%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 02:15:23 PM UTC 2026
% Result : Theorem 0.25s 0.54s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 67 ( 23 ~; 31 |; 5 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ! [X1,X2] :
( equalish(X1,X2)
<=> ! [X3] :
( a_member_of(X3,X1)
<=> a_member_of(X3,X2) ) )
=> ! [X1,X2] :
( equalish(X1,X2)
<=> equalish(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(c_0_1,negated_conjecture,
~ ( ! [X1,X2] :
( equalish(X1,X2)
<=> ! [X3] :
( a_member_of(X3,X1)
<=> a_member_of(X3,X2) ) )
=> ! [X1,X2] :
( equalish(X1,X2)
<=> equalish(X2,X1) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(c_0_2,negated_conjecture,
! [X4,X5,X6,X7,X8,X9] :
( ( equalish(esk3_0,esk2_0)
| equalish(esk2_0,esk3_0) )
& ( ~ equalish(esk3_0,esk2_0)
| ~ equalish(esk2_0,esk3_0) )
& ( equalish(X8,X9)
| a_member_of(esk1_2(X8,X9),X9)
| a_member_of(esk1_2(X8,X9),X8) )
& ( equalish(X8,X9)
| ~ a_member_of(esk1_2(X8,X9),X9)
| ~ a_member_of(esk1_2(X8,X9),X8) )
& ( ~ equalish(X4,X5)
| a_member_of(X7,X4)
| ~ a_member_of(X7,X5) )
& ( ~ equalish(X4,X5)
| a_member_of(X6,X5)
| ~ a_member_of(X6,X4) ) ),
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)],[c_0_1])])])])])])]) ).
cnf(c_0_3,negated_conjecture,
( ~ equalish(X2,X3)
| ~ a_member_of(X1,X2)
| a_member_of(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
( equalish(esk3_0,esk2_0)
| equalish(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( ~ equalish(X3,X2)
| ~ a_member_of(X1,X2)
| a_member_of(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
( ~ a_member_of(X1,esk2_0)
| a_member_of(X1,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_5]) ).
cnf(c_0_7,negated_conjecture,
( equalish(X1,X2)
| a_member_of(esk1_2(X1,X2),X2)
| a_member_of(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8,negated_conjecture,
( equalish(esk2_0,X1)
| a_member_of(esk1_2(esk2_0,X1),X1)
| a_member_of(esk1_2(esk2_0,X1),esk3_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,negated_conjecture,
( ~ a_member_of(esk1_2(X1,X2),X2)
| ~ a_member_of(esk1_2(X1,X2),X1)
| equalish(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
( equalish(esk2_0,esk3_0)
| a_member_of(esk1_2(esk2_0,esk3_0),esk3_0) ),
inference(ef,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( ~ a_member_of(esk1_2(esk2_0,esk3_0),esk2_0)
| equalish(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,negated_conjecture,
( ~ a_member_of(X1,esk3_0)
| a_member_of(X1,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_4]),c_0_3]) ).
cnf(c_0_13,negated_conjecture,
( equalish(X1,esk2_0)
| a_member_of(esk1_2(X1,esk2_0),X1)
| a_member_of(esk1_2(X1,esk2_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_14,negated_conjecture,
( ~ equalish(esk3_0,esk2_0)
| ~ equalish(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
equalish(esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( equalish(esk3_0,esk2_0)
| a_member_of(esk1_2(esk3_0,esk2_0),esk3_0) ),
inference(ef,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
~ equalish(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_18,negated_conjecture,
( ~ a_member_of(esk1_2(X1,esk2_0),X1)
| ~ a_member_of(esk1_2(X1,esk2_0),esk3_0)
| equalish(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
a_member_of(esk1_2(esk3_0,esk2_0),esk3_0),
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_19])]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n013.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:37:21 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.51 Running first-order theorem proving
% 0.25/0.51 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
% 0.25/0.54 % Version: 3.5.1
% 0.25/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.54 % Starting sh5l with 300s (1) cores
% 0.25/0.54 % new_bool_1 with pid 41307 completed with status 0
% 0.25/0.54 % Result found by new_bool_1
% 0.25/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.54 % Search class: FGHNF-FFSF22-SFFFFFNN
% 0.25/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.54 % SubtermCWHack with pid 41312 completed with status 0
% 0.25/0.54 % Result found by SubtermCWHack
% 0.25/0.54 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.54 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.54 % Search class: FGHNF-FFSF22-SFFFFFNN
% 0.25/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.54 % Preprocessing time : 0.001 s
% 0.25/0.54
% 0.25/0.54 % Proof found!
% 0.25/0.54 % SZS status Theorem
% 0.25/0.54 % SZS output start CNFRefutation
% See solution above
% 0.25/0.54 % Parsed axioms : 1
% 0.25/0.54 % Removed by relevancy pruning/SinE : 0
% 0.25/0.54 % Initial clauses : 6
% 0.25/0.54 % Removed in clause preprocessing : 0
% 0.25/0.54 % Initial clauses in saturation : 6
% 0.25/0.54 % Processed clauses : 23
% 0.25/0.54 % ...of these trivial : 0
% 0.25/0.54 % ...subsumed : 3
% 0.25/0.54 % ...remaining for further processing : 20
% 0.25/0.54 % Other redundant clauses eliminated : 0
% 0.25/0.54 % Clauses deleted for lack of memory : 0
% 0.25/0.54 % Backward-subsumed : 1
% 0.25/0.54 % Backward-rewritten : 5
% 0.25/0.54 % Generated clauses : 30
% 0.25/0.54 % ...of the previous two non-redundant : 21
% 0.25/0.54 % ...aggressively subsumed : 0
% 0.25/0.54 % Contextual simplify-reflections : 4
% 0.25/0.54 % Paramodulations : 23
% 0.25/0.54 % Factorizations : 6
% 0.25/0.54 % NegExts : 0
% 0.25/0.54 % Equation resolutions : 0
% 0.25/0.54 % Disequality decompositions : 0
% 0.25/0.54 % Total rewrite steps : 9
% 0.25/0.54 % ...of those cached : 5
% 0.25/0.54 % Propositional unsat checks : 0
% 0.25/0.54 % Propositional check models : 0
% 0.25/0.54 % Propositional check unsatisfiable : 0
% 0.25/0.54 % Propositional clauses : 0
% 0.25/0.54 % Propositional clauses after purity: 0
% 0.25/0.54 % Propositional unsat core size : 0
% 0.25/0.54 % Propositional preprocessing time : 0.000
% 0.25/0.54 % Propositional encoding time : 0.000
% 0.25/0.54 % Propositional solver time : 0.000
% 0.25/0.54 % Success case prop preproc time : 0.000
% 0.25/0.54 % Success case prop encoding time : 0.000
% 0.25/0.54 % Success case prop solver time : 0.000
% 0.25/0.54 % Current number of processed clauses : 13
% 0.25/0.54 % Positive orientable unit clauses : 3
% 0.25/0.54 % Positive unorientable unit clauses: 0
% 0.25/0.54 % Negative unit clauses : 1
% 0.25/0.54 % Non-unit-clauses : 9
% 0.25/0.54 % Current number of unprocessed clauses: 4
% 0.25/0.54 % ...number of literals in the above : 9
% 0.25/0.54 % Current number of archived formulas : 0
% 0.25/0.54 % Current number of archived clauses : 7
% 0.25/0.54 % Clause-clause subsumption calls (NU) : 27
% 0.25/0.54 % Rec. Clause-clause subsumption calls : 22
% 0.25/0.54 % Non-unit clause-clause subsumptions : 7
% 0.25/0.54 % Unit Clause-clause subsumption calls : 7
% 0.25/0.54 % Rewrite failures with RHS unbound : 0
% 0.25/0.54 % BW rewrite match attempts : 8
% 0.25/0.54 % BW rewrite match successes : 3
% 0.25/0.54 % Condensation attempts : 0
% 0.25/0.54 % Condensation successes : 0
% 0.25/0.54 % Termbank termtop insertions : 943
% 0.25/0.54 % Search garbage collected termcells : 221
% 0.25/0.54
% 0.25/0.54 % -------------------------------------------------
% 0.25/0.54 % User time : 0.004 s
% 0.25/0.54 % System time : 0.002 s
% 0.25/0.54 % Total time : 0.006 s
% 0.25/0.54 % Maximum resident set size: 3628 pages
% 0.25/0.54
% 0.25/0.54 % -------------------------------------------------
% 0.25/0.54 % User time : 0.005 s
% 0.25/0.54 % System time : 0.008 s
% 0.25/0.54 % Total time : 0.013 s
% 0.25/0.54 % Maximum resident set size: 4608 pages
% 0.25/0.54 % E exiting
%------------------------------------------------------------------------------