%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET023-3 : 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 : n015.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 02:13:09 PM UTC 2026
% Result : Unsatisfiable 0.37s 0.69s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 27 ( 11 unt; 0 nHn; 22 RR)
% Number of literals : 47 ( 14 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(ordered_pair_predicate3,axiom,
( ~ ordered_pair_predicate(X1)
| X1 = ordered_pair(f2(X1),f3(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate3) ).
cnf(ordered_pair_predicate1,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(f2(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate1) ).
cnf(ordered_pair_predicate2,axiom,
( ~ ordered_pair_predicate(X1)
| little_set(f3(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate2) ).
cnf(prove_second_component_is_small,negated_conjecture,
~ little_set(second(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_component_is_small) ).
cnf(an_ordered_pair_predicate,hypothesis,
ordered_pair_predicate(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).
cnf(c_0_8,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
inference(fof_simplification,[status(thm)],[property_of_second]) ).
cnf(c_0_9,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_10,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_11,plain,
( ~ ordered_pair_predicate(X1)
| X1 = ordered_pair(f2(X1),f3(X1)) ),
inference(fof_simplification,[status(thm)],[ordered_pair_predicate3]) ).
cnf(c_0_12,plain,
( ~ little_set(X2)
| ~ little_set(X1)
| second(ordered_pair(X1,X2)) = X2 ),
c_0_8 ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( ~ ordered_pair_predicate(X1)
| X1 = ordered_pair(f2(X1),f3(X1)) ),
c_0_11 ).
cnf(c_0_15,plain,
( ~ ordered_pair_predicate(X1)
| little_set(f2(X1)) ),
inference(fof_simplification,[status(thm)],[ordered_pair_predicate1]) ).
cnf(c_0_16,plain,
( ~ ordered_pair_predicate(X1)
| little_set(f3(X1)) ),
inference(fof_simplification,[status(thm)],[ordered_pair_predicate2]) ).
cnf(c_0_17,plain,
( ~ little_set(X1)
| ~ little_set(X2)
| second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X2 ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( ~ ordered_pair_predicate(X1)
| X1 = non_ordered_pair(non_ordered_pair(f2(X1),f2(X1)),non_ordered_pair(f2(X1),f3(X1))) ),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_19,plain,
( ~ ordered_pair_predicate(X1)
| little_set(f2(X1)) ),
c_0_15 ).
cnf(c_0_20,plain,
( ~ ordered_pair_predicate(X1)
| little_set(f3(X1)) ),
c_0_16 ).
cnf(c_0_21,negated_conjecture,
~ little_set(second(a)),
inference(fof_simplification,[status(thm)],[prove_second_component_is_small]) ).
cnf(c_0_22,plain,
( ~ ordered_pair_predicate(X1)
| f3(X1) = second(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
~ little_set(second(a)),
c_0_21 ).
cnf(c_0_24,plain,
( ~ ordered_pair_predicate(X1)
| little_set(second(X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_25,hypothesis,
ordered_pair_predicate(a),
an_ordered_pair_predicate ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET023-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n015.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 21 04:47:05 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.48 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
% 0.37/0.69 % Version: 3.5.1
% 0.37/0.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/0.69 % Starting new_bool_3 with 300s (1) cores
% 0.37/0.69 % Starting new_bool_1 with 300s (1) cores
% 0.37/0.69 % Starting sh5l with 300s (1) cores
% 0.37/0.69 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 588174 completed with status 0
% 0.37/0.69 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.37/0.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.37/0.69 % No SInE strategy applied
% 0.37/0.69 % Search class: FGHSF-FFLS31-MFFFFFNN
% 0.37/0.69 % partial match(1): FGHSM-FFLS31-MFFFFFNN
% 0.37/0.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.37/0.69 % Starting SubtermCWHack with 136s (1) cores
% 0.37/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.37/0.69 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 224s (1) cores
% 0.37/0.69 % Starting new_bool_3 with 216s (1) cores
% 0.37/0.69 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2i with 136s (1) cores
% 0.37/0.69 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 588186 completed with status 0
% 0.37/0.69 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.37/0.69 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.37/0.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.37/0.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.37/0.69 % No SInE strategy applied
% 0.37/0.69 % Search class: FGHSF-FFLS31-MFFFFFNN
% 0.37/0.69 % partial match(1): FGHSM-FFLS31-MFFFFFNN
% 0.37/0.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.37/0.69 % Starting SubtermCWHack with 136s (1) cores
% 0.37/0.69 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.37/0.69 % Preprocessing time : 0.003 s
% 0.37/0.69 % Presaturation interreduction done
% 0.37/0.69
% 0.37/0.69 % Proof found!
% 0.37/0.69 % SZS status Unsatisfiable
% 0.37/0.69 % SZS output start CNFRefutation
% See solution above
% 0.37/0.69 % Parsed axioms : 150
% 0.37/0.69 % Removed by relevancy pruning/SinE : 0
% 0.37/0.69 % Initial clauses : 150
% 0.37/0.69 % Removed in clause preprocessing : 6
% 0.37/0.69 % Initial clauses in saturation : 144
% 0.37/0.69 % Processed clauses : 744
% 0.37/0.69 % ...of these trivial : 6
% 0.37/0.69 % ...subsumed : 97
% 0.37/0.69 % ...remaining for further processing : 641
% 0.37/0.69 % Other redundant clauses eliminated : 18
% 0.37/0.69 % Clauses deleted for lack of memory : 0
% 0.37/0.69 % Backward-subsumed : 3
% 0.37/0.69 % Backward-rewritten : 0
% 0.37/0.69 % Generated clauses : 2552
% 0.37/0.69 % ...of the previous two non-redundant : 2377
% 0.37/0.69 % ...aggressively subsumed : 0
% 0.37/0.69 % Contextual simplify-reflections : 15
% 0.37/0.69 % Paramodulations : 2529
% 0.37/0.69 % Factorizations : 2
% 0.37/0.69 % NegExts : 0
% 0.37/0.69 % Equation resolutions : 21
% 0.37/0.69 % Disequality decompositions : 0
% 0.37/0.69 % Total rewrite steps : 326
% 0.37/0.69 % ...of those cached : 250
% 0.37/0.69 % Propositional unsat checks : 0
% 0.37/0.69 % Propositional check models : 0
% 0.37/0.69 % Propositional check unsatisfiable : 0
% 0.37/0.69 % Propositional clauses : 0
% 0.37/0.69 % Propositional clauses after purity: 0
% 0.37/0.69 % Propositional unsat core size : 0
% 0.37/0.69 % Propositional preprocessing time : 0.000
% 0.37/0.69 % Propositional encoding time : 0.000
% 0.37/0.69 % Propositional solver time : 0.000
% 0.37/0.69 % Success case prop preproc time : 0.000
% 0.37/0.69 % Success case prop encoding time : 0.000
% 0.37/0.69 % Success case prop solver time : 0.000
% 0.37/0.69 % Current number of processed clauses : 480
% 0.37/0.69 % Positive orientable unit clauses : 62
% 0.37/0.69 % Positive unorientable unit clauses: 0
% 0.37/0.69 % Negative unit clauses : 3
% 0.37/0.69 % Non-unit-clauses : 415
% 0.37/0.69 % Current number of unprocessed clauses: 1917
% 0.37/0.69 % ...number of literals in the above : 4950
% 0.37/0.69 % Current number of archived formulas : 0
% 0.37/0.69 % Current number of archived clauses : 153
% 0.37/0.69 % Clause-clause subsumption calls (NU) : 25371
% 0.37/0.69 % Rec. Clause-clause subsumption calls : 16851
% 0.37/0.69 % Non-unit clause-clause subsumptions : 82
% 0.37/0.69 % Unit Clause-clause subsumption calls : 1636
% 0.37/0.69 % Rewrite failures with RHS unbound : 0
% 0.37/0.69 % BW rewrite match attempts : 10
% 0.37/0.69 % BW rewrite match successes : 0
% 0.37/0.69 % Condensation attempts : 0
% 0.37/0.69 % Condensation successes : 0
% 0.37/0.69 % Termbank termtop insertions : 45251
% 0.37/0.69 % Search garbage collected termcells : 340
% 0.37/0.69
% 0.37/0.69 % -------------------------------------------------
% 0.37/0.69 % User time : 0.132 s
% 0.37/0.69 % System time : 0.014 s
% 0.37/0.69 % Total time : 0.146 s
% 0.37/0.69 % Maximum resident set size: 3768 pages
% 0.37/0.69
% 0.37/0.69 % -------------------------------------------------
% 0.37/0.69 % User time : 0.451 s
% 0.37/0.69 % System time : 0.039 s
% 0.37/0.69 % Total time : 0.490 s
% 0.37/0.69 % Maximum resident set size: 4608 pages
% 0.37/0.69 % E exiting
%------------------------------------------------------------------------------