%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW382+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:25 PM UTC 2026
% Result : Theorem 52.35s 10.94s
% Output : CNFRefutation 52.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 37 unt; 0 def)
% Number of atoms : 84 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 30 ~; 23 |; 0 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 12 con; 0-3 aty)
% Number of variables : 80 ( 6 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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_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(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(fact_Diff__cancel,axiom,
! [X15,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X15),X15) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__cancel) ).
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(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_13,plain,
! [X454,X455,X456,X457,X458,X459] : hAPP(c_Set_Oimage(X459,X458,X457),hAPP(c_Set_Oimage(X456,X459,X455),X454)) = hAPP(c_Set_Oimage(X456,X458,hAPP(hAPP(c_COMBB(X459,X458,X456),X457),X455)),X454),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(c_0_14,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(assume_negation,[status(cth)],[conj_7]) ).
fof(c_0_15,plain,
! [X341,X342,X343,X344] :
( c_Hoare__Mirabelle_Ohoare__derivs(X344,X341,X342)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X344,X341,X343)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X344,X343,X342) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut])])]) ).
cnf(c_0_16,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_17,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_13]) ).
fof(c_0_18,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)],[c_0_14]) ).
fof(c_0_19,plain,
! [X6994,X6995] : hAPP(c_Set_OCollect(X6995),hAPP(c_fequal,X6994)) = hAPP(hAPP(c_Set_Oinsert(X6995),X6994),c_Orderings_Obot__class_Obot(tc_fun(X6995,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).
fof(c_0_20,plain,
! [X6859,X6860] : hAPP(c_Set_OCollect(X6860),X6859) = X6859,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X1264,X1265] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1265,tc_HOL_Obool)),X1264),X1264) = c_Orderings_Obot__class_Obot(tc_fun(X1265,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).
cnf(c_0_22,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,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_16,c_0_17]) ).
fof(c_0_24,plain,
! [X326,X327] : c_Hoare__Mirabelle_Ohoare__derivs(X327,X326,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X327),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_empty]) ).
fof(c_0_25,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_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_26,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_27,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_F,X1)
| 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) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,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_24]) ).
fof(c_0_31,plain,
! [X632] :
( 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,X632)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,X632))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_MGF])])]) ).
fof(c_0_32,plain,
! [X882,X883] :
( hBOOL(hAPP(c_Com_OWT,X882))
| hAPP(c_Com_Obody,X883) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X882)
| ~ c_Com_OWT__bodies ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_WT__bodiesD])])]) ).
cnf(c_0_33,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_25]) ).
cnf(c_0_34,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool)) = hAPP(c_fequal,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_35,hypothesis,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,X2,X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_F,X2)
| 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) ),
inference(spm,[status(thm)],[c_0_22,c_0_29]) ).
cnf(c_0_36,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_37,plain,
( ~ hBOOL(hAPP(c_Com_OWT,X1))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| 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)))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,hypothesis,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(split_conjunct,[status(thm)],[conj_0]) ).
cnf(c_0_39,hypothesis,
c_Com_OWT__bodies,
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_40,plain,
( hAPP(c_Com_Obody,X1) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X2)
| ~ c_Com_OWT__bodies
| hBOOL(hAPP(c_Com_OWT,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_17]),c_0_28]),c_0_34]) ).
cnf(c_0_42,hypothesis,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),X1)
| 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) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,plain,
( ~ hBOOL(hAPP(c_Com_OWT,X1))
| 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)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_44,plain,
( hAPP(c_Com_Obody,X2) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X1)
| hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_39])]) ).
cnf(c_0_45,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_46,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),
inference(rw,[status(thm)],[c_0_28,c_0_28]) ).
cnf(c_0_48,plain,
( ~ hBOOL(hAPP(c_Com_OWT,X1))
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_28]),c_0_28]) ).
cnf(c_0_49,hypothesis,
( hAPP(c_Com_Obody,X1) != hAPP(c_Com_Obody,v_pn)
| hBOOL(hAPP(c_Com_OWT,v_y)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),X1),X1),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,v_y))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
( ~ hBOOL(hAPP(c_Com_OWT,X1))
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),tc_HOL_Obool),tc_HOL_Obool),hAPP(c_fequal,hAPP(c_Hoare__Mirabelle_OMGT,X1))) ),
inference(rw,[status(thm)],[c_0_48,c_0_34]) ).
cnf(c_0_52,hypothesis,
hBOOL(hAPP(c_Com_OWT,v_y)),
inference(er,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW382+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 09:50:19 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.35/10.94 % Version: 3.5.1
% 52.35/10.94 % Preprocessing class: FMLMSLSMSSSNFFN.
% 52.35/10.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 52.35/10.94 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 52.35/10.94 % Starting new_bool_3 with 300s (1) cores
% 52.35/10.94 % Starting new_bool_1 with 300s (1) cores
% 52.35/10.94 % Starting sh5l with 300s (1) cores
% 52.35/10.94 % SAT001_MinMin_p005000_rr_RG with pid 3775049 completed with status 0
% 52.35/10.94 % Result found by SAT001_MinMin_p005000_rr_RG
% 52.35/10.94 % Preprocessing class: FMLMSLSMSSSNFFN.
% 52.35/10.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 52.35/10.94 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 52.35/10.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 52.35/10.94 % No SInE strategy applied
% 52.35/10.94 % Search class: FGHSM-SMLM33-DFFFFFNN
% 52.35/10.94 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 52.35/10.94 % Starting SubtermCWHack with 135s (1) cores
% 52.35/10.94 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 52.35/10.94 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 52.35/10.94 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 52.35/10.94 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 52.35/10.94 % SAT001_MinMin_p005000_rr_RG with pid 3775090 completed with status 0
% 52.35/10.94 % Result found by SAT001_MinMin_p005000_rr_RG
% 52.35/10.94 % Preprocessing class: FMLMSLSMSSSNFFN.
% 52.35/10.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 52.35/10.94 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 52.35/10.94 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 52.35/10.94 % No SInE strategy applied
% 52.35/10.94 % Search class: FGHSM-SMLM33-DFFFFFNN
% 52.35/10.94 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 52.35/10.94 % Starting SubtermCWHack with 135s (1) cores
% 52.35/10.94 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 52.35/10.94 % Preprocessing time : 0.334 s
% 52.35/10.94 % Presaturation interreduction done
% 52.35/10.94
% 52.35/10.94 % Proof found!
% 52.35/10.94 % SZS status Theorem
% 52.35/10.94 % SZS output start CNFRefutation
% See solution above
% 52.35/10.94 % Parsed axioms : 5250
% 52.35/10.94 % Removed by relevancy pruning/SinE : 0
% 52.35/10.94 % Initial clauses : 7553
% 52.35/10.94 % Removed in clause preprocessing : 231
% 52.35/10.94 % Initial clauses in saturation : 7322
% 52.35/10.94 % Processed clauses : 12402
% 52.35/10.94 % ...of these trivial : 286
% 52.35/10.94 % ...subsumed : 2203
% 52.35/10.94 % ...remaining for further processing : 9913
% 52.35/10.94 % Other redundant clauses eliminated : 620
% 52.35/10.94 % Clauses deleted for lack of memory : 0
% 52.35/10.94 % Backward-subsumed : 104
% 52.35/10.94 % Backward-rewritten : 317
% 52.35/10.94 % Generated clauses : 21704
% 52.35/10.94 % ...of the previous two non-redundant : 19971
% 52.35/10.94 % ...aggressively subsumed : 0
% 52.35/10.94 % Contextual simplify-reflections : 40
% 52.35/10.94 % Paramodulations : 21093
% 52.35/10.94 % Factorizations : 4
% 52.35/10.94 % NegExts : 0
% 52.35/10.94 % Equation resolutions : 673
% 52.35/10.94 % Disequality decompositions : 0
% 52.35/10.94 % Total rewrite steps : 10620
% 52.35/10.94 % ...of those cached : 8023
% 52.35/10.94 % Propositional unsat checks : 2
% 52.35/10.94 % Propositional check models : 2
% 52.35/10.94 % Propositional check unsatisfiable : 0
% 52.35/10.94 % Propositional clauses : 0
% 52.35/10.94 % Propositional clauses after purity: 0
% 52.35/10.94 % Propositional unsat core size : 0
% 52.35/10.94 % Propositional preprocessing time : 0.000
% 52.35/10.94 % Propositional encoding time : 0.148
% 52.35/10.94 % Propositional solver time : 0.052
% 52.35/10.94 % Success case prop preproc time : 0.000
% 52.35/10.94 % Success case prop encoding time : 0.000
% 52.35/10.94 % Success case prop solver time : 0.000
% 52.35/10.94 % Current number of processed clauses : 3076
% 52.35/10.94 % Positive orientable unit clauses : 938
% 52.35/10.94 % Positive unorientable unit clauses: 1
% 52.35/10.94 % Negative unit clauses : 239
% 52.35/10.94 % Non-unit-clauses : 1898
% 52.35/10.94 % Current number of unprocessed clauses: 17334
% 52.35/10.94 % ...number of literals in the above : 40507
% 52.35/10.94 % Current number of archived formulas : 0
% 52.35/10.94 % Current number of archived clauses : 6389
% 52.35/10.94 % Clause-clause subsumption calls (NU) : 4589412
% 52.35/10.94 % Rec. Clause-clause subsumption calls : 1954209
% 52.35/10.94 % Non-unit clause-clause subsumptions : 1692
% 52.35/10.94 % Unit Clause-clause subsumption calls : 26778
% 52.35/10.94 % Rewrite failures with RHS unbound : 0
% 52.35/10.94 % BW rewrite match attempts : 29911
% 52.35/10.94 % BW rewrite match successes : 557
% 52.35/10.94 % Condensation attempts : 0
% 52.35/10.94 % Condensation successes : 0
% 52.35/10.94 % Termbank termtop insertions : 1654812
% 52.35/10.94 % Search garbage collected termcells : 99423
% 52.35/10.94
% 52.35/10.94 % -------------------------------------------------
% 52.35/10.94 % User time : 9.357 s
% 52.35/10.94 % System time : 0.247 s
% 52.35/10.94 % Total time : 9.604 s
% 52.35/10.94 % Maximum resident set size: 42636 pages
% 52.35/10.94
% 52.35/10.94 % -------------------------------------------------
% 52.35/10.94 % User time : 34.130 s
% 52.35/10.94 % System time : 1.092 s
% 52.35/10.94 % Total time : 35.222 s
% 52.35/10.94 % Maximum resident set size: 12288 pages
% 52.35/10.94 % E exiting
%------------------------------------------------------------------------------