%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET747+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 : n011.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 02:15:08 PM UTC 2026
% Result : Theorem 218.56s 32.94s
% Output : CNFRefutation 218.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 65 ( 23 unt; 0 def)
% Number of atoms : 321 ( 12 equ)
% Maximal formula atoms : 55 ( 4 avg)
% Number of connectives : 404 ( 148 ~; 181 |; 63 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-5 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-7 aty)
% Number of variables : 221 ( 0 sgn 95 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thII38,conjecture,
! [X6,X10,X1,X2,X11,X15,X16,X17] :
( ( decreasing(X10,X2,X16,X11,X17)
& increasing(X6,X1,X15,X2,X16)
& maps(X10,X2,X11)
& maps(X6,X1,X2) )
=> decreasing(compose_function(X10,X6,X1,X2,X11),X1,X15,X11,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII38) ).
fof(increasing_function,axiom,
! [X6,X1,X15,X2,X16] :
( increasing(X6,X1,X15,X2,X16)
<=> ! [X13,X7,X14,X8] :
( ( apply(X6,X14,X8)
& apply(X6,X13,X7)
& apply(X15,X13,X14)
& member(X8,X2)
& member(X14,X1)
& member(X7,X2)
& member(X13,X1) )
=> apply(X16,X7,X8) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',increasing_function) ).
fof(decreasing_function,axiom,
! [X6,X1,X15,X2,X16] :
( decreasing(X6,X1,X15,X2,X16)
<=> ! [X13,X7,X14,X8] :
( ( apply(X6,X14,X8)
& apply(X6,X13,X7)
& apply(X15,X13,X14)
& member(X8,X2)
& member(X14,X1)
& member(X7,X2)
& member(X13,X1) )
=> apply(X16,X8,X7) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',decreasing_function) ).
fof(compose_function,axiom,
! [X10,X6,X1,X2,X11,X3,X12] :
( ( member(X12,X11)
& member(X3,X1) )
=> ( apply(compose_function(X10,X6,X1,X2,X11),X3,X12)
<=> ? [X5] :
( apply(X10,X5,X12)
& apply(X6,X3,X5)
& member(X5,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(maps,axiom,
! [X6,X1,X2] :
( maps(X6,X1,X2)
<=> ( ! [X3,X7,X8] :
( ( member(X8,X2)
& member(X7,X2)
& member(X3,X1) )
=> ( ( apply(X6,X3,X8)
& apply(X6,X3,X7) )
=> X7 = X8 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X5] :
( apply(X6,X3,X5)
& member(X5,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).
fof(c_0_5,negated_conjecture,
~ ! [X6,X10,X1,X2,X11,X15,X16,X17] :
( ( decreasing(X10,X2,X16,X11,X17)
& increasing(X6,X1,X15,X2,X16)
& maps(X10,X2,X11)
& maps(X6,X1,X2) )
=> decreasing(compose_function(X10,X6,X1,X2,X11),X1,X15,X11,X17) ),
inference(assume_negation,[status(cth)],[thII38]) ).
fof(c_0_6,plain,
! [X53,X54,X55,X56,X57,X58,X59,X60,X61,X62,X63,X64,X65,X66] :
( ( increasing(X62,X63,X64,X65,X66)
| ~ apply(X66,esk15_5(X62,X63,X64,X65,X66),esk17_5(X62,X63,X64,X65,X66)) )
& ( increasing(X62,X63,X64,X65,X66)
| apply(X62,esk16_5(X62,X63,X64,X65,X66),esk17_5(X62,X63,X64,X65,X66)) )
& ( increasing(X62,X63,X64,X65,X66)
| apply(X62,esk14_5(X62,X63,X64,X65,X66),esk15_5(X62,X63,X64,X65,X66)) )
& ( increasing(X62,X63,X64,X65,X66)
| apply(X64,esk14_5(X62,X63,X64,X65,X66),esk16_5(X62,X63,X64,X65,X66)) )
& ( increasing(X62,X63,X64,X65,X66)
| member(esk17_5(X62,X63,X64,X65,X66),X65) )
& ( increasing(X62,X63,X64,X65,X66)
| member(esk16_5(X62,X63,X64,X65,X66),X63) )
& ( increasing(X62,X63,X64,X65,X66)
| member(esk15_5(X62,X63,X64,X65,X66),X65) )
& ( increasing(X62,X63,X64,X65,X66)
| member(esk14_5(X62,X63,X64,X65,X66),X63) )
& ( apply(X57,X59,X61)
| ~ apply(X53,X60,X61)
| ~ apply(X53,X58,X59)
| ~ apply(X55,X58,X60)
| ~ member(X61,X56)
| ~ member(X60,X54)
| ~ member(X59,X56)
| ~ member(X58,X54)
| ~ increasing(X53,X54,X55,X56,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)],[increasing_function])])])])])])]) ).
fof(c_0_7,negated_conjecture,
( ~ decreasing(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)
& decreasing(esk2_0,esk4_0,esk7_0,esk5_0,esk8_0)
& increasing(esk1_0,esk3_0,esk6_0,esk4_0,esk7_0)
& maps(esk2_0,esk4_0,esk5_0)
& maps(esk1_0,esk3_0,esk4_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,plain,
! [X26,X27,X28,X29,X30,X31,X32,X33,X34,X35,X36,X37,X38,X39] :
( ( decreasing(X35,X36,X37,X38,X39)
| ~ apply(X39,esk12_5(X35,X36,X37,X38,X39),esk10_5(X35,X36,X37,X38,X39)) )
& ( decreasing(X35,X36,X37,X38,X39)
| apply(X35,esk11_5(X35,X36,X37,X38,X39),esk12_5(X35,X36,X37,X38,X39)) )
& ( decreasing(X35,X36,X37,X38,X39)
| apply(X35,esk9_5(X35,X36,X37,X38,X39),esk10_5(X35,X36,X37,X38,X39)) )
& ( decreasing(X35,X36,X37,X38,X39)
| apply(X37,esk9_5(X35,X36,X37,X38,X39),esk11_5(X35,X36,X37,X38,X39)) )
& ( decreasing(X35,X36,X37,X38,X39)
| member(esk12_5(X35,X36,X37,X38,X39),X38) )
& ( decreasing(X35,X36,X37,X38,X39)
| member(esk11_5(X35,X36,X37,X38,X39),X36) )
& ( decreasing(X35,X36,X37,X38,X39)
| member(esk10_5(X35,X36,X37,X38,X39),X38) )
& ( decreasing(X35,X36,X37,X38,X39)
| member(esk9_5(X35,X36,X37,X38,X39),X36) )
& ( apply(X30,X34,X32)
| ~ apply(X26,X33,X34)
| ~ apply(X26,X31,X32)
| ~ apply(X28,X31,X33)
| ~ member(X34,X29)
| ~ member(X33,X27)
| ~ member(X32,X29)
| ~ member(X31,X27)
| ~ decreasing(X26,X27,X28,X29,X30) ) ),
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)],[decreasing_function])])])])])])]) ).
cnf(c_0_9,plain,
( ~ apply(X1,X8,X9)
| ~ apply(X1,X6,X7)
| ~ apply(X3,X6,X8)
| ~ member(X9,X4)
| ~ member(X8,X2)
| ~ member(X7,X4)
| ~ member(X6,X2)
| ~ increasing(X1,X2,X3,X4,X5)
| apply(X5,X7,X9) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
increasing(esk1_0,esk3_0,esk6_0,esk4_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
~ decreasing(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( decreasing(X2,X3,X1,X4,X5)
| apply(X1,esk9_5(X2,X3,X1,X4,X5),esk11_5(X2,X3,X1,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( decreasing(X1,X2,X3,X4,X5)
| member(esk11_5(X1,X2,X3,X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( decreasing(X1,X2,X3,X4,X5)
| member(esk9_5(X1,X2,X3,X4,X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_15,plain,
! [X44,X45,X46,X47,X48,X49,X50,X52] :
( ( ~ member(X50,X48)
| ~ member(X49,X46)
| apply(compose_function(X44,X45,X46,X47,X48),X49,X50)
| ~ apply(X44,X52,X50)
| ~ apply(X45,X49,X52)
| ~ member(X52,X47) )
& ( ~ member(X50,X48)
| ~ member(X49,X46)
| ~ apply(compose_function(X44,X45,X46,X47,X48),X49,X50)
| apply(X44,esk13_7(X44,X45,X46,X47,X48,X49,X50),X50) )
& ( ~ member(X50,X48)
| ~ member(X49,X46)
| ~ apply(compose_function(X44,X45,X46,X47,X48),X49,X50)
| apply(X45,X49,esk13_7(X44,X45,X46,X47,X48,X49,X50)) )
& ( ~ member(X50,X48)
| ~ member(X49,X46)
| ~ apply(compose_function(X44,X45,X46,X47,X48),X49,X50)
| member(esk13_7(X44,X45,X46,X47,X48,X49,X50),X47) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[compose_function])])])])])]) ).
cnf(c_0_16,plain,
( decreasing(X1,X2,X3,X4,X5)
| apply(X1,esk11_5(X1,X2,X3,X4,X5),esk12_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( decreasing(X1,X2,X3,X4,X5)
| member(esk12_5(X1,X2,X3,X4,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_18,plain,
! [X71,X72,X73,X74,X76,X77,X78,X79,X80,X81,X83] :
( ( maps(X79,X80,X81)
| ~ apply(X79,esk19_3(X79,X80,X81),X83)
| ~ member(X83,X81)
| esk21_3(X79,X80,X81) != esk22_3(X79,X80,X81) )
& ( maps(X79,X80,X81)
| ~ apply(X79,esk19_3(X79,X80,X81),X83)
| ~ member(X83,X81)
| apply(X79,esk20_3(X79,X80,X81),esk22_3(X79,X80,X81)) )
& ( maps(X79,X80,X81)
| ~ apply(X79,esk19_3(X79,X80,X81),X83)
| ~ member(X83,X81)
| apply(X79,esk20_3(X79,X80,X81),esk21_3(X79,X80,X81)) )
& ( maps(X79,X80,X81)
| ~ apply(X79,esk19_3(X79,X80,X81),X83)
| ~ member(X83,X81)
| member(esk22_3(X79,X80,X81),X81) )
& ( maps(X79,X80,X81)
| ~ apply(X79,esk19_3(X79,X80,X81),X83)
| ~ member(X83,X81)
| member(esk21_3(X79,X80,X81),X81) )
& ( maps(X79,X80,X81)
| ~ apply(X79,esk19_3(X79,X80,X81),X83)
| ~ member(X83,X81)
| member(esk20_3(X79,X80,X81),X80) )
& ( maps(X79,X80,X81)
| member(esk19_3(X79,X80,X81),X80)
| esk21_3(X79,X80,X81) != esk22_3(X79,X80,X81) )
& ( maps(X79,X80,X81)
| member(esk19_3(X79,X80,X81),X80)
| apply(X79,esk20_3(X79,X80,X81),esk22_3(X79,X80,X81)) )
& ( maps(X79,X80,X81)
| member(esk19_3(X79,X80,X81),X80)
| apply(X79,esk20_3(X79,X80,X81),esk21_3(X79,X80,X81)) )
& ( maps(X79,X80,X81)
| member(esk19_3(X79,X80,X81),X80)
| member(esk22_3(X79,X80,X81),X81) )
& ( maps(X79,X80,X81)
| member(esk19_3(X79,X80,X81),X80)
| member(esk21_3(X79,X80,X81),X81) )
& ( maps(X79,X80,X81)
| member(esk19_3(X79,X80,X81),X80)
| member(esk20_3(X79,X80,X81),X80) )
& ( ~ maps(X71,X72,X73)
| X77 = X78
| ~ apply(X71,X76,X78)
| ~ apply(X71,X76,X77)
| ~ member(X78,X73)
| ~ member(X77,X73)
| ~ member(X76,X72) )
& ( ~ maps(X71,X72,X73)
| ~ member(X74,X72)
| apply(X71,X74,esk18_4(X71,X72,X73,X74)) )
& ( ~ maps(X71,X72,X73)
| ~ member(X74,X72)
| member(esk18_4(X71,X72,X73,X74),X73) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[maps])])])])])])]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X3,esk3_0)
| ~ member(X1,esk4_0)
| ~ member(X4,esk3_0)
| ~ member(X2,esk4_0)
| ~ apply(esk1_0,X3,X1)
| ~ apply(esk1_0,X4,X2)
| ~ apply(esk6_0,X3,X4)
| apply(esk7_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_20,negated_conjecture,
apply(esk6_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_21,negated_conjecture,
member(esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk3_0),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_22,negated_conjecture,
member(esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk3_0),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_23,plain,
( ~ member(X7,X6)
| ~ member(X2,X4)
| ~ apply(compose_function(X3,X1,X4,X5,X6),X2,X7)
| apply(X1,X2,esk13_7(X3,X1,X4,X5,X6,X2,X7)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
apply(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_25,negated_conjecture,
member(esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk5_0),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_26,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| member(esk13_7(X1,X2,X3,X4,X5,X6,X7),X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,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_18]) ).
cnf(c_0_28,negated_conjecture,
maps(esk2_0,esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_29,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk18_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,plain,
( ~ maps(X1,X2,X3)
| ~ member(X4,X2)
| member(esk18_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,plain,
( ~ apply(X1,X8,X9)
| ~ apply(X1,X6,X7)
| ~ apply(X3,X6,X8)
| ~ member(X9,X4)
| ~ member(X8,X2)
| ~ member(X7,X4)
| ~ member(X6,X2)
| ~ decreasing(X1,X2,X3,X4,X5)
| apply(X5,X9,X7) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,negated_conjecture,
decreasing(esk2_0,esk4_0,esk7_0,esk5_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(X1,esk4_0)
| ~ member(X2,esk4_0)
| ~ apply(esk1_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X1)
| ~ apply(esk1_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X2)
| apply(esk7_0,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_34,negated_conjecture,
apply(esk1_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_21])]) ).
cnf(c_0_35,negated_conjecture,
member(esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_25]),c_0_21])]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(X3,esk4_0)
| ~ member(X1,esk5_0)
| ~ member(X2,esk5_0)
| ~ apply(esk2_0,X3,X1)
| ~ apply(esk2_0,X3,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( ~ member(X1,esk4_0)
| apply(esk2_0,X1,esk18_4(esk2_0,esk4_0,esk5_0,X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( ~ member(X1,esk4_0)
| member(esk18_4(esk2_0,esk4_0,esk5_0,X1),esk5_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_39,plain,
( ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| apply(X1,esk13_7(X1,X2,X3,X4,X5,X6,X7),X7) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_40,negated_conjecture,
maps(esk1_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_41,plain,
( decreasing(X1,X2,X3,X4,X5)
| apply(X1,esk9_5(X1,X2,X3,X4,X5),esk10_5(X1,X2,X3,X4,X5)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_42,plain,
( decreasing(X1,X2,X3,X4,X5)
| member(esk10_5(X1,X2,X3,X4,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_43,negated_conjecture,
( ~ member(X3,esk4_0)
| ~ member(X2,esk5_0)
| ~ member(X4,esk4_0)
| ~ member(X1,esk5_0)
| ~ apply(esk2_0,X3,X2)
| ~ apply(esk2_0,X4,X1)
| ~ apply(esk7_0,X3,X4)
| apply(esk8_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_44,negated_conjecture,
( ~ member(X1,esk4_0)
| ~ apply(esk1_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X1)
| apply(esk7_0,X1,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_45,negated_conjecture,
( ~ member(X2,esk4_0)
| ~ member(X1,esk5_0)
| ~ apply(esk2_0,X2,X1)
| X1 = esk18_4(esk2_0,esk4_0,esk5_0,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_46,negated_conjecture,
apply(esk2_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_24]),c_0_25]),c_0_21])]) ).
cnf(c_0_47,negated_conjecture,
( ~ member(X3,esk3_0)
| ~ member(X1,esk4_0)
| ~ member(X2,esk4_0)
| ~ apply(esk1_0,X3,X1)
| ~ apply(esk1_0,X3,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( ~ member(X1,esk3_0)
| apply(esk1_0,X1,esk18_4(esk1_0,esk3_0,esk4_0,X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_40]) ).
cnf(c_0_49,negated_conjecture,
( ~ member(X1,esk3_0)
| member(esk18_4(esk1_0,esk3_0,esk4_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_40]) ).
cnf(c_0_50,negated_conjecture,
apply(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
inference(spm,[status(thm)],[c_0_11,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
member(esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk5_0),
inference(spm,[status(thm)],[c_0_11,c_0_42]) ).
cnf(c_0_52,negated_conjecture,
( ~ member(X3,esk4_0)
| ~ member(X2,esk5_0)
| ~ member(X1,esk5_0)
| ~ apply(esk2_0,X3,X2)
| ~ apply(esk1_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X3)
| ~ apply(esk2_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),X1)
| apply(esk8_0,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_35])]) ).
cnf(c_0_53,negated_conjecture,
esk18_4(esk2_0,esk4_0,esk5_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk11_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))) = esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_25]),c_0_35])]) ).
cnf(c_0_54,negated_conjecture,
( ~ member(X2,esk3_0)
| ~ member(X1,esk4_0)
| ~ apply(esk1_0,X2,X1)
| X1 = esk18_4(esk1_0,esk3_0,esk4_0,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_55,negated_conjecture,
apply(esk1_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_50]),c_0_51]),c_0_22])]) ).
cnf(c_0_56,negated_conjecture,
member(esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_50]),c_0_51]),c_0_22])]) ).
cnf(c_0_57,negated_conjecture,
( ~ member(X2,esk4_0)
| ~ member(X1,esk5_0)
| ~ apply(esk2_0,X2,X1)
| ~ apply(esk1_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X2)
| apply(esk8_0,esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_37]),c_0_53]),c_0_53]),c_0_25]),c_0_35])]) ).
cnf(c_0_58,negated_conjecture,
esk18_4(esk1_0,esk3_0,esk4_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)) = esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_22])]) ).
cnf(c_0_59,negated_conjecture,
apply(esk2_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_50]),c_0_51]),c_0_22])]) ).
cnf(c_0_60,plain,
( ~ apply(X1,esk12_5(X2,X3,X4,X5,X1),esk10_5(X2,X3,X4,X5,X1))
| decreasing(X2,X3,X4,X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_61,negated_conjecture,
( ~ member(X1,esk5_0)
| ~ apply(esk2_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),X1)
| apply(esk8_0,esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_48]),c_0_58]),c_0_58]),c_0_56]),c_0_22])]) ).
cnf(c_0_62,negated_conjecture,
esk18_4(esk2_0,esk4_0,esk5_0,esk13_7(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0,esk9_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0))) = esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_59]),c_0_51]),c_0_56])]) ).
cnf(c_0_63,negated_conjecture,
~ apply(esk8_0,esk12_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0),esk10_5(compose_function(esk2_0,esk1_0,esk3_0,esk4_0,esk5_0),esk3_0,esk6_0,esk5_0,esk8_0)),
inference(spm,[status(thm)],[c_0_11,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_37]),c_0_62]),c_0_62]),c_0_51]),c_0_56])]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET747+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n011.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 05:35:25 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.56 Running first-order theorem proving
% 0.24/0.56 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
% 218.56/32.94 % Version: 3.5.1
% 218.56/32.94 % Preprocessing class: FSLSSMSSSSSNFFN.
% 218.56/32.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.56/32.94 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 218.56/32.94 % Starting new_bool_3 with 300s (1) cores
% 218.56/32.94 % Starting new_bool_1 with 300s (1) cores
% 218.56/32.94 % Starting sh5l with 300s (1) cores
% 218.56/32.94 % new_bool_3 with pid 1075801 completed with status 0
% 218.56/32.94 % Result found by new_bool_3
% 218.56/32.94 % Preprocessing class: FSLSSMSSSSSNFFN.
% 218.56/32.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.56/32.94 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 218.56/32.94 % Starting new_bool_3 with 300s (1) cores
% 218.56/32.94 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 218.56/32.94 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 218.56/32.94 % Search class: FGUSF-FFMS33-SFFFFFNN
% 218.56/32.94 % partial match(1): FGUSS-FFMS33-SFFFFFNN
% 218.56/32.94 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 218.56/32.94 % Starting SubtermCWHack with 31s (1) cores
% 218.56/32.94 % SubtermCWHack with pid 1075805 completed with status 8
% 218.56/32.94 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 150s (1) cores
% 218.56/32.94 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 1076223 completed with status 0
% 218.56/32.94 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 218.56/32.94 % Preprocessing class: FSLSSMSSSSSNFFN.
% 218.56/32.94 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 218.56/32.94 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 218.56/32.94 % Starting new_bool_3 with 300s (1) cores
% 218.56/32.94 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 218.56/32.94 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 218.56/32.94 % Search class: FGUSF-FFMS33-SFFFFFNN
% 218.56/32.94 % partial match(1): FGUSS-FFMS33-SFFFFFNN
% 218.56/32.94 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 218.56/32.94 % Starting SubtermCWHack with 31s (1) cores
% 218.56/32.94 % SubtermCWHack with pid 1075805 completed with status 8
% 218.56/32.94 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 150s (1) cores
% 218.56/32.94 % Preprocessing time : 0.003 s
% 218.56/32.94 % Presaturation interreduction done
% 218.56/32.94
% 218.56/32.94 % Proof found!
% 218.56/32.94 % SZS status Theorem
% 218.56/32.94 % SZS output start CNFRefutation
% See solution above
% 218.56/32.94 % Parsed axioms : 29
% 218.56/32.94 % Removed by relevancy pruning/SinE : 24
% 218.56/32.94 % Initial clauses : 42
% 218.56/32.94 % Removed in clause preprocessing : 0
% 218.56/32.94 % Initial clauses in saturation : 42
% 218.56/32.94 % Processed clauses : 172
% 218.56/32.94 % ...of these trivial : 0
% 218.56/32.94 % ...subsumed : 2
% 218.56/32.94 % ...remaining for further processing : 170
% 218.56/32.94 % Other redundant clauses eliminated : 0
% 218.56/32.94 % Clauses deleted for lack of memory : 0
% 218.56/32.94 % Backward-subsumed : 0
% 218.56/32.94 % Backward-rewritten : 0
% 218.56/32.94 % Generated clauses : 844
% 218.56/32.94 % ...of the previous two non-redundant : 780
% 218.56/32.94 % ...aggressively subsumed : 0
% 218.56/32.94 % Contextual simplify-reflections : 2
% 218.56/32.94 % Paramodulations : 844
% 218.56/32.94 % Factorizations : 0
% 218.56/32.94 % NegExts : 0
% 218.56/32.94 % Equation resolutions : 0
% 218.56/32.94 % Disequality decompositions : 0
% 218.56/32.94 % Total rewrite steps : 197
% 218.56/32.94 % ...of those cached : 183
% 218.56/32.94 % Propositional unsat checks : 0
% 218.56/32.94 % Propositional check models : 0
% 218.56/32.94 % Propositional check unsatisfiable : 0
% 218.56/32.94 % Propositional clauses : 0
% 218.56/32.94 % Propositional clauses after purity: 0
% 218.56/32.94 % Propositional unsat core size : 0
% 218.56/32.94 % Propositional preprocessing time : 0.000
% 218.56/32.94 % Propositional encoding time : 0.000
% 218.56/32.94 % Propositional solver time : 0.000
% 218.56/32.94 % Success case prop preproc time : 0.000
% 218.56/32.94 % Success case prop encoding time : 0.000
% 218.56/32.94 % Success case prop solver time : 0.000
% 218.56/32.94 % Current number of processed clauses : 128
% 218.56/32.94 % Positive orientable unit clauses : 21
% 218.56/32.94 % Positive unorientable unit clauses: 0
% 218.56/32.94 % Negative unit clauses : 2
% 218.56/32.94 % Non-unit-clauses : 105
% 218.56/32.94 % Current number of unprocessed clauses: 685
% 218.56/32.94 % ...number of literals in the above : 5439
% 218.56/32.94 % Current number of archived formulas : 0
% 218.56/32.94 % Current number of archived clauses : 42
% 218.56/32.94 % Clause-clause subsumption calls (NU) : 2202
% 218.56/32.94 % Rec. Clause-clause subsumption calls : 128
% 218.56/32.94 % Non-unit clause-clause subsumptions : 4
% 218.56/32.94 % Unit Clause-clause subsumption calls : 0
% 218.56/32.94 % Rewrite failures with RHS unbound : 0
% 218.56/32.94 % BW rewrite match attempts : 13
% 218.56/32.94 % BW rewrite match successes : 0
% 218.56/32.94 % Condensation attempts : 0
% 218.56/32.94 % Condensation successes : 0
% 218.56/32.94 % Termbank termtop insertions : 45948
% 218.56/32.94 % Search garbage collected termcells : 1215
% 218.56/32.94
% 218.56/32.94 % -------------------------------------------------
% 218.56/32.94 % User time : 30.578 s
% 218.56/32.94 % System time : 0.586 s
% 218.56/32.94 % Total time : 31.164 s
% 218.56/32.94 % Maximum resident set size: 3692 pages
% 218.56/32.94
% 218.56/32.94 % -------------------------------------------------
% 218.56/32.94 % User time : 30.587 s
% 218.56/32.94 % System time : 0.591 s
% 218.56/32.94 % Total time : 31.177 s
% 218.56/32.94 % Maximum resident set size: 4608 pages
% 218.56/32.94 % E exiting
%------------------------------------------------------------------------------