%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET021-7 : 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 : n012.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 02:13:08 PM UTC 2026
% Result : Unsatisfiable 0.15s 1.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 44 ( 16 unt; 14 nHn; 28 RR)
% Number of literals : 78 ( 49 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 33 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(corollary_2_to_cartesian_product,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
cnf(existence_of_1st_and_2nd_3,axiom,
( second(X1) = X1
| member(ordered_pair(first(X1),second(X1)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_3) ).
cnf(existence_of_1st_and_2nd_5,axiom,
( second(X1) = X1
| ordered_pair(first(X1),second(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_5) ).
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(ordered_pair_determines_components2,axiom,
( ~ member(X2,universal_class)
| ordered_pair(X1,X2) != ordered_pair(X3,X4)
| X2 = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_determines_components2) ).
cnf(existence_of_1st_and_2nd_2,axiom,
( first(X1) = X1
| member(ordered_pair(first(X1),second(X1)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).
cnf(existence_of_1st_and_2nd_4,axiom,
( first(X1) = X1
| ordered_pair(first(X1),second(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_sets2_1,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_1) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_sets2_2,negated_conjecture,
second(ordered_pair(u,v)) != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_2) ).
cnf(ordered_pair_determines_components1,axiom,
( ~ member(X1,universal_class)
| ordered_pair(X1,X2) != ordered_pair(X3,X4)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
cnf(ordered_pair_is_set,axiom,
member(ordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_is_set) ).
cnf(c_0_11,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,universal_class) ),
inference(fof_simplification,[status(thm)],[corollary_2_to_cartesian_product]) ).
cnf(c_0_12,axiom,
( second(X1) = X1
| member(ordered_pair(first(X1),second(X1)),cross_product(universal_class,universal_class)) ),
existence_of_1st_and_2nd_3 ).
cnf(c_0_13,axiom,
( second(X1) = X1
| ordered_pair(first(X1),second(X1)) = X1 ),
existence_of_1st_and_2nd_5 ).
cnf(c_0_14,plain,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[cartesian_product4]) ).
cnf(c_0_15,plain,
( ~ member(X2,universal_class)
| ordered_pair(X1,X2) != ordered_pair(X3,X4)
| X2 = X4 ),
inference(fof_simplification,[status(thm)],[ordered_pair_determines_components2]) ).
cnf(c_0_16,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,universal_class) ),
c_0_11 ).
cnf(c_0_17,plain,
( member(X1,cross_product(universal_class,universal_class))
| second(X1) = X1 ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,axiom,
( first(X1) = X1
| member(ordered_pair(first(X1),second(X1)),cross_product(universal_class,universal_class)) ),
existence_of_1st_and_2nd_2 ).
cnf(c_0_19,axiom,
( first(X1) = X1
| ordered_pair(first(X1),second(X1)) = X1 ),
existence_of_1st_and_2nd_4 ).
cnf(c_0_20,plain,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
c_0_14 ).
cnf(c_0_21,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
prove_unique_1st_and_2nd_in_pair_of_sets2_1 ).
cnf(c_0_22,plain,
( ~ member(X2,universal_class)
| ordered_pair(X1,X2) != ordered_pair(X3,X4)
| X2 = X4 ),
c_0_15 ).
cnf(c_0_23,plain,
( member(X2,universal_class)
| second(ordered_pair(X1,X2)) = ordered_pair(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,negated_conjecture,
second(ordered_pair(u,v)) != v,
inference(fof_simplification,[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_sets2_2]) ).
cnf(c_0_25,plain,
( member(X1,cross_product(universal_class,universal_class))
| first(X1) = X1 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( second(ordered_pair(X1,X2)) = X2
| second(ordered_pair(X1,X2)) = ordered_pair(X1,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13])]),c_0_23]) ).
cnf(c_0_28,negated_conjecture,
second(ordered_pair(u,v)) != v,
c_0_24 ).
cnf(c_0_29,plain,
( member(X2,universal_class)
| first(ordered_pair(X1,X2)) = ordered_pair(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_30,plain,
( ~ member(X1,universal_class)
| ordered_pair(X1,X2) != ordered_pair(X3,X4)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[ordered_pair_determines_components1]) ).
cnf(c_0_31,negated_conjecture,
ordered_pair(first(ordered_pair(u,v)),ordered_pair(u,v)) = ordered_pair(u,v),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_32,plain,
( second(ordered_pair(X1,X2)) = X2
| first(ordered_pair(X1,X2)) = ordered_pair(X1,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19])]),c_0_29]) ).
cnf(c_0_33,plain,
( ~ member(X1,universal_class)
| ordered_pair(X1,X2) != ordered_pair(X3,X4)
| X1 = X3 ),
c_0_30 ).
cnf(c_0_34,negated_conjecture,
ordered_pair(ordered_pair(u,v),ordered_pair(u,v)) = ordered_pair(u,v),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_28]) ).
cnf(c_0_35,axiom,
member(ordered_pair(X1,X2),universal_class),
ordered_pair_is_set ).
cnf(c_0_36,negated_conjecture,
( ordered_pair(u,v) != ordered_pair(X1,X2)
| ordered_pair(u,v) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_37,negated_conjecture,
ordered_pair(u,v) = u,
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_38,negated_conjecture,
member(v,universal_class),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_39,negated_conjecture,
ordered_pair(u,v) != v,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_28]) ).
cnf(c_0_40,negated_conjecture,
( ordered_pair(X2,X1) != u
| v = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_37]),c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
ordered_pair(u,u) = u,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_42,negated_conjecture,
u != v,
inference(rw,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET021-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 04:43:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.15/1.40 % Version: 3.5.1
% 0.15/1.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/1.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/1.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/1.40 % Starting new_bool_3 with 300s (1) cores
% 0.15/1.40 % Starting new_bool_1 with 300s (1) cores
% 0.15/1.40 % Starting sh5l with 300s (1) cores
% 0.15/1.40 % new_bool_3 with pid 1582496 completed with status 0
% 0.15/1.40 % Result found by new_bool_3
% 0.15/1.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/1.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/1.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/1.40 % Starting new_bool_3 with 300s (1) cores
% 0.15/1.40 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/1.40 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/1.40 % Search class: FGHSM-FFMS21-MFFFFFNN
% 0.15/1.40 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/1.40 % Starting SubtermCWHack with 31s (1) cores
% 0.15/1.40 % SubtermCWHack with pid 1582499 completed with status 0
% 0.15/1.40 % Result found by SubtermCWHack
% 0.15/1.40 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/1.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/1.40 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/1.40 % Starting new_bool_3 with 300s (1) cores
% 0.15/1.40 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/1.40 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/1.40 % Search class: FGHSM-FFMS21-MFFFFFNN
% 0.15/1.40 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/1.40 % Starting SubtermCWHack with 31s (1) cores
% 0.15/1.40 % Preprocessing time : 0.002 s
% 0.15/1.40
% 0.15/1.40 % Proof found!
% 0.15/1.40 % SZS status Unsatisfiable
% 0.15/1.40 % SZS output start CNFRefutation
% See solution above
% 0.15/1.40 % Parsed axioms : 159
% 0.15/1.40 % Removed by relevancy pruning/SinE : 95
% 0.15/1.40 % Initial clauses : 64
% 0.15/1.40 % Removed in clause preprocessing : 0
% 0.15/1.40 % Initial clauses in saturation : 64
% 0.15/1.40 % Processed clauses : 7706
% 0.15/1.40 % ...of these trivial : 435
% 0.15/1.40 % ...subsumed : 6212
% 0.15/1.40 % ...remaining for further processing : 1059
% 0.15/1.40 % Other redundant clauses eliminated : 262
% 0.15/1.40 % Clauses deleted for lack of memory : 0
% 0.15/1.40 % Backward-subsumed : 82
% 0.15/1.40 % Backward-rewritten : 74
% 0.15/1.40 % Generated clauses : 102486
% 0.15/1.40 % ...of the previous two non-redundant : 60764
% 0.15/1.40 % ...aggressively subsumed : 0
% 0.15/1.40 % Contextual simplify-reflections : 15
% 0.15/1.40 % Paramodulations : 102203
% 0.15/1.40 % Factorizations : 6
% 0.15/1.40 % NegExts : 0
% 0.15/1.40 % Equation resolutions : 277
% 0.15/1.40 % Disequality decompositions : 0
% 0.15/1.40 % Total rewrite steps : 60080
% 0.15/1.40 % ...of those cached : 58077
% 0.15/1.40 % Propositional unsat checks : 0
% 0.15/1.40 % Propositional check models : 0
% 0.15/1.40 % Propositional check unsatisfiable : 0
% 0.15/1.40 % Propositional clauses : 0
% 0.15/1.40 % Propositional clauses after purity: 0
% 0.15/1.40 % Propositional unsat core size : 0
% 0.15/1.40 % Propositional preprocessing time : 0.000
% 0.15/1.40 % Propositional encoding time : 0.000
% 0.15/1.40 % Propositional solver time : 0.000
% 0.15/1.40 % Success case prop preproc time : 0.000
% 0.15/1.40 % Success case prop encoding time : 0.000
% 0.15/1.40 % Success case prop solver time : 0.000
% 0.15/1.40 % Current number of processed clauses : 901
% 0.15/1.40 % Positive orientable unit clauses : 146
% 0.15/1.40 % Positive unorientable unit clauses: 4
% 0.15/1.40 % Negative unit clauses : 15
% 0.15/1.40 % Non-unit-clauses : 736
% 0.15/1.40 % Current number of unprocessed clauses: 52327
% 0.15/1.40 % ...number of literals in the above : 171911
% 0.15/1.40 % Current number of archived formulas : 0
% 0.15/1.40 % Current number of archived clauses : 156
% 0.15/1.40 % Clause-clause subsumption calls (NU) : 87551
% 0.15/1.40 % Rec. Clause-clause subsumption calls : 73214
% 0.15/1.40 % Non-unit clause-clause subsumptions : 5274
% 0.15/1.40 % Unit Clause-clause subsumption calls : 2543
% 0.15/1.40 % Rewrite failures with RHS unbound : 0
% 0.15/1.40 % BW rewrite match attempts : 160
% 0.15/1.40 % BW rewrite match successes : 70
% 0.15/1.40 % Condensation attempts : 0
% 0.15/1.40 % Condensation successes : 0
% 0.15/1.40 % Termbank termtop insertions : 1249569
% 0.15/1.40 % Search garbage collected termcells : 517
% 0.15/1.40
% 0.15/1.40 % -------------------------------------------------
% 0.15/1.40 % User time : 0.914 s
% 0.15/1.40 % System time : 0.039 s
% 0.15/1.40 % Total time : 0.952 s
% 0.15/1.40 % Maximum resident set size: 3704 pages
% 0.15/1.40
% 0.15/1.40 % -------------------------------------------------
% 0.15/1.40 % User time : 0.917 s
% 0.15/1.40 % System time : 0.044 s
% 0.15/1.40 % Total time : 0.961 s
% 0.15/1.40 % Maximum resident set size: 4608 pages
% 0.15/1.40 % E exiting
%------------------------------------------------------------------------------