%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU173+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 : 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 02:24:07 PM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 4 unt; 0 def)
% Number of atoms : 86 ( 6 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 96 ( 35 ~; 33 |; 12 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 1 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) )
& ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(l71_subset_1,conjecture,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_5,plain,
! [X1,X2] :
( ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) )
& ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
inference(assume_negation,[status(cth)],[l71_subset_1]) ).
fof(c_0_7,plain,
! [X10,X11] :
( ( ~ empty(X10)
| element(X11,X10)
| ~ empty(X11) )
& ( ~ empty(X10)
| empty(X11)
| ~ element(X11,X10) )
& ( empty(X10)
| element(X11,X10)
| ~ in(X11,X10) )
& ( empty(X10)
| in(X11,X10)
| ~ element(X11,X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,plain,
! [X47,X48] :
( ~ empty(X48)
| ~ in(X47,X48) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_9,negated_conjecture,
! [X9] :
( ~ element(esk1_0,powerset(esk2_0))
& ( in(X9,esk2_0)
| ~ in(X9,esk1_0) ) ),
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_6])])])])]) ).
cnf(c_0_10,plain,
( ~ in(X1,X2)
| empty(X2)
| element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X21,X22,X23,X24,X25,X26] :
( ( X26 = powerset(X25)
| subset(esk6_2(X25,X26),X25)
| in(esk6_2(X25,X26),X26) )
& ( X26 = powerset(X25)
| ~ subset(esk6_2(X25,X26),X25)
| ~ in(esk6_2(X25,X26),X26) )
& ( X22 != powerset(X21)
| in(X24,X22)
| ~ subset(X24,X21) )
& ( X22 != powerset(X21)
| subset(X23,X21)
| ~ in(X23,X22) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_zfmisc_1])])])])])])]) ).
fof(c_0_13,plain,
! [X31,X32,X33,X34,X35] :
( ( subset(X34,X35)
| ~ in(esk7_2(X34,X35),X35) )
& ( subset(X34,X35)
| in(esk7_2(X34,X35),X34) )
& ( in(X33,X32)
| ~ in(X33,X31)
| ~ subset(X31,X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])]) ).
cnf(c_0_14,negated_conjecture,
~ element(esk1_0,powerset(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(csr,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( X3 != powerset(X2)
| ~ subset(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(X1,esk1_0)
| in(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| in(esk7_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
~ in(esk1_0,powerset(esk2_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( ~ subset(X1,X2)
| in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( ~ in(esk7_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( in(esk7_2(esk1_0,X1),esk2_0)
| subset(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
~ subset(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU173+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 05:56:30 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.39 Running first-order theorem proving
% 0.07/0.39 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
% 0.12/0.43 % Version: 3.5.1
% 0.12/0.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.43 % Starting sh5l with 300s (1) cores
% 0.12/0.43 % new_bool_3 with pid 3555424 completed with status 0
% 0.12/0.43 % Result found by new_bool_3
% 0.12/0.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.43 % Search class: FGHSM-FFMS31-SFFFFFNN
% 0.12/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.43 % SubtermCWHack with pid 3555429 completed with status 0
% 0.12/0.43 % Result found by SubtermCWHack
% 0.12/0.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.43 % Search class: FGHSM-FFMS31-SFFFFFNN
% 0.12/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.43 % Preprocessing time : 0.002 s
% 0.12/0.43
% 0.12/0.43 % Proof found!
% 0.12/0.43 % SZS status Theorem
% 0.12/0.43 % SZS output start CNFRefutation
% See solution above
% 0.12/0.43 % Parsed axioms : 113
% 0.12/0.43 % Removed by relevancy pruning/SinE : 58
% 0.12/0.43 % Initial clauses : 92
% 0.12/0.43 % Removed in clause preprocessing : 0
% 0.12/0.43 % Initial clauses in saturation : 92
% 0.12/0.43 % Processed clauses : 294
% 0.12/0.43 % ...of these trivial : 7
% 0.12/0.43 % ...subsumed : 137
% 0.12/0.43 % ...remaining for further processing : 150
% 0.12/0.43 % Other redundant clauses eliminated : 17
% 0.12/0.43 % Clauses deleted for lack of memory : 0
% 0.12/0.43 % Backward-subsumed : 1
% 0.12/0.43 % Backward-rewritten : 3
% 0.12/0.43 % Generated clauses : 540
% 0.12/0.43 % ...of the previous two non-redundant : 366
% 0.12/0.43 % ...aggressively subsumed : 0
% 0.12/0.43 % Contextual simplify-reflections : 1
% 0.12/0.43 % Paramodulations : 524
% 0.12/0.43 % Factorizations : 0
% 0.12/0.43 % NegExts : 0
% 0.12/0.43 % Equation resolutions : 17
% 0.12/0.43 % Disequality decompositions : 0
% 0.12/0.43 % Total rewrite steps : 199
% 0.12/0.43 % ...of those cached : 153
% 0.12/0.43 % Propositional unsat checks : 0
% 0.12/0.43 % Propositional check models : 0
% 0.12/0.43 % Propositional check unsatisfiable : 0
% 0.12/0.43 % Propositional clauses : 0
% 0.12/0.43 % Propositional clauses after purity: 0
% 0.12/0.43 % Propositional unsat core size : 0
% 0.12/0.43 % Propositional preprocessing time : 0.000
% 0.12/0.43 % Propositional encoding time : 0.000
% 0.12/0.43 % Propositional solver time : 0.000
% 0.12/0.43 % Success case prop preproc time : 0.000
% 0.12/0.43 % Success case prop encoding time : 0.000
% 0.12/0.43 % Success case prop solver time : 0.000
% 0.12/0.43 % Current number of processed clauses : 133
% 0.12/0.43 % Positive orientable unit clauses : 33
% 0.12/0.43 % Positive unorientable unit clauses: 2
% 0.12/0.43 % Negative unit clauses : 23
% 0.12/0.43 % Non-unit-clauses : 75
% 0.12/0.43 % Current number of unprocessed clauses: 162
% 0.12/0.43 % ...number of literals in the above : 377
% 0.12/0.43 % Current number of archived formulas : 0
% 0.12/0.43 % Current number of archived clauses : 4
% 0.12/0.43 % Clause-clause subsumption calls (NU) : 467
% 0.12/0.43 % Rec. Clause-clause subsumption calls : 397
% 0.12/0.43 % Non-unit clause-clause subsumptions : 57
% 0.12/0.43 % Unit Clause-clause subsumption calls : 229
% 0.12/0.43 % Rewrite failures with RHS unbound : 0
% 0.12/0.43 % BW rewrite match attempts : 24
% 0.12/0.43 % BW rewrite match successes : 11
% 0.12/0.43 % Condensation attempts : 0
% 0.12/0.43 % Condensation successes : 0
% 0.12/0.43 % Termbank termtop insertions : 9456
% 0.12/0.43 % Search garbage collected termcells : 1557
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.014 s
% 0.12/0.43 % System time : 0.003 s
% 0.12/0.43 % Total time : 0.018 s
% 0.12/0.43 % Maximum resident set size: 3940 pages
% 0.12/0.43
% 0.12/0.43 % -------------------------------------------------
% 0.12/0.43 % User time : 0.018 s
% 0.12/0.43 % System time : 0.007 s
% 0.12/0.43 % Total time : 0.025 s
% 0.12/0.43 % Maximum resident set size: 4864 pages
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------