%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET727+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 02:15:05 PM UTC 2026
% Result : Theorem 218.25s 32.76s
% Output : CNFRefutation 218.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 78 ( 24 unt; 0 def)
% Number of atoms : 297 ( 32 equ)
% Maximal formula atoms : 55 ( 3 avg)
% Number of connectives : 349 ( 130 ~; 153 |; 51 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-7 aty)
% Number of variables : 182 ( 0 sgn 79 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thII18,conjecture,
! [X6,X10,X9,X1,X2] :
( ( identity(compose_function(X6,X9,X2,X1,X2),X2)
& identity(compose_function(X10,X6,X1,X2,X1),X1)
& maps(X9,X2,X1)
& maps(X10,X2,X1)
& maps(X6,X1,X2) )
=> equal_maps(inverse_function(X6,X1,X2),X9,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII18) ).
fof(maps,axiom,
! [X6,X1,X2] :
( maps(X6,X1,X2)
<=> ( ! [X3,X7,X8] :
( ( member(X8,X2)
& member(X7,X2)
& member(X3,X1) )
=> ( ( apply(X6,X3,X8)
& apply(X6,X3,X7) )
=> X7 = X8 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X5] :
( apply(X6,X3,X5)
& member(X5,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).
fof(equal_maps,axiom,
! [X6,X10,X1,X2] :
( equal_maps(X6,X10,X1,X2)
<=> ! [X3,X7,X8] :
( ( member(X8,X2)
& member(X7,X2)
& member(X3,X1) )
=> ( ( apply(X10,X3,X8)
& apply(X6,X3,X7) )
=> X7 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',equal_maps) ).
fof(identity,axiom,
! [X6,X1] :
( identity(X6,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X6,X3,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',identity) ).
fof(compose_function,axiom,
! [X10,X6,X1,X2,X11,X3,X12] :
( ( member(X12,X11)
& member(X3,X1) )
=> ( apply(compose_function(X10,X6,X1,X2,X11),X3,X12)
<=> ? [X5] :
( apply(X10,X5,X12)
& apply(X6,X3,X5)
& member(X5,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(inverse_function,axiom,
! [X6,X1,X2,X3,X5] :
( ( member(X5,X2)
& member(X3,X1) )
=> ( apply(X6,X3,X5)
<=> apply(inverse_function(X6,X1,X2),X5,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_function) ).
fof(c_0_6,negated_conjecture,
~ ! [X6,X10,X9,X1,X2] :
( ( identity(compose_function(X6,X9,X2,X1,X2),X2)
& identity(compose_function(X10,X6,X1,X2,X1),X1)
& maps(X9,X2,X1)
& maps(X10,X2,X1)
& maps(X6,X1,X2) )
=> equal_maps(inverse_function(X6,X1,X2),X9,X2,X1) ),
inference(assume_negation,[status(cth)],[thII18]) ).
fof(c_0_7,plain,
! [X56,X57,X58,X59,X61,X62,X63,X64,X65,X66,X68] :
( ( maps(X64,X65,X66)
| ~ apply(X64,esk12_3(X64,X65,X66),X68)
| ~ member(X68,X66)
| esk14_3(X64,X65,X66) != esk15_3(X64,X65,X66) )
& ( maps(X64,X65,X66)
| ~ apply(X64,esk12_3(X64,X65,X66),X68)
| ~ member(X68,X66)
| apply(X64,esk13_3(X64,X65,X66),esk15_3(X64,X65,X66)) )
& ( maps(X64,X65,X66)
| ~ apply(X64,esk12_3(X64,X65,X66),X68)
| ~ member(X68,X66)
| apply(X64,esk13_3(X64,X65,X66),esk14_3(X64,X65,X66)) )
& ( maps(X64,X65,X66)
| ~ apply(X64,esk12_3(X64,X65,X66),X68)
| ~ member(X68,X66)
| member(esk15_3(X64,X65,X66),X66) )
& ( maps(X64,X65,X66)
| ~ apply(X64,esk12_3(X64,X65,X66),X68)
| ~ member(X68,X66)
| member(esk14_3(X64,X65,X66),X66) )
& ( maps(X64,X65,X66)
| ~ apply(X64,esk12_3(X64,X65,X66),X68)
| ~ member(X68,X66)
| member(esk13_3(X64,X65,X66),X65) )
& ( maps(X64,X65,X66)
| member(esk12_3(X64,X65,X66),X65)
| esk14_3(X64,X65,X66) != esk15_3(X64,X65,X66) )
& ( maps(X64,X65,X66)
| member(esk12_3(X64,X65,X66),X65)
| apply(X64,esk13_3(X64,X65,X66),esk15_3(X64,X65,X66)) )
& ( maps(X64,X65,X66)
| member(esk12_3(X64,X65,X66),X65)
| apply(X64,esk13_3(X64,X65,X66),esk14_3(X64,X65,X66)) )
& ( maps(X64,X65,X66)
| member(esk12_3(X64,X65,X66),X65)
| member(esk15_3(X64,X65,X66),X66) )
& ( maps(X64,X65,X66)
| member(esk12_3(X64,X65,X66),X65)
| member(esk14_3(X64,X65,X66),X66) )
& ( maps(X64,X65,X66)
| member(esk12_3(X64,X65,X66),X65)
| member(esk13_3(X64,X65,X66),X65) )
& ( ~ maps(X56,X57,X58)
| X62 = X63
| ~ apply(X56,X61,X63)
| ~ apply(X56,X61,X62)
| ~ member(X63,X58)
| ~ member(X62,X58)
| ~ member(X61,X57) )
& ( ~ maps(X56,X57,X58)
| ~ member(X59,X57)
| apply(X56,X59,esk11_4(X56,X57,X58,X59)) )
& ( ~ maps(X56,X57,X58)
| ~ member(X59,X57)
| member(esk11_4(X56,X57,X58,X59),X58) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[maps])])])])])])]) ).
fof(c_0_8,negated_conjecture,
( ~ equal_maps(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)
& identity(compose_function(esk1_0,esk3_0,esk5_0,esk4_0,esk5_0),esk5_0)
& identity(compose_function(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0),esk4_0)
& maps(esk3_0,esk5_0,esk4_0)
& maps(esk2_0,esk5_0,esk4_0)
& maps(esk1_0,esk4_0,esk5_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,plain,
! [X22,X23,X24,X25,X26,X27,X28,X29,X30,X31,X32] :
( ( equal_maps(X29,X30,X31,X32)
| esk7_4(X29,X30,X31,X32) != esk8_4(X29,X30,X31,X32) )
& ( equal_maps(X29,X30,X31,X32)
| apply(X30,esk6_4(X29,X30,X31,X32),esk8_4(X29,X30,X31,X32)) )
& ( equal_maps(X29,X30,X31,X32)
| apply(X29,esk6_4(X29,X30,X31,X32),esk7_4(X29,X30,X31,X32)) )
& ( equal_maps(X29,X30,X31,X32)
| member(esk8_4(X29,X30,X31,X32),X32) )
& ( equal_maps(X29,X30,X31,X32)
| member(esk7_4(X29,X30,X31,X32),X32) )
& ( equal_maps(X29,X30,X31,X32)
| member(esk6_4(X29,X30,X31,X32),X31) )
& ( X27 = X28
| ~ apply(X23,X26,X28)
| ~ apply(X22,X26,X27)
| ~ member(X28,X25)
| ~ member(X27,X25)
| ~ member(X26,X24)
| ~ equal_maps(X22,X23,X24,X25) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_maps])])])])])])]) ).
fof(c_0_10,plain,
! [X41,X42,X43,X44,X45] :
( ( identity(X44,X45)
| ~ apply(X44,esk9_2(X44,X45),esk9_2(X44,X45)) )
& ( identity(X44,X45)
| member(esk9_2(X44,X45),X45) )
& ( apply(X41,X43,X43)
| ~ member(X43,X42)
| ~ identity(X41,X42) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[identity])])])])])])]) ).
cnf(c_0_11,plain,
( ~ maps(X6,X2,X4)
| ~ apply(X6,X1,X5)
| ~ apply(X6,X1,X3)
| ~ member(X5,X4)
| ~ member(X3,X4)
| ~ member(X1,X2)
| X3 = X5 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
maps(esk3_0,esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
~ equal_maps(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( equal_maps(X2,X1,X3,X4)
| apply(X1,esk6_4(X2,X1,X3,X4),esk8_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk8_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk6_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk11_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,plain,
( ~ maps(X1,X2,X3)
| ~ member(X4,X2)
| member(esk11_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_19,plain,
! [X47,X48,X49,X50,X51,X52,X53,X55] :
( ( ~ member(X53,X51)
| ~ member(X52,X49)
| apply(compose_function(X47,X48,X49,X50,X51),X52,X53)
| ~ apply(X47,X55,X53)
| ~ apply(X48,X52,X55)
| ~ member(X55,X50) )
& ( ~ member(X53,X51)
| ~ member(X52,X49)
| ~ apply(compose_function(X47,X48,X49,X50,X51),X52,X53)
| apply(X47,esk10_7(X47,X48,X49,X50,X51,X52,X53),X53) )
& ( ~ member(X53,X51)
| ~ member(X52,X49)
| ~ apply(compose_function(X47,X48,X49,X50,X51),X52,X53)
| apply(X48,X52,esk10_7(X47,X48,X49,X50,X51,X52,X53)) )
& ( ~ member(X53,X51)
| ~ member(X52,X49)
| ~ apply(compose_function(X47,X48,X49,X50,X51),X52,X53)
| member(esk10_7(X47,X48,X49,X50,X51,X52,X53),X50) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[compose_function])])])])])]) ).
cnf(c_0_20,plain,
( ~ member(X3,X2)
| ~ identity(X1,X2)
| apply(X1,X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
identity(compose_function(esk1_0,esk3_0,esk5_0,esk4_0,esk5_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,negated_conjecture,
( ~ member(X3,esk5_0)
| ~ member(X1,esk4_0)
| ~ member(X2,esk4_0)
| ~ apply(esk3_0,X3,X1)
| ~ apply(esk3_0,X3,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_23,negated_conjecture,
apply(esk3_0,esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_24,negated_conjecture,
member(esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk4_0),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_25,negated_conjecture,
member(esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk5_0),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( ~ member(X1,esk5_0)
| apply(esk3_0,X1,esk11_4(esk3_0,esk5_0,esk4_0,X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(X1,esk5_0)
| member(esk11_4(esk3_0,esk5_0,esk4_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_28,plain,
( ~ member(X7,X6)
| ~ member(X2,X4)
| ~ apply(compose_function(X3,X1,X4,X5,X6),X2,X7)
| apply(X1,X2,esk10_7(X3,X1,X4,X5,X6,X2,X7)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( ~ member(X1,esk5_0)
| apply(compose_function(esk1_0,esk3_0,esk5_0,esk4_0,esk5_0),X1,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_30,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| member(esk10_7(X1,X2,X3,X4,X5,X6,X7),X4) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,negated_conjecture,
( ~ member(X1,esk4_0)
| ~ apply(esk3_0,esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),X1)
| X1 = esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
fof(c_0_32,plain,
! [X36,X37,X38,X39,X40] :
( ( ~ member(X40,X38)
| ~ member(X39,X37)
| apply(X36,X39,X40)
| ~ apply(inverse_function(X36,X37,X38),X40,X39) )
& ( ~ member(X40,X38)
| ~ member(X39,X37)
| apply(inverse_function(X36,X37,X38),X40,X39)
| ~ apply(X36,X39,X40) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inverse_function])])])]) ).
cnf(c_0_33,plain,
( equal_maps(X1,X2,X3,X4)
| apply(X1,esk6_4(X1,X2,X3,X4),esk7_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk7_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(X2,esk5_0)
| ~ member(X1,esk4_0)
| ~ apply(esk3_0,X2,X1)
| X1 = esk11_4(esk3_0,esk5_0,esk4_0,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_27]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(X1,esk5_0)
| apply(esk3_0,X1,esk10_7(esk1_0,esk3_0,esk5_0,esk4_0,esk5_0,X1,X1)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( ~ member(X1,esk5_0)
| member(esk10_7(esk1_0,esk3_0,esk5_0,esk4_0,esk5_0,X1,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_38,negated_conjecture,
( ~ member(esk11_4(esk3_0,esk5_0,esk4_0,esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)),esk4_0)
| esk11_4(esk3_0,esk5_0,esk4_0,esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)) = esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_25])]) ).
cnf(c_0_39,negated_conjecture,
maps(esk1_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_40,plain,
( ~ member(X4,X3)
| ~ member(X5,X2)
| ~ apply(inverse_function(X1,X2,X3),X4,X5)
| apply(X1,X5,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,negated_conjecture,
apply(inverse_function(esk1_0,esk4_0,esk5_0),esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)),
inference(spm,[status(thm)],[c_0_13,c_0_33]) ).
cnf(c_0_42,negated_conjecture,
member(esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk4_0),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_43,negated_conjecture,
maps(esk2_0,esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_44,negated_conjecture,
identity(compose_function(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_45,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| apply(X1,esk10_7(X1,X2,X3,X4,X5,X6,X7),X7) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_46,negated_conjecture,
( ~ member(X1,esk5_0)
| esk11_4(esk3_0,esk5_0,esk4_0,X1) = esk10_7(esk1_0,esk3_0,esk5_0,esk4_0,esk5_0,X1,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_47,negated_conjecture,
esk11_4(esk3_0,esk5_0,esk4_0,esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)) = esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_27]),c_0_25])]) ).
cnf(c_0_48,negated_conjecture,
( ~ member(X3,esk4_0)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ apply(esk1_0,X3,X1)
| ~ apply(esk1_0,X3,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_11,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
apply(esk1_0,esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_25])]) ).
cnf(c_0_50,negated_conjecture,
( ~ member(X3,esk5_0)
| ~ member(X1,esk4_0)
| ~ member(X2,esk4_0)
| ~ apply(esk2_0,X3,X1)
| ~ apply(esk2_0,X3,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_11,c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( ~ member(X1,esk5_0)
| apply(esk2_0,X1,esk11_4(esk2_0,esk5_0,esk4_0,X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( ~ member(X1,esk5_0)
| member(esk11_4(esk2_0,esk5_0,esk4_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_43]) ).
cnf(c_0_53,negated_conjecture,
( ~ member(X1,esk4_0)
| apply(compose_function(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0),X1,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(X1,esk4_0)
| apply(esk1_0,X1,esk11_4(esk1_0,esk4_0,esk5_0,X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_55,negated_conjecture,
( ~ member(X1,esk4_0)
| member(esk11_4(esk1_0,esk4_0,esk5_0,X1),esk5_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_39]) ).
cnf(c_0_56,negated_conjecture,
( ~ member(X1,esk5_0)
| apply(esk1_0,esk10_7(esk1_0,esk3_0,esk5_0,esk4_0,esk5_0,X1,X1),X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_29]) ).
cnf(c_0_57,negated_conjecture,
esk10_7(esk1_0,esk3_0,esk5_0,esk4_0,esk5_0,esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)) = esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_25]),c_0_47]) ).
cnf(c_0_58,negated_conjecture,
( ~ member(X1,esk5_0)
| ~ apply(esk1_0,esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),X1)
| X1 = esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_25]),c_0_42])]) ).
cnf(c_0_59,negated_conjecture,
( ~ member(X2,esk5_0)
| ~ member(X1,esk4_0)
| ~ apply(esk2_0,X2,X1)
| X1 = esk11_4(esk2_0,esk5_0,esk4_0,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_60,negated_conjecture,
( ~ member(X1,esk4_0)
| apply(esk2_0,esk10_7(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0,X1,X1),X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( ~ member(X1,esk4_0)
| member(esk10_7(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0,X1,X1),esk5_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( ~ member(X2,esk4_0)
| ~ member(X1,esk5_0)
| ~ apply(esk1_0,X2,X1)
| X1 = esk11_4(esk1_0,esk4_0,esk5_0,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_54]),c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( ~ member(X1,esk4_0)
| apply(esk1_0,X1,esk10_7(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0,X1,X1)) ),
inference(spm,[status(thm)],[c_0_28,c_0_53]) ).
cnf(c_0_64,negated_conjecture,
apply(esk1_0,esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_25])]) ).
cnf(c_0_65,negated_conjecture,
( ~ member(esk11_4(esk1_0,esk4_0,esk5_0,esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)),esk5_0)
| esk11_4(esk1_0,esk4_0,esk5_0,esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)) = esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_54]),c_0_42])]) ).
cnf(c_0_66,negated_conjecture,
( ~ member(X1,esk4_0)
| esk11_4(esk2_0,esk5_0,esk4_0,esk10_7(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0,X1,X1)) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( ~ member(X1,esk4_0)
| esk10_7(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0,X1,X1) = esk11_4(esk1_0,esk4_0,esk5_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_61]) ).
cnf(c_0_68,negated_conjecture,
esk11_4(esk1_0,esk4_0,esk5_0,esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)) = esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_64]),c_0_25]),c_0_24])]) ).
cnf(c_0_69,negated_conjecture,
esk11_4(esk1_0,esk4_0,esk5_0,esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)) = esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_55]),c_0_42])]) ).
cnf(c_0_70,negated_conjecture,
esk11_4(esk2_0,esk5_0,esk4_0,esk10_7(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0,esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0))) = esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(spm,[status(thm)],[c_0_66,c_0_24]) ).
cnf(c_0_71,negated_conjecture,
esk10_7(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0,esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)) = esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_24]),c_0_68]) ).
cnf(c_0_72,plain,
( esk7_4(X1,X2,X3,X4) != esk8_4(X1,X2,X3,X4)
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_73,negated_conjecture,
esk11_4(esk2_0,esk5_0,esk4_0,esk10_7(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0,esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0))) = esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(spm,[status(thm)],[c_0_66,c_0_42]) ).
cnf(c_0_74,negated_conjecture,
esk10_7(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0,esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)) = esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_42]),c_0_69]) ).
cnf(c_0_75,negated_conjecture,
esk11_4(esk2_0,esk5_0,esk4_0,esk6_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0)) = esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
esk8_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0) != esk7_4(inverse_function(esk1_0,esk4_0,esk5_0),esk3_0,esk5_0,esk4_0),
inference(spm,[status(thm)],[c_0_13,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET727+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:34:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 218.25/32.76 % Version: 3.5.1
% 218.25/32.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 218.25/32.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.25/32.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 218.25/32.76 % Starting new_bool_3 with 300s (1) cores
% 218.25/32.76 % Starting new_bool_1 with 300s (1) cores
% 218.25/32.76 % Starting sh5l with 300s (1) cores
% 218.25/32.76 % new_bool_1 with pid 1074122 completed with status 0
% 218.25/32.76 % Result found by new_bool_1
% 218.25/32.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 218.25/32.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.25/32.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 218.25/32.76 % Starting new_bool_3 with 300s (1) cores
% 218.25/32.76 % Starting new_bool_1 with 300s (1) cores
% 218.25/32.76 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 218.25/32.76 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 218.25/32.76 % Search class: FGUSF-FFMS33-SFFFFFNN
% 218.25/32.76 % partial match(1): FGUSS-FFMS33-SFFFFFNN
% 218.25/32.76 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 218.25/32.76 % Starting SubtermCWHack with 31s (1) cores
% 218.25/32.76 % SubtermCWHack with pid 1074125 completed with status 8
% 218.25/32.76 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 150s (1) cores
% 218.25/32.76 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 1074134 completed with status 0
% 218.25/32.76 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 218.25/32.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 218.25/32.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.25/32.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 218.25/32.76 % Starting new_bool_3 with 300s (1) cores
% 218.25/32.76 % Starting new_bool_1 with 300s (1) cores
% 218.25/32.76 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 218.25/32.76 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 218.25/32.76 % Search class: FGUSF-FFMS33-SFFFFFNN
% 218.25/32.76 % partial match(1): FGUSS-FFMS33-SFFFFFNN
% 218.25/32.76 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 218.25/32.76 % Starting SubtermCWHack with 31s (1) cores
% 218.25/32.76 % SubtermCWHack with pid 1074125 completed with status 8
% 218.25/32.76 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 150s (1) cores
% 218.25/32.76 % Preprocessing time : 0.003 s
% 218.25/32.76 % Presaturation interreduction done
% 218.25/32.76
% 218.25/32.76 % Proof found!
% 218.25/32.76 % SZS status Theorem
% 218.25/32.76 % SZS output start CNFRefutation
% See solution above
% 218.25/32.76 % Parsed axioms : 29
% 218.25/32.76 % Removed by relevancy pruning/SinE : 23
% 218.25/32.76 % Initial clauses : 37
% 218.25/32.76 % Removed in clause preprocessing : 0
% 218.25/32.76 % Initial clauses in saturation : 37
% 218.25/32.76 % Processed clauses : 177
% 218.25/32.76 % ...of these trivial : 4
% 218.25/32.76 % ...subsumed : 2
% 218.25/32.76 % ...remaining for further processing : 171
% 218.25/32.76 % Other redundant clauses eliminated : 0
% 218.25/32.76 % Clauses deleted for lack of memory : 0
% 218.25/32.76 % Backward-subsumed : 0
% 218.25/32.76 % Backward-rewritten : 7
% 218.25/32.76 % Generated clauses : 629
% 218.25/32.76 % ...of the previous two non-redundant : 570
% 218.25/32.76 % ...aggressively subsumed : 0
% 218.25/32.76 % Contextual simplify-reflections : 7
% 218.25/32.76 % Paramodulations : 629
% 218.25/32.76 % Factorizations : 0
% 218.25/32.76 % NegExts : 0
% 218.25/32.76 % Equation resolutions : 0
% 218.25/32.76 % Disequality decompositions : 0
% 218.25/32.76 % Total rewrite steps : 230
% 218.25/32.76 % ...of those cached : 215
% 218.25/32.76 % Propositional unsat checks : 0
% 218.25/32.76 % Propositional check models : 0
% 218.25/32.76 % Propositional check unsatisfiable : 0
% 218.25/32.76 % Propositional clauses : 0
% 218.25/32.76 % Propositional clauses after purity: 0
% 218.25/32.76 % Propositional unsat core size : 0
% 218.25/32.76 % Propositional preprocessing time : 0.000
% 218.25/32.76 % Propositional encoding time : 0.000
% 218.25/32.76 % Propositional solver time : 0.000
% 218.25/32.76 % Success case prop preproc time : 0.000
% 218.25/32.76 % Success case prop encoding time : 0.000
% 218.25/32.76 % Success case prop solver time : 0.000
% 218.25/32.76 % Current number of processed clauses : 127
% 218.25/32.76 % Positive orientable unit clauses : 20
% 218.25/32.76 % Positive unorientable unit clauses: 0
% 218.25/32.76 % Negative unit clauses : 2
% 218.25/32.76 % Non-unit-clauses : 105
% 218.25/32.76 % Current number of unprocessed clauses: 463
% 218.25/32.76 % ...number of literals in the above : 2571
% 218.25/32.76 % Current number of archived formulas : 0
% 218.25/32.76 % Current number of archived clauses : 44
% 218.25/32.76 % Clause-clause subsumption calls (NU) : 2744
% 218.25/32.76 % Rec. Clause-clause subsumption calls : 837
% 218.25/32.76 % Non-unit clause-clause subsumptions : 9
% 218.25/32.76 % Unit Clause-clause subsumption calls : 27
% 218.25/32.76 % Rewrite failures with RHS unbound : 0
% 218.25/32.76 % BW rewrite match attempts : 37
% 218.25/32.76 % BW rewrite match successes : 5
% 218.25/32.76 % Condensation attempts : 0
% 218.25/32.76 % Condensation successes : 0
% 218.25/32.76 % Termbank termtop insertions : 29664
% 218.25/32.76 % Search garbage collected termcells : 1057
% 218.25/32.76
% 218.25/32.76 % -------------------------------------------------
% 218.25/32.76 % User time : 30.636 s
% 218.25/32.76 % System time : 0.485 s
% 218.25/32.76 % Total time : 31.121 s
% 218.25/32.76 % Maximum resident set size: 3692 pages
% 218.25/32.76
% 218.25/32.76 % -------------------------------------------------
% 218.25/32.76 % User time : 30.640 s
% 218.25/32.76 % System time : 0.494 s
% 218.25/32.76 % Total time : 31.134 s
% 218.25/32.76 % Maximum resident set size: 4608 pages
% 218.25/32.76 % E exiting
%------------------------------------------------------------------------------