%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET729+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 : n017.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 13.57s 2.78s
% Output : CNFRefutation 13.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 8
% Syntax : Number of formulae : 127 ( 6 unt; 0 def)
% Number of atoms : 717 ( 53 equ)
% Maximal formula atoms : 55 ( 5 avg)
% Number of connectives : 1009 ( 419 ~; 515 |; 54 &)
% ( 10 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 2 con; 0-7 aty)
% Number of variables : 497 ( 1 sgn 94 !; 3 ?)
% 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(thII20,conjecture,
! [X6,X1] :
( maps(X6,X1,X1)
=> ( ( inverse_predicate(X6,X6,X1,X1)
& one_to_one(X6,X1,X1) )
<=> identity(compose_function(X6,X6,X1,X1,X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII20) ).
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(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(inverse_predicate,axiom,
! [X10,X6,X1,X2] :
( inverse_predicate(X10,X6,X1,X2)
<=> ! [X3,X5] :
( ( member(X5,X2)
& member(X3,X1) )
=> ( apply(X6,X3,X5)
<=> apply(X10,X5,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_predicate) ).
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(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_8,plain,
! [X67,X68,X69,X70,X72,X73,X74,X75,X76,X77,X79] :
( ( maps(X75,X76,X77)
| ~ apply(X75,esk12_3(X75,X76,X77),X79)
| ~ member(X79,X77)
| esk14_3(X75,X76,X77) != esk15_3(X75,X76,X77) )
& ( maps(X75,X76,X77)
| ~ apply(X75,esk12_3(X75,X76,X77),X79)
| ~ member(X79,X77)
| apply(X75,esk13_3(X75,X76,X77),esk15_3(X75,X76,X77)) )
& ( maps(X75,X76,X77)
| ~ apply(X75,esk12_3(X75,X76,X77),X79)
| ~ member(X79,X77)
| apply(X75,esk13_3(X75,X76,X77),esk14_3(X75,X76,X77)) )
& ( maps(X75,X76,X77)
| ~ apply(X75,esk12_3(X75,X76,X77),X79)
| ~ member(X79,X77)
| member(esk15_3(X75,X76,X77),X77) )
& ( maps(X75,X76,X77)
| ~ apply(X75,esk12_3(X75,X76,X77),X79)
| ~ member(X79,X77)
| member(esk14_3(X75,X76,X77),X77) )
& ( maps(X75,X76,X77)
| ~ apply(X75,esk12_3(X75,X76,X77),X79)
| ~ member(X79,X77)
| member(esk13_3(X75,X76,X77),X76) )
& ( maps(X75,X76,X77)
| member(esk12_3(X75,X76,X77),X76)
| esk14_3(X75,X76,X77) != esk15_3(X75,X76,X77) )
& ( maps(X75,X76,X77)
| member(esk12_3(X75,X76,X77),X76)
| apply(X75,esk13_3(X75,X76,X77),esk15_3(X75,X76,X77)) )
& ( maps(X75,X76,X77)
| member(esk12_3(X75,X76,X77),X76)
| apply(X75,esk13_3(X75,X76,X77),esk14_3(X75,X76,X77)) )
& ( maps(X75,X76,X77)
| member(esk12_3(X75,X76,X77),X76)
| member(esk15_3(X75,X76,X77),X77) )
& ( maps(X75,X76,X77)
| member(esk12_3(X75,X76,X77),X76)
| member(esk14_3(X75,X76,X77),X77) )
& ( maps(X75,X76,X77)
| member(esk12_3(X75,X76,X77),X76)
| member(esk13_3(X75,X76,X77),X76) )
& ( ~ maps(X67,X68,X69)
| X73 = X74
| ~ apply(X67,X72,X74)
| ~ apply(X67,X72,X73)
| ~ member(X74,X69)
| ~ member(X73,X69)
| ~ member(X72,X68) )
& ( ~ maps(X67,X68,X69)
| ~ member(X70,X68)
| apply(X67,X70,esk11_4(X67,X68,X69,X70)) )
& ( ~ maps(X67,X68,X69)
| ~ member(X70,X68)
| member(esk11_4(X67,X68,X69,X70),X69) ) ),
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_9,plain,
! [X25,X26,X27,X28,X29,X30,X31,X33] :
( ( ~ member(X31,X29)
| ~ member(X30,X27)
| apply(compose_function(X25,X26,X27,X28,X29),X30,X31)
| ~ apply(X25,X33,X31)
| ~ apply(X26,X30,X33)
| ~ member(X33,X28) )
& ( ~ member(X31,X29)
| ~ member(X30,X27)
| ~ apply(compose_function(X25,X26,X27,X28,X29),X30,X31)
| apply(X25,esk4_7(X25,X26,X27,X28,X29,X30,X31),X31) )
& ( ~ member(X31,X29)
| ~ member(X30,X27)
| ~ apply(compose_function(X25,X26,X27,X28,X29),X30,X31)
| apply(X26,X30,esk4_7(X25,X26,X27,X28,X29,X30,X31)) )
& ( ~ member(X31,X29)
| ~ member(X30,X27)
| ~ apply(compose_function(X25,X26,X27,X28,X29),X30,X31)
| member(esk4_7(X25,X26,X27,X28,X29,X30,X31),X28) ) ),
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_10,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_8]) ).
cnf(c_0_11,plain,
( ~ member(X7,X6)
| ~ member(X2,X4)
| ~ apply(compose_function(X3,X1,X4,X5,X6),X2,X7)
| apply(X1,X2,esk4_7(X3,X1,X4,X5,X6,X2,X7)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( ~ member(X7,X4)
| ~ member(X8,X6)
| ~ member(X7,X9)
| ~ member(X1,X10)
| ~ member(esk4_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 = esk4_7(X2,X3,X4,X5,X6,X7,X8) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| member(esk4_7(X1,X2,X3,X4,X5,X6,X7),X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,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 = esk4_7(X2,X3,X4,X5,X6,X7,X8) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk11_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_16,negated_conjecture,
~ ! [X6,X1] :
( maps(X6,X1,X1)
=> ( ( inverse_predicate(X6,X6,X1,X1)
& one_to_one(X6,X1,X1) )
<=> identity(compose_function(X6,X6,X1,X1,X1),X1) ) ),
inference(assume_negation,[status(cth)],[thII20]) ).
cnf(c_0_17,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) = esk4_7(X5,X1,X6,X7,X8,X4,X9) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ maps(X1,X2,X3)
| ~ member(X4,X2)
| member(esk11_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_19,negated_conjecture,
( ( identity(compose_function(esk1_0,esk1_0,esk2_0,esk2_0,esk2_0),esk2_0)
| inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0) )
& ( identity(compose_function(esk1_0,esk1_0,esk2_0,esk2_0,esk2_0),esk2_0)
| one_to_one(esk1_0,esk2_0,esk2_0) )
& ( ~ identity(compose_function(esk1_0,esk1_0,esk2_0,esk2_0,esk2_0),esk2_0)
| ~ inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0)
| ~ one_to_one(esk1_0,esk2_0,esk2_0) )
& maps(esk1_0,esk2_0,esk2_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
cnf(c_0_20,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) = esk4_7(X5,X1,X6,X3,X7,X4,X8) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
maps(esk1_0,esk2_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X19,X20,X21,X22,X23] :
( ( identity(X22,X23)
| ~ apply(X22,esk3_2(X22,X23),esk3_2(X22,X23)) )
& ( identity(X22,X23)
| member(esk3_2(X22,X23),X23) )
& ( apply(X19,X21,X21)
| ~ member(X21,X20)
| ~ identity(X19,X20) ) ),
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_23,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_10,c_0_15]) ).
fof(c_0_24,plain,
! [X83,X84,X85,X86,X88,X89,X90,X92] :
( ( surjective(X88,X89,X90)
| ~ apply(X88,X92,esk17_3(X88,X89,X90))
| ~ member(X92,X89) )
& ( surjective(X88,X89,X90)
| member(esk17_3(X88,X89,X90),X90) )
& ( ~ surjective(X83,X84,X85)
| ~ member(X86,X85)
| apply(X83,esk16_4(X83,X84,X85,X86),X86) )
& ( ~ surjective(X83,X84,X85)
| ~ member(X86,X85)
| member(esk16_4(X83,X84,X85,X86),X84) ) ),
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_25,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| apply(X1,esk4_7(X1,X2,X3,X4,X5,X6,X7),X7) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,X4)
| ~ member(X6,X5)
| ~ member(X2,esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| ~ apply(compose_function(X3,esk1_0,X4,esk2_0,X5),X2,X6)
| esk11_4(esk1_0,X1,esk2_0,X2) = esk4_7(X3,esk1_0,X4,esk2_0,X5,X2,X6) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( ~ member(X3,X2)
| ~ identity(X1,X2)
| apply(X1,X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( identity(compose_function(esk1_0,esk1_0,esk2_0,esk2_0,esk2_0),esk2_0)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,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_23,c_0_18]) ).
cnf(c_0_30,plain,
( ~ surjective(X1,X2,X3)
| ~ member(X4,X3)
| apply(X1,esk16_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X34,X35,X36,X37,X38,X39,X40,X41,X42,X43] :
( ( inverse_predicate(X40,X41,X42,X43)
| apply(X40,esk6_4(X40,X41,X42,X43),esk5_4(X40,X41,X42,X43))
| apply(X41,esk5_4(X40,X41,X42,X43),esk6_4(X40,X41,X42,X43)) )
& ( inverse_predicate(X40,X41,X42,X43)
| ~ apply(X40,esk6_4(X40,X41,X42,X43),esk5_4(X40,X41,X42,X43))
| ~ apply(X41,esk5_4(X40,X41,X42,X43),esk6_4(X40,X41,X42,X43)) )
& ( inverse_predicate(X40,X41,X42,X43)
| member(esk6_4(X40,X41,X42,X43),X43) )
& ( inverse_predicate(X40,X41,X42,X43)
| member(esk5_4(X40,X41,X42,X43),X42) )
& ( ~ inverse_predicate(X34,X35,X36,X37)
| ~ member(X39,X37)
| ~ member(X38,X36)
| apply(X35,X38,X39)
| ~ apply(X34,X39,X38) )
& ( ~ inverse_predicate(X34,X35,X36,X37)
| ~ member(X39,X37)
| ~ member(X38,X36)
| apply(X34,X39,X38)
| ~ apply(X35,X38,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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inverse_predicate])])])])])])]) ).
cnf(c_0_32,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X5)
| ~ member(X4,X6)
| ~ member(X3,esk2_0)
| ~ maps(esk1_0,X2,esk2_0)
| ~ apply(compose_function(X1,esk1_0,X5,esk2_0,X6),X3,X4)
| apply(X1,esk11_4(esk1_0,X2,esk2_0,X3),X4) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(X1,esk2_0)
| apply(compose_function(esk1_0,esk1_0,esk2_0,esk2_0,esk2_0),X1,X1)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( ~ member(X6,X5)
| ~ member(X6,X3)
| ~ member(esk16_4(X1,X4,X5,X6),X2)
| ~ member(esk16_4(X1,X4,X5,X6),X7)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X7,X3)
| ~ surjective(X1,X4,X5)
| esk11_4(X1,X2,X3,esk16_4(X1,X4,X5,X6)) = X6 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ~ surjective(X1,X2,X3)
| ~ member(X4,X3)
| member(esk16_4(X1,X2,X3,X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,plain,
( inverse_predicate(X2,X1,X3,X4)
| apply(X2,esk6_4(X2,X1,X3,X4),esk5_4(X2,X1,X3,X4))
| apply(X1,esk5_4(X2,X1,X3,X4),esk6_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| apply(esk1_0,esk11_4(esk1_0,X1,esk2_0,X2),X2)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( ~ member(X6,X5)
| ~ member(X6,X3)
| ~ member(esk16_4(X1,X4,X5,X6),X2)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X4,X3)
| ~ surjective(X1,X4,X5)
| esk11_4(X1,X2,X3,esk16_4(X1,X4,X5,X6)) = X6 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( ~ member(esk5_4(X4,X1,X5,X6),X2)
| ~ member(esk5_4(X4,X1,X5,X6),X7)
| ~ member(esk6_4(X4,X1,X5,X6),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X7,X3)
| apply(X4,esk6_4(X4,X1,X5,X6),esk5_4(X4,X1,X5,X6))
| inverse_predicate(X4,X1,X5,X6)
| esk11_4(X1,X2,X3,esk5_4(X4,X1,X5,X6)) = esk6_4(X4,X1,X5,X6) ),
inference(spm,[status(thm)],[c_0_29,c_0_36]) ).
cnf(c_0_40,plain,
( inverse_predicate(X1,X2,X3,X4)
| member(esk5_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
( ~ member(X1,X3)
| ~ member(X1,esk2_0)
| ~ member(esk16_4(esk1_0,X2,X3,X1),X4)
| ~ member(esk16_4(esk1_0,X2,X3,X1),esk2_0)
| ~ maps(esk1_0,X2,esk2_0)
| ~ maps(esk1_0,X4,esk2_0)
| ~ surjective(esk1_0,X2,X3)
| apply(esk1_0,X1,esk16_4(esk1_0,X2,X3,X1))
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_42,plain,
! [X93,X94,X95,X96,X97,X98,X99,X100,X101] :
( ( injective(X99,X100,X101)
| esk18_3(X99,X100,X101) != esk19_3(X99,X100,X101) )
& ( injective(X99,X100,X101)
| apply(X99,esk19_3(X99,X100,X101),esk20_3(X99,X100,X101)) )
& ( injective(X99,X100,X101)
| apply(X99,esk18_3(X99,X100,X101),esk20_3(X99,X100,X101)) )
& ( injective(X99,X100,X101)
| member(esk20_3(X99,X100,X101),X101) )
& ( injective(X99,X100,X101)
| member(esk19_3(X99,X100,X101),X100) )
& ( injective(X99,X100,X101)
| member(esk18_3(X99,X100,X101),X100) )
& ( X96 = X97
| ~ apply(X93,X97,X98)
| ~ apply(X93,X96,X98)
| ~ member(X98,X95)
| ~ member(X97,X94)
| ~ member(X96,X94)
| ~ injective(X93,X94,X95) ) ),
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_43,plain,
( ~ member(esk5_4(X4,X1,X5,X6),X2)
| ~ member(esk6_4(X4,X1,X5,X6),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X5,X3)
| apply(X4,esk6_4(X4,X1,X5,X6),esk5_4(X4,X1,X5,X6))
| inverse_predicate(X4,X1,X5,X6)
| esk11_4(X1,X2,X3,esk5_4(X4,X1,X5,X6)) = esk6_4(X4,X1,X5,X6) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
( inverse_predicate(X1,X2,X3,X4)
| member(esk6_4(X1,X2,X3,X4),X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_45,plain,
( ~ member(esk6_4(X1,X4,X5,X6),X2)
| ~ member(esk6_4(X1,X4,X5,X6),X7)
| ~ member(esk5_4(X1,X4,X5,X6),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X7,X3)
| apply(X4,esk5_4(X1,X4,X5,X6),esk6_4(X1,X4,X5,X6))
| inverse_predicate(X1,X4,X5,X6)
| esk11_4(X1,X2,X3,esk6_4(X1,X4,X5,X6)) = esk5_4(X1,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_29,c_0_36]) ).
cnf(c_0_46,negated_conjecture,
( ~ member(X1,X3)
| ~ member(X1,esk2_0)
| ~ member(esk16_4(esk1_0,X2,X3,X1),esk2_0)
| ~ maps(esk1_0,X2,esk2_0)
| ~ surjective(esk1_0,X2,X3)
| apply(esk1_0,X1,esk16_4(esk1_0,X2,X3,X1))
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_35]) ).
cnf(c_0_47,plain,
( injective(X1,X2,X3)
| apply(X1,esk19_3(X1,X2,X3),esk20_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
( injective(X1,X2,X3)
| apply(X1,esk18_3(X1,X2,X3),esk20_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
( ~ member(esk5_4(X4,X1,X5,X3),X2)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X5,X3)
| apply(X4,esk6_4(X4,X1,X5,X3),esk5_4(X4,X1,X5,X3))
| inverse_predicate(X4,X1,X5,X3)
| esk11_4(X1,X2,X3,esk5_4(X4,X1,X5,X3)) = esk6_4(X4,X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
( ~ member(esk6_4(X1,X4,X5,X6),X2)
| ~ member(esk5_4(X1,X4,X5,X6),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X6,X3)
| apply(X4,esk5_4(X1,X4,X5,X6),esk6_4(X1,X4,X5,X6))
| inverse_predicate(X1,X4,X5,X6)
| esk11_4(X1,X2,X3,esk6_4(X1,X4,X5,X6)) = esk5_4(X1,X4,X5,X6) ),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( ~ member(X4,X3)
| ~ member(X4,X5)
| ~ member(X1,X6)
| ~ member(X4,esk2_0)
| ~ member(esk16_4(esk1_0,X2,X3,X4),X6)
| ~ member(esk16_4(esk1_0,X2,X3,X4),esk2_0)
| ~ maps(esk1_0,X5,X6)
| ~ maps(esk1_0,X2,esk2_0)
| ~ apply(esk1_0,X4,X1)
| ~ surjective(esk1_0,X2,X3)
| one_to_one(esk1_0,esk2_0,esk2_0)
| X1 = esk16_4(esk1_0,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_10,c_0_46]) ).
cnf(c_0_52,plain,
( ~ member(esk19_3(X1,X4,X5),X2)
| ~ member(esk19_3(X1,X4,X5),X6)
| ~ member(esk20_3(X1,X4,X5),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X6,X3)
| injective(X1,X4,X5)
| esk11_4(X1,X2,X3,esk19_3(X1,X4,X5)) = esk20_3(X1,X4,X5) ),
inference(spm,[status(thm)],[c_0_29,c_0_47]) ).
cnf(c_0_53,plain,
( injective(X1,X2,X3)
| member(esk19_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,plain,
( ~ member(esk18_3(X1,X4,X5),X2)
| ~ member(esk18_3(X1,X4,X5),X6)
| ~ member(esk20_3(X1,X4,X5),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X6,X3)
| injective(X1,X4,X5)
| esk11_4(X1,X2,X3,esk18_3(X1,X4,X5)) = esk20_3(X1,X4,X5) ),
inference(spm,[status(thm)],[c_0_29,c_0_48]) ).
cnf(c_0_55,plain,
( injective(X1,X2,X3)
| member(esk18_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_56,plain,
( ~ apply(X2,esk6_4(X2,X1,X3,X4),esk5_4(X2,X1,X3,X4))
| ~ apply(X1,esk5_4(X2,X1,X3,X4),esk6_4(X2,X1,X3,X4))
| inverse_predicate(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_57,plain,
( ~ maps(X1,X2,X3)
| apply(X4,esk6_4(X4,X1,X2,X3),esk5_4(X4,X1,X2,X3))
| inverse_predicate(X4,X1,X2,X3)
| esk11_4(X1,X2,X3,esk5_4(X4,X1,X2,X3)) = esk6_4(X4,X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_40]) ).
cnf(c_0_58,plain,
( ~ member(esk6_4(X1,X4,X3,X5),X2)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X5,X3)
| apply(X4,esk5_4(X1,X4,X3,X5),esk6_4(X1,X4,X3,X5))
| inverse_predicate(X1,X4,X3,X5)
| esk11_4(X1,X2,X3,esk6_4(X1,X4,X3,X5)) = esk5_4(X1,X4,X3,X5) ),
inference(spm,[status(thm)],[c_0_50,c_0_40]) ).
cnf(c_0_59,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X4)
| ~ member(X1,X5)
| ~ member(X3,esk2_0)
| ~ member(esk16_4(esk1_0,esk2_0,X2,X3),X5)
| ~ maps(esk1_0,X4,X5)
| ~ apply(esk1_0,X3,X1)
| ~ surjective(esk1_0,esk2_0,X2)
| one_to_one(esk1_0,esk2_0,esk2_0)
| X1 = esk16_4(esk1_0,esk2_0,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_35]),c_0_21])]) ).
cnf(c_0_60,plain,
( ~ member(esk19_3(X1,X4,X5),X2)
| ~ member(esk20_3(X1,X4,X5),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X4,X3)
| injective(X1,X4,X5)
| esk11_4(X1,X2,X3,esk19_3(X1,X4,X5)) = esk20_3(X1,X4,X5) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_61,plain,
( ~ member(esk18_3(X1,X4,X5),X2)
| ~ member(esk20_3(X1,X4,X5),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X4,X3)
| injective(X1,X4,X5)
| esk11_4(X1,X2,X3,esk18_3(X1,X4,X5)) = esk20_3(X1,X4,X5) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,plain,
( ~ maps(X1,X2,X3)
| ~ apply(X1,esk5_4(X4,X1,X2,X3),esk6_4(X4,X1,X2,X3))
| inverse_predicate(X4,X1,X2,X3)
| esk11_4(X1,X2,X3,esk5_4(X4,X1,X2,X3)) = esk6_4(X4,X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,plain,
( ~ maps(X1,X2,X3)
| apply(X4,esk5_4(X1,X4,X3,X2),esk6_4(X1,X4,X3,X2))
| inverse_predicate(X1,X4,X3,X2)
| esk11_4(X1,X2,X3,esk6_4(X1,X4,X3,X2)) = esk5_4(X1,X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_44]) ).
cnf(c_0_64,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X4)
| ~ member(X1,esk2_0)
| ~ member(X3,esk2_0)
| ~ maps(esk1_0,X4,esk2_0)
| ~ apply(esk1_0,X3,X1)
| ~ surjective(esk1_0,esk2_0,X2)
| one_to_one(esk1_0,esk2_0,esk2_0)
| X1 = esk16_4(esk1_0,esk2_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_35]) ).
cnf(c_0_65,negated_conjecture,
( ~ member(esk19_3(esk1_0,X1,X2),X3)
| ~ member(esk20_3(esk1_0,X1,X2),esk2_0)
| ~ member(esk19_3(esk1_0,X1,X2),esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| ~ maps(esk1_0,X3,esk2_0)
| apply(esk1_0,esk20_3(esk1_0,X1,X2),esk19_3(esk1_0,X1,X2))
| injective(esk1_0,X1,X2)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( ~ member(esk18_3(esk1_0,X1,X2),X3)
| ~ member(esk20_3(esk1_0,X1,X2),esk2_0)
| ~ member(esk18_3(esk1_0,X1,X2),esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| ~ maps(esk1_0,X3,esk2_0)
| apply(esk1_0,esk20_3(esk1_0,X1,X2),esk18_3(esk1_0,X1,X2))
| injective(esk1_0,X1,X2)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_61]) ).
cnf(c_0_67,plain,
( ~ apply(X3,X1,esk17_3(X3,X2,X4))
| ~ member(X1,X2)
| surjective(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_68,plain,
( ~ maps(X1,X2,X3)
| ~ maps(X4,X3,X2)
| inverse_predicate(X1,X4,X3,X2)
| esk11_4(X4,X3,X2,esk5_4(X1,X4,X3,X2)) = esk6_4(X1,X4,X3,X2)
| esk11_4(X1,X2,X3,esk6_4(X1,X4,X3,X2)) = esk5_4(X1,X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X1,esk2_0)
| ~ member(X3,esk2_0)
| ~ apply(esk1_0,X3,X1)
| ~ surjective(esk1_0,esk2_0,X2)
| one_to_one(esk1_0,esk2_0,esk2_0)
| X1 = esk16_4(esk1_0,esk2_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_64,c_0_21]) ).
cnf(c_0_70,negated_conjecture,
( ~ member(esk20_3(esk1_0,X1,X2),esk2_0)
| ~ member(esk19_3(esk1_0,X1,X2),esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| apply(esk1_0,esk20_3(esk1_0,X1,X2),esk19_3(esk1_0,X1,X2))
| injective(esk1_0,X1,X2)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_53]) ).
cnf(c_0_71,negated_conjecture,
( ~ member(esk20_3(esk1_0,X1,X2),esk2_0)
| ~ member(esk18_3(esk1_0,X1,X2),esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| apply(esk1_0,esk20_3(esk1_0,X1,X2),esk18_3(esk1_0,X1,X2))
| injective(esk1_0,X1,X2)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_66,c_0_55]) ).
cnf(c_0_72,plain,
( ~ member(X8,X5)
| ~ member(esk17_3(X1,X2,X3),X7)
| ~ member(esk4_7(X1,X4,X5,X6,X7,X8,esk17_3(X1,X2,X3)),X2)
| ~ apply(compose_function(X1,X4,X5,X6,X7),X8,esk17_3(X1,X2,X3))
| surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_25]) ).
cnf(c_0_73,negated_conjecture,
( ~ maps(X1,esk2_0,esk2_0)
| inverse_predicate(X1,esk1_0,esk2_0,esk2_0)
| esk11_4(X1,esk2_0,esk2_0,esk6_4(X1,esk1_0,esk2_0,esk2_0)) = esk5_4(X1,esk1_0,esk2_0,esk2_0)
| esk11_4(esk1_0,esk2_0,esk2_0,esk5_4(X1,esk1_0,esk2_0,esk2_0)) = esk6_4(X1,esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_21]) ).
cnf(c_0_74,negated_conjecture,
( ~ member(esk20_3(esk1_0,X2,X3),X1)
| ~ member(esk19_3(esk1_0,X2,X3),esk2_0)
| ~ member(esk20_3(esk1_0,X2,X3),esk2_0)
| ~ maps(esk1_0,X2,esk2_0)
| ~ surjective(esk1_0,esk2_0,X1)
| injective(esk1_0,X2,X3)
| one_to_one(esk1_0,esk2_0,esk2_0)
| esk16_4(esk1_0,esk2_0,X1,esk20_3(esk1_0,X2,X3)) = esk19_3(esk1_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
( ~ member(esk20_3(esk1_0,X2,X3),X1)
| ~ member(esk18_3(esk1_0,X2,X3),esk2_0)
| ~ member(esk20_3(esk1_0,X2,X3),esk2_0)
| ~ maps(esk1_0,X2,esk2_0)
| ~ surjective(esk1_0,esk2_0,X1)
| injective(esk1_0,X2,X3)
| one_to_one(esk1_0,esk2_0,esk2_0)
| esk16_4(esk1_0,esk2_0,X1,esk20_3(esk1_0,X2,X3)) = esk18_3(esk1_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_69,c_0_71]) ).
cnf(c_0_76,plain,
( esk18_3(X1,X2,X3) != esk19_3(X1,X2,X3)
| injective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_77,plain,
( ~ member(X7,X5)
| ~ member(esk17_3(X1,X2,X3),X6)
| ~ apply(compose_function(X1,X4,X5,X2,X6),X7,esk17_3(X1,X2,X3))
| surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_72,c_0_13]) ).
fof(c_0_78,plain,
! [X46,X47,X48] :
( ( one_to_one(X46,X47,X48)
| ~ surjective(X46,X47,X48)
| ~ injective(X46,X47,X48) )
& ( ~ one_to_one(X46,X47,X48)
| surjective(X46,X47,X48) )
& ( ~ one_to_one(X46,X47,X48)
| injective(X46,X47,X48) ) ),
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_79,negated_conjecture,
( identity(compose_function(esk1_0,esk1_0,esk2_0,esk2_0,esk2_0),esk2_0)
| inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_80,negated_conjecture,
( inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0)
| esk11_4(esk1_0,esk2_0,esk2_0,esk5_4(esk1_0,esk1_0,esk2_0,esk2_0)) = esk6_4(esk1_0,esk1_0,esk2_0,esk2_0)
| esk11_4(esk1_0,esk2_0,esk2_0,esk6_4(esk1_0,esk1_0,esk2_0,esk2_0)) = esk5_4(esk1_0,esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_73,c_0_21]) ).
cnf(c_0_81,negated_conjecture,
( ~ member(esk20_3(esk1_0,X1,X2),X3)
| ~ member(esk18_3(esk1_0,X1,X2),esk2_0)
| ~ member(esk19_3(esk1_0,X1,X2),esk2_0)
| ~ member(esk20_3(esk1_0,X1,X2),esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| ~ surjective(esk1_0,esk2_0,X3)
| injective(esk1_0,X1,X2)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_82,plain,
( injective(X1,X2,X3)
| member(esk20_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_83,negated_conjecture,
( ~ member(esk17_3(esk1_0,esk2_0,X1),esk2_0)
| surjective(esk1_0,esk2_0,X1)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_77,c_0_33]) ).
cnf(c_0_84,plain,
( surjective(X1,X2,X3)
| member(esk17_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_85,plain,
( ~ one_to_one(X1,X2,X3)
| surjective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_86,negated_conjecture,
( ~ member(X1,esk2_0)
| apply(compose_function(esk1_0,esk1_0,esk2_0,esk2_0,esk2_0),X1,X1)
| inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
( apply(esk1_0,esk6_4(esk1_0,esk1_0,esk2_0,esk2_0),esk5_4(esk1_0,esk1_0,esk2_0,esk2_0))
| inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0)
| esk11_4(esk1_0,esk2_0,esk2_0,esk5_4(esk1_0,esk1_0,esk2_0,esk2_0)) = esk6_4(esk1_0,esk1_0,esk2_0,esk2_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_80]),c_0_21])]),c_0_44]) ).
cnf(c_0_88,negated_conjecture,
( ~ member(esk20_3(esk1_0,X1,esk2_0),X2)
| ~ member(esk18_3(esk1_0,X1,esk2_0),esk2_0)
| ~ member(esk19_3(esk1_0,X1,esk2_0),esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| ~ surjective(esk1_0,esk2_0,X2)
| injective(esk1_0,X1,esk2_0)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
surjective(esk1_0,esk2_0,esk2_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_90,plain,
( ~ surjective(X1,X2,X3)
| ~ injective(X1,X2,X3)
| one_to_one(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_91,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| apply(esk1_0,esk11_4(esk1_0,X1,esk2_0,X2),X2)
| inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_86]) ).
cnf(c_0_92,negated_conjecture,
( ~ apply(esk1_0,esk5_4(esk1_0,esk1_0,esk2_0,esk2_0),esk6_4(esk1_0,esk1_0,esk2_0,esk2_0))
| inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0)
| esk11_4(esk1_0,esk2_0,esk2_0,esk5_4(esk1_0,esk1_0,esk2_0,esk2_0)) = esk6_4(esk1_0,esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_56,c_0_87]) ).
cnf(c_0_93,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_42]) ).
cnf(c_0_94,plain,
( ~ one_to_one(X1,X2,X3)
| injective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_95,negated_conjecture,
( ~ member(esk18_3(esk1_0,X1,esk2_0),esk2_0)
| ~ member(esk19_3(esk1_0,X1,esk2_0),esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| injective(esk1_0,X1,esk2_0)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_82]),c_0_89])]) ).
cnf(c_0_96,negated_conjecture,
( ~ injective(esk1_0,esk2_0,esk2_0)
| one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_90,c_0_89]) ).
cnf(c_0_97,negated_conjecture,
( inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0)
| esk11_4(esk1_0,esk2_0,esk2_0,esk5_4(esk1_0,esk1_0,esk2_0,esk2_0)) = esk6_4(esk1_0,esk1_0,esk2_0,esk2_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_80]),c_0_21])]),c_0_44]),c_0_92]) ).
cnf(c_0_98,plain,
( ~ member(X1,X4)
| ~ member(X2,X4)
| ~ member(X6,X5)
| ~ apply(X3,X1,X6)
| ~ apply(X3,X2,X6)
| ~ one_to_one(X3,X4,X5)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
one_to_one(esk1_0,esk2_0,esk2_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_53]),c_0_21])]),c_0_55]),c_0_96]) ).
cnf(c_0_100,negated_conjecture,
( apply(esk1_0,esk6_4(esk1_0,esk1_0,esk2_0,esk2_0),esk5_4(esk1_0,esk1_0,esk2_0,esk2_0))
| inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_97]),c_0_21])]),c_0_40]) ).
cnf(c_0_101,negated_conjecture,
( apply(esk1_0,esk5_4(esk1_0,esk1_0,esk2_0,esk2_0),esk6_4(esk1_0,esk1_0,esk2_0,esk2_0))
| inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_97]),c_0_21])]),c_0_40]) ).
cnf(c_0_102,negated_conjecture,
( ~ member(X1,esk2_0)
| ~ member(X2,esk2_0)
| ~ member(X3,esk2_0)
| ~ apply(esk1_0,X1,X3)
| ~ apply(esk1_0,X2,X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_103,plain,
( ~ inverse_predicate(X4,X1,X5,X6)
| ~ member(X3,X6)
| ~ member(X2,X5)
| ~ apply(X1,X2,X3)
| apply(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_104,negated_conjecture,
inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_100]),c_0_101]) ).
cnf(c_0_105,negated_conjecture,
( ~ member(X4,X3)
| ~ member(X1,esk2_0)
| ~ member(X4,esk2_0)
| ~ member(esk16_4(esk1_0,X2,X3,X4),esk2_0)
| ~ apply(esk1_0,X1,X4)
| ~ surjective(esk1_0,X2,X3)
| X1 = esk16_4(esk1_0,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_102,c_0_30]) ).
cnf(c_0_106,negated_conjecture,
( ~ member(X2,esk2_0)
| ~ member(X1,esk2_0)
| ~ apply(esk1_0,X2,X1)
| apply(esk1_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_107,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X1,esk2_0)
| ~ member(X3,esk2_0)
| ~ apply(esk1_0,X1,X3)
| ~ surjective(esk1_0,esk2_0,X2)
| X1 = esk16_4(esk1_0,esk2_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_105,c_0_35]) ).
cnf(c_0_108,negated_conjecture,
( ~ member(X3,X1)
| ~ member(X3,esk2_0)
| ~ member(esk11_4(esk1_0,X1,X2,X3),esk2_0)
| ~ maps(esk1_0,X1,X2)
| apply(esk1_0,esk11_4(esk1_0,X1,X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_106,c_0_15]) ).
cnf(c_0_109,negated_conjecture,
( ~ member(X3,X1)
| ~ member(X3,X4)
| ~ member(X3,esk2_0)
| ~ member(esk11_4(esk1_0,X1,X2,X3),esk2_0)
| ~ maps(esk1_0,X1,X2)
| ~ surjective(esk1_0,esk2_0,X4)
| esk11_4(esk1_0,X1,X2,X3) = esk16_4(esk1_0,esk2_0,X4,X3) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_110,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,X3)
| ~ member(X2,esk2_0)
| ~ maps(esk1_0,X1,esk2_0)
| ~ surjective(esk1_0,esk2_0,X3)
| esk11_4(esk1_0,X1,esk2_0,X2) = esk16_4(esk1_0,esk2_0,X3,X2) ),
inference(spm,[status(thm)],[c_0_109,c_0_18]) ).
cnf(c_0_111,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_112,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,X3)
| ~ member(X1,esk2_0)
| ~ maps(esk1_0,X3,esk2_0)
| ~ surjective(esk1_0,esk2_0,X2)
| apply(esk1_0,X1,esk16_4(esk1_0,esk2_0,X2,X1)) ),
inference(spm,[status(thm)],[c_0_15,c_0_110]) ).
cnf(c_0_113,plain,
( ~ member(X7,X9)
| ~ member(X6,X3)
| ~ member(X7,X5)
| ~ member(esk16_4(X1,X8,X9,X7),X4)
| ~ apply(X2,X6,esk16_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_111,c_0_30]) ).
cnf(c_0_114,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,esk2_0)
| ~ surjective(esk1_0,esk2_0,X2)
| apply(esk1_0,X1,esk16_4(esk1_0,esk2_0,X2,X1)) ),
inference(spm,[status(thm)],[c_0_112,c_0_21]) ).
cnf(c_0_115,negated_conjecture,
( ~ member(X4,X5)
| ~ member(X4,X1)
| ~ member(X4,X3)
| ~ member(X4,esk2_0)
| ~ member(esk16_4(esk1_0,esk2_0,X5,X4),X2)
| ~ surjective(esk1_0,esk2_0,X5)
| apply(compose_function(esk1_0,esk1_0,X1,X2,X3),X4,X4) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_116,negated_conjecture,
( ~ member(X3,X4)
| ~ member(X3,X1)
| ~ member(X3,X2)
| ~ member(X3,esk2_0)
| ~ surjective(esk1_0,esk2_0,X4)
| apply(compose_function(esk1_0,esk1_0,X1,esk2_0,X2),X3,X3) ),
inference(spm,[status(thm)],[c_0_115,c_0_35]) ).
cnf(c_0_117,plain,
( ~ apply(X1,esk3_2(X1,X2),esk3_2(X1,X2))
| identity(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_118,negated_conjecture,
( ~ member(X3,X1)
| ~ member(X3,X2)
| ~ member(X3,esk2_0)
| apply(compose_function(esk1_0,esk1_0,X1,esk2_0,X2),X3,X3) ),
inference(spm,[status(thm)],[c_0_116,c_0_89]) ).
cnf(c_0_119,negated_conjecture,
( ~ member(esk3_2(compose_function(esk1_0,esk1_0,X1,esk2_0,X2),X3),X1)
| ~ member(esk3_2(compose_function(esk1_0,esk1_0,X1,esk2_0,X2),X3),X2)
| ~ member(esk3_2(compose_function(esk1_0,esk1_0,X1,esk2_0,X2),X3),esk2_0)
| identity(compose_function(esk1_0,esk1_0,X1,esk2_0,X2),X3) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_120,plain,
( identity(X1,X2)
| member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_121,negated_conjecture,
( ~ identity(compose_function(esk1_0,esk1_0,esk2_0,esk2_0,esk2_0),esk2_0)
| ~ inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0)
| ~ one_to_one(esk1_0,esk2_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_122,negated_conjecture,
( ~ member(esk3_2(compose_function(esk1_0,esk1_0,X1,esk2_0,X2),esk2_0),X1)
| ~ member(esk3_2(compose_function(esk1_0,esk1_0,X1,esk2_0,X2),esk2_0),X2)
| identity(compose_function(esk1_0,esk1_0,X1,esk2_0,X2),esk2_0) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_123,negated_conjecture,
( ~ identity(compose_function(esk1_0,esk1_0,esk2_0,esk2_0,esk2_0),esk2_0)
| ~ inverse_predicate(esk1_0,esk1_0,esk2_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_99])]) ).
cnf(c_0_124,negated_conjecture,
( ~ member(esk3_2(compose_function(esk1_0,esk1_0,X1,esk2_0,esk2_0),esk2_0),X1)
| identity(compose_function(esk1_0,esk1_0,X1,esk2_0,esk2_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_122,c_0_120]) ).
cnf(c_0_125,negated_conjecture,
~ identity(compose_function(esk1_0,esk1_0,esk2_0,esk2_0,esk2_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_104])]) ).
cnf(c_0_126,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_120]),c_0_125]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET729+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.49 % Computer : n017.cluster.edu
% 0.19/0.49 % Model : x86_64 x86_64
% 0.19/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.49 % Memory : 8046.5625MB
% 0.19/0.49 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 05:29:57 UTC 2026
% 0.19/0.50 % CPUTime :
% 0.19/0.50 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.58 Running first-order theorem proving
% 0.24/0.58 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
% 13.57/2.78 % Version: 3.5.1
% 13.57/2.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 13.57/2.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.57/2.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.57/2.78 % Starting new_bool_3 with 300s (1) cores
% 13.57/2.78 % Starting new_bool_1 with 300s (1) cores
% 13.57/2.78 % Starting sh5l with 300s (1) cores
% 13.57/2.78 % sh5l with pid 1529940 completed with status 0
% 13.57/2.78 % Result found by sh5l
% 13.57/2.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 13.57/2.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.57/2.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.57/2.78 % Starting new_bool_3 with 300s (1) cores
% 13.57/2.78 % Starting new_bool_1 with 300s (1) cores
% 13.57/2.78 % Starting sh5l with 300s (1) cores
% 13.57/2.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 13.57/2.78 % SinE strategy is gf500_gu_R04_F100_L20000
% 13.57/2.78 % Search class: FGHSF-FFMS33-SFFFFFNN
% 13.57/2.78 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 13.57/2.78 % Starting SubtermCWHack with 31s (1) cores
% 13.57/2.78 % SubtermCWHack with pid 1529948 completed with status 0
% 13.57/2.78 % Result found by SubtermCWHack
% 13.57/2.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 13.57/2.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.57/2.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.57/2.78 % Starting new_bool_3 with 300s (1) cores
% 13.57/2.78 % Starting new_bool_1 with 300s (1) cores
% 13.57/2.78 % Starting sh5l with 300s (1) cores
% 13.57/2.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 13.57/2.78 % SinE strategy is gf500_gu_R04_F100_L20000
% 13.57/2.78 % Search class: FGHSF-FFMS33-SFFFFFNN
% 13.57/2.78 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 13.57/2.78 % Starting SubtermCWHack with 31s (1) cores
% 13.57/2.78 % Preprocessing time : 0.003 s
% 13.57/2.78
% 13.57/2.78 % Proof found!
% 13.57/2.78 % SZS status Theorem
% 13.57/2.78 % SZS output start CNFRefutation
% See solution above
% 13.57/2.78 % Parsed axioms : 29
% 13.57/2.78 % Removed by relevancy pruning/SinE : 20
% 13.57/2.78 % Initial clauses : 58
% 13.57/2.78 % Removed in clause preprocessing : 0
% 13.57/2.78 % Initial clauses in saturation : 58
% 13.57/2.78 % Processed clauses : 1997
% 13.57/2.78 % ...of these trivial : 0
% 13.57/2.78 % ...subsumed : 1154
% 13.57/2.78 % ...remaining for further processing : 843
% 13.57/2.78 % Other redundant clauses eliminated : 0
% 13.57/2.78 % Clauses deleted for lack of memory : 0
% 13.57/2.78 % Backward-subsumed : 104
% 13.57/2.78 % Backward-rewritten : 365
% 13.57/2.78 % Generated clauses : 11471
% 13.57/2.78 % ...of the previous two non-redundant : 11270
% 13.57/2.78 % ...aggressively subsumed : 0
% 13.57/2.78 % Contextual simplify-reflections : 52
% 13.57/2.78 % Paramodulations : 11471
% 13.57/2.78 % Factorizations : 0
% 13.57/2.78 % NegExts : 0
% 13.57/2.78 % Equation resolutions : 0
% 13.57/2.78 % Disequality decompositions : 0
% 13.57/2.78 % Total rewrite steps : 1026
% 13.57/2.78 % ...of those cached : 1022
% 13.57/2.78 % Propositional unsat checks : 0
% 13.57/2.78 % Propositional check models : 0
% 13.57/2.78 % Propositional check unsatisfiable : 0
% 13.57/2.78 % Propositional clauses : 0
% 13.57/2.78 % Propositional clauses after purity: 0
% 13.57/2.78 % Propositional unsat core size : 0
% 13.57/2.78 % Propositional preprocessing time : 0.000
% 13.57/2.78 % Propositional encoding time : 0.000
% 13.57/2.78 % Propositional solver time : 0.000
% 13.57/2.78 % Success case prop preproc time : 0.000
% 13.57/2.78 % Success case prop encoding time : 0.000
% 13.57/2.78 % Success case prop solver time : 0.000
% 13.57/2.78 % Current number of processed clauses : 374
% 13.57/2.78 % Positive orientable unit clauses : 5
% 13.57/2.78 % Positive unorientable unit clauses: 0
% 13.57/2.78 % Negative unit clauses : 1
% 13.57/2.78 % Non-unit-clauses : 368
% 13.57/2.78 % Current number of unprocessed clauses: 9080
% 13.57/2.78 % ...number of literals in the above : 110288
% 13.57/2.78 % Current number of archived formulas : 0
% 13.57/2.78 % Current number of archived clauses : 469
% 13.57/2.78 % Clause-clause subsumption calls (NU) : 277400
% 13.57/2.78 % Rec. Clause-clause subsumption calls : 6514
% 13.57/2.78 % Non-unit clause-clause subsumptions : 1310
% 13.57/2.78 % Unit Clause-clause subsumption calls : 101
% 13.57/2.78 % Rewrite failures with RHS unbound : 0
% 13.57/2.78 % BW rewrite match attempts : 3
% 13.57/2.78 % BW rewrite match successes : 2
% 13.57/2.78 % Condensation attempts : 0
% 13.57/2.78 % Condensation successes : 0
% 13.57/2.78 % Termbank termtop insertions : 606145
% 13.57/2.78 % Search garbage collected termcells : 1563
% 13.57/2.78
% 13.57/2.78 % -------------------------------------------------
% 13.57/2.78 % User time : 1.366 s
% 13.57/2.78 % System time : 0.025 s
% 13.57/2.78 % Total time : 1.391 s
% 13.57/2.78 % Maximum resident set size: 3948 pages
% 13.57/2.78
% 13.57/2.78 % -------------------------------------------------
% 13.57/2.78 % User time : 1.370 s
% 13.57/2.78 % System time : 0.032 s
% 13.57/2.78 % Total time : 1.402 s
% 13.57/2.78 % Maximum resident set size: 4608 pages
% 13.57/2.78 % E exiting
%------------------------------------------------------------------------------