%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 02:12:58 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 14 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_idempotency_of_union,conjecture,
! [X1] : union(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
fof(subset_union,axiom,
! [X1,X2] :
( subset(X1,X2)
=> union(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] : union(X1,X1) = X1,
inference(assume_negation,[status(cth)],[prove_idempotency_of_union]) ).
fof(c_0_4,negated_conjecture,
union(esk1_0,esk1_0) != esk1_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_5,plain,
! [X5,X6] :
( union(X5,X6) = X6
| ~ subset(X5,X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_union])])]) ).
fof(c_0_6,plain,
! [X20] : subset(X20,X20),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
cnf(c_0_7,negated_conjecture,
union(esk1_0,esk1_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( ~ subset(X1,X2)
| union(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:42:31 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.43 % Version: 3.5.1
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.43 % Starting sh5l with 300s (1) cores
% 0.11/0.43 % new_bool_3 with pid 3425138 completed with status 0
% 0.11/0.43 % Result found by new_bool_3
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.43 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.11/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.43 % SubtermCWHack with pid 3425142 completed with status 0
% 0.11/0.43 % Result found by SubtermCWHack
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.43 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.11/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.43 % Preprocessing time : 0.001 s
% 0.11/0.43
% 0.11/0.43 % Proof found!
% 0.11/0.43 % SZS status Theorem
% 0.11/0.43 % SZS output start CNFRefutation
% See solution above
% 0.11/0.43 % Parsed axioms : 8
% 0.11/0.43 % Removed by relevancy pruning/SinE : 0
% 0.11/0.43 % Initial clauses : 17
% 0.11/0.43 % Removed in clause preprocessing : 2
% 0.11/0.43 % Initial clauses in saturation : 15
% 0.11/0.43 % Processed clauses : 8
% 0.11/0.43 % ...of these trivial : 0
% 0.11/0.43 % ...subsumed : 2
% 0.11/0.43 % ...remaining for further processing : 6
% 0.11/0.43 % Other redundant clauses eliminated : 2
% 0.11/0.43 % Clauses deleted for lack of memory : 0
% 0.11/0.43 % Backward-subsumed : 0
% 0.11/0.43 % Backward-rewritten : 0
% 0.11/0.43 % Generated clauses : 7
% 0.11/0.43 % ...of the previous two non-redundant : 2
% 0.11/0.43 % ...aggressively subsumed : 0
% 0.11/0.43 % Contextual simplify-reflections : 0
% 0.11/0.43 % Paramodulations : 5
% 0.11/0.43 % Factorizations : 0
% 0.11/0.43 % NegExts : 0
% 0.11/0.43 % Equation resolutions : 2
% 0.11/0.43 % Disequality decompositions : 0
% 0.11/0.43 % Total rewrite steps : 3
% 0.11/0.43 % ...of those cached : 1
% 0.11/0.43 % Propositional unsat checks : 0
% 0.11/0.43 % Propositional check models : 0
% 0.11/0.43 % Propositional check unsatisfiable : 0
% 0.11/0.43 % Propositional clauses : 0
% 0.11/0.43 % Propositional clauses after purity: 0
% 0.11/0.43 % Propositional unsat core size : 0
% 0.11/0.43 % Propositional preprocessing time : 0.000
% 0.11/0.43 % Propositional encoding time : 0.000
% 0.11/0.43 % Propositional solver time : 0.000
% 0.11/0.43 % Success case prop preproc time : 0.000
% 0.11/0.43 % Success case prop encoding time : 0.000
% 0.11/0.43 % Success case prop solver time : 0.000
% 0.11/0.43 % Current number of processed clauses : 4
% 0.11/0.43 % Positive orientable unit clauses : 1
% 0.11/0.43 % Positive unorientable unit clauses: 1
% 0.11/0.43 % Negative unit clauses : 1
% 0.11/0.43 % Non-unit-clauses : 1
% 0.11/0.43 % Current number of unprocessed clauses: 9
% 0.11/0.43 % ...number of literals in the above : 23
% 0.11/0.43 % Current number of archived formulas : 0
% 0.11/0.43 % Current number of archived clauses : 0
% 0.11/0.43 % Clause-clause subsumption calls (NU) : 0
% 0.11/0.43 % Rec. Clause-clause subsumption calls : 0
% 0.11/0.43 % Non-unit clause-clause subsumptions : 0
% 0.11/0.43 % Unit Clause-clause subsumption calls : 0
% 0.11/0.43 % Rewrite failures with RHS unbound : 0
% 0.11/0.43 % BW rewrite match attempts : 2
% 0.11/0.43 % BW rewrite match successes : 2
% 0.11/0.43 % Condensation attempts : 0
% 0.11/0.43 % Condensation successes : 0
% 0.11/0.43 % Termbank termtop insertions : 926
% 0.11/0.43 % Search garbage collected termcells : 276
% 0.11/0.43
% 0.11/0.43 % -------------------------------------------------
% 0.11/0.43 % User time : 0.005 s
% 0.11/0.43 % System time : 0.002 s
% 0.11/0.43 % Total time : 0.007 s
% 0.11/0.43 % Maximum resident set size: 3632 pages
% 0.11/0.43
% 0.11/0.43 % -------------------------------------------------
% 0.11/0.43 % User time : 0.005 s
% 0.11/0.43 % System time : 0.008 s
% 0.11/0.43 % Total time : 0.013 s
% 0.11/0.43 % Maximum resident set size: 4864 pages
% 0.11/0.43 % E exiting
%------------------------------------------------------------------------------