%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET754+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 02:15:09 PM UTC 2026
% Result : Theorem 0.14s 0.49s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 5 unt; 0 def)
% Number of atoms : 164 ( 4 equ)
% Maximal formula atoms : 55 ( 4 avg)
% Number of connectives : 198 ( 71 ~; 86 |; 31 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 114 ( 1 sgn 54 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(inverse_image2,axiom,
! [X6,X2,X3] :
( member(X3,inverse_image2(X6,X2))
<=> ? [X5] :
( apply(X6,X3,X5)
& member(X5,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',inverse_image2) ).
fof(maps,axiom,
! [X6,X1,X2] :
( maps(X6,X1,X2)
<=> ( ! [X3,X7,X8] :
( ( member(X8,X2)
& member(X7,X2)
& member(X3,X1) )
=> ( ( apply(X6,X3,X8)
& apply(X6,X3,X7) )
=> X7 = X8 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X5] :
( apply(X6,X3,X5)
& member(X5,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',maps) ).
fof(thIIa04,conjecture,
! [X6,X1,X2,X11] :
( ( subset(X11,X1)
& maps(X6,X1,X2) )
=> subset(X11,inverse_image2(X6,image2(X6,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa04) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(image2,axiom,
! [X6,X1,X5] :
( member(X5,image2(X6,X1))
<=> ? [X3] :
( apply(X6,X3,X5)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',image2) ).
fof(c_0_5,plain,
! [X27,X28,X29,X31,X32,X33,X34] :
( ( member(X33,inverse_image2(X31,X32))
| ~ apply(X31,X33,X34)
| ~ member(X34,X32) )
& ( ~ member(X29,inverse_image2(X27,X28))
| apply(X27,X29,esk6_3(X27,X28,X29)) )
& ( ~ member(X29,inverse_image2(X27,X28))
| member(esk6_3(X27,X28,X29),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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inverse_image2])])])])])])]) ).
fof(c_0_6,plain,
! [X43,X44,X45,X46,X48,X49,X50,X51,X52,X53,X55] :
( ( maps(X51,X52,X53)
| ~ apply(X51,esk9_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| esk11_3(X51,X52,X53) != esk12_3(X51,X52,X53) )
& ( maps(X51,X52,X53)
| ~ apply(X51,esk9_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| apply(X51,esk10_3(X51,X52,X53),esk12_3(X51,X52,X53)) )
& ( maps(X51,X52,X53)
| ~ apply(X51,esk9_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| apply(X51,esk10_3(X51,X52,X53),esk11_3(X51,X52,X53)) )
& ( maps(X51,X52,X53)
| ~ apply(X51,esk9_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| member(esk12_3(X51,X52,X53),X53) )
& ( maps(X51,X52,X53)
| ~ apply(X51,esk9_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| member(esk11_3(X51,X52,X53),X53) )
& ( maps(X51,X52,X53)
| ~ apply(X51,esk9_3(X51,X52,X53),X55)
| ~ member(X55,X53)
| member(esk10_3(X51,X52,X53),X52) )
& ( maps(X51,X52,X53)
| member(esk9_3(X51,X52,X53),X52)
| esk11_3(X51,X52,X53) != esk12_3(X51,X52,X53) )
& ( maps(X51,X52,X53)
| member(esk9_3(X51,X52,X53),X52)
| apply(X51,esk10_3(X51,X52,X53),esk12_3(X51,X52,X53)) )
& ( maps(X51,X52,X53)
| member(esk9_3(X51,X52,X53),X52)
| apply(X51,esk10_3(X51,X52,X53),esk11_3(X51,X52,X53)) )
& ( maps(X51,X52,X53)
| member(esk9_3(X51,X52,X53),X52)
| member(esk12_3(X51,X52,X53),X53) )
& ( maps(X51,X52,X53)
| member(esk9_3(X51,X52,X53),X52)
| member(esk11_3(X51,X52,X53),X53) )
& ( maps(X51,X52,X53)
| member(esk9_3(X51,X52,X53),X52)
| member(esk10_3(X51,X52,X53),X52) )
& ( ~ maps(X43,X44,X45)
| X49 = X50
| ~ apply(X43,X48,X50)
| ~ apply(X43,X48,X49)
| ~ member(X50,X45)
| ~ member(X49,X45)
| ~ member(X48,X44) )
& ( ~ maps(X43,X44,X45)
| ~ member(X46,X44)
| apply(X43,X46,esk8_4(X43,X44,X45,X46)) )
& ( ~ maps(X43,X44,X45)
| ~ member(X46,X44)
| member(esk8_4(X43,X44,X45,X46),X45) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[maps])])])])])])]) ).
cnf(c_0_7,plain,
( ~ apply(X3,X4,X1)
| ~ member(X1,X2)
| member(X4,inverse_image2(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk8_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,negated_conjecture,
~ ! [X6,X1,X2,X11] :
( ( subset(X11,X1)
& maps(X6,X1,X2) )
=> subset(X11,inverse_image2(X6,image2(X6,X11))) ),
inference(assume_negation,[status(cth)],[thIIa04]) ).
cnf(c_0_10,plain,
( ~ member(X1,X4)
| ~ member(esk8_4(X2,X4,X5,X1),X3)
| ~ maps(X2,X4,X5)
| member(X1,inverse_image2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( ~ maps(X1,X2,X3)
| ~ member(X4,X2)
| member(esk8_4(X1,X2,X3,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,negated_conjecture,
( ~ subset(esk4_0,inverse_image2(esk1_0,image2(esk1_0,esk4_0)))
& subset(esk4_0,esk2_0)
& maps(esk1_0,esk2_0,esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_13,plain,
! [X21,X22,X23,X24,X25] :
( ( subset(X24,X25)
| ~ member(esk5_2(X24,X25),X25) )
& ( subset(X24,X25)
| member(esk5_2(X24,X25),X24) )
& ( member(X23,X22)
| ~ member(X23,X21)
| ~ subset(X21,X22) ) ),
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)],[subset])])])])])])]) ).
cnf(c_0_14,plain,
( ~ member(X1,X4)
| ~ maps(X2,X4,X3)
| member(X1,inverse_image2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
maps(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( ~ member(esk5_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(X1,esk2_0)
| member(X1,inverse_image2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
subset(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X35,X36,X37,X39,X40,X41,X42] :
( ( member(X41,image2(X39,X40))
| ~ apply(X39,X42,X41)
| ~ member(X42,X40) )
& ( ~ member(X37,image2(X35,X36))
| apply(X35,esk7_3(X35,X36,X37),X37) )
& ( ~ member(X37,image2(X35,X36))
| member(esk7_3(X35,X36,X37),X36) ) ),
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)],[image2])])])])])])]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(esk5_2(X1,inverse_image2(esk1_0,esk3_0)),esk2_0)
| subset(X1,inverse_image2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ member(X2,inverse_image2(X1,X3))
| apply(X1,X2,esk6_3(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_24,plain,
( ~ apply(X3,X1,X4)
| ~ member(X1,X2)
| member(X4,image2(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( ~ member(esk5_2(X1,inverse_image2(esk1_0,esk3_0)),esk4_0)
| subset(X1,inverse_image2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( subset(X1,X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,plain,
( ~ member(X1,inverse_image2(X2,X4))
| ~ member(esk6_3(X2,X4,X1),X3)
| member(X1,inverse_image2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_23]) ).
cnf(c_0_28,plain,
( ~ member(X3,X4)
| ~ member(X3,inverse_image2(X1,X2))
| member(esk6_3(X1,X2,X3),image2(X1,X4)) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
subset(esk4_0,inverse_image2(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( ~ member(X1,X3)
| ~ member(X1,inverse_image2(X2,X4))
| member(X1,inverse_image2(X2,image2(X2,X3))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,inverse_image2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X1,esk4_0)
| member(X1,inverse_image2(esk1_0,image2(esk1_0,X2))) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(esk5_2(X1,inverse_image2(esk1_0,image2(esk1_0,X2))),X2)
| ~ member(esk5_2(X1,inverse_image2(esk1_0,image2(esk1_0,X2))),esk4_0)
| subset(X1,inverse_image2(esk1_0,image2(esk1_0,X2))) ),
inference(spm,[status(thm)],[c_0_16,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( ~ member(esk5_2(esk4_0,inverse_image2(esk1_0,image2(esk1_0,X1))),X1)
| subset(esk4_0,inverse_image2(esk1_0,image2(esk1_0,X1))) ),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_35,negated_conjecture,
~ subset(esk4_0,inverse_image2(esk1_0,image2(esk1_0,esk4_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET754+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:33:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.49 % Version: 3.5.1
% 0.14/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.49 % Starting sh5l with 300s (1) cores
% 0.14/0.49 % new_bool_1 with pid 278857 completed with status 0
% 0.14/0.49 % Result found by new_bool_1
% 0.14/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.49 % Search class: FGUSF-FFMF32-SFFFFFNN
% 0.14/0.49 % partial match(1): FGHSF-FFMF32-SFFFFFNN
% 0.14/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.49 % SubtermCWHack with pid 278861 completed with status 0
% 0.14/0.49 % Result found by SubtermCWHack
% 0.14/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.49 % Search class: FGUSF-FFMF32-SFFFFFNN
% 0.14/0.49 % partial match(1): FGHSF-FFMF32-SFFFFFNN
% 0.14/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.49 % Preprocessing time : 0.002 s
% 0.14/0.49
% 0.14/0.49 % Proof found!
% 0.14/0.49 % SZS status Theorem
% 0.14/0.49 % SZS output start CNFRefutation
% See solution above
% 0.14/0.49 % Parsed axioms : 29
% 0.14/0.49 % Removed by relevancy pruning/SinE : 24
% 0.14/0.49 % Initial clauses : 27
% 0.14/0.49 % Removed in clause preprocessing : 0
% 0.14/0.49 % Initial clauses in saturation : 27
% 0.14/0.49 % Processed clauses : 496
% 0.14/0.49 % ...of these trivial : 1
% 0.14/0.49 % ...subsumed : 254
% 0.14/0.49 % ...remaining for further processing : 241
% 0.14/0.49 % Other redundant clauses eliminated : 0
% 0.14/0.49 % Clauses deleted for lack of memory : 0
% 0.14/0.49 % Backward-subsumed : 0
% 0.14/0.49 % Backward-rewritten : 0
% 0.14/0.49 % Generated clauses : 2357
% 0.14/0.49 % ...of the previous two non-redundant : 2344
% 0.14/0.49 % ...aggressively subsumed : 0
% 0.14/0.49 % Contextual simplify-reflections : 0
% 0.14/0.49 % Paramodulations : 2357
% 0.14/0.49 % Factorizations : 0
% 0.14/0.49 % NegExts : 0
% 0.14/0.49 % Equation resolutions : 0
% 0.14/0.49 % Disequality decompositions : 0
% 0.14/0.49 % Total rewrite steps : 10
% 0.14/0.49 % ...of those cached : 3
% 0.14/0.49 % Propositional unsat checks : 0
% 0.14/0.49 % Propositional check models : 0
% 0.14/0.49 % Propositional check unsatisfiable : 0
% 0.14/0.49 % Propositional clauses : 0
% 0.14/0.49 % Propositional clauses after purity: 0
% 0.14/0.49 % Propositional unsat core size : 0
% 0.14/0.49 % Propositional preprocessing time : 0.000
% 0.14/0.49 % Propositional encoding time : 0.000
% 0.14/0.49 % Propositional solver time : 0.000
% 0.14/0.49 % Success case prop preproc time : 0.000
% 0.14/0.49 % Success case prop encoding time : 0.000
% 0.14/0.49 % Success case prop solver time : 0.000
% 0.14/0.49 % Current number of processed clauses : 241
% 0.14/0.49 % Positive orientable unit clauses : 25
% 0.14/0.49 % Positive unorientable unit clauses: 0
% 0.14/0.49 % Negative unit clauses : 1
% 0.14/0.49 % Non-unit-clauses : 215
% 0.14/0.49 % Current number of unprocessed clauses: 1830
% 0.14/0.49 % ...number of literals in the above : 7646
% 0.14/0.49 % Current number of archived formulas : 0
% 0.14/0.49 % Current number of archived clauses : 0
% 0.14/0.49 % Clause-clause subsumption calls (NU) : 9102
% 0.14/0.49 % Rec. Clause-clause subsumption calls : 6813
% 0.14/0.49 % Non-unit clause-clause subsumptions : 254
% 0.14/0.49 % Unit Clause-clause subsumption calls : 79
% 0.14/0.49 % Rewrite failures with RHS unbound : 0
% 0.14/0.49 % BW rewrite match attempts : 19
% 0.14/0.49 % BW rewrite match successes : 0
% 0.14/0.49 % Condensation attempts : 0
% 0.14/0.49 % Condensation successes : 0
% 0.14/0.49 % Termbank termtop insertions : 53036
% 0.14/0.49 % Search garbage collected termcells : 861
% 0.14/0.49
% 0.14/0.49 % -------------------------------------------------
% 0.14/0.49 % User time : 0.063 s
% 0.14/0.49 % System time : 0.003 s
% 0.14/0.49 % Total time : 0.066 s
% 0.14/0.49 % Maximum resident set size: 3692 pages
% 0.14/0.49
% 0.14/0.49 % -------------------------------------------------
% 0.14/0.49 % User time : 0.064 s
% 0.14/0.49 % System time : 0.009 s
% 0.14/0.49 % Total time : 0.073 s
% 0.14/0.49 % Maximum resident set size: 4864 pages
% 0.14/0.49 % E exiting
%------------------------------------------------------------------------------