).
cnf(i_0_2247,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[1924]) ).
cnf(i_0_2248,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[1925]) ).
cnf(i_0_2249,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[1926]) ).
cnf(i_0_2250,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[1927]) ).
cnf(i_0_2251,plain,
( X1 = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(equality_inference,[],[1996]) ).
cnf(i_0_2252,plain,
( X1 = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(equality_inference,[],[1997]) ).
cnf(i_0_2253,plain,
X1 = X1,
inference(equality_inference,[],[2016]) ).
cnf(i_0_2254,plain,
X1 = X1,
inference(equality_inference,[],[2017]) ).
cnf(i_0_2255,plain,
X1 = X1,
inference(equality_inference,[],[2047]) ).
cnf(i_0_2256,plain,
$false,
inference(scs_inference,[],[i_0_1194,i_0_1269,i_0_1134]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV844-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 06:03:31 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.77/2.73 % Version : CSE_E---1.7
% 1.77/2.73 % Problem : theBenchmark.p
% 1.77/2.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.77/2.73 % SZS output start CNFRefutation
% See solution above
% 1.87/2.81 % Total time : 2.382s
%------------------------------------------------------------------------------