%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET724+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 : n006.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 02:15:04 PM UTC 2026
% Result : Theorem 1.29s 0.66s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 68 ( 8 unt; 0 def)
% Number of atoms : 435 ( 32 equ)
% Maximal formula atoms : 55 ( 6 avg)
% Number of connectives : 639 ( 272 ~; 303 |; 51 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-7 aty)
% Number of variables : 271 ( 0 sgn 75 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thII15,conjecture,
! [X6,X10,X9,X1,X2,X11] :
( ( equal_maps(compose_function(X10,X6,X1,X2,X11),compose_function(X9,X6,X1,X2,X11),X1,X11)
& surjective(X6,X1,X2)
& maps(X9,X2,X11)
& maps(X10,X2,X11)
& maps(X6,X1,X2) )
=> equal_maps(X10,X9,X2,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII15) ).
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(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(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(surjective,axiom,
! [X6,X1,X2] :
( surjective(X6,X1,X2)
<=> ! [X5] :
( member(X5,X2)
=> ? [X4] :
( apply(X6,X4,X5)
& member(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(c_0_5,negated_conjecture,
~ ! [X6,X10,X9,X1,X2,X11] :
( ( equal_maps(compose_function(X10,X6,X1,X2,X11),compose_function(X9,X6,X1,X2,X11),X1,X11)
& surjective(X6,X1,X2)
& maps(X9,X2,X11)
& maps(X10,X2,X11)
& maps(X6,X1,X2) )
=> equal_maps(X10,X9,X2,X11) ),
inference(assume_negation,[status(cth)],[thII15]) ).
fof(c_0_6,plain,
! [X23,X24,X25,X26,X27,X28,X29,X30,X31,X32,X33] :
( ( equal_maps(X30,X31,X32,X33)
| esk8_4(X30,X31,X32,X33) != esk9_4(X30,X31,X32,X33) )
& ( equal_maps(X30,X31,X32,X33)
| apply(X31,esk7_4(X30,X31,X32,X33),esk9_4(X30,X31,X32,X33)) )
& ( equal_maps(X30,X31,X32,X33)
| apply(X30,esk7_4(X30,X31,X32,X33),esk8_4(X30,X31,X32,X33)) )
& ( equal_maps(X30,X31,X32,X33)
| member(esk9_4(X30,X31,X32,X33),X33) )
& ( equal_maps(X30,X31,X32,X33)
| member(esk8_4(X30,X31,X32,X33),X33) )
& ( equal_maps(X30,X31,X32,X33)
| member(esk7_4(X30,X31,X32,X33),X32) )
& ( X28 = X29
| ~ apply(X24,X27,X29)
| ~ apply(X23,X27,X28)
| ~ member(X29,X26)
| ~ member(X28,X26)
| ~ member(X27,X25)
| ~ equal_maps(X23,X24,X25,X26) ) ),
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_7,negated_conjecture,
( ~ equal_maps(esk2_0,esk3_0,esk5_0,esk6_0)
& equal_maps(compose_function(esk2_0,esk1_0,esk4_0,esk5_0,esk6_0),compose_function(esk3_0,esk1_0,esk4_0,esk5_0,esk6_0),esk4_0,esk6_0)
& surjective(esk1_0,esk4_0,esk5_0)
& maps(esk3_0,esk5_0,esk6_0)
& maps(esk2_0,esk5_0,esk6_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_5])])])]) ).
fof(c_0_8,plain,
! [X37,X38,X39,X40,X41,X42,X43,X45] :
( ( ~ member(X43,X41)
| ~ member(X42,X39)
| apply(compose_function(X37,X38,X39,X40,X41),X42,X43)
| ~ apply(X37,X45,X43)
| ~ apply(X38,X42,X45)
| ~ member(X45,X40) )
& ( ~ member(X43,X41)
| ~ member(X42,X39)
| ~ apply(compose_function(X37,X38,X39,X40,X41),X42,X43)
| apply(X37,esk10_7(X37,X38,X39,X40,X41,X42,X43),X43) )
& ( ~ member(X43,X41)
| ~ member(X42,X39)
| ~ apply(compose_function(X37,X38,X39,X40,X41),X42,X43)
| apply(X38,X42,esk10_7(X37,X38,X39,X40,X41,X42,X43)) )
& ( ~ member(X43,X41)
| ~ member(X42,X39)
| ~ apply(compose_function(X37,X38,X39,X40,X41),X42,X43)
| member(esk10_7(X37,X38,X39,X40,X41,X42,X43),X40) ) ),
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])])])])])]) ).
fof(c_0_9,plain,
! [X59,X60,X61,X62,X64,X65,X66,X67,X68,X69,X71] :
( ( maps(X67,X68,X69)
| ~ apply(X67,esk14_3(X67,X68,X69),X71)
| ~ member(X71,X69)
| esk16_3(X67,X68,X69) != esk17_3(X67,X68,X69) )
& ( maps(X67,X68,X69)
| ~ apply(X67,esk14_3(X67,X68,X69),X71)
| ~ member(X71,X69)
| apply(X67,esk15_3(X67,X68,X69),esk17_3(X67,X68,X69)) )
& ( maps(X67,X68,X69)
| ~ apply(X67,esk14_3(X67,X68,X69),X71)
| ~ member(X71,X69)
| apply(X67,esk15_3(X67,X68,X69),esk16_3(X67,X68,X69)) )
& ( maps(X67,X68,X69)
| ~ apply(X67,esk14_3(X67,X68,X69),X71)
| ~ member(X71,X69)
| member(esk17_3(X67,X68,X69),X69) )
& ( maps(X67,X68,X69)
| ~ apply(X67,esk14_3(X67,X68,X69),X71)
| ~ member(X71,X69)
| member(esk16_3(X67,X68,X69),X69) )
& ( maps(X67,X68,X69)
| ~ apply(X67,esk14_3(X67,X68,X69),X71)
| ~ member(X71,X69)
| member(esk15_3(X67,X68,X69),X68) )
& ( maps(X67,X68,X69)
| member(esk14_3(X67,X68,X69),X68)
| esk16_3(X67,X68,X69) != esk17_3(X67,X68,X69) )
& ( maps(X67,X68,X69)
| member(esk14_3(X67,X68,X69),X68)
| apply(X67,esk15_3(X67,X68,X69),esk17_3(X67,X68,X69)) )
& ( maps(X67,X68,X69)
| member(esk14_3(X67,X68,X69),X68)
| apply(X67,esk15_3(X67,X68,X69),esk16_3(X67,X68,X69)) )
& ( maps(X67,X68,X69)
| member(esk14_3(X67,X68,X69),X68)
| member(esk17_3(X67,X68,X69),X69) )
& ( maps(X67,X68,X69)
| member(esk14_3(X67,X68,X69),X68)
| member(esk16_3(X67,X68,X69),X69) )
& ( maps(X67,X68,X69)
| member(esk14_3(X67,X68,X69),X68)
| member(esk15_3(X67,X68,X69),X68) )
& ( ~ maps(X59,X60,X61)
| X65 = X66
| ~ apply(X59,X64,X66)
| ~ apply(X59,X64,X65)
| ~ member(X66,X61)
| ~ member(X65,X61)
| ~ member(X64,X60) )
& ( ~ maps(X59,X60,X61)
| ~ member(X62,X60)
| apply(X59,X62,esk13_4(X59,X60,X61,X62)) )
& ( ~ maps(X59,X60,X61)
| ~ member(X62,X60)
| member(esk13_4(X59,X60,X61,X62),X61) ) ),
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])])])])])])]) ).
cnf(c_0_10,plain,
( ~ apply(X2,X5,X7)
| ~ apply(X1,X5,X6)
| ~ member(X7,X4)
| ~ member(X6,X4)
| ~ member(X5,X3)
| ~ equal_maps(X1,X2,X3,X4)
| X6 = X7 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
equal_maps(compose_function(esk2_0,esk1_0,esk4_0,esk5_0,esk6_0),compose_function(esk3_0,esk1_0,esk4_0,esk5_0,esk6_0),esk4_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( ~ member(X6,X8)
| ~ member(X4,X7)
| ~ apply(X5,X1,X6)
| ~ apply(X3,X4,X1)
| ~ member(X1,X2)
| apply(compose_function(X5,X3,X7,X2,X8),X4,X6) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk13_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( ~ member(X3,esk4_0)
| ~ member(X1,esk6_0)
| ~ member(X2,esk6_0)
| ~ apply(compose_function(esk2_0,esk1_0,esk4_0,esk5_0,esk6_0),X3,X1)
| ~ apply(compose_function(esk3_0,esk1_0,esk4_0,esk5_0,esk6_0),X3,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(X9,X7)
| ~ member(X9,X4)
| ~ member(X6,X3)
| ~ member(esk13_4(X1,X7,X8,X9),X5)
| ~ maps(X1,X7,X8)
| ~ apply(X2,X6,X9)
| apply(compose_function(X1,X2,X3,X4,X5),X6,esk13_4(X1,X7,X8,X9)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
( ~ member(X4,X2)
| ~ member(X4,esk5_0)
| ~ member(X5,esk4_0)
| ~ member(X1,esk6_0)
| ~ member(esk13_4(esk3_0,X2,X3,X4),esk6_0)
| ~ maps(esk3_0,X2,X3)
| ~ apply(esk1_0,X5,X4)
| ~ apply(compose_function(esk2_0,esk1_0,esk4_0,esk5_0,esk6_0),X5,X1)
| X1 = esk13_4(esk3_0,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(X3,X1)
| ~ member(X6,X4)
| ~ member(X3,esk5_0)
| ~ member(X6,esk5_0)
| ~ member(X7,esk4_0)
| ~ member(esk13_4(esk2_0,X1,X2,X3),esk6_0)
| ~ member(esk13_4(esk3_0,X4,X5,X6),esk6_0)
| ~ maps(esk2_0,X1,X2)
| ~ maps(esk3_0,X4,X5)
| ~ apply(esk1_0,X7,X3)
| ~ apply(esk1_0,X7,X6)
| esk13_4(esk2_0,X1,X2,X3) = esk13_4(esk3_0,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_18,plain,
( ~ maps(X1,X2,X3)
| ~ member(X4,X2)
| member(esk13_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X3,X1)
| ~ member(X5,X4)
| ~ member(X3,esk5_0)
| ~ member(X5,esk5_0)
| ~ member(X6,esk4_0)
| ~ member(esk13_4(esk2_0,X1,X2,X3),esk6_0)
| ~ maps(esk2_0,X1,X2)
| ~ maps(esk3_0,X4,esk6_0)
| ~ apply(esk1_0,X6,X3)
| ~ apply(esk1_0,X6,X5)
| esk13_4(esk2_0,X1,X2,X3) = esk13_4(esk3_0,X4,esk6_0,X5) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_20,plain,
! [X46,X47,X48,X49,X51,X52,X53,X55] :
( ( surjective(X51,X52,X53)
| ~ apply(X51,X55,esk12_3(X51,X52,X53))
| ~ member(X55,X52) )
& ( surjective(X51,X52,X53)
| member(esk12_3(X51,X52,X53),X53) )
& ( ~ surjective(X46,X47,X48)
| ~ member(X49,X48)
| apply(X46,esk11_4(X46,X47,X48,X49),X49) )
& ( ~ surjective(X46,X47,X48)
| ~ member(X49,X48)
| member(esk11_4(X46,X47,X48,X49),X47) ) ),
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)],[surjective])])])])])])]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X4,X3)
| ~ member(X2,esk5_0)
| ~ member(X4,esk5_0)
| ~ member(X5,esk4_0)
| ~ maps(esk2_0,X1,esk6_0)
| ~ maps(esk3_0,X3,esk6_0)
| ~ apply(esk1_0,X5,X2)
| ~ apply(esk1_0,X5,X4)
| esk13_4(esk2_0,X1,esk6_0,X2) = esk13_4(esk3_0,X3,esk6_0,X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_22,plain,
( ~ surjective(X1,X2,X3)
| ~ member(X4,X3)
| apply(X1,esk11_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( ~ member(X4,X6)
| ~ member(X2,X1)
| ~ member(X4,X3)
| ~ member(X2,esk5_0)
| ~ member(X4,esk5_0)
| ~ member(esk11_4(esk1_0,X5,X6,X4),esk4_0)
| ~ maps(esk2_0,X1,esk6_0)
| ~ maps(esk3_0,X3,esk6_0)
| ~ apply(esk1_0,esk11_4(esk1_0,X5,X6,X4),X2)
| ~ surjective(esk1_0,X5,X6)
| esk13_4(esk2_0,X1,esk6_0,X2) = esk13_4(esk3_0,X3,esk6_0,X4) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(X2,X5)
| ~ member(X2,X1)
| ~ member(X2,X3)
| ~ member(X2,esk5_0)
| ~ member(esk11_4(esk1_0,X4,X5,X2),esk4_0)
| ~ maps(esk2_0,X1,esk6_0)
| ~ maps(esk3_0,X3,esk6_0)
| ~ surjective(esk1_0,X4,X5)
| esk13_4(esk2_0,X1,esk6_0,X2) = esk13_4(esk3_0,X3,esk6_0,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_25,plain,
( ~ surjective(X1,X2,X3)
| ~ member(X4,X3)
| member(esk11_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( ~ member(X2,X4)
| ~ member(X2,X1)
| ~ member(X2,X3)
| ~ member(X2,esk5_0)
| ~ maps(esk2_0,X1,esk6_0)
| ~ maps(esk3_0,X3,esk6_0)
| ~ surjective(esk1_0,esk4_0,X4)
| esk13_4(esk2_0,X1,esk6_0,X2) = esk13_4(esk3_0,X3,esk6_0,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
surjective(esk1_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,X3)
| ~ member(X2,esk5_0)
| ~ maps(esk2_0,X1,esk6_0)
| ~ maps(esk3_0,X3,esk6_0)
| esk13_4(esk2_0,X1,esk6_0,X2) = esk13_4(esk3_0,X3,esk6_0,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ member(X1,esk5_0)
| ~ maps(esk2_0,X2,esk6_0)
| ~ maps(esk3_0,X3,esk6_0)
| apply(esk3_0,X1,esk13_4(esk2_0,X2,esk6_0,X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
maps(esk3_0,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_31,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_9]) ).
cnf(c_0_32,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,esk5_0)
| ~ maps(esk2_0,X2,esk6_0)
| apply(esk3_0,X1,esk13_4(esk2_0,X2,esk6_0,X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X4)
| ~ member(X1,X5)
| ~ member(X3,esk5_0)
| ~ member(esk13_4(esk2_0,X2,esk6_0,X3),X5)
| ~ maps(esk3_0,X4,X5)
| ~ maps(esk2_0,X2,esk6_0)
| ~ apply(esk3_0,X3,X1)
| X1 = esk13_4(esk2_0,X2,esk6_0,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X4)
| ~ member(X1,esk6_0)
| ~ member(X3,esk5_0)
| ~ maps(esk3_0,X4,esk6_0)
| ~ maps(esk2_0,X2,esk6_0)
| ~ apply(esk3_0,X3,X1)
| X1 = esk13_4(esk2_0,X2,esk6_0,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X1,esk6_0)
| ~ member(X3,esk5_0)
| ~ maps(esk2_0,X2,esk6_0)
| ~ apply(esk3_0,X3,X1)
| X1 = esk13_4(esk2_0,X2,esk6_0,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_36,plain,
( equal_maps(X1,X2,X3,X4)
| apply(X1,esk7_4(X1,X2,X3,X4),esk8_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_37,plain,
( equal_maps(X2,X1,X3,X4)
| apply(X1,esk7_4(X2,X1,X3,X4),esk9_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_38,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ member(X1,esk5_0)
| ~ maps(esk3_0,X2,esk6_0)
| ~ maps(esk2_0,X3,esk6_0)
| apply(esk2_0,X1,esk13_4(esk3_0,X2,esk6_0,X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_39,negated_conjecture,
maps(esk2_0,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_40,negated_conjecture,
( ~ member(esk7_4(esk3_0,X2,X3,X4),X1)
| ~ member(esk8_4(esk3_0,X2,X3,X4),esk6_0)
| ~ member(esk7_4(esk3_0,X2,X3,X4),esk5_0)
| ~ maps(esk2_0,X1,esk6_0)
| equal_maps(esk3_0,X2,X3,X4)
| esk13_4(esk2_0,X1,esk6_0,esk7_4(esk3_0,X2,X3,X4)) = esk8_4(esk3_0,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( ~ member(esk7_4(X2,esk3_0,X3,X4),X1)
| ~ member(esk9_4(X2,esk3_0,X3,X4),esk6_0)
| ~ member(esk7_4(X2,esk3_0,X3,X4),esk5_0)
| ~ maps(esk2_0,X1,esk6_0)
| equal_maps(X2,esk3_0,X3,X4)
| esk13_4(esk2_0,X1,esk6_0,esk7_4(X2,esk3_0,X3,X4)) = esk9_4(X2,esk3_0,X3,X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_42,plain,
( esk8_4(X1,X2,X3,X4) != esk9_4(X1,X2,X3,X4)
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_43,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,esk5_0)
| ~ maps(esk3_0,X2,esk6_0)
| apply(esk2_0,X1,esk13_4(esk3_0,X2,esk6_0,X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( ~ member(esk7_4(esk3_0,esk3_0,X1,X2),X3)
| ~ member(esk9_4(esk3_0,esk3_0,X1,X2),esk6_0)
| ~ member(esk8_4(esk3_0,esk3_0,X1,X2),esk6_0)
| ~ member(esk7_4(esk3_0,esk3_0,X1,X2),esk5_0)
| ~ maps(esk2_0,X3,esk6_0)
| equal_maps(esk3_0,esk3_0,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_45,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk9_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_46,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk8_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_47,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X4)
| ~ member(X1,X5)
| ~ member(X3,esk5_0)
| ~ member(esk13_4(esk3_0,X2,esk6_0,X3),X5)
| ~ maps(esk2_0,X4,X5)
| ~ maps(esk3_0,X2,esk6_0)
| ~ apply(esk2_0,X3,X1)
| X1 = esk13_4(esk3_0,X2,esk6_0,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
( ~ member(esk7_4(esk3_0,esk3_0,X1,esk6_0),X2)
| ~ member(esk7_4(esk3_0,esk3_0,X1,esk6_0),esk5_0)
| ~ maps(esk2_0,X2,esk6_0)
| equal_maps(esk3_0,esk3_0,X1,esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_49,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk7_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_50,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X4)
| ~ member(X1,esk6_0)
| ~ member(X3,esk5_0)
| ~ maps(esk2_0,X4,esk6_0)
| ~ maps(esk3_0,X2,esk6_0)
| ~ apply(esk2_0,X3,X1)
| X1 = esk13_4(esk3_0,X2,esk6_0,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_18]) ).
cnf(c_0_51,negated_conjecture,
( ~ member(esk7_4(esk3_0,esk3_0,esk5_0,esk6_0),X1)
| ~ maps(esk2_0,X1,esk6_0)
| equal_maps(esk3_0,esk3_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X1,esk6_0)
| ~ member(X3,esk5_0)
| ~ maps(esk3_0,X2,esk6_0)
| ~ apply(esk2_0,X3,X1)
| X1 = esk13_4(esk3_0,X2,esk6_0,X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_39]) ).
cnf(c_0_53,negated_conjecture,
equal_maps(esk3_0,esk3_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_49]),c_0_39])]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(esk7_4(X2,esk2_0,X3,X4),X1)
| ~ member(esk9_4(X2,esk2_0,X3,X4),esk6_0)
| ~ member(esk7_4(X2,esk2_0,X3,X4),esk5_0)
| ~ maps(esk3_0,X1,esk6_0)
| equal_maps(X2,esk2_0,X3,X4)
| esk13_4(esk3_0,X1,esk6_0,esk7_4(X2,esk2_0,X3,X4)) = esk9_4(X2,esk2_0,X3,X4) ),
inference(spm,[status(thm)],[c_0_52,c_0_37]) ).
cnf(c_0_55,negated_conjecture,
( ~ member(X3,esk5_0)
| ~ member(X1,esk6_0)
| ~ member(X2,esk6_0)
| ~ apply(esk3_0,X3,X1)
| ~ apply(esk3_0,X3,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_10,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( ~ member(esk7_4(X1,esk2_0,X2,X3),X4)
| ~ member(esk9_4(X1,esk2_0,X2,X3),esk6_0)
| ~ member(esk7_4(X1,esk2_0,X2,X3),esk5_0)
| ~ maps(esk3_0,X4,esk6_0)
| apply(esk3_0,esk7_4(X1,esk2_0,X2,X3),esk9_4(X1,esk2_0,X2,X3))
| equal_maps(X1,esk2_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
( ~ member(X1,esk6_0)
| ~ member(esk7_4(esk3_0,X2,X3,X4),esk5_0)
| ~ member(esk8_4(esk3_0,X2,X3,X4),esk6_0)
| ~ apply(esk3_0,esk7_4(esk3_0,X2,X3,X4),X1)
| equal_maps(esk3_0,X2,X3,X4)
| X1 = esk8_4(esk3_0,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_55,c_0_36]) ).
cnf(c_0_58,negated_conjecture,
( ~ member(esk9_4(X1,esk2_0,X2,X3),esk6_0)
| ~ member(esk7_4(X1,esk2_0,X2,X3),esk5_0)
| ~ maps(esk3_0,X2,esk6_0)
| apply(esk3_0,esk7_4(X1,esk2_0,X2,X3),esk9_4(X1,esk2_0,X2,X3))
| equal_maps(X1,esk2_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_56,c_0_49]) ).
cnf(c_0_59,negated_conjecture,
( ~ member(esk9_4(esk3_0,esk2_0,X1,X2),esk6_0)
| ~ member(esk7_4(esk3_0,esk2_0,X1,X2),esk5_0)
| ~ member(esk8_4(esk3_0,esk2_0,X1,X2),esk6_0)
| ~ maps(esk3_0,X1,esk6_0)
| equal_maps(esk3_0,esk2_0,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_42]) ).
cnf(c_0_60,negated_conjecture,
( ~ member(esk7_4(esk3_0,esk2_0,X1,esk6_0),esk5_0)
| ~ maps(esk3_0,X1,esk6_0)
| equal_maps(esk3_0,esk2_0,X1,esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_45]),c_0_46]) ).
cnf(c_0_61,negated_conjecture,
equal_maps(esk3_0,esk2_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_49]),c_0_30])]) ).
cnf(c_0_62,negated_conjecture,
( ~ member(X3,esk5_0)
| ~ member(X1,esk6_0)
| ~ member(X2,esk6_0)
| ~ apply(esk3_0,X3,X1)
| ~ apply(esk2_0,X3,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_10,c_0_61]) ).
cnf(c_0_63,negated_conjecture,
( ~ member(X1,esk6_0)
| ~ member(esk7_4(esk2_0,X2,X3,X4),esk5_0)
| ~ member(esk8_4(esk2_0,X2,X3,X4),esk6_0)
| ~ apply(esk3_0,esk7_4(esk2_0,X2,X3,X4),X1)
| equal_maps(esk2_0,X2,X3,X4)
| X1 = esk8_4(esk2_0,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_62,c_0_36]) ).
cnf(c_0_64,negated_conjecture,
( ~ member(esk9_4(esk2_0,esk3_0,X1,X2),esk6_0)
| ~ member(esk7_4(esk2_0,esk3_0,X1,X2),esk5_0)
| ~ member(esk8_4(esk2_0,esk3_0,X1,X2),esk6_0)
| equal_maps(esk2_0,esk3_0,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_37]),c_0_42]) ).
cnf(c_0_65,negated_conjecture,
( ~ member(esk7_4(esk2_0,esk3_0,X1,esk6_0),esk5_0)
| equal_maps(esk2_0,esk3_0,X1,esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_45]),c_0_46]) ).
cnf(c_0_66,negated_conjecture,
~ equal_maps(esk2_0,esk3_0,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_49]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET724+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:33:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 1.29/0.66 % Version: 3.5.1
% 1.29/0.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.29/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.29/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.29/0.66 % Starting new_bool_3 with 300s (1) cores
% 1.29/0.66 % Starting new_bool_1 with 300s (1) cores
% 1.29/0.66 % Starting sh5l with 300s (1) cores
% 1.29/0.66 % new_bool_3 with pid 2101216 completed with status 0
% 1.29/0.66 % Result found by new_bool_3
% 1.29/0.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.29/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.29/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.29/0.66 % Starting new_bool_3 with 300s (1) cores
% 1.29/0.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.29/0.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.29/0.66 % Search class: FGUSF-FFMS33-SFFFFFNN
% 1.29/0.66 % partial match(1): FGUSS-FFMS33-SFFFFFNN
% 1.29/0.66 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.29/0.66 % Starting SubtermCWHack with 31s (1) cores
% 1.29/0.66 % SubtermCWHack with pid 2101219 completed with status 0
% 1.29/0.66 % Result found by SubtermCWHack
% 1.29/0.66 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.29/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.29/0.66 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.29/0.66 % Starting new_bool_3 with 300s (1) cores
% 1.29/0.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.29/0.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.29/0.66 % Search class: FGUSF-FFMS33-SFFFFFNN
% 1.29/0.66 % partial match(1): FGUSS-FFMS33-SFFFFFNN
% 1.29/0.66 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.29/0.66 % Starting SubtermCWHack with 31s (1) cores
% 1.29/0.66 % Preprocessing time : 0.001 s
% 1.29/0.66
% 1.29/0.66 % Proof found!
% 1.29/0.66 % SZS status Theorem
% 1.29/0.66 % SZS output start CNFRefutation
% See solution above
% 1.29/0.67 % Parsed axioms : 29
% 1.29/0.67 % Removed by relevancy pruning/SinE : 22
% 1.29/0.67 % Initial clauses : 46
% 1.29/0.67 % Removed in clause preprocessing : 0
% 1.29/0.67 % Initial clauses in saturation : 46
% 1.29/0.67 % Processed clauses : 928
% 1.29/0.67 % ...of these trivial : 0
% 1.29/0.67 % ...subsumed : 376
% 1.29/0.67 % ...remaining for further processing : 552
% 1.29/0.67 % Other redundant clauses eliminated : 0
% 1.29/0.67 % Clauses deleted for lack of memory : 0
% 1.29/0.67 % Backward-subsumed : 67
% 1.29/0.67 % Backward-rewritten : 1
% 1.29/0.67 % Generated clauses : 6818
% 1.29/0.67 % ...of the previous two non-redundant : 6753
% 1.29/0.67 % ...aggressively subsumed : 0
% 1.29/0.67 % Contextual simplify-reflections : 24
% 1.29/0.67 % Paramodulations : 6818
% 1.29/0.67 % Factorizations : 0
% 1.29/0.67 % NegExts : 0
% 1.29/0.67 % Equation resolutions : 0
% 1.29/0.67 % Disequality decompositions : 0
% 1.29/0.67 % Total rewrite steps : 22
% 1.29/0.67 % ...of those cached : 19
% 1.29/0.67 % Propositional unsat checks : 0
% 1.29/0.67 % Propositional check models : 0
% 1.29/0.67 % Propositional check unsatisfiable : 0
% 1.29/0.67 % Propositional clauses : 0
% 1.29/0.67 % Propositional clauses after purity: 0
% 1.29/0.67 % Propositional unsat core size : 0
% 1.29/0.67 % Propositional preprocessing time : 0.000
% 1.29/0.67 % Propositional encoding time : 0.000
% 1.29/0.67 % Propositional solver time : 0.000
% 1.29/0.67 % Success case prop preproc time : 0.000
% 1.29/0.67 % Success case prop encoding time : 0.000
% 1.29/0.67 % Success case prop solver time : 0.000
% 1.29/0.67 % Current number of processed clauses : 484
% 1.29/0.67 % Positive orientable unit clauses : 7
% 1.29/0.67 % Positive unorientable unit clauses: 0
% 1.29/0.67 % Negative unit clauses : 1
% 1.29/0.67 % Non-unit-clauses : 476
% 1.29/0.67 % Current number of unprocessed clauses: 5867
% 1.29/0.67 % ...number of literals in the above : 72234
% 1.29/0.67 % Current number of archived formulas : 0
% 1.29/0.67 % Current number of archived clauses : 68
% 1.29/0.67 % Clause-clause subsumption calls (NU) : 74524
% 1.29/0.67 % Rec. Clause-clause subsumption calls : 2894
% 1.29/0.67 % Non-unit clause-clause subsumptions : 467
% 1.29/0.67 % Unit Clause-clause subsumption calls : 10
% 1.29/0.67 % Rewrite failures with RHS unbound : 0
% 1.29/0.67 % BW rewrite match attempts : 5
% 1.29/0.67 % BW rewrite match successes : 1
% 1.29/0.67 % Condensation attempts : 0
% 1.29/0.67 % Condensation successes : 0
% 1.29/0.67 % Termbank termtop insertions : 338825
% 1.29/0.67 % Search garbage collected termcells : 1242
% 1.29/0.67
% 1.29/0.67 % -------------------------------------------------
% 1.29/0.67 % User time : 0.211 s
% 1.29/0.67 % System time : 0.011 s
% 1.29/0.67 % Total time : 0.222 s
% 1.29/0.67 % Maximum resident set size: 3692 pages
% 1.29/0.67
% 1.29/0.67 % -------------------------------------------------
% 1.29/0.67 % User time : 0.213 s
% 1.29/0.67 % System time : 0.016 s
% 1.29/0.67 % Total time : 0.229 s
% 1.29/0.67 % Maximum resident set size: 4608 pages
% 1.29/0.67 % E exiting
%------------------------------------------------------------------------------