%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET763+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 : n005.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 02:15:10 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 15 unt; 0 def)
% Number of atoms : 147 ( 4 equ)
% Maximal formula atoms : 55 ( 4 avg)
% Number of connectives : 173 ( 61 ~; 68 |; 34 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 84 ( 6 sgn 51 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIIa13,conjecture,
! [X6,X1,X2,X3] :
( ( equal_set(image2(X6,X3),empty_set)
& subset(X3,X1)
& maps(X6,X1,X2) )
=> equal_set(X3,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa13) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
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(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(c_0_6,negated_conjecture,
~ ! [X6,X1,X2,X3] :
( ( equal_set(image2(X6,X3),empty_set)
& subset(X3,X1)
& maps(X6,X1,X2) )
=> equal_set(X3,empty_set) ),
inference(assume_negation,[status(cth)],[thIIa13]) ).
fof(c_0_7,plain,
! [X21,X22] :
( ( equal_set(X21,X22)
| ~ subset(X22,X21)
| ~ subset(X21,X22) )
& ( ~ equal_set(X21,X22)
| subset(X22,X21) )
& ( ~ equal_set(X21,X22)
| subset(X21,X22) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
fof(c_0_8,negated_conjecture,
( ~ equal_set(esk4_0,empty_set)
& equal_set(image2(esk1_0,esk4_0),empty_set)
& 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_6])])])]) ).
fof(c_0_9,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(c_0_10,plain,
! [X32,X33,X34,X35,X36] :
( ( subset(X35,X36)
| ~ member(esk6_2(X35,X36),X36) )
& ( subset(X35,X36)
| member(esk6_2(X35,X36),X35) )
& ( member(X34,X33)
| ~ member(X34,X32)
| ~ subset(X32,X33) ) ),
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_11,plain,
( ~ equal_set(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
equal_set(image2(esk1_0,esk4_0),empty_set),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X23] : ~ member(X23,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])]) ).
fof(c_0_14,plain,
! [X24,X25,X26,X28,X29,X30,X31] :
( ( member(X30,image2(X28,X29))
| ~ apply(X28,X31,X30)
| ~ member(X31,X29) )
& ( ~ member(X26,image2(X24,X25))
| apply(X24,esk5_3(X24,X25,X26),X26) )
& ( ~ member(X26,image2(X24,X25))
| member(esk5_3(X24,X25,X26),X25) ) ),
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])])])])])])]) ).
fof(c_0_15,plain,
! [X38,X39,X40,X41,X43,X44,X45,X46,X47,X48,X50] :
( ( maps(X46,X47,X48)
| ~ apply(X46,esk8_3(X46,X47,X48),X50)
| ~ member(X50,X48)
| esk10_3(X46,X47,X48) != esk11_3(X46,X47,X48) )
& ( maps(X46,X47,X48)
| ~ apply(X46,esk8_3(X46,X47,X48),X50)
| ~ member(X50,X48)
| apply(X46,esk9_3(X46,X47,X48),esk11_3(X46,X47,X48)) )
& ( maps(X46,X47,X48)
| ~ apply(X46,esk8_3(X46,X47,X48),X50)
| ~ member(X50,X48)
| apply(X46,esk9_3(X46,X47,X48),esk10_3(X46,X47,X48)) )
& ( maps(X46,X47,X48)
| ~ apply(X46,esk8_3(X46,X47,X48),X50)
| ~ member(X50,X48)
| member(esk11_3(X46,X47,X48),X48) )
& ( maps(X46,X47,X48)
| ~ apply(X46,esk8_3(X46,X47,X48),X50)
| ~ member(X50,X48)
| member(esk10_3(X46,X47,X48),X48) )
& ( maps(X46,X47,X48)
| ~ apply(X46,esk8_3(X46,X47,X48),X50)
| ~ member(X50,X48)
| member(esk9_3(X46,X47,X48),X47) )
& ( maps(X46,X47,X48)
| member(esk8_3(X46,X47,X48),X47)
| esk10_3(X46,X47,X48) != esk11_3(X46,X47,X48) )
& ( maps(X46,X47,X48)
| member(esk8_3(X46,X47,X48),X47)
| apply(X46,esk9_3(X46,X47,X48),esk11_3(X46,X47,X48)) )
& ( maps(X46,X47,X48)
| member(esk8_3(X46,X47,X48),X47)
| apply(X46,esk9_3(X46,X47,X48),esk10_3(X46,X47,X48)) )
& ( maps(X46,X47,X48)
| member(esk8_3(X46,X47,X48),X47)
| member(esk11_3(X46,X47,X48),X48) )
& ( maps(X46,X47,X48)
| member(esk8_3(X46,X47,X48),X47)
| member(esk10_3(X46,X47,X48),X48) )
& ( maps(X46,X47,X48)
| member(esk8_3(X46,X47,X48),X47)
| member(esk9_3(X46,X47,X48),X47) )
& ( ~ maps(X38,X39,X40)
| X44 = X45
| ~ apply(X38,X43,X45)
| ~ apply(X38,X43,X44)
| ~ member(X45,X40)
| ~ member(X44,X40)
| ~ member(X43,X39) )
& ( ~ maps(X38,X39,X40)
| ~ member(X41,X39)
| apply(X38,X41,esk7_4(X38,X39,X40,X41)) )
& ( ~ maps(X38,X39,X40)
| ~ member(X41,X39)
| member(esk7_4(X38,X39,X40,X41),X40) ) ),
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_16,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
subset(image2(esk1_0,esk4_0),empty_set),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ apply(X3,X1,X4)
| ~ member(X1,X2)
| member(X4,image2(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ maps(X1,X3,X4)
| ~ member(X2,X3)
| apply(X1,X2,esk7_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
~ member(X1,image2(esk1_0,esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_22,plain,
( ~ member(X4,X2)
| ~ member(X4,X5)
| ~ maps(X1,X2,X3)
| member(esk7_4(X1,X2,X3,X4),image2(X1,X5)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
subset(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,plain,
( subset(X1,X2)
| member(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,negated_conjecture,
( ~ member(X3,X1)
| ~ member(X3,esk4_0)
| ~ maps(esk1_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
maps(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(X1,esk4_0)
| member(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
~ equal_set(esk4_0,empty_set),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_30,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
~ member(X1,esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_32,negated_conjecture,
~ subset(esk4_0,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
subset(esk4_0,X1),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET763+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:36:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.45 % Version: 3.5.1
% 0.10/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % new_bool_3 with pid 2660198 completed with status 0
% 0.10/0.45 % Result found by new_bool_3
% 0.10/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.45 % Search class: FGUSF-FFMS32-SFFFFFNN
% 0.10/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.45 % SubtermCWHack with pid 2660201 completed with status 0
% 0.10/0.45 % Result found by SubtermCWHack
% 0.10/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.45 % Search class: FGUSF-FFMS32-SFFFFFNN
% 0.10/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.45 % Preprocessing time : 0.002 s
% 0.10/0.45
% 0.10/0.45 % Proof found!
% 0.10/0.45 % SZS status Theorem
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 29
% 0.10/0.45 % Removed by relevancy pruning/SinE : 23
% 0.10/0.45 % Initial clauses : 29
% 0.10/0.45 % Removed in clause preprocessing : 0
% 0.10/0.45 % Initial clauses in saturation : 29
% 0.10/0.45 % Processed clauses : 312
% 0.10/0.45 % ...of these trivial : 17
% 0.10/0.45 % ...subsumed : 185
% 0.10/0.45 % ...remaining for further processing : 110
% 0.10/0.45 % Other redundant clauses eliminated : 0
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 4
% 0.10/0.45 % Backward-rewritten : 4
% 0.10/0.45 % Generated clauses : 544
% 0.10/0.45 % ...of the previous two non-redundant : 393
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 1
% 0.10/0.45 % Paramodulations : 544
% 0.10/0.45 % Factorizations : 0
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 0
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 167
% 0.10/0.45 % ...of those cached : 8
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 102
% 0.10/0.45 % Positive orientable unit clauses : 35
% 0.10/0.45 % Positive unorientable unit clauses: 0
% 0.10/0.45 % Negative unit clauses : 17
% 0.10/0.45 % Non-unit-clauses : 50
% 0.10/0.45 % Current number of unprocessed clauses: 109
% 0.10/0.45 % ...number of literals in the above : 240
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 8
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 193
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 166
% 0.10/0.45 % Non-unit clause-clause subsumptions : 7
% 0.10/0.45 % Unit Clause-clause subsumption calls : 67
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 141
% 0.10/0.45 % BW rewrite match successes : 4
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 8449
% 0.10/0.45 % Search garbage collected termcells : 807
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.011 s
% 0.10/0.45 % System time : 0.006 s
% 0.10/0.45 % Total time : 0.017 s
% 0.10/0.45 % Maximum resident set size: 3692 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.013 s
% 0.10/0.45 % System time : 0.011 s
% 0.10/0.45 % Total time : 0.024 s
% 0.10/0.45 % Maximum resident set size: 4864 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------