%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET728+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 : n001.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 6.16s 1.64s
% Output : CNFRefutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 67 ( 8 unt; 0 def)
% Number of atoms : 407 ( 29 equ)
% Maximal formula atoms : 55 ( 6 avg)
% Number of connectives : 587 ( 247 ~; 278 |; 49 &)
% ( 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 : 16 ( 16 usr; 5 con; 0-7 aty)
% Number of variables : 291 ( 0 sgn 69 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(thII19,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(X10,X9,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII19) ).
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(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(c_0_5,plain,
! [X51,X52,X53,X54,X56,X57,X58,X59,X60,X61,X63] :
( ( maps(X59,X60,X61)
| ~ apply(X59,esk12_3(X59,X60,X61),X63)
| ~ member(X63,X61)
| esk14_3(X59,X60,X61) != esk15_3(X59,X60,X61) )
& ( maps(X59,X60,X61)
| ~ apply(X59,esk12_3(X59,X60,X61),X63)
| ~ member(X63,X61)
| apply(X59,esk13_3(X59,X60,X61),esk15_3(X59,X60,X61)) )
& ( maps(X59,X60,X61)
| ~ apply(X59,esk12_3(X59,X60,X61),X63)
| ~ member(X63,X61)
| apply(X59,esk13_3(X59,X60,X61),esk14_3(X59,X60,X61)) )
& ( maps(X59,X60,X61)
| ~ apply(X59,esk12_3(X59,X60,X61),X63)
| ~ member(X63,X61)
| member(esk15_3(X59,X60,X61),X61) )
& ( maps(X59,X60,X61)
| ~ apply(X59,esk12_3(X59,X60,X61),X63)
| ~ member(X63,X61)
| member(esk14_3(X59,X60,X61),X61) )
& ( maps(X59,X60,X61)
| ~ apply(X59,esk12_3(X59,X60,X61),X63)
| ~ member(X63,X61)
| member(esk13_3(X59,X60,X61),X60) )
& ( maps(X59,X60,X61)
| member(esk12_3(X59,X60,X61),X60)
| esk14_3(X59,X60,X61) != esk15_3(X59,X60,X61) )
& ( maps(X59,X60,X61)
| member(esk12_3(X59,X60,X61),X60)
| apply(X59,esk13_3(X59,X60,X61),esk15_3(X59,X60,X61)) )
& ( maps(X59,X60,X61)
| member(esk12_3(X59,X60,X61),X60)
| apply(X59,esk13_3(X59,X60,X61),esk14_3(X59,X60,X61)) )
& ( maps(X59,X60,X61)
| member(esk12_3(X59,X60,X61),X60)
| member(esk15_3(X59,X60,X61),X61) )
& ( maps(X59,X60,X61)
| member(esk12_3(X59,X60,X61),X60)
| member(esk14_3(X59,X60,X61),X61) )
& ( maps(X59,X60,X61)
| member(esk12_3(X59,X60,X61),X60)
| member(esk13_3(X59,X60,X61),X60) )
& ( ~ maps(X51,X52,X53)
| X57 = X58
| ~ apply(X51,X56,X58)
| ~ apply(X51,X56,X57)
| ~ member(X58,X53)
| ~ member(X57,X53)
| ~ member(X56,X52) )
& ( ~ maps(X51,X52,X53)
| ~ member(X54,X52)
| apply(X51,X54,esk11_4(X51,X52,X53,X54)) )
& ( ~ maps(X51,X52,X53)
| ~ member(X54,X52)
| member(esk11_4(X51,X52,X53,X54),X53) ) ),
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_6,plain,
! [X42,X43,X44,X45,X46,X47,X48,X50] :
( ( ~ member(X48,X46)
| ~ member(X47,X44)
| apply(compose_function(X42,X43,X44,X45,X46),X47,X48)
| ~ apply(X42,X50,X48)
| ~ apply(X43,X47,X50)
| ~ member(X50,X45) )
& ( ~ member(X48,X46)
| ~ member(X47,X44)
| ~ apply(compose_function(X42,X43,X44,X45,X46),X47,X48)
| apply(X42,esk10_7(X42,X43,X44,X45,X46,X47,X48),X48) )
& ( ~ member(X48,X46)
| ~ member(X47,X44)
| ~ apply(compose_function(X42,X43,X44,X45,X46),X47,X48)
| apply(X43,X47,esk10_7(X42,X43,X44,X45,X46,X47,X48)) )
& ( ~ member(X48,X46)
| ~ member(X47,X44)
| ~ apply(compose_function(X42,X43,X44,X45,X46),X47,X48)
| member(esk10_7(X42,X43,X44,X45,X46,X47,X48),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(fof_nnf,[status(thm)],[compose_function])])])])])]) ).
cnf(c_0_7,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_5]) ).
cnf(c_0_8,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_6]) ).
cnf(c_0_9,plain,
( ~ member(X7,X4)
| ~ member(X8,X6)
| ~ member(X7,X9)
| ~ member(X1,X10)
| ~ member(esk10_7(X2,X3,X4,X5,X6,X7,X8),X10)
| ~ maps(X3,X9,X10)
| ~ apply(X3,X7,X1)
| ~ apply(compose_function(X2,X3,X4,X5,X6),X7,X8)
| X1 = esk10_7(X2,X3,X4,X5,X6,X7,X8) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,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_6]) ).
cnf(c_0_11,plain,
( ~ member(X7,X4)
| ~ member(X8,X6)
| ~ member(X7,X9)
| ~ member(X1,X5)
| ~ maps(X3,X9,X5)
| ~ apply(X3,X7,X1)
| ~ apply(compose_function(X2,X3,X4,X5,X6),X7,X8)
| X1 = esk10_7(X2,X3,X4,X5,X6,X7,X8) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk11_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_13,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(X10,X9,X2,X1) ),
inference(assume_negation,[status(cth)],[thII19]) ).
cnf(c_0_14,plain,
( ~ member(X4,X2)
| ~ member(X4,X6)
| ~ member(X9,X8)
| ~ member(X4,X10)
| ~ member(esk11_4(X1,X2,X3,X4),X7)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X10,X7)
| ~ apply(compose_function(X5,X1,X6,X7,X8),X4,X9)
| esk11_4(X1,X2,X3,X4) = esk10_7(X5,X1,X6,X7,X8,X4,X9) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( ~ maps(X1,X2,X3)
| ~ member(X4,X2)
| member(esk11_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_16,negated_conjecture,
( ~ equal_maps(esk2_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_13])])])]) ).
cnf(c_0_17,plain,
( ~ member(X4,X2)
| ~ member(X4,X6)
| ~ member(X8,X7)
| ~ member(X4,X9)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X9,X3)
| ~ apply(compose_function(X5,X1,X6,X3,X7),X4,X8)
| esk11_4(X1,X2,X3,X4) = esk10_7(X5,X1,X6,X3,X7,X4,X8) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
maps(esk3_0,esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X36,X37,X38,X39,X40] :
( ( identity(X39,X40)
| ~ apply(X39,esk9_2(X39,X40),esk9_2(X39,X40)) )
& ( identity(X39,X40)
| member(esk9_2(X39,X40),X40) )
& ( apply(X36,X38,X38)
| ~ member(X38,X37)
| ~ identity(X36,X37) ) ),
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_20,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_6]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,X4)
| ~ member(X6,X5)
| ~ member(X2,esk5_0)
| ~ maps(esk3_0,X1,esk4_0)
| ~ apply(compose_function(X3,esk3_0,X4,esk4_0,X5),X2,X6)
| esk11_4(esk3_0,X1,esk4_0,X2) = esk10_7(X3,esk3_0,X4,esk4_0,X5,X2,X6) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ member(X3,X2)
| ~ identity(X1,X2)
| apply(X1,X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
identity(compose_function(esk1_0,esk3_0,esk5_0,esk4_0,esk5_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
maps(esk1_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( ~ member(X5,X3)
| ~ member(X5,X6)
| ~ member(X1,X7)
| ~ member(esk11_4(X2,X3,X4,X5),X7)
| ~ maps(X2,X3,X4)
| ~ maps(X2,X6,X7)
| ~ apply(X2,X5,X1)
| X1 = esk11_4(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_26,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X5)
| ~ member(X4,X6)
| ~ member(X3,esk5_0)
| ~ maps(esk3_0,X2,esk4_0)
| ~ apply(compose_function(X1,esk3_0,X5,esk4_0,X6),X3,X4)
| apply(X1,esk11_4(esk3_0,X2,esk4_0,X3),X4) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,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_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,X4)
| ~ member(X6,X5)
| ~ member(X2,esk4_0)
| ~ maps(esk1_0,X1,esk5_0)
| ~ apply(compose_function(X3,esk1_0,X4,esk5_0,X5),X2,X6)
| esk11_4(esk1_0,X1,esk5_0,X2) = esk10_7(X3,esk1_0,X4,esk5_0,X5,X2,X6) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
identity(compose_function(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_30,plain,
( ~ member(X5,X3)
| ~ member(X5,X6)
| ~ member(X1,X4)
| ~ maps(X2,X3,X4)
| ~ maps(X2,X6,X4)
| ~ apply(X2,X5,X1)
| X1 = esk11_4(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_31,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,esk5_0)
| ~ maps(esk3_0,X1,esk4_0)
| apply(esk1_0,esk11_4(esk3_0,X1,esk4_0,X2),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X5)
| ~ member(X4,X6)
| ~ member(X3,esk4_0)
| ~ maps(esk1_0,X2,esk5_0)
| ~ apply(compose_function(X1,esk1_0,X5,esk5_0,X6),X3,X4)
| apply(X1,esk11_4(esk1_0,X2,esk5_0,X3),X4) ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_33,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_22,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( ~ member(X4,X3)
| ~ member(X4,X2)
| ~ member(X4,esk5_0)
| ~ member(esk11_4(esk3_0,X3,esk4_0,X4),X1)
| ~ member(esk11_4(esk3_0,X3,esk4_0,X4),X5)
| ~ maps(esk1_0,X1,X2)
| ~ maps(esk1_0,X5,X2)
| ~ maps(esk3_0,X3,esk4_0)
| esk11_4(esk1_0,X1,X2,esk11_4(esk3_0,X3,esk4_0,X4)) = X4 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,esk4_0)
| ~ maps(esk1_0,X1,esk5_0)
| apply(esk2_0,esk11_4(esk1_0,X1,esk5_0,X2),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(X4,X3)
| ~ member(X4,X2)
| ~ member(X4,esk5_0)
| ~ member(esk11_4(esk3_0,X3,esk4_0,X4),X1)
| ~ maps(esk1_0,X1,X2)
| ~ maps(esk1_0,esk4_0,X2)
| ~ maps(esk3_0,X3,esk4_0)
| esk11_4(esk1_0,X1,X2,esk11_4(esk3_0,X3,esk4_0,X4)) = X4 ),
inference(spm,[status(thm)],[c_0_34,c_0_15]) ).
cnf(c_0_37,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,esk5_0)
| ~ member(esk11_4(esk3_0,X2,esk4_0,X1),X3)
| ~ maps(esk3_0,X2,esk4_0)
| ~ maps(esk1_0,X3,esk5_0)
| apply(esk2_0,X1,esk11_4(esk3_0,X2,esk4_0,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_24])]),c_0_15]) ).
cnf(c_0_38,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,esk5_0)
| ~ maps(esk3_0,X2,esk4_0)
| apply(esk2_0,X1,esk11_4(esk3_0,X2,esk4_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_15]),c_0_24])]) ).
cnf(c_0_39,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X4)
| ~ member(X1,X5)
| ~ member(X3,esk5_0)
| ~ member(esk11_4(esk3_0,X2,esk4_0,X3),X5)
| ~ maps(esk2_0,X4,X5)
| ~ maps(esk3_0,X2,esk4_0)
| ~ apply(esk2_0,X3,X1)
| X1 = esk11_4(esk3_0,X2,esk4_0,X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X4)
| ~ member(X1,esk4_0)
| ~ member(X3,esk5_0)
| ~ maps(esk2_0,X4,esk4_0)
| ~ maps(esk3_0,X2,esk4_0)
| ~ apply(esk2_0,X3,X1)
| X1 = esk11_4(esk3_0,X2,esk4_0,X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_15]) ).
cnf(c_0_41,negated_conjecture,
maps(esk2_0,esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_42,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])])])])])])]) ).
cnf(c_0_43,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X1,esk4_0)
| ~ member(X3,esk5_0)
| ~ maps(esk3_0,X2,esk4_0)
| ~ apply(esk2_0,X3,X1)
| X1 = esk11_4(esk3_0,X2,esk4_0,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,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_42]) ).
cnf(c_0_45,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_42]) ).
cnf(c_0_46,negated_conjecture,
( ~ member(esk6_4(esk2_0,X2,X3,X4),X1)
| ~ member(esk7_4(esk2_0,X2,X3,X4),esk4_0)
| ~ member(esk6_4(esk2_0,X2,X3,X4),esk5_0)
| ~ maps(esk3_0,X1,esk4_0)
| equal_maps(esk2_0,X2,X3,X4)
| esk11_4(esk3_0,X1,esk4_0,esk6_4(esk2_0,X2,X3,X4)) = esk7_4(esk2_0,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( ~ member(esk6_4(X2,esk2_0,X3,X4),X1)
| ~ member(esk8_4(X2,esk2_0,X3,X4),esk4_0)
| ~ member(esk6_4(X2,esk2_0,X3,X4),esk5_0)
| ~ maps(esk3_0,X1,esk4_0)
| equal_maps(X2,esk2_0,X3,X4)
| esk11_4(esk3_0,X1,esk4_0,esk6_4(X2,esk2_0,X3,X4)) = esk8_4(X2,esk2_0,X3,X4) ),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_48,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_42]) ).
cnf(c_0_49,negated_conjecture,
( ~ member(esk6_4(esk2_0,esk2_0,X1,X2),X3)
| ~ member(esk8_4(esk2_0,esk2_0,X1,X2),esk4_0)
| ~ member(esk7_4(esk2_0,esk2_0,X1,X2),esk4_0)
| ~ member(esk6_4(esk2_0,esk2_0,X1,X2),esk5_0)
| ~ maps(esk3_0,X3,esk4_0)
| equal_maps(esk2_0,esk2_0,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_50,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk8_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk7_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,negated_conjecture,
( ~ member(esk6_4(esk2_0,esk2_0,X1,esk4_0),X2)
| ~ member(esk6_4(esk2_0,esk2_0,X1,esk4_0),esk5_0)
| ~ maps(esk3_0,X2,esk4_0)
| equal_maps(esk2_0,esk2_0,X1,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_53,plain,
( equal_maps(X1,X2,X3,X4)
| member(esk6_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(esk6_4(esk2_0,esk2_0,esk5_0,esk4_0),X1)
| ~ maps(esk3_0,X1,esk4_0)
| equal_maps(esk2_0,esk2_0,esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_55,plain,
( ~ member(esk6_4(X4,X1,X5,X6),X2)
| ~ member(esk6_4(X4,X1,X5,X6),X7)
| ~ member(esk8_4(X4,X1,X5,X6),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X7,X3)
| equal_maps(X4,X1,X5,X6)
| esk11_4(X1,X2,X3,esk6_4(X4,X1,X5,X6)) = esk8_4(X4,X1,X5,X6) ),
inference(spm,[status(thm)],[c_0_30,c_0_45]) ).
cnf(c_0_56,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_42]) ).
cnf(c_0_57,negated_conjecture,
equal_maps(esk2_0,esk2_0,esk5_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_53]),c_0_18])]) ).
cnf(c_0_58,plain,
( ~ member(esk6_4(X4,X1,X5,X6),X2)
| ~ member(esk8_4(X4,X1,X5,X6),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X5,X3)
| equal_maps(X4,X1,X5,X6)
| esk11_4(X1,X2,X3,esk6_4(X4,X1,X5,X6)) = esk8_4(X4,X1,X5,X6) ),
inference(spm,[status(thm)],[c_0_55,c_0_53]) ).
cnf(c_0_59,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_56,c_0_57]) ).
cnf(c_0_60,negated_conjecture,
( ~ member(esk6_4(X1,esk3_0,X2,X3),X4)
| ~ member(esk8_4(X1,esk3_0,X2,X3),esk4_0)
| ~ member(esk6_4(X1,esk3_0,X2,X3),esk5_0)
| ~ maps(esk3_0,X2,esk4_0)
| ~ maps(esk3_0,X4,esk4_0)
| apply(esk2_0,esk6_4(X1,esk3_0,X2,X3),esk8_4(X1,esk3_0,X2,X3))
| equal_maps(X1,esk3_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
( ~ member(X1,esk4_0)
| ~ member(esk6_4(esk2_0,X2,X3,X4),esk5_0)
| ~ member(esk7_4(esk2_0,X2,X3,X4),esk4_0)
| ~ apply(esk2_0,esk6_4(esk2_0,X2,X3,X4),X1)
| equal_maps(esk2_0,X2,X3,X4)
| X1 = esk7_4(esk2_0,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_59,c_0_44]) ).
cnf(c_0_62,negated_conjecture,
( ~ member(esk8_4(X1,esk3_0,X2,X3),esk4_0)
| ~ member(esk6_4(X1,esk3_0,X2,X3),esk5_0)
| ~ maps(esk3_0,X2,esk4_0)
| apply(esk2_0,esk6_4(X1,esk3_0,X2,X3),esk8_4(X1,esk3_0,X2,X3))
| equal_maps(X1,esk3_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_60,c_0_53]) ).
cnf(c_0_63,negated_conjecture,
( ~ member(esk8_4(esk2_0,esk3_0,X1,X2),esk4_0)
| ~ member(esk6_4(esk2_0,esk3_0,X1,X2),esk5_0)
| ~ member(esk7_4(esk2_0,esk3_0,X1,X2),esk4_0)
| ~ maps(esk3_0,X1,esk4_0)
| equal_maps(esk2_0,esk3_0,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_48]) ).
cnf(c_0_64,negated_conjecture,
( ~ member(esk6_4(esk2_0,esk3_0,X1,esk4_0),esk5_0)
| ~ maps(esk3_0,X1,esk4_0)
| equal_maps(esk2_0,esk3_0,X1,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_50]),c_0_51]) ).
cnf(c_0_65,negated_conjecture,
~ equal_maps(esk2_0,esk3_0,esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_53]),c_0_18])]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET728+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n001.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:40:00 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.48 Running first-order theorem proving
% 0.17/0.48 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
% 6.16/1.63 % Version: 3.5.1
% 6.16/1.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.16/1.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.16/1.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.16/1.63 % Starting new_bool_3 with 300s (1) cores
% 6.16/1.63 % Starting new_bool_1 with 300s (1) cores
% 6.16/1.63 % Starting sh5l with 300s (1) cores
% 6.16/1.63 % new_bool_3 with pid 2300906 completed with status 0
% 6.16/1.63 % Result found by new_bool_3
% 6.16/1.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.16/1.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.16/1.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.16/1.63 % Starting new_bool_3 with 300s (1) cores
% 6.16/1.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.16/1.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.16/1.63 % Search class: FGUSF-FFMS33-SFFFFFNN
% 6.16/1.63 % partial match(1): FGUSS-FFMS33-SFFFFFNN
% 6.16/1.63 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 6.16/1.63 % Starting SubtermCWHack with 31s (1) cores
% 6.16/1.63 % SubtermCWHack with pid 2300909 completed with status 0
% 6.16/1.64 % Result found by SubtermCWHack
% 6.16/1.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.16/1.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.16/1.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.16/1.64 % Starting new_bool_3 with 300s (1) cores
% 6.16/1.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.16/1.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.16/1.64 % Search class: FGUSF-FFMS33-SFFFFFNN
% 6.16/1.64 % partial match(1): FGUSS-FFMS33-SFFFFFNN
% 6.16/1.64 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 6.16/1.64 % Starting SubtermCWHack with 31s (1) cores
% 6.16/1.64 % Preprocessing time : 0.001 s
% 6.16/1.64
% 6.16/1.64 % Proof found!
% 6.16/1.64 % SZS status Theorem
% 6.16/1.64 % SZS output start CNFRefutation
% See solution above
% 6.16/1.64 % Parsed axioms : 29
% 6.16/1.64 % Removed by relevancy pruning/SinE : 24
% 6.16/1.64 % Initial clauses : 35
% 6.16/1.64 % Removed in clause preprocessing : 0
% 6.16/1.64 % Initial clauses in saturation : 35
% 6.16/1.64 % Processed clauses : 1251
% 6.16/1.64 % ...of these trivial : 0
% 6.16/1.64 % ...subsumed : 573
% 6.16/1.64 % ...remaining for further processing : 678
% 6.16/1.64 % Other redundant clauses eliminated : 0
% 6.16/1.64 % Clauses deleted for lack of memory : 0
% 6.16/1.64 % Backward-subsumed : 81
% 6.16/1.64 % Backward-rewritten : 1
% 6.16/1.64 % Generated clauses : 9304
% 6.16/1.64 % ...of the previous two non-redundant : 9116
% 6.16/1.64 % ...aggressively subsumed : 0
% 6.16/1.64 % Contextual simplify-reflections : 40
% 6.16/1.64 % Paramodulations : 9304
% 6.16/1.64 % Factorizations : 0
% 6.16/1.64 % NegExts : 0
% 6.16/1.64 % Equation resolutions : 0
% 6.16/1.64 % Disequality decompositions : 0
% 6.16/1.64 % Total rewrite steps : 175
% 6.16/1.64 % ...of those cached : 167
% 6.16/1.64 % Propositional unsat checks : 0
% 6.16/1.64 % Propositional check models : 0
% 6.16/1.64 % Propositional check unsatisfiable : 0
% 6.16/1.64 % Propositional clauses : 0
% 6.16/1.64 % Propositional clauses after purity: 0
% 6.16/1.64 % Propositional unsat core size : 0
% 6.16/1.64 % Propositional preprocessing time : 0.000
% 6.16/1.64 % Propositional encoding time : 0.000
% 6.16/1.64 % Propositional solver time : 0.000
% 6.16/1.64 % Success case prop preproc time : 0.000
% 6.16/1.64 % Success case prop encoding time : 0.000
% 6.16/1.64 % Success case prop solver time : 0.000
% 6.16/1.64 % Current number of processed clauses : 596
% 6.16/1.64 % Positive orientable unit clauses : 8
% 6.16/1.64 % Positive unorientable unit clauses: 0
% 6.16/1.64 % Negative unit clauses : 1
% 6.16/1.64 % Non-unit-clauses : 587
% 6.16/1.64 % Current number of unprocessed clauses: 7842
% 6.16/1.64 % ...number of literals in the above : 89017
% 6.16/1.64 % Current number of archived formulas : 0
% 6.16/1.64 % Current number of archived clauses : 82
% 6.16/1.64 % Clause-clause subsumption calls (NU) : 122292
% 6.16/1.64 % Rec. Clause-clause subsumption calls : 3990
% 6.16/1.64 % Non-unit clause-clause subsumptions : 694
% 6.16/1.64 % Unit Clause-clause subsumption calls : 149
% 6.16/1.64 % Rewrite failures with RHS unbound : 0
% 6.16/1.64 % BW rewrite match attempts : 7
% 6.16/1.64 % BW rewrite match successes : 1
% 6.16/1.64 % Condensation attempts : 0
% 6.16/1.64 % Condensation successes : 0
% 6.16/1.64 % Termbank termtop insertions : 496966
% 6.16/1.64 % Search garbage collected termcells : 1020
% 6.16/1.64
% 6.16/1.64 % -------------------------------------------------
% 6.16/1.64 % User time : 0.510 s
% 6.16/1.64 % System time : 0.014 s
% 6.16/1.64 % Total time : 0.524 s
% 6.16/1.64 % Maximum resident set size: 3692 pages
% 6.16/1.64
% 6.16/1.64 % -------------------------------------------------
% 6.16/1.64 % User time : 0.513 s
% 6.16/1.64 % System time : 0.022 s
% 6.16/1.64 % Total time : 0.535 s
% 6.16/1.64 % Maximum resident set size: 4864 pages
% 6.16/1.64 % E exiting
%------------------------------------------------------------------------------