%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW382+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.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 05:32:14 PM UTC 2026
% Result : Theorem 11.78s 8.06s
% Output : CNFRefutation 11.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 35 unt; 0 def)
% Number of atoms : 93 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 31 ~; 26 |; 0 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 12 con; 0-3 aty)
% Number of variables : 96 ( 17 sgn 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_bot__fun__def,axiom,
! [X16,X13,X5] :
( class_Orderings_Obot(X5)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X13,X5)),X16) = c_Orderings_Obot__class_Obot(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(fact_singleton__conv2,axiom,
! [X6,X5] : hAPP(c_Set_OCollect(X5),hAPP(c_fequal,X6)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__conv2) ).
fof(fact_Collect__def,axiom,
! [X33,X5] : hAPP(c_Set_OCollect(X5),X33) = X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(conj_7,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_7) ).
fof(fact_image__image,axiom,
! [X15,X1,X22,X2,X5,X13] : hAPP(c_Set_Oimage(X13,X5,X2),hAPP(c_Set_Oimage(X22,X13,X1),X15)) = hAPP(c_Set_Oimage(X22,X5,hAPP(hAPP(c_COMBB(X13,X5,X22),X2),X1)),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_empty,axiom,
! [X4,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty) ).
fof(fact_MGF,axiom,
! [X18] :
( c_Hoare__Mirabelle_Ostate__not__singleton
=> ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,X18))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X18)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_MGF) ).
fof(fact_WT__bodiesD,axiom,
! [X42,X49] :
( c_Com_OWT__bodies
=> ( hAPP(c_Com_Obody,X49) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X42)
=> hBOOL(hAPP(c_Com_OWT,X42)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT__bodiesD) ).
fof(fact_cut,axiom,
! [X4,X7,X9,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X5,X9,X7)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X9)
=> c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut) ).
fof(conj_6,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),v_F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(conj_0,hypothesis,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(conj_1,hypothesis,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(conj_5,hypothesis,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
fof(c_0_15,plain,
! [X17281,X17282,X17283] :
( ~ class_Orderings_Obot(X17283)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17282,X17283)),X17281) = c_Orderings_Obot__class_Obot(X17283) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).
fof(c_0_16,plain,
! [X16962,X16963] :
( hAPP(X16963,esk1_2(X16962,X16963)) != hAPP(X16962,esk1_2(X16962,X16963))
| X16963 = X16962 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
cnf(c_0_17,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
fof(c_0_19,plain,
! [X23633,X23634] : hAPP(c_Set_OCollect(X23634),hAPP(c_fequal,X23633)) = hAPP(hAPP(c_Set_Oinsert(X23634),X23633),c_Orderings_Obot__class_Obot(tc_fun(X23634,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).
fof(c_0_20,plain,
! [X23498,X23499] : hAPP(c_Set_OCollect(X23499),X23498) = X23498,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
cnf(c_0_21,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_Orderings_Obot__class_Obot(tc_HOL_Obool),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_23,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_7])]) ).
cnf(c_0_24,plain,
hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X17093,X17094,X17095,X17096,X17097,X17098] : hAPP(c_Set_Oimage(X17098,X17097,X17096),hAPP(c_Set_Oimage(X17095,X17098,X17094),X17093)) = hAPP(c_Set_Oimage(X17095,X17097,hAPP(hAPP(c_COMBB(X17098,X17097,X17095),X17096),X17094)),X17093),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(c_0_27,plain,
! [X16965,X16966] : c_Hoare__Mirabelle_Ohoare__derivs(X16966,X16965,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X16966),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_empty]) ).
cnf(c_0_28,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hAPP(X1,esk1_2(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X1)) != c_Orderings_Obot__class_Obot(tc_HOL_Obool) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_29,plain,
! [X17271] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ hBOOL(hAPP(c_Com_OWT,X17271))
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X17271)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_MGF])]) ).
fof(c_0_30,plain,
! [X17521,X17522] :
( ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X17522) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X17521)
| hBOOL(hAPP(c_Com_OWT,X17521)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT__bodiesD])]) ).
cnf(c_0_31,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
hAPP(c_fequal,X1) = hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_33,plain,
! [X16980,X16981,X16982,X16983] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X16983,X16982,X16981)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X16983,X16980,X16982)
| c_Hoare__Mirabelle_Ohoare__derivs(X16983,X16980,X16981) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut])]) ).
cnf(c_0_34,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),v_F),
inference(split_conjunct,[status(thm)],[conj_6]) ).
cnf(c_0_35,plain,
hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_Oimage(X4,X1,X5),X6)) = hAPP(c_Set_Oimage(X4,X2,hAPP(hAPP(c_COMBB(X1,X2,X4),X3),X5)),X6),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_38,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,hypothesis,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(split_conjunct,[status(thm)],[conj_0]) ).
cnf(c_0_40,hypothesis,
c_Com_OWT__bodies,
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_41,plain,
( hBOOL(hAPP(c_Com_OWT,X2))
| ~ c_Com_OWT__bodies
| hAPP(c_Com_Obody,X1) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_43,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),v_F),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_45,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_47,plain,
( hBOOL(hAPP(c_Com_OWT,X1))
| hAPP(c_Com_Obody,X2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_40])]) ).
cnf(c_0_48,hypothesis,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(split_conjunct,[status(thm)],[conj_5]) ).
cnf(c_0_49,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))),
inference(rw,[status(thm)],[c_0_42,c_0_35]) ).
cnf(c_0_50,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),c_Hoare__Mirabelle_OMGT),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Com_Ocom,c_Com_Ocom_OBODY),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))),X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_F,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_52,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X1)))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(rw,[status(thm)],[c_0_46,c_0_32]) ).
cnf(c_0_53,hypothesis,
( hBOOL(hAPP(c_Com_OWT,v_y))
| hAPP(c_Com_Obody,X1) != hAPP(c_Com_Obody,v_pn) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_F,hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X1,hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X2)))
| ~ hBOOL(hAPP(c_Com_OWT,X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,hypothesis,
hBOOL(hAPP(c_Com_OWT,v_y)),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW382+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 06:45:05 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 11.78/8.06 % Version : CSE_E---1.7
% 11.78/8.06 % Problem : theBenchmark.p
% 11.78/8.06 % SZS status Theorem for theBenchmark.p
% 11.78/8.06 % SZS output start CNFRefutation
% See solution above
% 11.78/8.08 % Total time : 7.042s
%------------------------------------------------------------------------------