%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU152+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 02:24:00 PM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 30 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 6 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l23_zfmisc_1,conjecture,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
inference(assume_negation,[status(cth)],[l23_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
( set_union2(singleton(esk1_0),esk2_0) != esk2_0
& in(esk1_0,esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_7,lemma,
! [X19,X20] :
( set_union2(X19,X20) = X20
| ~ subset(X19,X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])]) ).
cnf(c_0_8,negated_conjecture,
set_union2(singleton(esk1_0),esk2_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,lemma,
( ~ subset(X1,X2)
| set_union2(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
set_union2(esk2_0,singleton(esk1_0)) != esk2_0,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,lemma,
( ~ subset(X2,X1)
| set_union2(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_13,lemma,
! [X41,X42] :
( ( subset(singleton(X41),X42)
| ~ in(X41,X42) )
& ( in(X41,X42)
| ~ subset(singleton(X41),X42) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])])]) ).
cnf(c_0_14,negated_conjecture,
~ subset(singleton(esk1_0),esk2_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,lemma,
( ~ in(X1,X2)
| subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
in(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU152+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:58:58 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % new_bool_1 with pid 2335110 completed with status 0
% 0.14/0.43 % Result found by new_bool_1
% 0.14/0.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.43 % Search class: FGHSM-FFMF32-SFFFFFNN
% 0.14/0.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.43 % SubtermCWHack with pid 2335112 completed with status 0
% 0.14/0.43 % Result found by SubtermCWHack
% 0.14/0.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.43 % Search class: FGHSM-FFMF32-SFFFFFNN
% 0.14/0.43 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.43 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.43 % Preprocessing time : 0.002 s
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Theorem
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 75
% 0.14/0.43 % Removed by relevancy pruning/SinE : 33
% 0.14/0.43 % Initial clauses : 72
% 0.14/0.43 % Removed in clause preprocessing : 0
% 0.14/0.43 % Initial clauses in saturation : 72
% 0.14/0.43 % Processed clauses : 83
% 0.14/0.43 % ...of these trivial : 5
% 0.14/0.43 % ...subsumed : 22
% 0.14/0.43 % ...remaining for further processing : 56
% 0.14/0.43 % Other redundant clauses eliminated : 9
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 0
% 0.14/0.43 % Backward-rewritten : 1
% 0.14/0.43 % Generated clauses : 119
% 0.14/0.43 % ...of the previous two non-redundant : 61
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 0
% 0.14/0.43 % Paramodulations : 111
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 9
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 59
% 0.14/0.43 % ...of those cached : 37
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 48
% 0.14/0.43 % Positive orientable unit clauses : 20
% 0.14/0.43 % Positive unorientable unit clauses: 2
% 0.14/0.43 % Negative unit clauses : 8
% 0.14/0.43 % Non-unit-clauses : 18
% 0.14/0.43 % Current number of unprocessed clauses: 50
% 0.14/0.43 % ...number of literals in the above : 132
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 1
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 32
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 32
% 0.14/0.43 % Non-unit clause-clause subsumptions : 8
% 0.14/0.43 % Unit Clause-clause subsumption calls : 11
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 21
% 0.14/0.43 % BW rewrite match successes : 16
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 4946
% 0.14/0.43 % Search garbage collected termcells : 1200
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.008 s
% 0.14/0.43 % System time : 0.001 s
% 0.14/0.43 % Total time : 0.009 s
% 0.14/0.43 % Maximum resident set size: 3692 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.012 s
% 0.14/0.43 % System time : 0.005 s
% 0.14/0.43 % Total time : 0.016 s
% 0.14/0.43 % Maximum resident set size: 4864 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------