%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET084-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 02:13:30 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 13 unt; 3 nHn; 19 RR)
% Number of literals : 41 ( 18 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_singleton_identified_by_element2_1,negated_conjecture,
singleton(x) = singleton(y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(corollary_to_unordered_pair_axiom2,axiom,
( unordered_pair(X2,X1) != null_class
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
cnf(null_unordered_pair,axiom,
( member(X2,universal_class)
| member(X1,universal_class)
| unordered_pair(X1,X2) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_unordered_pair) ).
cnf(only_member_in_singleton,axiom,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
cnf(unordered_pair3,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(prove_singleton_identified_by_element2_2,negated_conjecture,
member(y,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_2) ).
cnf(prove_singleton_identified_by_element2_3,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_3) ).
cnf(c_0_8,negated_conjecture,
singleton(x) = singleton(y),
prove_singleton_identified_by_element2_1 ).
cnf(c_0_9,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_10,plain,
( unordered_pair(X2,X1) != null_class
| ~ member(X1,universal_class) ),
inference(fof_simplification,[status(thm)],[corollary_to_unordered_pair_axiom2]) ).
cnf(c_0_11,negated_conjecture,
unordered_pair(x,x) = unordered_pair(y,y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
cnf(c_0_12,axiom,
( member(X2,universal_class)
| member(X1,universal_class)
| unordered_pair(X1,X2) = null_class ),
null_unordered_pair ).
cnf(c_0_13,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[only_member_in_singleton]) ).
cnf(c_0_14,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(fof_simplification,[status(thm)],[unordered_pair3]) ).
cnf(c_0_15,plain,
( unordered_pair(X2,X1) != null_class
| ~ member(X1,universal_class) ),
c_0_10 ).
cnf(c_0_16,negated_conjecture,
( member(x,universal_class)
| unordered_pair(y,y) = null_class ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
member(y,universal_class),
prove_singleton_identified_by_element2_2 ).
cnf(c_0_18,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
c_0_13 ).
cnf(c_0_19,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
c_0_14 ).
cnf(c_0_20,negated_conjecture,
member(x,universal_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_21,negated_conjecture,
x != y,
inference(fof_simplification,[status(thm)],[prove_singleton_identified_by_element2_3]) ).
cnf(c_0_22,plain,
( ~ member(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_23,negated_conjecture,
member(x,unordered_pair(y,y)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_11]),c_0_20])]) ).
cnf(c_0_24,negated_conjecture,
x != y,
c_0_21 ).
cnf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET084-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 04:51:04 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.45 % Version: 3.5.1
% 0.12/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.45 % Starting sh5l with 300s (1) cores
% 0.12/0.45 % new_bool_3 with pid 1721949 completed with status 0
% 0.12/0.45 % Result found by new_bool_3
% 0.12/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.45 % Search class: FGHSM-FFMS21-MFFFFFNN
% 0.12/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.45 % SubtermCWHack with pid 1721952 completed with status 0
% 0.12/0.45 % Result found by SubtermCWHack
% 0.12/0.45 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.45 % Search class: FGHSM-FFMS21-MFFFFFNN
% 0.12/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.45 % Preprocessing time : 0.002 s
% 0.12/0.45
% 0.12/0.45 % Proof found!
% 0.12/0.45 % SZS status Unsatisfiable
% 0.12/0.45 % SZS output start CNFRefutation
% See solution above
% 0.12/0.45 % Parsed axioms : 129
% 0.12/0.45 % Removed by relevancy pruning/SinE : 83
% 0.12/0.45 % Initial clauses : 46
% 0.12/0.45 % Removed in clause preprocessing : 0
% 0.12/0.45 % Initial clauses in saturation : 46
% 0.12/0.45 % Processed clauses : 114
% 0.12/0.45 % ...of these trivial : 7
% 0.12/0.45 % ...subsumed : 38
% 0.12/0.45 % ...remaining for further processing : 69
% 0.12/0.45 % Other redundant clauses eliminated : 2
% 0.12/0.45 % Clauses deleted for lack of memory : 0
% 0.12/0.45 % Backward-subsumed : 2
% 0.12/0.45 % Backward-rewritten : 4
% 0.12/0.45 % Generated clauses : 472
% 0.12/0.45 % ...of the previous two non-redundant : 276
% 0.12/0.45 % ...aggressively subsumed : 0
% 0.12/0.45 % Contextual simplify-reflections : 0
% 0.12/0.45 % Paramodulations : 470
% 0.12/0.45 % Factorizations : 0
% 0.12/0.45 % NegExts : 0
% 0.12/0.45 % Equation resolutions : 2
% 0.12/0.45 % Disequality decompositions : 0
% 0.12/0.45 % Total rewrite steps : 230
% 0.12/0.45 % ...of those cached : 177
% 0.12/0.45 % Propositional unsat checks : 0
% 0.12/0.45 % Propositional check models : 0
% 0.12/0.45 % Propositional check unsatisfiable : 0
% 0.12/0.45 % Propositional clauses : 0
% 0.12/0.45 % Propositional clauses after purity: 0
% 0.12/0.45 % Propositional unsat core size : 0
% 0.12/0.45 % Propositional preprocessing time : 0.000
% 0.12/0.45 % Propositional encoding time : 0.000
% 0.12/0.45 % Propositional solver time : 0.000
% 0.12/0.45 % Success case prop preproc time : 0.000
% 0.12/0.45 % Success case prop encoding time : 0.000
% 0.12/0.45 % Success case prop solver time : 0.000
% 0.12/0.45 % Current number of processed clauses : 61
% 0.12/0.45 % Positive orientable unit clauses : 28
% 0.12/0.45 % Positive unorientable unit clauses: 2
% 0.12/0.45 % Negative unit clauses : 4
% 0.12/0.45 % Non-unit-clauses : 27
% 0.12/0.45 % Current number of unprocessed clauses: 204
% 0.12/0.45 % ...number of literals in the above : 477
% 0.12/0.45 % Current number of archived formulas : 0
% 0.12/0.45 % Current number of archived clauses : 6
% 0.12/0.45 % Clause-clause subsumption calls (NU) : 115
% 0.12/0.45 % Rec. Clause-clause subsumption calls : 108
% 0.12/0.45 % Non-unit clause-clause subsumptions : 30
% 0.12/0.45 % Unit Clause-clause subsumption calls : 54
% 0.12/0.45 % Rewrite failures with RHS unbound : 0
% 0.12/0.45 % BW rewrite match attempts : 18
% 0.12/0.45 % BW rewrite match successes : 13
% 0.12/0.45 % Condensation attempts : 0
% 0.12/0.45 % Condensation successes : 0
% 0.12/0.45 % Termbank termtop insertions : 4992
% 0.12/0.45 % Search garbage collected termcells : 452
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.009 s
% 0.12/0.45 % System time : 0.002 s
% 0.12/0.45 % Total time : 0.011 s
% 0.12/0.45 % Maximum resident set size: 3736 pages
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.013 s
% 0.12/0.45 % System time : 0.007 s
% 0.12/0.45 % Total time : 0.020 s
% 0.12/0.45 % Maximum resident set size: 4864 pages
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------