%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET755+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 : n012.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 0.02s 0.42s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 4 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 24 ~; 23 |; 15 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 59 ( 0 sgn 28 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIIa05,conjecture,
! [X6,X1,X2,X3,X5] :
( ( subset(X3,X5)
& subset(X5,X2)
& subset(X3,X2)
& maps(X6,X1,X2) )
=> subset(inverse_image2(X6,X3),inverse_image2(X6,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa05) ).
fof(inverse_image2,axiom,
! [X6,X2,X3] :
( member(X3,inverse_image2(X6,X2))
<=> ? [X5] :
( apply(X6,X3,X5)
& member(X5,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_image2) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(c_0_3,negated_conjecture,
~ ! [X6,X1,X2,X3,X5] :
( ( subset(X3,X5)
& subset(X5,X2)
& subset(X3,X2)
& maps(X6,X1,X2) )
=> subset(inverse_image2(X6,X3),inverse_image2(X6,X5)) ),
inference(assume_negation,[status(cth)],[thIIa05]) ).
fof(c_0_4,plain,
! [X28,X29,X30,X32,X33,X34,X35] :
( ( member(X34,inverse_image2(X32,X33))
| ~ apply(X32,X34,X35)
| ~ member(X35,X33) )
& ( ~ member(X30,inverse_image2(X28,X29))
| apply(X28,X30,esk7_3(X28,X29,X30)) )
& ( ~ member(X30,inverse_image2(X28,X29))
| member(esk7_3(X28,X29,X30),X29) ) ),
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_5,plain,
! [X22,X23,X24,X25,X26] :
( ( subset(X25,X26)
| ~ member(esk6_2(X25,X26),X26) )
& ( subset(X25,X26)
| member(esk6_2(X25,X26),X25) )
& ( member(X24,X23)
| ~ member(X24,X22)
| ~ subset(X22,X23) ) ),
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])])])])])])]) ).
fof(c_0_6,negated_conjecture,
( ~ subset(inverse_image2(esk1_0,esk4_0),inverse_image2(esk1_0,esk5_0))
& subset(esk4_0,esk5_0)
& subset(esk5_0,esk3_0)
& subset(esk4_0,esk3_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_3])])])]) ).
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_4]) ).
cnf(c_0_8,plain,
( ~ member(X2,inverse_image2(X1,X3))
| apply(X1,X2,esk7_3(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ member(X1,inverse_image2(X2,X4))
| ~ member(esk7_3(X2,X4,X1),X3)
| member(X1,inverse_image2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( ~ member(X1,inverse_image2(X2,X3))
| ~ member(esk7_3(X2,X3,X1),esk4_0)
| member(X1,inverse_image2(X2,esk5_0)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
( ~ member(X3,inverse_image2(X1,X2))
| member(esk7_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,plain,
( ~ member(esk6_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
( ~ member(X1,inverse_image2(X2,esk4_0))
| member(X1,inverse_image2(X2,esk5_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(esk6_2(X1,inverse_image2(X2,esk5_0)),inverse_image2(X2,esk4_0))
| subset(X1,inverse_image2(X2,esk5_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| member(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,negated_conjecture,
~ subset(inverse_image2(esk1_0,esk4_0),inverse_image2(esk1_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
subset(inverse_image2(X1,esk4_0),inverse_image2(X1,esk5_0)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET755+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:35:37 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.02/0.39 Running first-order theorem proving
% 0.02/0.39 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
% 0.02/0.41 % Version: 3.5.1
% 0.02/0.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.02/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.02/0.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.02/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.02/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.02/0.41 % Starting sh5l with 300s (1) cores
% 0.02/0.41 % new_bool_1 with pid 1654851 completed with status 0
% 0.02/0.41 % Result found by new_bool_1
% 0.02/0.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.02/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.02/0.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.02/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.02/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.02/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.02/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.02/0.41 % Search class: FGUSF-FFMS32-SFFFFFNN
% 0.02/0.41 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.02/0.41 % Starting SubtermCWHack with 31s (1) cores
% 0.02/0.41 % SubtermCWHack with pid 1654854 completed with status 0
% 0.02/0.42 % Result found by SubtermCWHack
% 0.02/0.42 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.02/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.02/0.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.02/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.02/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.02/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.02/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.02/0.42 % Search class: FGUSF-FFMS32-SFFFFFNN
% 0.02/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.02/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.02/0.42 % Preprocessing time : 0.001 s
% 0.02/0.42
% 0.02/0.42 % Proof found!
% 0.02/0.42 % SZS status Theorem
% 0.02/0.42 % SZS output start CNFRefutation
% See solution above
% 0.02/0.42 % Parsed axioms : 29
% 0.02/0.42 % Removed by relevancy pruning/SinE : 25
% 0.02/0.42 % Initial clauses : 26
% 0.02/0.42 % Removed in clause preprocessing : 0
% 0.02/0.42 % Initial clauses in saturation : 26
% 0.02/0.42 % Processed clauses : 50
% 0.02/0.42 % ...of these trivial : 0
% 0.02/0.42 % ...subsumed : 4
% 0.02/0.42 % ...remaining for further processing : 46
% 0.02/0.42 % Other redundant clauses eliminated : 0
% 0.02/0.42 % Clauses deleted for lack of memory : 0
% 0.02/0.42 % Backward-subsumed : 0
% 0.02/0.42 % Backward-rewritten : 1
% 0.02/0.42 % Generated clauses : 64
% 0.02/0.42 % ...of the previous two non-redundant : 58
% 0.02/0.42 % ...aggressively subsumed : 0
% 0.02/0.42 % Contextual simplify-reflections : 0
% 0.02/0.42 % Paramodulations : 64
% 0.02/0.42 % Factorizations : 0
% 0.02/0.42 % NegExts : 0
% 0.02/0.42 % Equation resolutions : 0
% 0.02/0.42 % Disequality decompositions : 0
% 0.02/0.42 % Total rewrite steps : 4
% 0.02/0.42 % ...of those cached : 0
% 0.02/0.42 % Propositional unsat checks : 0
% 0.02/0.42 % Propositional check models : 0
% 0.02/0.42 % Propositional check unsatisfiable : 0
% 0.02/0.42 % Propositional clauses : 0
% 0.02/0.42 % Propositional clauses after purity: 0
% 0.02/0.42 % Propositional unsat core size : 0
% 0.02/0.42 % Propositional preprocessing time : 0.000
% 0.02/0.42 % Propositional encoding time : 0.000
% 0.02/0.42 % Propositional solver time : 0.000
% 0.02/0.42 % Success case prop preproc time : 0.000
% 0.02/0.42 % Success case prop encoding time : 0.000
% 0.02/0.42 % Success case prop solver time : 0.000
% 0.02/0.42 % Current number of processed clauses : 45
% 0.02/0.42 % Positive orientable unit clauses : 8
% 0.02/0.42 % Positive unorientable unit clauses: 0
% 0.02/0.42 % Negative unit clauses : 0
% 0.02/0.42 % Non-unit-clauses : 37
% 0.02/0.42 % Current number of unprocessed clauses: 34
% 0.02/0.42 % ...number of literals in the above : 116
% 0.02/0.42 % Current number of archived formulas : 0
% 0.02/0.42 % Current number of archived clauses : 1
% 0.02/0.42 % Clause-clause subsumption calls (NU) : 149
% 0.02/0.42 % Rec. Clause-clause subsumption calls : 109
% 0.02/0.42 % Non-unit clause-clause subsumptions : 4
% 0.02/0.42 % Unit Clause-clause subsumption calls : 17
% 0.02/0.42 % Rewrite failures with RHS unbound : 0
% 0.02/0.42 % BW rewrite match attempts : 6
% 0.02/0.42 % BW rewrite match successes : 1
% 0.02/0.42 % Condensation attempts : 0
% 0.02/0.42 % Condensation successes : 0
% 0.02/0.42 % Termbank termtop insertions : 3195
% 0.02/0.42 % Search garbage collected termcells : 815
% 0.02/0.42
% 0.02/0.42 % -------------------------------------------------
% 0.02/0.42 % User time : 0.006 s
% 0.02/0.42 % System time : 0.002 s
% 0.02/0.42 % Total time : 0.008 s
% 0.02/0.42 % Maximum resident set size: 3948 pages
% 0.02/0.42
% 0.02/0.42 % -------------------------------------------------
% 0.02/0.42 % User time : 0.008 s
% 0.02/0.42 % System time : 0.006 s
% 0.02/0.42 % Total time : 0.014 s
% 0.02/0.42 % Maximum resident set size: 4864 pages
% 0.02/0.42 % E exiting
%------------------------------------------------------------------------------