%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET042-3 : 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 : n009.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 02:13:15 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 33 ( 11 unt; 0 nHn; 33 RR)
% Number of literals : 80 ( 9 equ; 53 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cross_product4,axiom,
( ~ member(second(X1),X3)
| ~ member(first(X1),X2)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1)
| member(X1,cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',cross_product4) ).
cnf(ordered_pairs_are_small2,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pairs_are_small2) ).
cnf(prove_ordered_pair_is_in_cross_product,negated_conjecture,
~ member(ordered_pair(a,b),cross_product(set_a,set_b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_is_in_cross_product) ).
cnf(a2,axiom,
( ~ member(X1,X2)
| little_set(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(property_of_second,axiom,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_second) ).
cnf(member_of_set_b,hypothesis,
member(b,set_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set_b) ).
cnf(member_of_set_a,hypothesis,
member(a,set_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set_a) ).
cnf(property_of_first,axiom,
( ~ little_set(X2)
| ~ little_set(X1)
| first(ordered_pair(X1,X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_first) ).
cnf(ordered_pair_predicate4,axiom,
( X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2)
| ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate4) ).
cnf(c_0_9,plain,
( ~ member(second(X1),X3)
| ~ member(first(X1),X2)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1)
| member(X1,cross_product(X2,X3)) ),
inference(fof_simplification,[status(thm)],[cross_product4]) ).
cnf(c_0_10,plain,
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
inference(fof_simplification,[status(thm)],[ordered_pairs_are_small2]) ).
cnf(c_0_11,negated_conjecture,
~ member(ordered_pair(a,b),cross_product(set_a,set_b)),
inference(fof_simplification,[status(thm)],[prove_ordered_pair_is_in_cross_product]) ).
cnf(c_0_12,plain,
( ~ member(second(X1),X3)
| ~ member(first(X1),X2)
| ~ ordered_pair_predicate(X1)
| ~ little_set(X1)
| member(X1,cross_product(X2,X3)) ),
c_0_9 ).
cnf(c_0_13,plain,
( ~ ordered_pair_predicate(X1)
| little_set(X1) ),
c_0_10 ).
cnf(c_0_14,plain,
( ~ member(X1,X2)
| little_set(X1) ),
inference(fof_simplification,[status(thm)],[a2]) ).
cnf(c_0_15,negated_conjecture,
~ member(ordered_pair(a,b),cross_product(set_a,set_b)),
c_0_11 ).
cnf(c_0_16,plain,
( ~ member(second(X1),X3)
| ~ member(first(X1),X2)
| ~ ordered_pair_predicate(X1)
| member(X1,cross_product(X2,X3)) ),
inference(csr,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[property_of_second]) ).
cnf(c_0_18,plain,
( ~ member(X1,X2)
| little_set(X1) ),
c_0_14 ).
cnf(c_0_19,hypothesis,
member(b,set_b),
member_of_set_b ).
cnf(c_0_20,hypothesis,
member(a,set_a),
member_of_set_a ).
cnf(c_0_21,negated_conjecture,
( ~ member(second(ordered_pair(a,b)),set_b)
| ~ member(first(ordered_pair(a,b)),set_a)
| ~ ordered_pair_predicate(ordered_pair(a,b)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
c_0_17 ).
cnf(c_0_23,hypothesis,
little_set(b),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,hypothesis,
little_set(a),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_25,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| first(ordered_pair(X1,X2)) = X1 ),
inference(fof_simplification,[status(thm)],[property_of_first]) ).
cnf(c_0_26,plain,
( X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2)
| ordered_pair_predicate(X1) ),
inference(fof_simplification,[status(thm)],[ordered_pair_predicate4]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(first(ordered_pair(a,b)),set_a)
| ~ ordered_pair_predicate(ordered_pair(a,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_19]),c_0_23]),c_0_24])]) ).
cnf(c_0_28,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| first(ordered_pair(X1,X2)) = X1 ),
c_0_25 ).
cnf(c_0_29,plain,
( X1 != ordered_pair(X2,X3)
| ~ little_set(X3)
| ~ little_set(X2)
| ordered_pair_predicate(X1) ),
c_0_26 ).
cnf(c_0_30,negated_conjecture,
~ ordered_pair_predicate(ordered_pair(a,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]),c_0_23]),c_0_24])]) ).
cnf(c_0_31,plain,
( ~ little_set(X1)
| ~ little_set(X2)
| ordered_pair_predicate(ordered_pair(X1,X2)) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET042-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n009.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 04:47:13 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
% 0.12/0.46 % Version: 3.5.1
% 0.12/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.46 % Starting sh5l with 300s (1) cores
% 0.12/0.46 % new_bool_3 with pid 868711 completed with status 0
% 0.12/0.46 % Result found by new_bool_3
% 0.12/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.46 % Search class: FHUSS-FFMF21-SFFFFFNN
% 0.12/0.46 % partial match(1): FHUSM-FFMF21-SFFFFFNN
% 0.12/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.46 % SubtermCWHack with pid 868716 completed with status 0
% 0.12/0.46 % Result found by SubtermCWHack
% 0.12/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.46 % Search class: FHUSS-FFMF21-SFFFFFNN
% 0.12/0.46 % partial match(1): FHUSM-FFMF21-SFFFFFNN
% 0.12/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.46 % Preprocessing time : 0.002 s
% 0.12/0.46
% 0.12/0.46 % Proof found!
% 0.12/0.46 % SZS status Unsatisfiable
% 0.12/0.46 % SZS output start CNFRefutation
% See solution above
% 0.12/0.46 % Parsed axioms : 170
% 0.12/0.46 % Removed by relevancy pruning/SinE : 122
% 0.12/0.46 % Initial clauses : 48
% 0.12/0.46 % Removed in clause preprocessing : 0
% 0.12/0.46 % Initial clauses in saturation : 48
% 0.12/0.46 % Processed clauses : 149
% 0.12/0.46 % ...of these trivial : 3
% 0.12/0.46 % ...subsumed : 19
% 0.12/0.46 % ...remaining for further processing : 127
% 0.12/0.46 % Other redundant clauses eliminated : 8
% 0.12/0.46 % Clauses deleted for lack of memory : 0
% 0.12/0.46 % Backward-subsumed : 2
% 0.12/0.46 % Backward-rewritten : 0
% 0.12/0.46 % Generated clauses : 295
% 0.12/0.46 % ...of the previous two non-redundant : 276
% 0.12/0.46 % ...aggressively subsumed : 0
% 0.12/0.46 % Contextual simplify-reflections : 4
% 0.12/0.46 % Paramodulations : 285
% 0.12/0.46 % Factorizations : 0
% 0.12/0.46 % NegExts : 0
% 0.12/0.46 % Equation resolutions : 10
% 0.12/0.46 % Disequality decompositions : 0
% 0.12/0.46 % Total rewrite steps : 17
% 0.12/0.46 % ...of those cached : 7
% 0.12/0.46 % Propositional unsat checks : 0
% 0.12/0.46 % Propositional check models : 0
% 0.12/0.46 % Propositional check unsatisfiable : 0
% 0.12/0.46 % Propositional clauses : 0
% 0.12/0.46 % Propositional clauses after purity: 0
% 0.12/0.46 % Propositional unsat core size : 0
% 0.12/0.46 % Propositional preprocessing time : 0.000
% 0.12/0.46 % Propositional encoding time : 0.000
% 0.12/0.46 % Propositional solver time : 0.000
% 0.12/0.46 % Success case prop preproc time : 0.000
% 0.12/0.46 % Success case prop encoding time : 0.000
% 0.12/0.46 % Success case prop solver time : 0.000
% 0.12/0.46 % Current number of processed clauses : 117
% 0.12/0.46 % Positive orientable unit clauses : 10
% 0.12/0.46 % Positive unorientable unit clauses: 0
% 0.12/0.46 % Negative unit clauses : 2
% 0.12/0.46 % Non-unit-clauses : 105
% 0.12/0.46 % Current number of unprocessed clauses: 175
% 0.12/0.46 % ...number of literals in the above : 555
% 0.12/0.46 % Current number of archived formulas : 0
% 0.12/0.46 % Current number of archived clauses : 2
% 0.12/0.46 % Clause-clause subsumption calls (NU) : 992
% 0.12/0.46 % Rec. Clause-clause subsumption calls : 687
% 0.12/0.46 % Non-unit clause-clause subsumptions : 24
% 0.12/0.46 % Unit Clause-clause subsumption calls : 7
% 0.12/0.46 % Rewrite failures with RHS unbound : 0
% 0.12/0.46 % BW rewrite match attempts : 13
% 0.12/0.46 % BW rewrite match successes : 0
% 0.12/0.46 % Condensation attempts : 0
% 0.12/0.46 % Condensation successes : 0
% 0.12/0.46 % Termbank termtop insertions : 7556
% 0.12/0.46 % Search garbage collected termcells : 698
% 0.12/0.46
% 0.12/0.46 % -------------------------------------------------
% 0.12/0.46 % User time : 0.015 s
% 0.12/0.46 % System time : 0.004 s
% 0.12/0.46 % Total time : 0.019 s
% 0.12/0.46 % Maximum resident set size: 3784 pages
% 0.12/0.46
% 0.12/0.46 % -------------------------------------------------
% 0.12/0.46 % User time : 0.019 s
% 0.12/0.46 % System time : 0.010 s
% 0.12/0.46 % Total time : 0.028 s
% 0.12/0.46 % Maximum resident set size: 4608 pages
% 0.12/0.46 % E exiting
%------------------------------------------------------------------------------