%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET232-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:13:57 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 18 ( 7 unt; 5 nHn; 14 RR)
% Number of literals : 30 ( 4 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cartesian_product4,axiom,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
cnf(cartesian_product1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
cnf(not_subclass_members1,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(prove_cross_product_property7_2,negated_conjecture,
~ member(first(not_subclass_element(cross_product(x,y),z)),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property7_2) ).
cnf(prove_cross_product_property7_1,negated_conjecture,
~ subclass(cross_product(x,y),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property7_1) ).
cnf(c_0_5,plain,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[cartesian_product4]) ).
cnf(c_0_6,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[cartesian_product1]) ).
cnf(c_0_7,plain,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
c_0_5 ).
cnf(c_0_8,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_9,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
c_0_6 ).
cnf(c_0_10,plain,
( subclass(cross_product(X1,X2),X3)
| ordered_pair(first(not_subclass_element(cross_product(X1,X2),X3)),second(not_subclass_element(cross_product(X1,X2),X3))) = not_subclass_element(cross_product(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
~ member(first(not_subclass_element(cross_product(x,y),z)),x),
inference(fof_simplification,[status(thm)],[prove_cross_product_property7_2]) ).
cnf(c_0_12,plain,
( ~ member(not_subclass_element(cross_product(X1,X2),X3),cross_product(X4,X5))
| subclass(cross_product(X1,X2),X3)
| member(first(not_subclass_element(cross_product(X1,X2),X3)),X4) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
~ subclass(cross_product(x,y),z),
inference(fof_simplification,[status(thm)],[prove_cross_product_property7_1]) ).
cnf(c_0_14,negated_conjecture,
~ member(first(not_subclass_element(cross_product(x,y),z)),x),
c_0_11 ).
cnf(c_0_15,plain,
( subclass(cross_product(X1,X2),X3)
| member(first(not_subclass_element(cross_product(X1,X2),X3)),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_16,negated_conjecture,
~ subclass(cross_product(x,y),z),
c_0_13 ).
cnf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET232-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:02:36 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.12/0.43 % Version: 3.5.1
% 0.12/0.43 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.43 % Starting sh5l with 300s (1) cores
% 0.12/0.43 % new_bool_3 with pid 2303726 completed with status 0
% 0.12/0.43 % Result found by new_bool_3
% 0.12/0.43 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.43 % Search class: FGUSS-FFSF21-MFFFFFNN
% 0.12/0.43 % partial match(1): FGUSS-FFSF22-MFFFFFNN
% 0.12/0.43 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.43 % SubtermCWHack with pid 2303729 completed with status 0
% 0.12/0.43 % Result found by SubtermCWHack
% 0.12/0.43 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.43 % Search class: FGUSS-FFSF21-MFFFFFNN
% 0.12/0.43 % partial match(1): FGUSS-FFSF22-MFFFFFNN
% 0.12/0.43 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.43 % Preprocessing time : 0.001 s
% 0.12/0.43
% 0.12/0.43 % Proof found!
% 0.12/0.43 % SZS status Unsatisfiable
% 0.12/0.43 % SZS output start CNFRefutation
% See solution above
% 0.12/0.43 % Parsed axioms : 114
% 0.12/0.43 % Removed by relevancy pruning/SinE : 97
% 0.12/0.43 % Initial clauses : 17
% 0.12/0.43 % Removed in clause preprocessing : 0
% 0.12/0.43 % Initial clauses in saturation : 17
% 0.12/0.43 % Processed clauses : 57
% 0.12/0.43 % ...of these trivial : 0
% 0.12/0.43 % ...subsumed : 14
% 0.12/0.43 % ...remaining for further processing : 43
% 0.12/0.43 % Other redundant clauses eliminated : 2
% 0.12/0.43 % Clauses deleted for lack of memory : 0
% 0.12/0.43 % Backward-subsumed : 0
% 0.12/0.43 % Backward-rewritten : 0
% 0.12/0.43 % Generated clauses : 121
% 0.12/0.43 % ...of the previous two non-redundant : 112
% 0.12/0.43 % ...aggressively subsumed : 0
% 0.12/0.43 % Contextual simplify-reflections : 0
% 0.12/0.43 % Paramodulations : 119
% 0.12/0.43 % Factorizations : 0
% 0.12/0.43 % NegExts : 0
% 0.12/0.43 % Equation resolutions : 2
% 0.12/0.43 % Disequality decompositions : 0
% 0.12/0.43 % Total rewrite steps : 4
% 0.12/0.43 % ...of those cached : 1
% 0.12/0.43 % Propositional unsat checks : 0
% 0.12/0.43 % Propositional check models : 0
% 0.12/0.43 % Propositional check unsatisfiable : 0
% 0.12/0.43 % Propositional clauses : 0
% 0.12/0.43 % Propositional clauses after purity: 0
% 0.12/0.43 % Propositional unsat core size : 0
% 0.12/0.43 % Propositional preprocessing time : 0.000
% 0.12/0.43 % Propositional encoding time : 0.000
% 0.12/0.43 % Propositional solver time : 0.000
% 0.12/0.43 % Success case prop preproc time : 0.000
% 0.12/0.43 % Success case prop encoding time : 0.000
% 0.12/0.43 % Success case prop solver time : 0.000
% 0.12/0.43 % Current number of processed clauses : 41
% 0.12/0.43 % Positive orientable unit clauses : 4
% 0.12/0.43 % Positive unorientable unit clauses: 0
% 0.12/0.43 % Negative unit clauses : 2
% 0.12/0.43 % Non-unit-clauses : 35
% 0.12/0.43 % Current number of unprocessed clauses: 58
% 0.12/0.43 % ...number of literals in the above : 268
% 0.12/0.43 % Current number of archived formulas : 0
% 0.12/0.43 % Current number of archived clauses : 0
% 0.12/0.43 % Clause-clause subsumption calls (NU) : 306
% 0.12/0.43 % Rec. Clause-clause subsumption calls : 205
% 0.12/0.43 % Non-unit clause-clause subsumptions : 14
% 0.12/0.43 % Unit Clause-clause subsumption calls : 0
% 0.12/0.43 % Rewrite failures with RHS unbound : 0
% 0.12/0.43 % BW rewrite match attempts : 2
% 0.12/0.43 % BW rewrite match successes : 0
% 0.12/0.43 % Condensation attempts : 0
% 0.12/0.43 % Condensation successes : 0
% 0.12/0.43 % Termbank termtop insertions : 3494
% 0.12/0.43 % Search garbage collected termcells : 478
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.006 s
% 0.12/0.43 % System time : 0.001 s
% 0.12/0.43 % Total time : 0.007 s
% 0.12/0.43 % Maximum resident set size: 3744 pages
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.010 s
% 0.12/0.43 % System time : 0.006 s
% 0.12/0.43 % Total time : 0.016 s
% 0.12/0.43 % Maximum resident set size: 4864 pages
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------