%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU094+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:23:48 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 92 ( 36 ~; 38 |; 9 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 33 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_finset_1,axiom,
! [X1,X2] :
( ( finite(X2)
& subset(X1,X2) )
=> finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
fof(t100_zfmisc_1,axiom,
! [X1] : subset(X1,powerset(union(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
fof(t24_finset_1,axiom,
! [X1] :
( finite(X1)
<=> finite(powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finset_1) ).
fof(t25_finset_1,conjecture,
! [X1] :
( ( ! [X2] :
( in(X2,X1)
=> finite(X2) )
& finite(X1) )
<=> finite(union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).
fof(l22_finset_1,axiom,
! [X1] :
( ( ! [X2] :
( in(X2,X1)
=> finite(X2) )
& finite(X1) )
=> finite(union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l22_finset_1) ).
fof(t92_zfmisc_1,axiom,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(c_0_6,plain,
! [X53,X54] :
( finite(X53)
| ~ finite(X54)
| ~ subset(X53,X54) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_finset_1])])]) ).
fof(c_0_7,plain,
! [X17] : subset(X17,powerset(union(X17))),
inference(variable_rename,[status(thm)],[t100_zfmisc_1]) ).
cnf(c_0_8,plain,
( ~ finite(X2)
| ~ subset(X1,X2)
| finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
subset(X1,powerset(union(X1))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X13] :
( ( finite(X13)
| ~ finite(powerset(X13)) )
& ( finite(powerset(X13))
| ~ finite(X13) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t24_finset_1])])]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( ! [X2] :
( in(X2,X1)
=> finite(X2) )
& finite(X1) )
<=> finite(union(X1)) ),
inference(assume_negation,[status(cth)],[t25_finset_1]) ).
cnf(c_0_12,plain,
( ~ finite(powerset(union(X1)))
| finite(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( ~ finite(X1)
| finite(powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,negated_conjecture,
! [X6] :
( ( finite(union(esk1_0))
| finite(X6)
| ~ in(X6,esk1_0) )
& ( finite(union(esk1_0))
| finite(esk1_0) )
& ( ~ finite(union(esk1_0))
| ~ finite(esk1_0)
| ~ finite(esk2_0) )
& ( ~ finite(union(esk1_0))
| ~ finite(esk1_0)
| in(esk2_0,esk1_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])]) ).
fof(c_0_15,plain,
! [X15] :
( ( finite(union(X15))
| ~ finite(X15)
| ~ finite(esk5_1(X15)) )
& ( finite(union(X15))
| ~ finite(X15)
| in(esk5_1(X15),X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l22_finset_1])])])])]) ).
cnf(c_0_16,plain,
( ~ finite(union(X1))
| finite(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( finite(union(esk1_0))
| finite(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( ~ in(X1,esk1_0)
| finite(union(esk1_0))
| finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( ~ finite(X1)
| finite(union(X1))
| in(esk5_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
finite(esk1_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,plain,
! [X18,X19] :
( subset(X18,union(X19))
| ~ in(X18,X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t92_zfmisc_1])])]) ).
cnf(c_0_22,negated_conjecture,
( ~ finite(union(esk1_0))
| ~ finite(esk1_0)
| in(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( ~ finite(X1)
| ~ finite(esk5_1(X1))
| finite(union(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( finite(union(esk1_0))
| finite(esk5_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_25,negated_conjecture,
( ~ finite(union(esk1_0))
| ~ finite(esk1_0)
| ~ finite(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,plain,
( ~ in(X1,X2)
| subset(X1,union(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( ~ finite(union(esk1_0))
| in(esk2_0,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_20])]) ).
cnf(c_0_28,negated_conjecture,
finite(union(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20])]) ).
cnf(c_0_29,negated_conjecture,
( ~ finite(esk2_0)
| ~ finite(union(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_20])]) ).
cnf(c_0_30,plain,
( ~ in(X1,X2)
| ~ finite(union(X2))
| finite(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
in(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
~ finite(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_28])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU094+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:49:53 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.42 % Version: 3.5.1
% 0.13/0.42 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % new_bool_3 with pid 1681004 completed with status 0
% 0.13/0.42 % Result found by new_bool_3
% 0.13/0.42 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.42 % Search class: FGHSM-FFMM11-SFFFFFNN
% 0.13/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.42 % SubtermCWHack with pid 1681007 completed with status 0
% 0.13/0.42 % Result found by SubtermCWHack
% 0.13/0.42 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.42 % Search class: FGHSM-FFMM11-SFFFFFNN
% 0.13/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.42 % Preprocessing time : 0.001 s
% 0.13/0.42
% 0.13/0.42 % Proof found!
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start CNFRefutation
% See solution above
% 0.13/0.42 % Parsed axioms : 60
% 0.13/0.42 % Removed by relevancy pruning/SinE : 28
% 0.13/0.42 % Initial clauses : 55
% 0.13/0.42 % Removed in clause preprocessing : 0
% 0.13/0.42 % Initial clauses in saturation : 55
% 0.13/0.42 % Processed clauses : 129
% 0.13/0.42 % ...of these trivial : 0
% 0.13/0.42 % ...subsumed : 21
% 0.13/0.42 % ...remaining for further processing : 108
% 0.13/0.42 % Other redundant clauses eliminated : 0
% 0.13/0.42 % Clauses deleted for lack of memory : 0
% 0.13/0.42 % Backward-subsumed : 0
% 0.13/0.42 % Backward-rewritten : 14
% 0.13/0.42 % Generated clauses : 106
% 0.13/0.42 % ...of the previous two non-redundant : 91
% 0.13/0.42 % ...aggressively subsumed : 0
% 0.13/0.42 % Contextual simplify-reflections : 1
% 0.13/0.42 % Paramodulations : 106
% 0.13/0.42 % Factorizations : 0
% 0.13/0.42 % NegExts : 0
% 0.13/0.42 % Equation resolutions : 0
% 0.13/0.42 % Disequality decompositions : 0
% 0.13/0.42 % Total rewrite steps : 32
% 0.13/0.42 % ...of those cached : 21
% 0.13/0.42 % Propositional unsat checks : 0
% 0.13/0.42 % Propositional check models : 0
% 0.13/0.42 % Propositional check unsatisfiable : 0
% 0.13/0.42 % Propositional clauses : 0
% 0.13/0.42 % Propositional clauses after purity: 0
% 0.13/0.42 % Propositional unsat core size : 0
% 0.13/0.42 % Propositional preprocessing time : 0.000
% 0.13/0.42 % Propositional encoding time : 0.000
% 0.13/0.42 % Propositional solver time : 0.000
% 0.13/0.42 % Success case prop preproc time : 0.000
% 0.13/0.42 % Success case prop encoding time : 0.000
% 0.13/0.42 % Success case prop solver time : 0.000
% 0.13/0.42 % Current number of processed clauses : 94
% 0.13/0.42 % Positive orientable unit clauses : 21
% 0.13/0.42 % Positive unorientable unit clauses: 0
% 0.13/0.42 % Negative unit clauses : 7
% 0.13/0.42 % Non-unit-clauses : 66
% 0.13/0.42 % Current number of unprocessed clauses: 13
% 0.13/0.42 % ...number of literals in the above : 38
% 0.13/0.42 % Current number of archived formulas : 0
% 0.13/0.42 % Current number of archived clauses : 14
% 0.13/0.42 % Clause-clause subsumption calls (NU) : 375
% 0.13/0.42 % Rec. Clause-clause subsumption calls : 343
% 0.13/0.42 % Non-unit clause-clause subsumptions : 10
% 0.13/0.42 % Unit Clause-clause subsumption calls : 17
% 0.13/0.42 % Rewrite failures with RHS unbound : 0
% 0.13/0.42 % BW rewrite match attempts : 8
% 0.13/0.42 % BW rewrite match successes : 4
% 0.13/0.42 % Condensation attempts : 0
% 0.13/0.42 % Condensation successes : 0
% 0.13/0.42 % Termbank termtop insertions : 4425
% 0.13/0.42 % Search garbage collected termcells : 670
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.007 s
% 0.13/0.42 % System time : 0.004 s
% 0.13/0.42 % Total time : 0.012 s
% 0.13/0.42 % Maximum resident set size: 3680 pages
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.011 s
% 0.13/0.42 % System time : 0.007 s
% 0.13/0.42 % Total time : 0.017 s
% 0.13/0.42 % Maximum resident set size: 4864 pages
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------