%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET144-6 : 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 : n026.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 02:13:43 PM UTC 2026
% Result : Unsatisfiable 5.90s 1.40s
% Output : CNFRefutation 5.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 27 ( 6 unt; 4 nHn; 21 RR)
% Number of literals : 55 ( 7 equ; 27 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(not_subclass_members2,axiom,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(not_subclass_members1,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(subclass_implies_equal,axiom,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(prove_commutativity_of_intersection_1,negated_conjecture,
intersection(x,y) != intersection(y,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity_of_intersection_1) ).
cnf(c_0_7,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_8,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_9,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_10,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_7 ).
cnf(c_0_11,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_8 ).
cnf(c_0_12,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_9 ).
cnf(c_0_13,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_14,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_15,plain,
( ~ member(not_subclass_element(X1,intersection(X2,X3)),X2)
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
| subclass(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( subclass(intersection(X1,X2),X3)
| member(not_subclass_element(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_14 ).
cnf(c_0_18,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).
cnf(c_0_19,plain,
( ~ member(not_subclass_element(intersection(X1,X2),intersection(X3,X1)),X3)
| subclass(intersection(X1,X2),intersection(X3,X1)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( subclass(intersection(X1,X2),X3)
| member(not_subclass_element(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
intersection(x,y) != intersection(y,x),
inference(fof_simplification,[status(thm)],[prove_commutativity_of_intersection_1]) ).
cnf(c_0_22,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
c_0_18 ).
cnf(c_0_23,plain,
subclass(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
intersection(x,y) != intersection(y,x),
c_0_21 ).
cnf(c_0_25,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET144-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n026.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 04:59:21 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 5.90/1.40 % Version: 3.5.1
% 5.90/1.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 5.90/1.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.90/1.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 5.90/1.40 % Starting new_bool_3 with 300s (1) cores
% 5.90/1.40 % Starting new_bool_1 with 300s (1) cores
% 5.90/1.40 % Starting sh5l with 300s (1) cores
% 5.90/1.40 % new_bool_3 with pid 1419496 completed with status 9
% 5.90/1.40 % new_bool_1 with pid 1419497 completed with status 9
% 5.90/1.40 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1419495 completed with status 0
% 5.90/1.40 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 5.90/1.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 5.90/1.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.90/1.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 5.90/1.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.90/1.40 % No SInE strategy applied
% 5.90/1.40 % Search class: FGHSM-FFLM31-DFFFFFNN
% 5.90/1.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.90/1.40 % Starting SubtermCWHack with 136s (1) cores
% 5.90/1.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 5.90/1.40 % Starting new_bool_3 with 311s (1) cores
% 5.90/1.40 % Starting new_bool_1 with 308s (1) cores
% 5.90/1.40 % Starting sh5l with 304s (1) cores
% 5.90/1.40 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1419505 completed with status 0
% 5.90/1.40 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 5.90/1.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 5.90/1.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.90/1.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 5.90/1.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.90/1.40 % No SInE strategy applied
% 5.90/1.40 % Search class: FGHSM-FFLM31-DFFFFFNN
% 5.90/1.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.90/1.40 % Starting SubtermCWHack with 136s (1) cores
% 5.90/1.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 5.90/1.40 % Preprocessing time : 0.003 s
% 5.90/1.40 % Presaturation interreduction done
% 5.90/1.40
% 5.90/1.40 % Proof found!
% 5.90/1.40 % SZS status Unsatisfiable
% 5.90/1.40 % SZS output start CNFRefutation
% See solution above
% 5.90/1.40 % Parsed axioms : 113
% 5.90/1.40 % Removed by relevancy pruning/SinE : 0
% 5.90/1.40 % Initial clauses : 113
% 5.90/1.40 % Removed in clause preprocessing : 17
% 5.90/1.40 % Initial clauses in saturation : 96
% 5.90/1.40 % Processed clauses : 4588
% 5.90/1.40 % ...of these trivial : 116
% 5.90/1.40 % ...subsumed : 3132
% 5.90/1.40 % ...remaining for further processing : 1340
% 5.90/1.40 % Other redundant clauses eliminated : 18
% 5.90/1.40 % Clauses deleted for lack of memory : 0
% 5.90/1.40 % Backward-subsumed : 44
% 5.90/1.40 % Backward-rewritten : 353
% 5.90/1.40 % Generated clauses : 21461
% 5.90/1.40 % ...of the previous two non-redundant : 17827
% 5.90/1.40 % ...aggressively subsumed : 0
% 5.90/1.40 % Contextual simplify-reflections : 26
% 5.90/1.40 % Paramodulations : 21429
% 5.90/1.40 % Factorizations : 14
% 5.90/1.40 % NegExts : 0
% 5.90/1.40 % Equation resolutions : 18
% 5.90/1.40 % Disequality decompositions : 0
% 5.90/1.40 % Total rewrite steps : 7084
% 5.90/1.40 % ...of those cached : 6350
% 5.90/1.40 % Propositional unsat checks : 0
% 5.90/1.40 % Propositional check models : 0
% 5.90/1.40 % Propositional check unsatisfiable : 0
% 5.90/1.40 % Propositional clauses : 0
% 5.90/1.40 % Propositional clauses after purity: 0
% 5.90/1.40 % Propositional unsat core size : 0
% 5.90/1.40 % Propositional preprocessing time : 0.000
% 5.90/1.40 % Propositional encoding time : 0.000
% 5.90/1.40 % Propositional solver time : 0.000
% 5.90/1.40 % Success case prop preproc time : 0.000
% 5.90/1.40 % Success case prop encoding time : 0.000
% 5.90/1.40 % Success case prop solver time : 0.000
% 5.90/1.40 % Current number of processed clauses : 844
% 5.90/1.40 % Positive orientable unit clauses : 109
% 5.90/1.40 % Positive unorientable unit clauses: 1
% 5.90/1.40 % Negative unit clauses : 11
% 5.90/1.40 % Non-unit-clauses : 723
% 5.90/1.40 % Current number of unprocessed clauses: 13103
% 5.90/1.40 % ...number of literals in the above : 46506
% 5.90/1.40 % Current number of archived formulas : 0
% 5.90/1.40 % Current number of archived clauses : 509
% 5.90/1.40 % Clause-clause subsumption calls (NU) : 119038
% 5.90/1.40 % Rec. Clause-clause subsumption calls : 72713
% 5.90/1.40 % Non-unit clause-clause subsumptions : 2467
% 5.90/1.40 % Unit Clause-clause subsumption calls : 4790
% 5.90/1.40 % Rewrite failures with RHS unbound : 0
% 5.90/1.40 % BW rewrite match attempts : 508
% 5.90/1.40 % BW rewrite match successes : 385
% 5.90/1.40 % Condensation attempts : 0
% 5.90/1.40 % Condensation successes : 0
% 5.90/1.40 % Termbank termtop insertions : 825699
% 5.90/1.40 % Search garbage collected termcells : 185
% 5.90/1.40
% 5.90/1.40 % -------------------------------------------------
% 5.90/1.40 % User time : 0.910 s
% 5.90/1.40 % System time : 0.024 s
% 5.90/1.40 % Total time : 0.935 s
% 5.90/1.40 % Maximum resident set size: 4000 pages
% 5.90/1.40
% 5.90/1.40 % -------------------------------------------------
% 5.90/1.40 % User time : 4.547 s
% 5.90/1.40 % System time : 0.212 s
% 5.90/1.40 % Total time : 4.759 s
% 5.90/1.40 % Maximum resident set size: 4864 pages
% 5.90/1.40 % E exiting
%------------------------------------------------------------------------------