%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET715+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 02:18:01 PM UTC 2026
% Result : Theorem 1.44s 0.65s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 82 ( 7 unt; 0 def)
% Number of atoms : 485 ( 23 equ)
% Maximal formula atoms : 55 ( 5 avg)
% Number of connectives : 717 ( 314 ~; 336 |; 49 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-7 aty)
% Number of variables : 377 ( 6 sgn 90 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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/sandbox/benchmark/Axioms/SET006+1.ax',inverse_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/sandbox/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/sandbox/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(thII06,conjecture,
! [X6,X1,X2] :
( ( one_to_one(X6,X1,X2)
& maps(X6,X1,X2) )
=> identity(compose_function(X6,inverse_function(X6,X1,X2),X2,X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII06) ).
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/sandbox/benchmark/Axioms/SET006+1.ax',one_to_one) ).
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/sandbox/benchmark/Axioms/SET006+1.ax',injective) ).
fof(identity,axiom,
! [X6,X1] :
( identity(X6,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X6,X3,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',identity) ).
fof(c_0_8,plain,
! [X26,X27,X28,X29,X30,X31,X32,X34] :
( ( ~ member(X32,X30)
| ~ member(X31,X28)
| apply(compose_function(X26,X27,X28,X29,X30),X31,X32)
| ~ apply(X26,X34,X32)
| ~ apply(X27,X31,X34)
| ~ member(X34,X29) )
& ( ~ member(X32,X30)
| ~ member(X31,X28)
| ~ apply(compose_function(X26,X27,X28,X29,X30),X31,X32)
| apply(X26,esk5_7(X26,X27,X28,X29,X30,X31,X32),X32) )
& ( ~ member(X32,X30)
| ~ member(X31,X28)
| ~ apply(compose_function(X26,X27,X28,X29,X30),X31,X32)
| apply(X27,X31,esk5_7(X26,X27,X28,X29,X30,X31,X32)) )
& ( ~ member(X32,X30)
| ~ member(X31,X28)
| ~ apply(compose_function(X26,X27,X28,X29,X30),X31,X32)
| member(esk5_7(X26,X27,X28,X29,X30,X31,X32),X29) ) ),
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,
! [X35,X36,X37,X38,X39] :
( ( ~ member(X39,X37)
| ~ member(X38,X36)
| apply(X35,X38,X39)
| ~ apply(inverse_function(X35,X36,X37),X39,X38) )
& ( ~ member(X39,X37)
| ~ member(X38,X36)
| apply(inverse_function(X35,X36,X37),X39,X38)
| ~ apply(X35,X38,X39) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inverse_function])])])]) ).
cnf(c_0_10,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_11,plain,
( ~ member(X3,X5)
| ~ member(X2,X4)
| ~ apply(X1,X2,X3)
| apply(inverse_function(X1,X4,X5),X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X43,X44,X45,X46,X48,X49,X50,X51,X52,X53,X55] :
( ( maps(X51,X52,X53)
| ~ apply(X51,esk7_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| esk9_3(X51,X52,X53) != esk10_3(X51,X52,X53) )
& ( maps(X51,X52,X53)
| ~ apply(X51,esk7_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| apply(X51,esk8_3(X51,X52,X53),esk10_3(X51,X52,X53)) )
& ( maps(X51,X52,X53)
| ~ apply(X51,esk7_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| apply(X51,esk8_3(X51,X52,X53),esk9_3(X51,X52,X53)) )
& ( maps(X51,X52,X53)
| ~ apply(X51,esk7_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| member(esk10_3(X51,X52,X53),X53) )
& ( maps(X51,X52,X53)
| ~ apply(X51,esk7_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| member(esk9_3(X51,X52,X53),X53) )
& ( maps(X51,X52,X53)
| ~ apply(X51,esk7_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| member(esk8_3(X51,X52,X53),X52) )
& ( maps(X51,X52,X53)
| member(esk7_3(X51,X52,X53),X52)
| esk9_3(X51,X52,X53) != esk10_3(X51,X52,X53) )
& ( maps(X51,X52,X53)
| member(esk7_3(X51,X52,X53),X52)
| apply(X51,esk8_3(X51,X52,X53),esk10_3(X51,X52,X53)) )
& ( maps(X51,X52,X53)
| member(esk7_3(X51,X52,X53),X52)
| apply(X51,esk8_3(X51,X52,X53),esk9_3(X51,X52,X53)) )
& ( maps(X51,X52,X53)
| member(esk7_3(X51,X52,X53),X52)
| member(esk10_3(X51,X52,X53),X53) )
& ( maps(X51,X52,X53)
| member(esk7_3(X51,X52,X53),X52)
| member(esk9_3(X51,X52,X53),X53) )
& ( maps(X51,X52,X53)
| member(esk7_3(X51,X52,X53),X52)
| member(esk8_3(X51,X52,X53),X52) )
& ( ~ maps(X43,X44,X45)
| X49 = X50
| ~ apply(X43,X48,X50)
| ~ apply(X43,X48,X49)
| ~ member(X50,X45)
| ~ member(X49,X45)
| ~ member(X48,X44) )
& ( ~ maps(X43,X44,X45)
| ~ member(X46,X44)
| apply(X43,X46,esk6_4(X43,X44,X45,X46)) )
& ( ~ maps(X43,X44,X45)
| ~ member(X46,X44)
| member(esk6_4(X43,X44,X45,X46),X45) ) ),
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_13,plain,
( ~ member(X9,X2)
| ~ member(X10,X3)
| ~ member(X10,X6)
| ~ member(X8,X5)
| ~ member(X9,X7)
| ~ apply(X1,X9,X10)
| ~ apply(X4,X8,X10)
| apply(compose_function(inverse_function(X1,X2,X3),X4,X5,X6,X7),X8,X9) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk6_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X59,X60,X61,X62,X64,X65,X66,X68] :
( ( surjective(X64,X65,X66)
| ~ apply(X64,X68,esk12_3(X64,X65,X66))
| ~ member(X68,X65) )
& ( surjective(X64,X65,X66)
| member(esk12_3(X64,X65,X66),X66) )
& ( ~ surjective(X59,X60,X61)
| ~ member(X62,X61)
| apply(X59,esk11_4(X59,X60,X61,X62),X62) )
& ( ~ surjective(X59,X60,X61)
| ~ member(X62,X61)
| member(esk11_4(X59,X60,X61,X62),X60) ) ),
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_16,plain,
( ~ member(X8,X10)
| ~ member(X9,X2)
| ~ member(X8,X5)
| ~ member(X9,X7)
| ~ member(esk6_4(X4,X10,X11,X8),X3)
| ~ member(esk6_4(X4,X10,X11,X8),X6)
| ~ maps(X4,X10,X11)
| ~ apply(X1,X9,esk6_4(X4,X10,X11,X8))
| apply(compose_function(inverse_function(X1,X2,X3),X4,X5,X6,X7),X8,X9) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,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_9]) ).
cnf(c_0_18,plain,
( ~ surjective(X1,X2,X3)
| ~ member(X4,X3)
| apply(X1,esk11_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ member(X7,X8)
| ~ member(X7,X2)
| ~ member(X7,X4)
| ~ member(X7,X6)
| ~ member(esk6_4(X1,X8,X9,X7),X3)
| ~ member(esk6_4(X1,X8,X9,X7),X5)
| ~ maps(X1,X8,X9)
| apply(compose_function(inverse_function(X1,X2,X3),X1,X4,X5,X6),X7,X7) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_20,plain,
( ~ maps(X1,X2,X3)
| ~ member(X4,X2)
| member(esk6_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_21,negated_conjecture,
~ ! [X6,X1,X2] :
( ( one_to_one(X6,X1,X2)
& maps(X6,X1,X2) )
=> identity(compose_function(X6,inverse_function(X6,X1,X2),X2,X1,X2),X2) ),
inference(assume_negation,[status(cth)],[thII06]) ).
cnf(c_0_22,plain,
( ~ member(X2,X6)
| ~ member(X2,X3)
| ~ member(esk11_4(inverse_function(X1,X3,X4),X5,X6,X2),X4)
| ~ surjective(inverse_function(X1,X3,X4),X5,X6)
| apply(X1,X2,esk11_4(inverse_function(X1,X3,X4),X5,X6,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( ~ surjective(X1,X2,X3)
| ~ member(X4,X3)
| member(esk11_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( ~ apply(X3,X1,esk12_3(X3,X2,X4))
| ~ member(X1,X2)
| surjective(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| apply(X1,esk5_7(X1,X2,X3,X4,X5,X6,X7),X7) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,plain,
( ~ member(X7,X8)
| ~ member(X7,X2)
| ~ member(X7,X4)
| ~ member(X7,X6)
| ~ member(esk6_4(X1,X8,X5,X7),X3)
| ~ maps(X1,X8,X5)
| apply(compose_function(inverse_function(X1,X2,X3),X1,X4,X5,X6),X7,X7) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_27,negated_conjecture,
( ~ identity(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),esk3_0,esk2_0,esk3_0),esk3_0)
& one_to_one(esk1_0,esk2_0,esk3_0)
& maps(esk1_0,esk2_0,esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_28,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_12]) ).
cnf(c_0_29,plain,
( ~ member(X2,X5)
| ~ member(X2,X3)
| ~ surjective(inverse_function(X1,X3,X4),X4,X5)
| apply(X1,X2,esk11_4(inverse_function(X1,X3,X4),X4,X5,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( ~ member(X8,X5)
| ~ member(esk12_3(X1,X2,X3),X7)
| ~ member(esk5_7(X1,X4,X5,X6,X7,X8,esk12_3(X1,X2,X3)),X2)
| ~ apply(compose_function(X1,X4,X5,X6,X7),X8,esk12_3(X1,X2,X3))
| surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| member(esk5_7(X1,X2,X3,X4,X5,X6,X7),X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,plain,
( ~ member(X6,X7)
| ~ member(X6,X2)
| ~ member(X6,X4)
| ~ member(X6,X5)
| ~ maps(X1,X7,X3)
| apply(compose_function(inverse_function(X1,X2,X3),X1,X4,X3,X5),X6,X6) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_33,negated_conjecture,
maps(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( ~ member(X6,X5)
| ~ member(X6,X3)
| ~ member(X6,X7)
| ~ member(X1,X8)
| ~ member(esk11_4(inverse_function(X2,X3,X4),X4,X5,X6),X8)
| ~ maps(X2,X7,X8)
| ~ apply(X2,X6,X1)
| ~ surjective(inverse_function(X2,X3,X4),X4,X5)
| X1 = esk11_4(inverse_function(X2,X3,X4),X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( ~ member(X7,X5)
| ~ member(esk12_3(X1,X2,X3),X6)
| ~ apply(compose_function(X1,X4,X5,X2,X6),X7,esk12_3(X1,X2,X3))
| surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(X4,X1)
| ~ member(X4,X2)
| ~ member(X4,X3)
| ~ member(X4,esk2_0)
| apply(compose_function(inverse_function(esk1_0,X1,esk3_0),esk1_0,X2,esk3_0,X3),X4,X4) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
( ~ member(X6,X5)
| ~ member(X6,X3)
| ~ member(X6,X7)
| ~ member(X1,X4)
| ~ maps(X2,X7,X4)
| ~ apply(X2,X6,X1)
| ~ surjective(inverse_function(X2,X3,X4),X4,X5)
| X1 = esk11_4(inverse_function(X2,X3,X4),X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_34,c_0_23]) ).
cnf(c_0_38,negated_conjecture,
( ~ member(esk12_3(inverse_function(esk1_0,X1,esk3_0),esk3_0,X2),X1)
| ~ member(esk12_3(inverse_function(esk1_0,X1,esk3_0),esk3_0,X2),X4)
| ~ member(esk12_3(inverse_function(esk1_0,X1,esk3_0),esk3_0,X2),X3)
| ~ member(esk12_3(inverse_function(esk1_0,X1,esk3_0),esk3_0,X2),esk2_0)
| surjective(inverse_function(esk1_0,X1,esk3_0),esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( surjective(X1,X2,X3)
| member(esk12_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_40,plain,
! [X40,X41,X42] :
( ( one_to_one(X40,X41,X42)
| ~ surjective(X40,X41,X42)
| ~ injective(X40,X41,X42) )
& ( ~ one_to_one(X40,X41,X42)
| surjective(X40,X41,X42) )
& ( ~ one_to_one(X40,X41,X42)
| injective(X40,X41,X42) ) ),
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_41,plain,
( ~ member(X4,X2)
| ~ member(X4,X7)
| ~ member(X4,X5)
| ~ member(X4,X8)
| ~ member(esk6_4(X1,X2,X3,X4),X6)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X8,X6)
| ~ surjective(inverse_function(X1,X5,X6),X6,X7)
| esk6_4(X1,X2,X3,X4) = esk11_4(inverse_function(X1,X5,X6),X6,X7,X4) ),
inference(spm,[status(thm)],[c_0_37,c_0_14]) ).
cnf(c_0_42,negated_conjecture,
( ~ member(esk12_3(inverse_function(esk1_0,X1,esk3_0),esk3_0,esk2_0),X1)
| ~ member(esk12_3(inverse_function(esk1_0,X1,esk3_0),esk3_0,esk2_0),X3)
| ~ member(esk12_3(inverse_function(esk1_0,X1,esk3_0),esk3_0,esk2_0),X2)
| surjective(inverse_function(esk1_0,X1,esk3_0),esk3_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_43,plain,
! [X69,X70,X71,X72,X73,X74,X75,X76,X77] :
( ( injective(X75,X76,X77)
| esk13_3(X75,X76,X77) != esk14_3(X75,X76,X77) )
& ( injective(X75,X76,X77)
| apply(X75,esk14_3(X75,X76,X77),esk15_3(X75,X76,X77)) )
& ( injective(X75,X76,X77)
| apply(X75,esk13_3(X75,X76,X77),esk15_3(X75,X76,X77)) )
& ( injective(X75,X76,X77)
| member(esk15_3(X75,X76,X77),X77) )
& ( injective(X75,X76,X77)
| member(esk14_3(X75,X76,X77),X76) )
& ( injective(X75,X76,X77)
| member(esk13_3(X75,X76,X77),X76) )
& ( X72 = X73
| ~ apply(X69,X73,X74)
| ~ apply(X69,X72,X74)
| ~ member(X74,X71)
| ~ member(X73,X70)
| ~ member(X72,X70)
| ~ injective(X69,X70,X71) ) ),
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])])])])])])]) ).
cnf(c_0_44,plain,
( ~ one_to_one(X1,X2,X3)
| injective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,negated_conjecture,
one_to_one(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_46,plain,
( ~ member(X4,X2)
| ~ member(X4,X6)
| ~ member(X4,X5)
| ~ member(X4,X7)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X7,X3)
| ~ surjective(inverse_function(X1,X5,X3),X3,X6)
| esk6_4(X1,X2,X3,X4) = esk11_4(inverse_function(X1,X5,X3),X3,X6,X4) ),
inference(spm,[status(thm)],[c_0_41,c_0_20]) ).
cnf(c_0_47,negated_conjecture,
( ~ member(esk12_3(inverse_function(esk1_0,X1,esk3_0),esk3_0,esk2_0),X1)
| ~ member(esk12_3(inverse_function(esk1_0,X1,esk3_0),esk3_0,esk2_0),X2)
| surjective(inverse_function(esk1_0,X1,esk3_0),esk3_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_48,plain,
( ~ member(X5,X3)
| ~ member(X5,X6)
| ~ member(X1,X7)
| ~ member(esk6_4(X2,X3,X4,X5),X7)
| ~ maps(X2,X3,X4)
| ~ maps(X2,X6,X7)
| ~ apply(X2,X5,X1)
| X1 = esk6_4(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_28,c_0_14]) ).
cnf(c_0_49,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_43]) ).
cnf(c_0_50,negated_conjecture,
injective(esk1_0,esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,X4)
| ~ member(X2,X3)
| ~ member(X2,esk2_0)
| ~ maps(esk1_0,X1,esk3_0)
| ~ surjective(inverse_function(esk1_0,X3,esk3_0),esk3_0,X4)
| esk6_4(esk1_0,X1,esk3_0,X2) = esk11_4(inverse_function(esk1_0,X3,esk3_0),esk3_0,X4,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_33]) ).
cnf(c_0_52,negated_conjecture,
( ~ member(esk12_3(inverse_function(esk1_0,X1,esk3_0),esk3_0,esk2_0),X1)
| surjective(inverse_function(esk1_0,X1,esk3_0),esk3_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_39]) ).
cnf(c_0_53,plain,
( ~ member(X5,X3)
| ~ member(X5,X6)
| ~ member(X1,X4)
| ~ maps(X2,X3,X4)
| ~ maps(X2,X6,X4)
| ~ apply(X2,X5,X1)
| X1 = esk6_4(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_48,c_0_20]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(X1,esk2_0)
| ~ member(X2,esk2_0)
| ~ member(X3,esk3_0)
| ~ apply(esk1_0,X1,X3)
| ~ apply(esk1_0,X2,X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X1)
| ~ member(X3,X4)
| ~ member(X3,esk2_0)
| ~ maps(esk1_0,X2,esk3_0)
| ~ surjective(inverse_function(esk1_0,X1,esk3_0),esk3_0,X4)
| apply(inverse_function(esk1_0,X1,esk3_0),esk6_4(esk1_0,X2,esk3_0,X3),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
surjective(inverse_function(esk1_0,esk2_0,esk3_0),esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_52,c_0_39]) ).
cnf(c_0_57,plain,
( ~ member(X6,X5)
| ~ member(X6,X3)
| ~ member(esk11_4(X1,X4,X5,X6),X2)
| ~ member(esk11_4(X1,X4,X5,X6),X7)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X7,X3)
| ~ surjective(X1,X4,X5)
| esk6_4(X1,X2,X3,esk11_4(X1,X4,X5,X6)) = X6 ),
inference(spm,[status(thm)],[c_0_53,c_0_18]) ).
cnf(c_0_58,negated_conjecture,
( ~ member(X4,X3)
| ~ member(X1,esk2_0)
| ~ member(X4,esk3_0)
| ~ member(esk11_4(esk1_0,X2,X3,X4),esk2_0)
| ~ apply(esk1_0,X1,X4)
| ~ surjective(esk1_0,X2,X3)
| X1 = esk11_4(esk1_0,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_54,c_0_18]) ).
cnf(c_0_59,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,esk2_0)
| ~ maps(esk1_0,X1,esk3_0)
| apply(inverse_function(esk1_0,esk2_0,esk3_0),esk6_4(esk1_0,X1,esk3_0,X2),X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
( ~ member(X6,X5)
| ~ member(X6,X3)
| ~ member(esk11_4(X1,X4,X5,X6),X2)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X4,X3)
| ~ surjective(X1,X4,X5)
| esk6_4(X1,X2,X3,esk11_4(X1,X4,X5,X6)) = X6 ),
inference(spm,[status(thm)],[c_0_57,c_0_23]) ).
cnf(c_0_61,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X1,esk2_0)
| ~ member(X3,esk3_0)
| ~ apply(esk1_0,X1,X3)
| ~ surjective(esk1_0,esk2_0,X2)
| X1 = esk11_4(esk1_0,esk2_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_58,c_0_23]) ).
cnf(c_0_62,negated_conjecture,
( ~ member(X1,X3)
| ~ member(X1,esk3_0)
| ~ member(esk11_4(esk1_0,X2,X3,X1),X4)
| ~ member(esk11_4(esk1_0,X2,X3,X1),esk2_0)
| ~ maps(esk1_0,X2,esk3_0)
| ~ maps(esk1_0,X4,esk3_0)
| ~ surjective(esk1_0,X2,X3)
| apply(inverse_function(esk1_0,esk2_0,esk3_0),X1,esk11_4(esk1_0,X2,X3,X1)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X4)
| ~ member(X3,esk3_0)
| ~ member(esk11_4(esk1_0,X1,X2,X3),esk2_0)
| ~ surjective(esk1_0,X1,X2)
| ~ surjective(esk1_0,esk2_0,X4)
| esk11_4(esk1_0,X1,X2,X3) = esk11_4(esk1_0,esk2_0,X4,X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_18]) ).
cnf(c_0_64,negated_conjecture,
( ~ member(X1,X3)
| ~ member(X1,esk3_0)
| ~ member(esk11_4(esk1_0,X2,X3,X1),esk2_0)
| ~ maps(esk1_0,X2,esk3_0)
| ~ surjective(esk1_0,X2,X3)
| apply(inverse_function(esk1_0,esk2_0,esk3_0),X1,esk11_4(esk1_0,X2,X3,X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_23]) ).
cnf(c_0_65,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,X3)
| ~ member(X2,esk3_0)
| ~ surjective(esk1_0,esk2_0,X1)
| ~ surjective(esk1_0,esk2_0,X3)
| esk11_4(esk1_0,esk2_0,X1,X2) = esk11_4(esk1_0,esk2_0,X3,X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_23]) ).
cnf(c_0_66,plain,
( ~ one_to_one(X1,X2,X3)
| surjective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_67,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ member(X1,esk3_0)
| ~ surjective(esk1_0,esk2_0,X2)
| ~ surjective(esk1_0,esk2_0,X3)
| apply(inverse_function(esk1_0,esk2_0,esk3_0),X1,esk11_4(esk1_0,esk2_0,X2,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_33])]),c_0_23]) ).
cnf(c_0_68,negated_conjecture,
surjective(esk1_0,esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_66,c_0_45]) ).
cnf(c_0_69,plain,
( ~ member(X7,X9)
| ~ member(X6,X3)
| ~ member(X7,X5)
| ~ member(esk11_4(X1,X8,X9,X7),X4)
| ~ apply(X2,X6,esk11_4(X1,X8,X9,X7))
| ~ surjective(X1,X8,X9)
| apply(compose_function(X1,X2,X3,X4,X5),X6,X7) ),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_70,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,esk3_0)
| ~ surjective(esk1_0,esk2_0,X2)
| apply(inverse_function(esk1_0,esk2_0,esk3_0),X1,esk11_4(esk1_0,esk2_0,X2,X1)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( ~ member(X4,X5)
| ~ member(X4,X1)
| ~ member(X4,X3)
| ~ member(X4,esk3_0)
| ~ member(esk11_4(esk1_0,esk2_0,X5,X4),X2)
| ~ surjective(esk1_0,esk2_0,X5)
| apply(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,X2,X3),X4,X4) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
fof(c_0_72,plain,
! [X20,X21,X22,X23,X24] :
( ( identity(X23,X24)
| ~ apply(X23,esk4_2(X23,X24),esk4_2(X23,X24)) )
& ( identity(X23,X24)
| member(esk4_2(X23,X24),X24) )
& ( apply(X20,X22,X22)
| ~ member(X22,X21)
| ~ identity(X20,X21) ) ),
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_73,negated_conjecture,
( ~ member(X3,X4)
| ~ member(X3,X1)
| ~ member(X3,X2)
| ~ member(X3,esk3_0)
| ~ surjective(esk1_0,esk2_0,X4)
| apply(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,X2),X3,X3) ),
inference(spm,[status(thm)],[c_0_71,c_0_23]) ).
cnf(c_0_74,plain,
( ~ apply(X1,esk4_2(X1,X2),esk4_2(X1,X2))
| identity(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( ~ member(X3,X1)
| ~ member(X3,X2)
| ~ member(X3,esk3_0)
| apply(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,X2),X3,X3) ),
inference(spm,[status(thm)],[c_0_73,c_0_68]) ).
cnf(c_0_76,negated_conjecture,
( ~ member(esk4_2(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,X2),X3),X1)
| ~ member(esk4_2(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,X2),X3),X2)
| ~ member(esk4_2(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,X2),X3),esk3_0)
| identity(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,X2),X3) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_77,plain,
( identity(X1,X2)
| member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( ~ member(esk4_2(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,X2),esk3_0),X1)
| ~ member(esk4_2(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,X2),esk3_0),X2)
| identity(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,X2),esk3_0) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_79,negated_conjecture,
( ~ member(esk4_2(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,esk3_0),esk3_0),X1)
| identity(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),X1,esk2_0,esk3_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_78,c_0_77]) ).
cnf(c_0_80,negated_conjecture,
~ identity(compose_function(esk1_0,inverse_function(esk1_0,esk2_0,esk3_0),esk3_0,esk2_0,esk3_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_77]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET715+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 05:36:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 1.44/0.65 % Version: 3.5.1
% 1.44/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.44/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.44/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.44/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.44/0.65 % Starting sh5l with 300s (1) cores
% 1.44/0.65 % new_bool_1 with pid 1472925 completed with status 0
% 1.44/0.65 % Result found by new_bool_1
% 1.44/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.44/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.44/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.44/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.44/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.44/0.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.44/0.65 % Search class: FGUSF-FFMF33-SFFFFFNN
% 1.44/0.65 % partial match(1): FGUSM-FFMF33-SFFFFFNN
% 1.44/0.65 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.44/0.65 % Starting SubtermCWHack with 28s (1) cores
% 1.44/0.65 % SubtermCWHack with pid 1472928 completed with status 0
% 1.44/0.65 % Result found by SubtermCWHack
% 1.44/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.44/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.44/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.44/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.44/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.44/0.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.44/0.65 % Search class: FGUSF-FFMF33-SFFFFFNN
% 1.44/0.65 % partial match(1): FGUSM-FFMF33-SFFFFFNN
% 1.44/0.65 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.44/0.65 % Starting SubtermCWHack with 28s (1) cores
% 1.44/0.65 % Preprocessing time : 0.001 s
% 1.44/0.65
% 1.44/0.65 % Proof found!
% 1.44/0.65 % SZS status Theorem
% 1.44/0.65 % SZS output start CNFRefutation
% See solution above
% 1.44/0.65 % Parsed axioms : 29
% 1.44/0.65 % Removed by relevancy pruning/SinE : 21
% 1.44/0.65 % Initial clauses : 41
% 1.44/0.65 % Removed in clause preprocessing : 0
% 1.44/0.65 % Initial clauses in saturation : 41
% 1.44/0.65 % Processed clauses : 904
% 1.44/0.65 % ...of these trivial : 0
% 1.44/0.65 % ...subsumed : 407
% 1.44/0.65 % ...remaining for further processing : 497
% 1.44/0.65 % Other redundant clauses eliminated : 0
% 1.44/0.65 % Clauses deleted for lack of memory : 0
% 1.44/0.65 % Backward-subsumed : 50
% 1.44/0.65 % Backward-rewritten : 0
% 1.44/0.65 % Generated clauses : 5291
% 1.44/0.65 % ...of the previous two non-redundant : 5218
% 1.44/0.65 % ...aggressively subsumed : 0
% 1.44/0.65 % Contextual simplify-reflections : 11
% 1.44/0.65 % Paramodulations : 5291
% 1.44/0.65 % Factorizations : 0
% 1.44/0.65 % NegExts : 0
% 1.44/0.65 % Equation resolutions : 0
% 1.44/0.65 % Disequality decompositions : 0
% 1.44/0.65 % Total rewrite steps : 53
% 1.44/0.65 % ...of those cached : 48
% 1.44/0.65 % Propositional unsat checks : 0
% 1.44/0.65 % Propositional check models : 0
% 1.44/0.65 % Propositional check unsatisfiable : 0
% 1.44/0.65 % Propositional clauses : 0
% 1.44/0.65 % Propositional clauses after purity: 0
% 1.44/0.65 % Propositional unsat core size : 0
% 1.44/0.65 % Propositional preprocessing time : 0.000
% 1.44/0.65 % Propositional encoding time : 0.000
% 1.44/0.65 % Propositional solver time : 0.000
% 1.44/0.65 % Success case prop preproc time : 0.000
% 1.44/0.65 % Success case prop encoding time : 0.000
% 1.44/0.65 % Success case prop solver time : 0.000
% 1.44/0.65 % Current number of processed clauses : 447
% 1.44/0.65 % Positive orientable unit clauses : 7
% 1.44/0.65 % Positive unorientable unit clauses: 0
% 1.44/0.65 % Negative unit clauses : 1
% 1.44/0.65 % Non-unit-clauses : 439
% 1.44/0.65 % Current number of unprocessed clauses: 4338
% 1.44/0.65 % ...number of literals in the above : 49658
% 1.44/0.65 % Current number of archived formulas : 0
% 1.44/0.65 % Current number of archived clauses : 50
% 1.44/0.65 % Clause-clause subsumption calls (NU) : 62884
% 1.44/0.65 % Rec. Clause-clause subsumption calls : 2405
% 1.44/0.65 % Non-unit clause-clause subsumptions : 468
% 1.44/0.65 % Unit Clause-clause subsumption calls : 24
% 1.44/0.65 % Rewrite failures with RHS unbound : 0
% 1.44/0.65 % BW rewrite match attempts : 2
% 1.44/0.65 % BW rewrite match successes : 0
% 1.44/0.65 % Condensation attempts : 0
% 1.44/0.65 % Condensation successes : 0
% 1.44/0.65 % Termbank termtop insertions : 279472
% 1.44/0.65 % Search garbage collected termcells : 1126
% 1.44/0.65
% 1.44/0.65 % -------------------------------------------------
% 1.44/0.65 % User time : 0.189 s
% 1.44/0.65 % System time : 0.010 s
% 1.44/0.65 % Total time : 0.199 s
% 1.44/0.65 % Maximum resident set size: 3948 pages
% 1.44/0.65
% 1.44/0.65 % -------------------------------------------------
% 1.44/0.65 % User time : 0.192 s
% 1.44/0.65 % System time : 0.013 s
% 1.44/0.65 % Total time : 0.206 s
% 1.44/0.65 % Maximum resident set size: 4864 pages
% 1.44/0.65 % E exiting
%------------------------------------------------------------------------------