%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 02:13:06 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of clauses : 39 ( 24 unt; 11 nHn; 29 RR)
% Number of literals : 60 ( 37 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(unordered_pair_3,axiom,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_3) ).
cnf(unordered_pair_1,axiom,
member(X1,unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_1) ).
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = unordered_pair(singleton_set(X1),unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
cnf(equal_ordered_pairs,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pairs) ).
cnf(singleton_2,axiom,
( ~ member(X1,singleton_set(X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_2) ).
cnf(singleton_1,axiom,
member(X1,singleton_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_1) ).
cnf(unordered_pair_2,axiom,
member(X1,unordered_pair(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_2) ).
cnf(prove_second_components_equal,negated_conjecture,
r1 != r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_components_equal) ).
cnf(c_0_8,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_3]) ).
cnf(c_0_9,axiom,
member(X1,unordered_pair(X1,X2)),
unordered_pair_1 ).
cnf(c_0_10,axiom,
ordered_pair(X1,X2) = unordered_pair(singleton_set(X1),unordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_11,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_8 ).
cnf(c_0_12,plain,
member(singleton_set(X1),ordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
equal_ordered_pairs ).
cnf(c_0_14,plain,
( ~ member(X1,ordered_pair(X2,X3))
| X1 = singleton_set(X2)
| X1 = unordered_pair(X2,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,hypothesis,
member(singleton_set(m1),ordered_pair(m2,r2)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( ~ member(X1,singleton_set(X2))
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[singleton_2]) ).
cnf(c_0_17,axiom,
member(X1,singleton_set(X1)),
singleton_1 ).
cnf(c_0_18,hypothesis,
( singleton_set(m1) = singleton_set(m2)
| singleton_set(m1) = unordered_pair(m2,r2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( ~ member(X1,singleton_set(X2))
| X1 = X2 ),
c_0_16 ).
cnf(c_0_20,hypothesis,
( member(m1,singleton_set(m2))
| singleton_set(m1) = unordered_pair(m2,r2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,hypothesis,
( m1 = m2
| singleton_set(m1) = unordered_pair(m2,r2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,hypothesis,
( ~ member(X1,unordered_pair(m2,r2))
| X1 = m1
| m1 = m2 ),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_23,axiom,
member(X1,unordered_pair(X2,X1)),
unordered_pair_2 ).
cnf(c_0_24,hypothesis,
m1 = m2,
inference(spm,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_25,plain,
member(unordered_pair(X1,X2),ordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_26,hypothesis,
ordered_pair(m2,r1) = ordered_pair(m2,r2),
inference(rw,[status(thm)],[c_0_13,c_0_24]) ).
cnf(c_0_27,hypothesis,
member(unordered_pair(m1,r1),ordered_pair(m2,r2)),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_28,hypothesis,
( ~ member(X1,ordered_pair(m2,r2))
| X1 = singleton_set(m2)
| X1 = unordered_pair(m2,r1) ),
inference(spm,[status(thm)],[c_0_14,c_0_26]) ).
cnf(c_0_29,hypothesis,
( singleton_set(m2) = unordered_pair(m2,r1)
| unordered_pair(m2,r1) = unordered_pair(m2,r2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_27]),c_0_24]),c_0_24]) ).
cnf(c_0_30,hypothesis,
( singleton_set(m2) = unordered_pair(m2,r2)
| unordered_pair(m2,r1) = unordered_pair(m2,r2) ),
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_31,hypothesis,
unordered_pair(m2,r1) = unordered_pair(m2,r2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
r1 != r2,
inference(fof_simplification,[status(thm)],[prove_second_components_equal]) ).
cnf(c_0_33,hypothesis,
member(r1,unordered_pair(m2,r2)),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
r1 != r2,
c_0_32 ).
cnf(c_0_35,hypothesis,
m2 = r1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_33]),c_0_34]) ).
cnf(c_0_36,hypothesis,
unordered_pair(r1,r1) = unordered_pair(r1,r2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_35]),c_0_35]) ).
cnf(c_0_37,hypothesis,
( ~ member(X1,unordered_pair(r1,r2))
| X1 = r1 ),
inference(spm,[status(thm)],[c_0_11,c_0_36]) ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_23]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 04:38:26 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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: FSSSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN 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 1446334 completed with status 0
% 0.12/0.45 % Result found by new_bool_3
% 0.12/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN 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: FGUSM-FFSF21-SFFFFFNN
% 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 1446339 completed with status 0
% 0.12/0.45 % Result found by SubtermCWHack
% 0.12/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN 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: FGUSM-FFSF21-SFFFFFNN
% 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 : 0.001 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 : 8
% 0.12/0.45 % Removed by relevancy pruning/SinE : 0
% 0.12/0.45 % Initial clauses : 8
% 0.12/0.45 % Removed in clause preprocessing : 0
% 0.12/0.45 % Initial clauses in saturation : 8
% 0.12/0.45 % Processed clauses : 81
% 0.12/0.45 % ...of these trivial : 16
% 0.12/0.45 % ...subsumed : 6
% 0.12/0.45 % ...remaining for further processing : 59
% 0.12/0.45 % Other redundant clauses eliminated : 0
% 0.12/0.45 % Clauses deleted for lack of memory : 0
% 0.12/0.45 % Backward-subsumed : 0
% 0.12/0.45 % Backward-rewritten : 34
% 0.12/0.45 % Generated clauses : 241
% 0.12/0.45 % ...of the previous two non-redundant : 191
% 0.12/0.45 % ...aggressively subsumed : 0
% 0.12/0.45 % Contextual simplify-reflections : 0
% 0.12/0.45 % Paramodulations : 239
% 0.12/0.45 % Factorizations : 2
% 0.12/0.45 % NegExts : 0
% 0.12/0.45 % Equation resolutions : 0
% 0.12/0.45 % Disequality decompositions : 0
% 0.12/0.45 % Total rewrite steps : 218
% 0.12/0.45 % ...of those cached : 171
% 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 : 25
% 0.12/0.45 % Positive orientable unit clauses : 19
% 0.12/0.45 % Positive unorientable unit clauses: 0
% 0.12/0.45 % Negative unit clauses : 1
% 0.12/0.45 % Non-unit-clauses : 5
% 0.12/0.45 % Current number of unprocessed clauses: 92
% 0.12/0.45 % ...number of literals in the above : 215
% 0.12/0.45 % Current number of archived formulas : 0
% 0.12/0.45 % Current number of archived clauses : 34
% 0.12/0.45 % Clause-clause subsumption calls (NU) : 52
% 0.12/0.45 % Rec. Clause-clause subsumption calls : 50
% 0.12/0.45 % Non-unit clause-clause subsumptions : 5
% 0.12/0.45 % Unit Clause-clause subsumption calls : 4
% 0.12/0.45 % Rewrite failures with RHS unbound : 0
% 0.12/0.45 % BW rewrite match attempts : 7
% 0.12/0.45 % BW rewrite match successes : 4
% 0.12/0.45 % Condensation attempts : 0
% 0.12/0.45 % Condensation successes : 0
% 0.12/0.45 % Termbank termtop insertions : 3507
% 0.12/0.45 % Search garbage collected termcells : 8
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.005 s
% 0.12/0.45 % System time : 0.002 s
% 0.12/0.45 % Total time : 0.007 s
% 0.12/0.45 % Maximum resident set size: 3632 pages
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.005 s
% 0.12/0.45 % System time : 0.005 s
% 0.12/0.45 % Total time : 0.010 s
% 0.12/0.45 % Maximum resident set size: 4864 pages
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------