%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET725+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 6.21s 1.59s
% Output : CNFRefutation 6.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 79 ( 10 unt; 0 def)
% Number of atoms : 459 ( 28 equ)
% Maximal formula atoms : 55 ( 5 avg)
% Number of connectives : 655 ( 275 ~; 308 |; 56 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-7 aty)
% Number of variables : 320 ( 1 sgn 84 !; 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(thII16,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) )
=> one_to_one(X6,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII16) ).
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(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(surjective,axiom,
! [X6,X1,X2] :
( surjective(X6,X1,X2)
<=> ! [X5] :
( member(X5,X2)
=> ? [X4] :
( apply(X6,X4,X5)
& member(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(one_to_one,axiom,
! [X6,X1,X2] :
( one_to_one(X6,X1,X2)
<=> ( surjective(X6,X1,X2)
& injective(X6,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',one_to_one) ).
fof(c_0_7,plain,
! [X40,X41,X42,X43,X45,X46,X47,X48,X49,X50,X52] :
( ( maps(X48,X49,X50)
| ~ apply(X48,esk9_3(X48,X49,X50),X52)
| ~ member(X52,X50)
| esk11_3(X48,X49,X50) != esk12_3(X48,X49,X50) )
& ( maps(X48,X49,X50)
| ~ apply(X48,esk9_3(X48,X49,X50),X52)
| ~ member(X52,X50)
| apply(X48,esk10_3(X48,X49,X50),esk12_3(X48,X49,X50)) )
& ( maps(X48,X49,X50)
| ~ apply(X48,esk9_3(X48,X49,X50),X52)
| ~ member(X52,X50)
| apply(X48,esk10_3(X48,X49,X50),esk11_3(X48,X49,X50)) )
& ( maps(X48,X49,X50)
| ~ apply(X48,esk9_3(X48,X49,X50),X52)
| ~ member(X52,X50)
| member(esk12_3(X48,X49,X50),X50) )
& ( maps(X48,X49,X50)
| ~ apply(X48,esk9_3(X48,X49,X50),X52)
| ~ member(X52,X50)
| member(esk11_3(X48,X49,X50),X50) )
& ( maps(X48,X49,X50)
| ~ apply(X48,esk9_3(X48,X49,X50),X52)
| ~ member(X52,X50)
| member(esk10_3(X48,X49,X50),X49) )
& ( maps(X48,X49,X50)
| member(esk9_3(X48,X49,X50),X49)
| esk11_3(X48,X49,X50) != esk12_3(X48,X49,X50) )
& ( maps(X48,X49,X50)
| member(esk9_3(X48,X49,X50),X49)
| apply(X48,esk10_3(X48,X49,X50),esk12_3(X48,X49,X50)) )
& ( maps(X48,X49,X50)
| member(esk9_3(X48,X49,X50),X49)
| apply(X48,esk10_3(X48,X49,X50),esk11_3(X48,X49,X50)) )
& ( maps(X48,X49,X50)
| member(esk9_3(X48,X49,X50),X49)
| member(esk12_3(X48,X49,X50),X50) )
& ( maps(X48,X49,X50)
| member(esk9_3(X48,X49,X50),X49)
| member(esk11_3(X48,X49,X50),X50) )
& ( maps(X48,X49,X50)
| member(esk9_3(X48,X49,X50),X49)
| member(esk10_3(X48,X49,X50),X49) )
& ( ~ maps(X40,X41,X42)
| X46 = X47
| ~ apply(X40,X45,X47)
| ~ apply(X40,X45,X46)
| ~ member(X47,X42)
| ~ member(X46,X42)
| ~ member(X45,X41) )
& ( ~ maps(X40,X41,X42)
| ~ member(X43,X41)
| apply(X40,X43,esk8_4(X40,X41,X42,X43)) )
& ( ~ maps(X40,X41,X42)
| ~ member(X43,X41)
| member(esk8_4(X40,X41,X42,X43),X42) ) ),
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_8,plain,
! [X31,X32,X33,X34,X35,X36,X37,X39] :
( ( ~ member(X37,X35)
| ~ member(X36,X33)
| apply(compose_function(X31,X32,X33,X34,X35),X36,X37)
| ~ apply(X31,X39,X37)
| ~ apply(X32,X36,X39)
| ~ member(X39,X34) )
& ( ~ member(X37,X35)
| ~ member(X36,X33)
| ~ apply(compose_function(X31,X32,X33,X34,X35),X36,X37)
| apply(X31,esk7_7(X31,X32,X33,X34,X35,X36,X37),X37) )
& ( ~ member(X37,X35)
| ~ member(X36,X33)
| ~ apply(compose_function(X31,X32,X33,X34,X35),X36,X37)
| apply(X32,X36,esk7_7(X31,X32,X33,X34,X35,X36,X37)) )
& ( ~ member(X37,X35)
| ~ member(X36,X33)
| ~ apply(compose_function(X31,X32,X33,X34,X35),X36,X37)
| member(esk7_7(X31,X32,X33,X34,X35,X36,X37),X34) ) ),
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_9,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_7]) ).
cnf(c_0_10,plain,
( ~ member(X7,X6)
| ~ member(X2,X4)
| ~ apply(compose_function(X3,X1,X4,X5,X6),X2,X7)
| apply(X1,X2,esk7_7(X3,X1,X4,X5,X6,X2,X7)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( ~ member(X7,X4)
| ~ member(X8,X6)
| ~ member(X7,X9)
| ~ member(X1,X10)
| ~ member(esk7_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 = esk7_7(X2,X3,X4,X5,X6,X7,X8) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| member(esk7_7(X1,X2,X3,X4,X5,X6,X7),X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,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 = esk7_7(X2,X3,X4,X5,X6,X7,X8) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk8_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_15,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) )
=> one_to_one(X6,X1,X2) ),
inference(assume_negation,[status(cth)],[thII16]) ).
cnf(c_0_16,plain,
( ~ member(X4,X2)
| ~ member(X4,X6)
| ~ member(X9,X8)
| ~ member(X4,X10)
| ~ member(esk8_4(X1,X2,X3,X4),X7)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X10,X7)
| ~ apply(compose_function(X5,X1,X6,X7,X8),X4,X9)
| esk8_4(X1,X2,X3,X4) = esk7_7(X5,X1,X6,X7,X8,X4,X9) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( ~ maps(X1,X2,X3)
| ~ member(X4,X2)
| member(esk8_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_18,negated_conjecture,
( ~ one_to_one(esk1_0,esk4_0,esk5_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_15])])])]) ).
cnf(c_0_19,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)
| esk8_4(X1,X2,X3,X4) = esk7_7(X5,X1,X6,X3,X7,X4,X8) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
maps(esk3_0,esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X25,X26,X27,X28,X29] :
( ( identity(X28,X29)
| ~ apply(X28,esk6_2(X28,X29),esk6_2(X28,X29)) )
& ( identity(X28,X29)
| member(esk6_2(X28,X29),X29) )
& ( apply(X25,X27,X27)
| ~ member(X27,X26)
| ~ identity(X25,X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[identity])])])])])])]) ).
cnf(c_0_22,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| apply(X1,esk7_7(X1,X2,X3,X4,X5,X6,X7),X7) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,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)
| esk8_4(esk3_0,X1,esk4_0,X2) = esk7_7(X3,esk3_0,X4,esk4_0,X5,X2,X6) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( ~ member(X3,X2)
| ~ identity(X1,X2)
| apply(X1,X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
identity(compose_function(esk1_0,esk3_0,esk5_0,esk4_0,esk5_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
maps(esk1_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
( ~ member(X5,X3)
| ~ member(X5,X6)
| ~ member(X1,X7)
| ~ member(esk8_4(X2,X3,X4,X5),X7)
| ~ maps(X2,X3,X4)
| ~ maps(X2,X6,X7)
| ~ apply(X2,X5,X1)
| X1 = esk8_4(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_28,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,esk8_4(esk3_0,X2,esk4_0,X3),X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,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_24,c_0_25]) ).
cnf(c_0_30,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)
| esk8_4(esk1_0,X1,esk5_0,X2) = esk7_7(X3,esk1_0,X4,esk5_0,X5,X2,X6) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
identity(compose_function(esk2_0,esk1_0,esk4_0,esk5_0,esk4_0),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,plain,
( ~ member(X5,X3)
| ~ member(X5,X6)
| ~ member(X1,X4)
| ~ maps(X2,X3,X4)
| ~ maps(X2,X6,X4)
| ~ apply(X2,X5,X1)
| X1 = esk8_4(X2,X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,esk5_0)
| ~ maps(esk3_0,X1,esk4_0)
| apply(esk1_0,esk8_4(esk3_0,X1,esk4_0,X2),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,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,esk8_4(esk1_0,X2,esk5_0,X3),X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_35,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_24,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(X4,X3)
| ~ member(X4,X2)
| ~ member(X4,esk5_0)
| ~ member(esk8_4(esk3_0,X3,esk4_0,X4),X1)
| ~ member(esk8_4(esk3_0,X3,esk4_0,X4),X5)
| ~ maps(esk1_0,X1,X2)
| ~ maps(esk1_0,X5,X2)
| ~ maps(esk3_0,X3,esk4_0)
| esk8_4(esk1_0,X1,X2,esk8_4(esk3_0,X3,esk4_0,X4)) = X4 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X2,esk4_0)
| ~ maps(esk1_0,X1,esk5_0)
| apply(esk2_0,esk8_4(esk1_0,X1,esk5_0,X2),X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( ~ member(X4,X3)
| ~ member(X4,X2)
| ~ member(X4,esk5_0)
| ~ member(esk8_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)
| esk8_4(esk1_0,X1,X2,esk8_4(esk3_0,X3,esk4_0,X4)) = X4 ),
inference(spm,[status(thm)],[c_0_36,c_0_17]) ).
fof(c_0_39,plain,
! [X66,X67,X68,X69,X70,X71,X72,X73,X74] :
( ( injective(X72,X73,X74)
| esk15_3(X72,X73,X74) != esk16_3(X72,X73,X74) )
& ( injective(X72,X73,X74)
| apply(X72,esk16_3(X72,X73,X74),esk17_3(X72,X73,X74)) )
& ( injective(X72,X73,X74)
| apply(X72,esk15_3(X72,X73,X74),esk17_3(X72,X73,X74)) )
& ( injective(X72,X73,X74)
| member(esk17_3(X72,X73,X74),X74) )
& ( injective(X72,X73,X74)
| member(esk16_3(X72,X73,X74),X73) )
& ( injective(X72,X73,X74)
| member(esk15_3(X72,X73,X74),X73) )
& ( X69 = X70
| ~ apply(X66,X70,X71)
| ~ apply(X66,X69,X71)
| ~ member(X71,X68)
| ~ member(X70,X67)
| ~ member(X69,X67)
| ~ injective(X66,X67,X68) ) ),
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_40,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,esk5_0)
| ~ member(esk8_4(esk3_0,X2,esk4_0,X1),X3)
| ~ maps(esk3_0,X2,esk4_0)
| ~ maps(esk1_0,X3,esk5_0)
| apply(esk2_0,X1,esk8_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_37,c_0_38]),c_0_26])]),c_0_17]) ).
cnf(c_0_41,plain,
( injective(X1,X2,X3)
| apply(X1,esk16_3(X1,X2,X3),esk17_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_42,plain,
( injective(X1,X2,X3)
| apply(X1,esk15_3(X1,X2,X3),esk17_3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,esk5_0)
| ~ maps(esk3_0,X2,esk4_0)
| apply(esk2_0,X1,esk8_4(esk3_0,X2,esk4_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_17]),c_0_26])]) ).
cnf(c_0_44,plain,
( ~ member(esk16_3(X1,X4,X5),X2)
| ~ member(esk16_3(X1,X4,X5),X6)
| ~ member(esk17_3(X1,X4,X5),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X6,X3)
| injective(X1,X4,X5)
| esk8_4(X1,X2,X3,esk16_3(X1,X4,X5)) = esk17_3(X1,X4,X5) ),
inference(spm,[status(thm)],[c_0_32,c_0_41]) ).
cnf(c_0_45,plain,
( injective(X1,X2,X3)
| member(esk16_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( ~ member(esk15_3(X1,X4,X5),X2)
| ~ member(esk15_3(X1,X4,X5),X6)
| ~ member(esk17_3(X1,X4,X5),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X6,X3)
| injective(X1,X4,X5)
| esk8_4(X1,X2,X3,esk15_3(X1,X4,X5)) = esk17_3(X1,X4,X5) ),
inference(spm,[status(thm)],[c_0_32,c_0_42]) ).
cnf(c_0_47,plain,
( injective(X1,X2,X3)
| member(esk15_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,negated_conjecture,
( ~ member(X3,X2)
| ~ member(X3,X4)
| ~ member(X1,X5)
| ~ member(X3,esk5_0)
| ~ member(esk8_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 = esk8_4(esk3_0,X2,esk4_0,X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_43]) ).
cnf(c_0_49,plain,
( ~ member(esk16_3(X1,X4,X5),X2)
| ~ member(esk17_3(X1,X4,X5),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X4,X3)
| injective(X1,X4,X5)
| esk8_4(X1,X2,X3,esk16_3(X1,X4,X5)) = esk17_3(X1,X4,X5) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
( ~ member(esk15_3(X1,X4,X5),X2)
| ~ member(esk17_3(X1,X4,X5),X3)
| ~ maps(X1,X2,X3)
| ~ maps(X1,X4,X3)
| injective(X1,X4,X5)
| esk8_4(X1,X2,X3,esk15_3(X1,X4,X5)) = esk17_3(X1,X4,X5) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_51,plain,
! [X56,X57,X58,X59,X61,X62,X63,X65] :
( ( surjective(X61,X62,X63)
| ~ apply(X61,X65,esk14_3(X61,X62,X63))
| ~ member(X65,X62) )
& ( surjective(X61,X62,X63)
| member(esk14_3(X61,X62,X63),X63) )
& ( ~ surjective(X56,X57,X58)
| ~ member(X59,X58)
| apply(X56,esk13_4(X56,X57,X58,X59),X59) )
& ( ~ surjective(X56,X57,X58)
| ~ member(X59,X58)
| member(esk13_4(X56,X57,X58,X59),X57) ) ),
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_52,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 = esk8_4(esk3_0,X2,esk4_0,X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_17]) ).
cnf(c_0_53,negated_conjecture,
maps(esk2_0,esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(esk16_3(esk1_0,X1,X2),X3)
| ~ member(esk17_3(esk1_0,X1,X2),esk5_0)
| ~ member(esk16_3(esk1_0,X1,X2),esk4_0)
| ~ maps(esk1_0,X1,esk5_0)
| ~ maps(esk1_0,X3,esk5_0)
| apply(esk2_0,esk17_3(esk1_0,X1,X2),esk16_3(esk1_0,X1,X2))
| injective(esk1_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( ~ member(esk15_3(esk1_0,X1,X2),X3)
| ~ member(esk17_3(esk1_0,X1,X2),esk5_0)
| ~ member(esk15_3(esk1_0,X1,X2),esk4_0)
| ~ maps(esk1_0,X1,esk5_0)
| ~ maps(esk1_0,X3,esk5_0)
| apply(esk2_0,esk17_3(esk1_0,X1,X2),esk15_3(esk1_0,X1,X2))
| injective(esk1_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_50]) ).
cnf(c_0_56,plain,
( ~ apply(X3,X1,esk14_3(X3,X2,X4))
| ~ member(X1,X2)
| surjective(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,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 = esk8_4(esk3_0,X2,esk4_0,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,negated_conjecture,
( ~ member(esk17_3(esk1_0,X1,X2),esk5_0)
| ~ member(esk16_3(esk1_0,X1,X2),esk4_0)
| ~ maps(esk1_0,X1,esk5_0)
| apply(esk2_0,esk17_3(esk1_0,X1,X2),esk16_3(esk1_0,X1,X2))
| injective(esk1_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_45]) ).
cnf(c_0_59,negated_conjecture,
( ~ member(esk17_3(esk1_0,X1,X2),esk5_0)
| ~ member(esk15_3(esk1_0,X1,X2),esk4_0)
| ~ maps(esk1_0,X1,esk5_0)
| apply(esk2_0,esk17_3(esk1_0,X1,X2),esk15_3(esk1_0,X1,X2))
| injective(esk1_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_47]) ).
cnf(c_0_60,plain,
( ~ member(X8,X5)
| ~ member(esk14_3(X1,X2,X3),X7)
| ~ member(esk7_7(X1,X4,X5,X6,X7,X8,esk14_3(X1,X2,X3)),X2)
| ~ apply(compose_function(X1,X4,X5,X6,X7),X8,esk14_3(X1,X2,X3))
| surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_56,c_0_22]) ).
cnf(c_0_61,negated_conjecture,
( ~ member(esk17_3(esk1_0,X2,X3),X1)
| ~ member(esk16_3(esk1_0,X2,X3),esk4_0)
| ~ member(esk17_3(esk1_0,X2,X3),esk5_0)
| ~ maps(esk1_0,X2,esk5_0)
| ~ maps(esk3_0,X1,esk4_0)
| injective(esk1_0,X2,X3)
| esk8_4(esk3_0,X1,esk4_0,esk17_3(esk1_0,X2,X3)) = esk16_3(esk1_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( ~ member(esk17_3(esk1_0,X2,X3),X1)
| ~ member(esk15_3(esk1_0,X2,X3),esk4_0)
| ~ member(esk17_3(esk1_0,X2,X3),esk5_0)
| ~ maps(esk1_0,X2,esk5_0)
| ~ maps(esk3_0,X1,esk4_0)
| injective(esk1_0,X2,X3)
| esk8_4(esk3_0,X1,esk4_0,esk17_3(esk1_0,X2,X3)) = esk15_3(esk1_0,X2,X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_59]) ).
cnf(c_0_63,plain,
( esk15_3(X1,X2,X3) != esk16_3(X1,X2,X3)
| injective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_64,plain,
! [X22,X23,X24] :
( ( one_to_one(X22,X23,X24)
| ~ surjective(X22,X23,X24)
| ~ injective(X22,X23,X24) )
& ( ~ one_to_one(X22,X23,X24)
| surjective(X22,X23,X24) )
& ( ~ one_to_one(X22,X23,X24)
| injective(X22,X23,X24) ) ),
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_65,plain,
( ~ member(X7,X5)
| ~ member(esk14_3(X1,X2,X3),X6)
| ~ apply(compose_function(X1,X4,X5,X2,X6),X7,esk14_3(X1,X2,X3))
| surjective(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_60,c_0_12]) ).
cnf(c_0_66,negated_conjecture,
( ~ member(esk17_3(esk1_0,X1,X2),X3)
| ~ member(esk15_3(esk1_0,X1,X2),esk4_0)
| ~ member(esk16_3(esk1_0,X1,X2),esk4_0)
| ~ member(esk17_3(esk1_0,X1,X2),esk5_0)
| ~ maps(esk1_0,X1,esk5_0)
| ~ maps(esk3_0,X3,esk4_0)
| injective(esk1_0,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_67,plain,
( injective(X1,X2,X3)
| member(esk17_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_68,negated_conjecture,
~ one_to_one(esk1_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_69,plain,
( ~ surjective(X1,X2,X3)
| ~ injective(X1,X2,X3)
| one_to_one(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( ~ member(esk14_3(esk1_0,esk4_0,X1),esk5_0)
| surjective(esk1_0,esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_29]) ).
cnf(c_0_71,plain,
( surjective(X1,X2,X3)
| member(esk14_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_72,negated_conjecture,
( ~ member(esk17_3(esk1_0,X1,esk5_0),X2)
| ~ member(esk15_3(esk1_0,X1,esk5_0),esk4_0)
| ~ member(esk16_3(esk1_0,X1,esk5_0),esk4_0)
| ~ maps(esk1_0,X1,esk5_0)
| ~ maps(esk3_0,X2,esk4_0)
| injective(esk1_0,X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( ~ injective(esk1_0,esk4_0,esk5_0)
| ~ surjective(esk1_0,esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
surjective(esk1_0,esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( ~ member(esk15_3(esk1_0,X1,esk5_0),esk4_0)
| ~ member(esk16_3(esk1_0,X1,esk5_0),esk4_0)
| ~ maps(esk1_0,X1,esk5_0)
| injective(esk1_0,X1,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_67]),c_0_20])]) ).
cnf(c_0_76,negated_conjecture,
~ injective(esk1_0,esk4_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).
cnf(c_0_77,negated_conjecture,
~ member(esk15_3(esk1_0,esk4_0,esk5_0),esk4_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_45]),c_0_26])]),c_0_76]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_47]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET725+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 % Computer : n001.cluster.edu
% 0.15/0.45 % Model : x86_64 x86_64
% 0.15/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.45 % Memory : 8046.5625MB
% 0.15/0.45 % OS : Linux 6.8.0-71-generic
% 0.15/0.45 % CPULimit : 300
% 0.15/0.45 % WCLimit : 300
% 0.15/0.45 % DateTime : Mon Sep 21 05:39:44 UTC 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 6.21/1.59 % Version: 3.5.1
% 6.21/1.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.21/1.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.21/1.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.21/1.59 % Starting new_bool_3 with 300s (1) cores
% 6.21/1.59 % Starting new_bool_1 with 300s (1) cores
% 6.21/1.59 % Starting sh5l with 300s (1) cores
% 6.21/1.59 % new_bool_1 with pid 2300484 completed with status 0
% 6.21/1.59 % Result found by new_bool_1
% 6.21/1.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.21/1.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.21/1.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.21/1.59 % Starting new_bool_3 with 300s (1) cores
% 6.21/1.59 % Starting new_bool_1 with 300s (1) cores
% 6.21/1.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.21/1.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.21/1.59 % Search class: FGUSF-FFMS33-SFFFFFNN
% 6.21/1.59 % partial match(1): FGUSS-FFMS33-SFFFFFNN
% 6.21/1.59 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 6.21/1.59 % Starting SubtermCWHack with 31s (1) cores
% 6.21/1.59 % SubtermCWHack with pid 2300487 completed with status 0
% 6.21/1.59 % Result found by SubtermCWHack
% 6.21/1.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.21/1.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.21/1.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.21/1.59 % Starting new_bool_3 with 300s (1) cores
% 6.21/1.59 % Starting new_bool_1 with 300s (1) cores
% 6.21/1.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.21/1.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.21/1.59 % Search class: FGUSF-FFMS33-SFFFFFNN
% 6.21/1.59 % partial match(1): FGUSS-FFMS33-SFFFFFNN
% 6.21/1.59 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 6.21/1.59 % Starting SubtermCWHack with 31s (1) cores
% 6.21/1.59 % Preprocessing time : 0.003 s
% 6.21/1.59
% 6.21/1.59 % Proof found!
% 6.21/1.59 % SZS status Theorem
% 6.21/1.59 % SZS output start CNFRefutation
% See solution above
% 6.21/1.59 % Parsed axioms : 29
% 6.21/1.59 % Removed by relevancy pruning/SinE : 22
% 6.21/1.59 % Initial clauses : 42
% 6.21/1.59 % Removed in clause preprocessing : 0
% 6.21/1.59 % Initial clauses in saturation : 42
% 6.21/1.59 % Processed clauses : 1512
% 6.21/1.59 % ...of these trivial : 0
% 6.21/1.59 % ...subsumed : 749
% 6.21/1.59 % ...remaining for further processing : 763
% 6.21/1.59 % Other redundant clauses eliminated : 0
% 6.21/1.59 % Clauses deleted for lack of memory : 0
% 6.21/1.59 % Backward-subsumed : 76
% 6.21/1.59 % Backward-rewritten : 2
% 6.21/1.59 % Generated clauses : 9139
% 6.21/1.59 % ...of the previous two non-redundant : 8937
% 6.21/1.59 % ...aggressively subsumed : 0
% 6.21/1.59 % Contextual simplify-reflections : 31
% 6.21/1.59 % Paramodulations : 9139
% 6.21/1.59 % Factorizations : 0
% 6.21/1.59 % NegExts : 0
% 6.21/1.59 % Equation resolutions : 0
% 6.21/1.59 % Disequality decompositions : 0
% 6.21/1.59 % Total rewrite steps : 261
% 6.21/1.59 % ...of those cached : 252
% 6.21/1.59 % Propositional unsat checks : 0
% 6.21/1.59 % Propositional check models : 0
% 6.21/1.59 % Propositional check unsatisfiable : 0
% 6.21/1.59 % Propositional clauses : 0
% 6.21/1.59 % Propositional clauses after purity: 0
% 6.21/1.59 % Propositional unsat core size : 0
% 6.21/1.59 % Propositional preprocessing time : 0.000
% 6.21/1.59 % Propositional encoding time : 0.000
% 6.21/1.59 % Propositional solver time : 0.000
% 6.21/1.59 % Success case prop preproc time : 0.000
% 6.21/1.59 % Success case prop encoding time : 0.000
% 6.21/1.59 % Success case prop solver time : 0.000
% 6.21/1.59 % Current number of processed clauses : 685
% 6.21/1.59 % Positive orientable unit clauses : 14
% 6.21/1.59 % Positive unorientable unit clauses: 0
% 6.21/1.59 % Negative unit clauses : 3
% 6.21/1.59 % Non-unit-clauses : 668
% 6.21/1.59 % Current number of unprocessed clauses: 7429
% 6.21/1.59 % ...number of literals in the above : 83610
% 6.21/1.59 % Current number of archived formulas : 0
% 6.21/1.59 % Current number of archived clauses : 78
% 6.21/1.59 % Clause-clause subsumption calls (NU) : 140262
% 6.21/1.59 % Rec. Clause-clause subsumption calls : 4624
% 6.21/1.59 % Non-unit clause-clause subsumptions : 856
% 6.21/1.59 % Unit Clause-clause subsumption calls : 554
% 6.21/1.59 % Rewrite failures with RHS unbound : 0
% 6.21/1.59 % BW rewrite match attempts : 11
% 6.21/1.59 % BW rewrite match successes : 2
% 6.21/1.59 % Condensation attempts : 0
% 6.21/1.59 % Condensation successes : 0
% 6.21/1.59 % Termbank termtop insertions : 484878
% 6.21/1.59 % Search garbage collected termcells : 1131
% 6.21/1.59
% 6.21/1.59 % -------------------------------------------------
% 6.21/1.59 % User time : 0.940 s
% 6.21/1.59 % System time : 0.023 s
% 6.21/1.59 % Total time : 0.963 s
% 6.21/1.59 % Maximum resident set size: 3692 pages
% 6.21/1.59
% 6.21/1.59 % -------------------------------------------------
% 6.21/1.59 % User time : 0.947 s
% 6.21/1.59 % System time : 0.027 s
% 6.21/1.59 % Total time : 0.974 s
% 6.21/1.59 % Maximum resident set size: 4608 pages
% 6.21/1.59 % E exiting
%------------------------------------------------------------------------------