%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET737+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 : n008.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 02:15:07 PM UTC 2026
% Result : Theorem 3.71s 1.04s
% Output : CNFRefutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 9 unt; 0 def)
% Number of atoms : 348 ( 19 equ)
% Maximal formula atoms : 55 ( 6 avg)
% Number of connectives : 486 ( 196 ~; 219 |; 57 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-7 aty)
% Number of variables : 244 ( 2 sgn 78 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thII28,conjecture,
! [X6,X10,X9,X1,X2,X11] :
( ( surjective(compose_function(X10,compose_function(X6,X9,X11,X1,X2),X11,X2,X11),X11,X11)
& injective(compose_function(X6,compose_function(X9,X10,X2,X11,X1),X2,X1,X2),X2,X2)
& injective(compose_function(X9,compose_function(X10,X6,X1,X2,X11),X1,X11,X1),X1,X1)
& maps(X9,X11,X1)
& maps(X10,X2,X11)
& maps(X6,X1,X2) )
=> one_to_one(X10,X2,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII28) ).
fof(injective,axiom,
! [X6,X1,X2] :
( injective(X6,X1,X2)
<=> ! [X13,X14,X5] :
( ( member(X5,X2)
& member(X14,X1)
& member(X13,X1) )
=> ( ( apply(X6,X14,X5)
& apply(X6,X13,X5) )
=> X13 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',injective) ).
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(one_to_one,axiom,
! [X6,X1,X2] :
( one_to_one(X6,X1,X2)
<=> ( surjective(X6,X1,X2)
& injective(X6,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',one_to_one) ).
fof(c_0_6,negated_conjecture,
~ ! [X6,X10,X9,X1,X2,X11] :
( ( surjective(compose_function(X10,compose_function(X6,X9,X11,X1,X2),X11,X2,X11),X11,X11)
& injective(compose_function(X6,compose_function(X9,X10,X2,X11,X1),X2,X1,X2),X2,X2)
& injective(compose_function(X9,compose_function(X10,X6,X1,X2,X11),X1,X11,X1),X1,X1)
& maps(X9,X11,X1)
& maps(X10,X2,X11)
& maps(X6,X1,X2) )
=> one_to_one(X10,X2,X11) ),
inference(assume_negation,[status(cth)],[thII28]) ).
fof(c_0_7,plain,
! [X45,X46,X47,X48,X49,X50,X51,X52,X53] :
( ( injective(X51,X52,X53)
| esk10_3(X51,X52,X53) != esk11_3(X51,X52,X53) )
& ( injective(X51,X52,X53)
| apply(X51,esk11_3(X51,X52,X53),esk12_3(X51,X52,X53)) )
& ( injective(X51,X52,X53)
| apply(X51,esk10_3(X51,X52,X53),esk12_3(X51,X52,X53)) )
& ( injective(X51,X52,X53)
| member(esk12_3(X51,X52,X53),X53) )
& ( injective(X51,X52,X53)
| member(esk11_3(X51,X52,X53),X52) )
& ( injective(X51,X52,X53)
| member(esk10_3(X51,X52,X53),X52) )
& ( X48 = X49
| ~ apply(X45,X49,X50)
| ~ apply(X45,X48,X50)
| ~ member(X50,X47)
| ~ member(X49,X46)
| ~ member(X48,X46)
| ~ injective(X45,X46,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)],[injective])])])])])])]) ).
fof(c_0_8,negated_conjecture,
( ~ one_to_one(esk2_0,esk5_0,esk6_0)
& surjective(compose_function(esk2_0,compose_function(esk1_0,esk3_0,esk6_0,esk4_0,esk5_0),esk6_0,esk5_0,esk6_0),esk6_0,esk6_0)
& injective(compose_function(esk1_0,compose_function(esk3_0,esk2_0,esk5_0,esk6_0,esk4_0),esk5_0,esk4_0,esk5_0),esk5_0,esk5_0)
& injective(compose_function(esk3_0,compose_function(esk2_0,esk1_0,esk4_0,esk5_0,esk6_0),esk4_0,esk6_0,esk4_0),esk4_0,esk4_0)
& maps(esk3_0,esk6_0,esk4_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_6])])])]) ).
fof(c_0_9,plain,
! [X36,X37,X38,X39,X40,X41,X42,X44] :
( ( ~ member(X42,X40)
| ~ member(X41,X38)
| apply(compose_function(X36,X37,X38,X39,X40),X41,X42)
| ~ apply(X36,X44,X42)
| ~ apply(X37,X41,X44)
| ~ member(X44,X39) )
& ( ~ member(X42,X40)
| ~ member(X41,X38)
| ~ apply(compose_function(X36,X37,X38,X39,X40),X41,X42)
| apply(X36,esk9_7(X36,X37,X38,X39,X40,X41,X42),X42) )
& ( ~ member(X42,X40)
| ~ member(X41,X38)
| ~ apply(compose_function(X36,X37,X38,X39,X40),X41,X42)
| apply(X37,X41,esk9_7(X36,X37,X38,X39,X40,X41,X42)) )
& ( ~ member(X42,X40)
| ~ member(X41,X38)
| ~ apply(compose_function(X36,X37,X38,X39,X40),X41,X42)
| member(esk9_7(X36,X37,X38,X39,X40,X41,X42),X39) ) ),
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_10,plain,
! [X57,X58,X59,X60,X62,X63,X64,X65,X66,X67,X69] :
( ( maps(X65,X66,X67)
| ~ apply(X65,esk14_3(X65,X66,X67),X69)
| ~ member(X69,X67)
| esk16_3(X65,X66,X67) != esk17_3(X65,X66,X67) )
& ( maps(X65,X66,X67)
| ~ apply(X65,esk14_3(X65,X66,X67),X69)
| ~ member(X69,X67)
| apply(X65,esk15_3(X65,X66,X67),esk17_3(X65,X66,X67)) )
& ( maps(X65,X66,X67)
| ~ apply(X65,esk14_3(X65,X66,X67),X69)
| ~ member(X69,X67)
| apply(X65,esk15_3(X65,X66,X67),esk16_3(X65,X66,X67)) )
& ( maps(X65,X66,X67)
| ~ apply(X65,esk14_3(X65,X66,X67),X69)
| ~ member(X69,X67)
| member(esk17_3(X65,X66,X67),X67) )
& ( maps(X65,X66,X67)
| ~ apply(X65,esk14_3(X65,X66,X67),X69)
| ~ member(X69,X67)
| member(esk16_3(X65,X66,X67),X67) )
& ( maps(X65,X66,X67)
| ~ apply(X65,esk14_3(X65,X66,X67),X69)
| ~ member(X69,X67)
| member(esk15_3(X65,X66,X67),X66) )
& ( maps(X65,X66,X67)
| member(esk14_3(X65,X66,X67),X66)
| esk16_3(X65,X66,X67) != esk17_3(X65,X66,X67) )
& ( maps(X65,X66,X67)
| member(esk14_3(X65,X66,X67),X66)
| apply(X65,esk15_3(X65,X66,X67),esk17_3(X65,X66,X67)) )
& ( maps(X65,X66,X67)
| member(esk14_3(X65,X66,X67),X66)
| apply(X65,esk15_3(X65,X66,X67),esk16_3(X65,X66,X67)) )
& ( maps(X65,X66,X67)
| member(esk14_3(X65,X66,X67),X66)
| member(esk17_3(X65,X66,X67),X67) )
& ( maps(X65,X66,X67)
| member(esk14_3(X65,X66,X67),X66)
| member(esk16_3(X65,X66,X67),X67) )
& ( maps(X65,X66,X67)
| member(esk14_3(X65,X66,X67),X66)
| member(esk15_3(X65,X66,X67),X66) )
& ( ~ maps(X57,X58,X59)
| X63 = X64
| ~ apply(X57,X62,X64)
| ~ apply(X57,X62,X63)
| ~ member(X64,X59)
| ~ member(X63,X59)
| ~ member(X62,X58) )
& ( ~ maps(X57,X58,X59)
| ~ member(X60,X58)
| apply(X57,X60,esk13_4(X57,X58,X59,X60)) )
& ( ~ maps(X57,X58,X59)
| ~ member(X60,X58)
| member(esk13_4(X57,X58,X59,X60),X59) ) ),
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_11,plain,
( ~ apply(X1,X5,X6)
| ~ apply(X1,X4,X6)
| ~ member(X6,X3)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ injective(X1,X2,X3)
| X4 = X5 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
injective(compose_function(esk1_0,compose_function(esk3_0,esk2_0,esk5_0,esk6_0,esk4_0),esk5_0,esk4_0,esk5_0),esk5_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,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_9]) ).
cnf(c_0_14,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk13_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ member(X3,esk5_0)
| ~ apply(compose_function(esk1_0,compose_function(esk3_0,esk2_0,esk5_0,esk6_0,esk4_0),esk5_0,esk4_0,esk5_0),X1,X3)
| ~ apply(compose_function(esk1_0,compose_function(esk3_0,esk2_0,esk5_0,esk6_0,esk4_0),esk5_0,esk4_0,esk5_0),X2,X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,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_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(X5,X3)
| ~ member(X5,esk4_0)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ member(esk13_4(esk1_0,X3,X4,X5),esk5_0)
| ~ maps(esk1_0,X3,X4)
| ~ apply(compose_function(esk3_0,esk2_0,esk5_0,esk6_0,esk4_0),X2,X5)
| ~ apply(compose_function(esk1_0,compose_function(esk3_0,esk2_0,esk5_0,esk6_0,esk4_0),esk5_0,esk4_0,esk5_0),X1,esk13_4(esk1_0,X3,X4,X5))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,negated_conjecture,
( ~ member(X3,X4)
| ~ member(X3,esk4_0)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ member(esk13_4(esk1_0,X4,X5,X3),esk5_0)
| ~ maps(esk1_0,X4,X5)
| ~ apply(compose_function(esk3_0,esk2_0,esk5_0,esk6_0,esk4_0),X1,X3)
| ~ apply(compose_function(esk3_0,esk2_0,esk5_0,esk6_0,esk4_0),X2,X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X5,X3)
| ~ member(X5,esk6_0)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ member(esk13_4(esk3_0,X3,X4,X5),X6)
| ~ member(esk13_4(esk3_0,X3,X4,X5),esk4_0)
| ~ member(esk13_4(esk1_0,X6,X7,esk13_4(esk3_0,X3,X4,X5)),esk5_0)
| ~ maps(esk3_0,X3,X4)
| ~ maps(esk1_0,X6,X7)
| ~ apply(esk2_0,X2,X5)
| ~ apply(compose_function(esk3_0,esk2_0,esk5_0,esk6_0,esk4_0),X1,esk13_4(esk3_0,X3,X4,X5))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
fof(c_0_20,plain,
! [X26,X27,X28,X29,X31,X32,X33,X35] :
( ( surjective(X31,X32,X33)
| ~ apply(X31,X35,esk8_3(X31,X32,X33))
| ~ member(X35,X32) )
& ( surjective(X31,X32,X33)
| member(esk8_3(X31,X32,X33),X33) )
& ( ~ surjective(X26,X27,X28)
| ~ member(X29,X28)
| apply(X26,esk7_4(X26,X27,X28,X29),X29) )
& ( ~ surjective(X26,X27,X28)
| ~ member(X29,X28)
| member(esk7_4(X26,X27,X28,X29),X27) ) ),
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(X3,X6)
| ~ member(X3,esk6_0)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ member(esk13_4(esk3_0,X6,X7,X3),X4)
| ~ member(esk13_4(esk3_0,X6,X7,X3),esk4_0)
| ~ member(esk13_4(esk1_0,X4,X5,esk13_4(esk3_0,X6,X7,X3)),esk5_0)
| ~ maps(esk3_0,X6,X7)
| ~ maps(esk1_0,X4,X5)
| ~ apply(esk2_0,X1,X3)
| ~ apply(esk2_0,X2,X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_22,plain,
( ~ maps(X1,X2,X3)
| ~ member(X4,X2)
| member(esk13_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,plain,
( ~ apply(X3,X1,esk8_3(X3,X2,X4))
| ~ member(X1,X2)
| surjective(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| apply(X1,esk9_7(X1,X2,X3,X4,X5,X6,X7),X7) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
( ~ member(X3,X5)
| ~ member(X3,esk6_0)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ member(esk13_4(esk3_0,X5,X6,X3),X4)
| ~ member(esk13_4(esk3_0,X5,X6,X3),esk4_0)
| ~ maps(esk3_0,X5,X6)
| ~ maps(esk1_0,X4,esk5_0)
| ~ apply(esk2_0,X1,X3)
| ~ apply(esk2_0,X2,X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ member(X8,X5)
| ~ member(esk8_3(X1,X2,X3),X7)
| ~ member(esk9_7(X1,X4,X5,X6,X7,X8,esk8_3(X1,X2,X3)),X2)
| ~ apply(compose_function(X1,X4,X5,X6,X7),X8,esk8_3(X1,X2,X3))
| surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| member(esk9_7(X1,X2,X3,X4,X5,X6,X7),X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( ~ member(X3,X5)
| ~ member(X3,esk6_0)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ member(esk13_4(esk3_0,X5,esk4_0,X3),X4)
| ~ maps(esk3_0,X5,esk4_0)
| ~ maps(esk1_0,X4,esk5_0)
| ~ apply(esk2_0,X1,X3)
| ~ apply(esk2_0,X2,X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
maps(esk1_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_30,plain,
( ~ member(X7,X5)
| ~ member(esk8_3(X1,X2,X3),X6)
| ~ apply(compose_function(X1,X4,X5,X2,X6),X7,esk8_3(X1,X2,X3))
| surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( ~ surjective(X1,X2,X3)
| ~ member(X4,X3)
| apply(X1,esk7_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( ~ member(X3,X4)
| ~ member(X3,esk6_0)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ maps(esk3_0,X4,esk4_0)
| ~ apply(esk2_0,X1,X3)
| ~ apply(esk2_0,X2,X3)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_29])]) ).
cnf(c_0_33,negated_conjecture,
maps(esk3_0,esk6_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_34,plain,
( ~ member(esk8_3(X1,X2,X3),X8)
| ~ member(esk8_3(X1,X2,X3),X6)
| ~ member(esk7_4(compose_function(X1,X4,X5,X2,X6),X7,X8,esk8_3(X1,X2,X3)),X5)
| ~ surjective(compose_function(X1,X4,X5,X2,X6),X7,X8)
| surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ~ surjective(X1,X2,X3)
| ~ member(X4,X3)
| member(esk7_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(X3,esk6_0)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ apply(esk2_0,X1,X3)
| ~ apply(esk2_0,X2,X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
( injective(X1,X2,X3)
| apply(X1,esk11_3(X1,X2,X3),esk12_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_38,plain,
! [X23,X24,X25] :
( ( one_to_one(X23,X24,X25)
| ~ surjective(X23,X24,X25)
| ~ injective(X23,X24,X25) )
& ( ~ one_to_one(X23,X24,X25)
| surjective(X23,X24,X25) )
& ( ~ one_to_one(X23,X24,X25)
| injective(X23,X24,X25) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_to_one])])])]) ).
cnf(c_0_39,plain,
( ~ member(esk8_3(X1,X2,X3),X7)
| ~ member(esk8_3(X1,X2,X3),X6)
| ~ surjective(compose_function(X1,X4,X5,X2,X6),X5,X7)
| surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
surjective(compose_function(esk2_0,compose_function(esk1_0,esk3_0,esk6_0,esk4_0,esk5_0),esk6_0,esk5_0,esk6_0),esk6_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_41,negated_conjecture,
( ~ member(X1,esk5_0)
| ~ member(esk12_3(esk2_0,X2,X3),esk6_0)
| ~ member(esk11_3(esk2_0,X2,X3),esk5_0)
| ~ apply(esk2_0,X1,esk12_3(esk2_0,X2,X3))
| injective(esk2_0,X2,X3)
| X1 = esk11_3(esk2_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( injective(X1,X2,X3)
| apply(X1,esk10_3(X1,X2,X3),esk12_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_43,plain,
( esk10_3(X1,X2,X3) != esk11_3(X1,X2,X3)
| injective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_44,negated_conjecture,
~ one_to_one(esk2_0,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_45,plain,
( ~ surjective(X1,X2,X3)
| ~ injective(X1,X2,X3)
| one_to_one(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,negated_conjecture,
( ~ member(esk8_3(esk2_0,esk5_0,X1),esk6_0)
| surjective(esk2_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
( surjective(X1,X2,X3)
| member(esk8_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_48,negated_conjecture,
( ~ member(esk10_3(esk2_0,X1,X2),esk5_0)
| ~ member(esk12_3(esk2_0,X1,X2),esk6_0)
| ~ member(esk11_3(esk2_0,X1,X2),esk5_0)
| injective(esk2_0,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_49,plain,
( injective(X1,X2,X3)
| member(esk12_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_50,negated_conjecture,
( ~ injective(esk2_0,esk5_0,esk6_0)
| ~ surjective(esk2_0,esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
surjective(esk2_0,esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( ~ member(esk10_3(esk2_0,X1,esk6_0),esk5_0)
| ~ member(esk11_3(esk2_0,X1,esk6_0),esk5_0)
| injective(esk2_0,X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( injective(X1,X2,X3)
| member(esk11_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_54,negated_conjecture,
~ injective(esk2_0,esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).
cnf(c_0_55,negated_conjecture,
~ member(esk10_3(esk2_0,esk5_0,esk6_0),esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_56,plain,
( injective(X1,X2,X3)
| member(esk10_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET737+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:35:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.71/1.04 % Version: 3.5.1
% 3.71/1.04 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.71/1.04 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.71/1.04 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.71/1.04 % Starting new_bool_3 with 300s (1) cores
% 3.71/1.04 % Starting new_bool_1 with 300s (1) cores
% 3.71/1.04 % Starting sh5l with 300s (1) cores
% 3.71/1.04 % new_bool_3 with pid 246277 completed with status 0
% 3.71/1.04 % Result found by new_bool_3
% 3.71/1.04 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.71/1.04 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.71/1.04 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.71/1.04 % Starting new_bool_3 with 300s (1) cores
% 3.71/1.04 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.71/1.04 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.71/1.04 % Search class: FGUSF-FFMM33-SFFFFFNN
% 3.71/1.04 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 3.71/1.04 % Starting SubtermCWHack with 31s (1) cores
% 3.71/1.04 % SubtermCWHack with pid 246280 completed with status 0
% 3.71/1.04 % Result found by SubtermCWHack
% 3.71/1.04 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.71/1.04 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.71/1.04 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.71/1.04 % Starting new_bool_3 with 300s (1) cores
% 3.71/1.04 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 3.71/1.04 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.71/1.04 % Search class: FGUSF-FFMM33-SFFFFFNN
% 3.71/1.04 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 3.71/1.04 % Starting SubtermCWHack with 31s (1) cores
% 3.71/1.04 % Preprocessing time : 0.002 s
% 3.71/1.04
% 3.71/1.04 % Proof found!
% 3.71/1.04 % SZS status Theorem
% 3.71/1.04 % SZS output start CNFRefutation
% See solution above
% 3.71/1.04 % Parsed axioms : 29
% 3.71/1.04 % Removed by relevancy pruning/SinE : 23
% 3.71/1.04 % Initial clauses : 40
% 3.71/1.04 % Removed in clause preprocessing : 0
% 3.71/1.04 % Initial clauses in saturation : 40
% 3.71/1.04 % Processed clauses : 1102
% 3.71/1.04 % ...of these trivial : 0
% 3.71/1.04 % ...subsumed : 513
% 3.71/1.04 % ...remaining for further processing : 589
% 3.71/1.04 % Other redundant clauses eliminated : 0
% 3.71/1.04 % Clauses deleted for lack of memory : 0
% 3.71/1.04 % Backward-subsumed : 38
% 3.71/1.04 % Backward-rewritten : 1
% 3.71/1.04 % Generated clauses : 7765
% 3.71/1.04 % ...of the previous two non-redundant : 7740
% 3.71/1.04 % ...aggressively subsumed : 0
% 3.71/1.04 % Contextual simplify-reflections : 3
% 3.71/1.04 % Paramodulations : 7765
% 3.71/1.04 % Factorizations : 0
% 3.71/1.04 % NegExts : 0
% 3.71/1.04 % Equation resolutions : 0
% 3.71/1.04 % Disequality decompositions : 0
% 3.71/1.04 % Total rewrite steps : 2
% 3.71/1.04 % ...of those cached : 0
% 3.71/1.04 % Propositional unsat checks : 0
% 3.71/1.04 % Propositional check models : 0
% 3.71/1.04 % Propositional check unsatisfiable : 0
% 3.71/1.04 % Propositional clauses : 0
% 3.71/1.04 % Propositional clauses after purity: 0
% 3.71/1.04 % Propositional unsat core size : 0
% 3.71/1.04 % Propositional preprocessing time : 0.000
% 3.71/1.04 % Propositional encoding time : 0.000
% 3.71/1.04 % Propositional solver time : 0.000
% 3.71/1.04 % Success case prop preproc time : 0.000
% 3.71/1.04 % Success case prop encoding time : 0.000
% 3.71/1.04 % Success case prop solver time : 0.000
% 3.71/1.04 % Current number of processed clauses : 550
% 3.71/1.04 % Positive orientable unit clauses : 7
% 3.71/1.04 % Positive unorientable unit clauses: 0
% 3.71/1.04 % Negative unit clauses : 3
% 3.71/1.04 % Non-unit-clauses : 540
% 3.71/1.04 % Current number of unprocessed clauses: 6642
% 3.71/1.04 % ...number of literals in the above : 95642
% 3.71/1.04 % Current number of archived formulas : 0
% 3.71/1.04 % Current number of archived clauses : 39
% 3.71/1.04 % Clause-clause subsumption calls (NU) : 162890
% 3.71/1.04 % Rec. Clause-clause subsumption calls : 4288
% 3.71/1.04 % Non-unit clause-clause subsumptions : 554
% 3.71/1.04 % Unit Clause-clause subsumption calls : 543
% 3.71/1.04 % Rewrite failures with RHS unbound : 0
% 3.71/1.04 % BW rewrite match attempts : 2
% 3.71/1.04 % BW rewrite match successes : 1
% 3.71/1.04 % Condensation attempts : 0
% 3.71/1.04 % Condensation successes : 0
% 3.71/1.04 % Termbank termtop insertions : 468244
% 3.71/1.04 % Search garbage collected termcells : 1090
% 3.71/1.04
% 3.71/1.04 % -------------------------------------------------
% 3.71/1.04 % User time : 0.575 s
% 3.71/1.04 % System time : 0.015 s
% 3.71/1.04 % Total time : 0.590 s
% 3.71/1.04 % Maximum resident set size: 3696 pages
% 3.71/1.04
% 3.71/1.04 % -------------------------------------------------
% 3.71/1.04 % User time : 0.577 s
% 3.71/1.04 % System time : 0.018 s
% 3.71/1.04 % Total time : 0.595 s
% 3.71/1.04 % Maximum resident set size: 4608 pages
% 3.71/1.04 % E exiting
%------------------------------------------------------------------------------