%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU159+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 : n010.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 02:24:02 PM UTC 2026
% Result : Theorem 185.86s 32.15s
% Output : CNFRefutation 185.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 101 ( 33 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 105 ( 37 ~; 51 |; 11 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 68 ( 4 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(t38_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X2,X3)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_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(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_4,plain,
! [X29,X30,X31,X32,X33,X34,X35,X36] :
( ( X36 = unordered_pair(X34,X35)
| esk6_3(X34,X35,X36) = X35
| esk6_3(X34,X35,X36) = X34
| in(esk6_3(X34,X35,X36),X36) )
& ( X36 = unordered_pair(X34,X35)
| ~ in(esk6_3(X34,X35,X36),X36)
| esk6_3(X34,X35,X36) != X35 )
& ( X36 = unordered_pair(X34,X35)
| ~ in(esk6_3(X34,X35,X36),X36)
| esk6_3(X34,X35,X36) != X34 )
& ( X31 != unordered_pair(X29,X30)
| in(X33,X31)
| X33 != X30 )
& ( X31 != unordered_pair(X29,X30)
| in(X33,X31)
| X33 != X29 )
& ( X31 != unordered_pair(X29,X30)
| X32 = X30
| X32 = X29
| ~ in(X32,X31) ) ),
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)],[d2_tarski])])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X2,X3)
& in(X1,X3) ) ),
inference(assume_negation,[status(cth)],[t38_zfmisc_1]) ).
cnf(c_0_6,plain,
( X2 != unordered_pair(X3,X4)
| ~ in(X1,X2)
| X1 = X4
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,plain,
! [X12,X13,X14,X15,X16] :
( ( subset(X15,X16)
| ~ in(esk4_2(X15,X16),X16) )
& ( subset(X15,X16)
| in(esk4_2(X15,X16),X15) )
& ( in(X14,X13)
| ~ in(X14,X12)
| ~ subset(X12,X13) ) ),
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])])])])])])]) ).
fof(c_0_8,negated_conjecture,
( ( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| in(esk2_0,esk3_0) )
& ( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| in(esk1_0,esk3_0) )
& ( ~ in(esk2_0,esk3_0)
| ~ in(esk1_0,esk3_0)
| ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
cnf(c_0_9,plain,
( ~ in(X1,unordered_pair(X3,X2))
| X1 = X3
| X1 = X2 ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| in(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( X3 != unordered_pair(X4,X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
| in(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( X3 != unordered_pair(X2,X4)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,plain,
( ~ in(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
( subset(unordered_pair(X1,X2),X3)
| esk4_2(unordered_pair(X1,X2),X3) = X1
| esk4_2(unordered_pair(X1,X2),X3) = X2 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_18,negated_conjecture,
( ~ in(X1,unordered_pair(esk1_0,esk2_0))
| in(X1,esk3_0)
| in(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_13])]) ).
cnf(c_0_20,negated_conjecture,
( ~ in(X1,unordered_pair(esk1_0,esk2_0))
| in(X1,esk3_0)
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_21,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_15])]) ).
cnf(c_0_22,plain,
( ~ in(X1,X3)
| subset(unordered_pair(X1,X2),X3)
| esk4_2(unordered_pair(X1,X2),X3) = X2 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
in(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(esk2_0,esk3_0)
| ~ in(esk1_0,esk3_0)
| ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
in(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( subset(unordered_pair(esk2_0,X1),esk3_0)
| esk4_2(unordered_pair(esk2_0,X1),esk3_0) = X1 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_27,plain,
! [X27,X28] : unordered_pair(X27,X28) = unordered_pair(X28,X27),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_28,negated_conjecture,
( ~ in(esk2_0,esk3_0)
| ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
( ~ in(X1,esk3_0)
| subset(unordered_pair(esk2_0,X1),esk3_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_30,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
~ subset(unordered_pair(esk1_0,esk2_0),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_23])]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU159+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n010.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
% 0.10/0.37 % DateTime : Mon Sep 21 05:53:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 185.86/32.15 % Version: 3.5.1
% 185.86/32.15 % Preprocessing class: FSLSSMSSSSSNFFN.
% 185.86/32.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 185.86/32.15 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 185.86/32.15 % Starting new_bool_3 with 300s (1) cores
% 185.86/32.15 % Starting new_bool_1 with 300s (1) cores
% 185.86/32.15 % Starting sh5l with 300s (1) cores
% 185.86/32.15 % new_bool_3 with pid 162086 completed with status 0
% 185.86/32.15 % Result found by new_bool_3
% 185.86/32.15 % Preprocessing class: FSLSSMSSSSSNFFN.
% 185.86/32.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 185.86/32.15 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 185.86/32.15 % Starting new_bool_3 with 300s (1) cores
% 185.86/32.15 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 185.86/32.15 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 185.86/32.15 % Search class: FGHSM-FFMF32-SFFFFFNN
% 185.86/32.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 185.86/32.15 % Starting SubtermCWHack with 28s (1) cores
% 185.86/32.15 % SubtermCWHack with pid 162092 completed with status 8
% 185.86/32.15 % Starting new_bool_3 with 31s (1) cores
% 185.86/32.15 % new_bool_3 with pid 162473 completed with status 0
% 185.86/32.15 % Result found by new_bool_3
% 185.86/32.15 % Preprocessing class: FSLSSMSSSSSNFFN.
% 185.86/32.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 185.86/32.15 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 185.86/32.15 % Starting new_bool_3 with 300s (1) cores
% 185.86/32.15 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 185.86/32.15 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 185.86/32.15 % Search class: FGHSM-FFMF32-SFFFFFNN
% 185.86/32.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 185.86/32.15 % Starting SubtermCWHack with 28s (1) cores
% 185.86/32.15 % SubtermCWHack with pid 162092 completed with status 8
% 185.86/32.15 % Starting new_bool_3 with 31s (1) cores
% 185.86/32.15 % Preprocessing time : 0.003 s
% 185.86/32.15 % Presaturation interreduction done
% 185.86/32.15
% 185.86/32.15 % Proof found!
% 185.86/32.15 % SZS status Theorem
% 185.86/32.15 % SZS output start CNFRefutation
% See solution above
% 185.86/32.15 % Parsed axioms : 89
% 185.86/32.15 % Removed by relevancy pruning/SinE : 44
% 185.86/32.15 % Initial clauses : 77
% 185.86/32.15 % Removed in clause preprocessing : 0
% 185.86/32.15 % Initial clauses in saturation : 77
% 185.86/32.15 % Processed clauses : 11366
% 185.86/32.15 % ...of these trivial : 450
% 185.86/32.15 % ...subsumed : 9411
% 185.86/32.15 % ...remaining for further processing : 1504
% 185.86/32.15 % Other redundant clauses eliminated : 143
% 185.86/32.15 % Clauses deleted for lack of memory : 0
% 185.86/32.15 % Backward-subsumed : 49
% 185.86/32.15 % Backward-rewritten : 95
% 185.86/32.15 % Generated clauses : 90497
% 185.86/32.15 % ...of the previous two non-redundant : 77165
% 185.86/32.15 % ...aggressively subsumed : 0
% 185.86/32.15 % Contextual simplify-reflections : 1
% 185.86/32.15 % Paramodulations : 89622
% 185.86/32.15 % Factorizations : 732
% 185.86/32.15 % NegExts : 0
% 185.86/32.15 % Equation resolutions : 146
% 185.86/32.15 % Disequality decompositions : 0
% 185.86/32.15 % Total rewrite steps : 39561
% 185.86/32.15 % ...of those cached : 36116
% 185.86/32.15 % Propositional unsat checks : 0
% 185.86/32.15 % Propositional check models : 0
% 185.86/32.15 % Propositional check unsatisfiable : 0
% 185.86/32.15 % Propositional clauses : 0
% 185.86/32.15 % Propositional clauses after purity: 0
% 185.86/32.15 % Propositional unsat core size : 0
% 185.86/32.15 % Propositional preprocessing time : 0.000
% 185.86/32.15 % Propositional encoding time : 0.000
% 185.86/32.15 % Propositional solver time : 0.000
% 185.86/32.15 % Success case prop preproc time : 0.000
% 185.86/32.15 % Success case prop encoding time : 0.000
% 185.86/32.15 % Success case prop solver time : 0.000
% 185.86/32.15 % Current number of processed clauses : 1276
% 185.86/32.15 % Positive orientable unit clauses : 240
% 185.86/32.15 % Positive unorientable unit clauses: 5
% 185.86/32.15 % Negative unit clauses : 171
% 185.86/32.15 % Non-unit-clauses : 860
% 185.86/32.15 % Current number of unprocessed clauses: 65705
% 185.86/32.15 % ...number of literals in the above : 221683
% 185.86/32.15 % Current number of archived formulas : 0
% 185.86/32.15 % Current number of archived clauses : 212
% 185.86/32.15 % Clause-clause subsumption calls (NU) : 71215
% 185.86/32.15 % Rec. Clause-clause subsumption calls : 42522
% 185.86/32.15 % Non-unit clause-clause subsumptions : 2689
% 185.86/32.15 % Unit Clause-clause subsumption calls : 4293
% 185.86/32.15 % Rewrite failures with RHS unbound : 0
% 185.86/32.15 % BW rewrite match attempts : 557
% 185.86/32.15 % BW rewrite match successes : 96
% 185.86/32.15 % Condensation attempts : 0
% 185.86/32.15 % Condensation successes : 0
% 185.86/32.15 % Termbank termtop insertions : 1291529
% 185.86/32.15 % Search garbage collected termcells : 1361
% 185.86/32.15
% 185.86/32.15 % -------------------------------------------------
% 185.86/32.15 % User time : 29.612 s
% 185.86/32.15 % System time : 1.263 s
% 185.86/32.15 % Total time : 30.876 s
% 185.86/32.15 % Maximum resident set size: 3708 pages
% 185.86/32.15
% 185.86/32.15 % -------------------------------------------------
% 185.86/32.15 % User time : 29.615 s
% 185.86/32.15 % System time : 1.271 s
% 185.86/32.15 % Total time : 30.886 s
% 185.86/32.15 % Maximum resident set size: 4864 pages
% 185.86/32.15 % E exiting
%------------------------------------------------------------------------------