%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT020-1 : 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 : n026.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 05:05:50 PM UTC 2026
% Result : Unsatisfiable 153.99s 118.65s
% Output : CNFRefutation 154.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 31
% Syntax : Number of clauses : 95 ( 39 unt; 9 nHn; 55 RR)
% Number of literals : 189 ( 42 equ; 93 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 7 con; 0-4 aty)
% Number of variables : 253 ( 60 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_IntE_1,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
cnf(cls_Int__assoc_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool)),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X2,tc_bool)),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
cnf(cls_Int__absorb2_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3) = X1
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
cnf(cls_subset__Un__eq_1,axiom,
( c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),X3) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
cnf(cls_Un__UNIV__left_0,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),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_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_UNIV__eq__I_0,axiom,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__eq__I_0) ).
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_Int__commute_0,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X2,tc_bool)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_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_INT__absorb_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X1,X2),tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X3,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X4,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__absorb_0) ).
cnf(cls_sup__idem_0,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
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(cls_INTER__UNIV__conv_I2_J_2,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1,X3,tc_fun(X4,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))
| hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1(X2,X1,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_2) ).
cnf(cls_irrefl__def_0,axiom,
( ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)))
| ~ c_Relation_Oirrefl(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_Relation_Otrans(v_F(X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_2,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_in__mkbot_0,axiom,
~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
cnf(cls_not__acc__down_0,axiom,
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3)))
| hBOOL(c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_rev__ImageI_0,axiom,
( hBOOL(c_in(X1,hAPP(c_Relation_OImage(X2,X3,X4),X5),X4))
| ~ hBOOL(c_in(c_Pair(X6,X1,X3,X4),X2,tc_prod(X3,X4)))
| ~ hBOOL(c_in(X6,X5,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
cnf(cls_conjecture_3,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_trans__def_0,axiom,
( hBOOL(c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)))
| ~ hBOOL(c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3)))
| ~ hBOOL(c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)))
| ~ c_Relation_Otrans(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_Relation_Oirrefl(v_F(X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_insert__absorb_0,axiom,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(c_in(X1,X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_Image__singleton__iff_0,axiom,
( hBOOL(c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)))
| ~ hBOOL(c_in(X2,hAPP(c_Relation_OImage(X5,X3,X4),hAPP(c_Set_Oinsert(X1,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
cnf(cls_conjecture_8,negated_conjecture,
( hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
cnf(cls_total__on__def_0,axiom,
( hBOOL(c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)))
| hBOOL(c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)))
| X2 = X1
| ~ hBOOL(c_in(X1,X5,X3))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Relation_Ototal__on(X5,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
cnf(cls_conjecture_4,negated_conjecture,
~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(c_0_31,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),X2),X3)) ),
cls_IntE_1 ).
cnf(c_0_32,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool)),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X2,tc_bool)),X4)),
cls_Int__assoc_0 ).
cnf(c_0_33,plain,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,tc_fun(X3,tc_bool)),X2)),X3)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3) = X1
| ~ c_lessequals(X1,X3,tc_fun(X2,tc_bool)) ),
cls_Int__absorb2_0 ).
cnf(c_0_35,axiom,
( c_lessequals(X1,X3,tc_fun(X2,tc_bool))
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_fun(X2,tc_bool)),X3) != X3 ),
cls_subset__Un__eq_1 ).
cnf(c_0_36,axiom,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),X2) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Un__UNIV__left_0 ).
cnf(c_0_37,plain,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(c_in(X1,X4,X3))
| ~ c_lessequals(X4,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X5,tc_fun(X3,tc_bool)),X2),tc_fun(X3,tc_bool)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != X2 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,axiom,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X2)),
cls_UNIV__I_0 ).
cnf(c_0_40,axiom,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1)) ),
cls_UNIV__eq__I_0 ).
cnf(c_0_41,axiom,
( hBOOL(c_in(X1,X2,X3))
| ~ hBOOL(hAPP(X2,X1)) ),
cls_mem__def_1 ).
cnf(c_0_42,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(X4,tc_fun(X3,tc_bool)),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_43,axiom,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_fun(X2,tc_bool)),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X2,tc_bool)),X1),
cls_Int__commute_0 ).
cnf(c_0_44,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1))) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_46,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(X3,tc_bool)),X4) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
( hBOOL(c_in(X1,X2,X3))
| c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)) != hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(X3,tc_bool)),X5) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X1,X2),tc_fun(X3,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X3,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,X1,X5,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X2,X4,X5)) ),
cls_INT__absorb_0 ).
cnf(c_0_50,plain,
( hBOOL(c_in(X1,hAPP(X2,X3),X4))
| c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,X2,X7,tc_fun(X4,tc_bool))
| ~ hBOOL(c_in(X3,X6,X7)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,axiom,
( hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__idem_0 ).
cnf(c_0_52,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_53,plain,
( hBOOL(c_in(X1,hAPP(X2,X3),X4))
| c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,X2,X7,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X6,X3)) ),
inference(spm,[status(thm)],[c_0_50,c_0_41]) ).
cnf(c_0_54,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X1) = X1,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,X1,X3,tc_fun(X4,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool))
| hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1(X2,X1,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)) ),
cls_INTER__UNIV__conv_I2_J_2 ).
cnf(c_0_56,axiom,
( ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2)))
| ~ c_Relation_Oirrefl(X3,X2) ),
cls_irrefl__def_0 ).
cnf(c_0_57,negated_conjecture,
( c_Relation_Otrans(v_F(X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt) ),
cls_conjecture_5 ).
cnf(c_0_58,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_2 ).
cnf(c_0_59,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_0 ).
cnf(c_0_60,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_1 ).
cnf(c_0_61,plain,
( hBOOL(c_in(X1,hAPP(X2,X3),X4))
| c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Lattices_Oupper__semilattice__class_Osup(X3,tc_bool),X2,X6,tc_fun(X4,tc_bool))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),X3,tc_fun(X4,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_36]),c_0_47]) ).
cnf(c_0_63,axiom,
~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X3,X2),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
cls_in__mkbot_0 ).
cnf(c_0_64,axiom,
( hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X1,X2,X3),X2,X3,X3),X1,tc_prod(X3,X3)))
| hBOOL(c_in(X2,c_Wellfounded_Oacc(X1,X3),X3)) ),
cls_not__acc__down_0 ).
cnf(c_0_65,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(hAPP(X1,c_Pair(X3,X3,X2,X2))) ),
inference(spm,[status(thm)],[c_0_56,c_0_41]) ).
cnf(c_0_66,axiom,
hBOOL(hAPP(hAPP(c_Set_Oinsert(X1,X2),X3),X1)),
cls_insert__code_1 ).
cnf(c_0_67,axiom,
( hBOOL(c_in(X1,hAPP(c_Relation_OImage(X2,X3,X4),X5),X4))
| ~ hBOOL(c_in(c_Pair(X6,X1,X3,X4),X2,tc_prod(X3,X4)))
| ~ hBOOL(c_in(X6,X5,X3)) ),
cls_rev__ImageI_0 ).
cnf(c_0_68,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
cls_conjecture_3 ).
cnf(c_0_69,axiom,
( hBOOL(c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)))
| ~ hBOOL(c_in(c_Pair(X5,X2,X3,X3),X4,tc_prod(X3,X3)))
| ~ hBOOL(c_in(c_Pair(X1,X5,X3,X3),X4,tc_prod(X3,X3)))
| ~ c_Relation_Otrans(X4,X3) ),
cls_trans__def_0 ).
cnf(c_0_70,negated_conjecture,
c_Relation_Otrans(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_71,negated_conjecture,
( c_Relation_Oirrefl(v_F(X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X1,hAPP(v_x,X1)),tc_Arrow__Order__Mirabelle_Oalt) ),
cls_conjecture_6 ).
cnf(c_0_72,plain,
( hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3))
| ~ hBOOL(X4) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_36]),c_0_47]) ).
cnf(c_0_73,plain,
hBOOL(c_in(X1,c_Wellfounded_Oacc(c_Arrow__Order__Mirabelle_Omkbot(X2,X1),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_74,plain,
~ c_Relation_Oirrefl(hAPP(c_Set_Oinsert(c_Pair(X1,X1,X2,X2),X3),X4),X2),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,axiom,
( hAPP(c_Set_Oinsert(X1,X2),X3) = X3
| ~ hBOOL(c_in(X1,X3,X2)) ),
cls_insert__absorb_0 ).
cnf(c_0_76,axiom,
( hBOOL(c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4)))
| ~ hBOOL(c_in(X2,hAPP(c_Relation_OImage(X5,X3,X4),hAPP(c_Set_Oinsert(X1,X3),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)))),X4)) ),
cls_Image__singleton__iff_0 ).
cnf(c_0_77,negated_conjecture,
( hBOOL(c_in(v_b,hAPP(c_Relation_OImage(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(c_in(v_a,X1,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_78,negated_conjecture,
( hBOOL(c_in(c_Pair(X1,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(X1,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_68]),c_0_70])]) ).
cnf(c_0_79,negated_conjecture,
c_Relation_Oirrefl(v_F(v_P),tc_Arrow__Order__Mirabelle_Oalt),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_80,negated_conjecture,
( hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Otrans(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt) ),
cls_conjecture_8 ).
cnf(c_0_81,axiom,
( hBOOL(c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)))
| hBOOL(c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)))
| X2 = X1
| ~ hBOOL(c_in(X1,X5,X3))
| ~ hBOOL(c_in(X2,X5,X3))
| ~ c_Relation_Ototal__on(X5,X4,X3) ),
cls_total__on__def_0 ).
cnf(c_0_82,plain,
hBOOL(c_in(X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ hBOOL(c_in(c_Pair(X3,X3,X2,X2),X1,X4)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,negated_conjecture,
( hBOOL(c_in(c_Pair(X1,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(v_a,hAPP(c_Set_Oinsert(X1,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
~ hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_78]),c_0_79])]) ).
cnf(c_0_86,negated_conjecture,
( X1 = X2
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_87,plain,
( X1 = X2
| hBOOL(c_in(c_Pair(X2,X1,X3,X3),X4,tc_prod(X3,X3)))
| hBOOL(c_in(c_Pair(X1,X2,X3,X3),X4,tc_prod(X3,X3)))
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_bool)),X4,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_82])]) ).
cnf(c_0_88,negated_conjecture,
~ hBOOL(c_in(v_a,hAPP(c_Set_Oinsert(v_b,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))),tc_Arrow__Order__Mirabelle_Oalt)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_79])]) ).
cnf(c_0_89,negated_conjecture,
( v_b = v_a
| ~ hBOOL(c_in(c_Pair(v_b,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,negated_conjecture,
( X1 = X2
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(spm,[status(thm)],[c_0_87,c_0_58]) ).
cnf(c_0_91,negated_conjecture,
~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
cls_conjecture_4 ).
cnf(c_0_92,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Set_Oinsert(v_b,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool))),v_a)),
inference(spm,[status(thm)],[c_0_88,c_0_41]) ).
cnf(c_0_93,negated_conjecture,
v_b = v_a,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.21 % Problem : SCT020-1 : TPTP v9.2.1. Released v4.1.0.
% 0.03/0.21 % 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
% 0.13/0.48 % Computer : n026.cluster.edu
% 0.13/0.48 % Model : x86_64 x86_64
% 0.13/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.48 % Memory : 8042.1875MB
% 0.13/0.48 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.48 % CPULimit : 300
% 0.13/0.48 % WCLimit : 300
% 0.13/0.48 % DateTime : Tue May 5 01:54:23 EDT 2026
% 0.13/0.48 % CPUTime :
% 0.13/0.49 % start to proof: theBenchmark
% 153.99/118.65 % Version : CSE_E---1.7
% 153.99/118.65 % Problem : theBenchmark.p
% 153.99/118.65 % SZS status Unsatisfiable for theBenchmark.p
% 153.99/118.65 % SZS output start CNFRefutation
% See solution above
% 154.29/118.95 % Total time : 106.155s
%------------------------------------------------------------------------------