%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET016+4 : 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 : n014.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 02:13:05 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 75 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 24 ~; 27 |; 9 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI50a,conjecture,
! [X1,X2,X6,X7] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
=> X1 = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI50a) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(unordered_pair,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( X3 = X2
| X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X6,X7] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X2)),unordered_pair(singleton(X6),unordered_pair(X6,X7)))
=> X1 = X6 ),
inference(assume_negation,[status(cth)],[thI50a]) ).
fof(c_0_6,plain,
! [X12,X13] :
( ( equal_set(X12,X13)
| ~ subset(X13,X12)
| ~ subset(X12,X13) )
& ( ~ equal_set(X12,X13)
| subset(X13,X12) )
& ( ~ equal_set(X12,X13)
| subset(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
fof(c_0_7,negated_conjecture,
( esk1_0 != esk3_0
& equal_set(unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)),unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0))) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,plain,
! [X19,X20,X21,X22,X23] :
( ( subset(X22,X23)
| ~ member(esk5_2(X22,X23),X23) )
& ( subset(X22,X23)
| member(esk5_2(X22,X23),X22) )
& ( member(X21,X20)
| ~ member(X21,X19)
| ~ subset(X19,X20) ) ),
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)],[subset])])])])])])]) ).
cnf(c_0_9,plain,
( ~ equal_set(X2,X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
equal_set(unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0)),unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X14,X15,X16] :
( ( member(X14,unordered_pair(X15,X16))
| X14 != X16 )
& ( member(X14,unordered_pair(X15,X16))
| X14 != X15 )
& ( X14 = X16
| X14 = X15
| ~ member(X14,unordered_pair(X15,X16)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])])]) ).
cnf(c_0_12,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
subset(unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0)),unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( X1 != X2
| member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X17,X18] :
( ( member(X17,singleton(X18))
| X17 != X18 )
& ( X17 = X18
| ~ member(X17,singleton(X18)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])])]) ).
cnf(c_0_16,negated_conjecture,
( ~ member(X1,unordered_pair(singleton(esk3_0),unordered_pair(esk3_0,esk4_0)))
| member(X1,unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
member(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( X1 != X2
| member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
member(singleton(esk3_0),unordered_pair(singleton(esk1_0),unordered_pair(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( singleton(esk3_0) = singleton(esk1_0)
| singleton(esk3_0) = unordered_pair(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( member(esk3_0,singleton(esk1_0))
| singleton(esk3_0) = unordered_pair(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
esk1_0 != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
singleton(esk3_0) = unordered_pair(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_27,negated_conjecture,
member(esk3_0,unordered_pair(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
esk2_0 = esk3_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_27]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
singleton(esk3_0) = unordered_pair(esk1_0,esk3_0),
inference(rw,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( ~ member(X1,unordered_pair(esk1_0,esk3_0))
| X1 = esk3_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_17]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 04:42:34 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.12/0.45 % Version: 3.5.1
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.45 % Starting sh5l with 300s (1) cores
% 0.12/0.45 % new_bool_3 with pid 3158200 completed with status 0
% 0.12/0.45 % Result found by new_bool_3
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.45 % Search class: FGUSF-FFSF21-SFFFFFNN
% 0.12/0.45 % partial match(1): FGHSF-FFSF21-SFFFFFNN
% 0.12/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.45 % SubtermCWHack with pid 3158204 completed with status 0
% 0.12/0.45 % Result found by SubtermCWHack
% 0.12/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.45 % Search class: FGUSF-FFSF21-SFFFFFNN
% 0.12/0.45 % partial match(1): FGHSF-FFSF21-SFFFFFNN
% 0.12/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.45 % Preprocessing time : 0.001 s
% 0.12/0.45
% 0.12/0.45 % Proof found!
% 0.12/0.45 % SZS status Theorem
% 0.12/0.45 % SZS output start CNFRefutation
% See solution above
% 0.12/0.45 % Parsed axioms : 12
% 0.12/0.45 % Removed by relevancy pruning/SinE : 7
% 0.12/0.45 % Initial clauses : 13
% 0.12/0.45 % Removed in clause preprocessing : 0
% 0.12/0.45 % Initial clauses in saturation : 13
% 0.12/0.45 % Processed clauses : 53
% 0.12/0.45 % ...of these trivial : 0
% 0.12/0.45 % ...subsumed : 6
% 0.12/0.45 % ...remaining for further processing : 47
% 0.12/0.45 % Other redundant clauses eliminated : 5
% 0.12/0.45 % Clauses deleted for lack of memory : 0
% 0.12/0.45 % Backward-subsumed : 0
% 0.12/0.45 % Backward-rewritten : 4
% 0.12/0.45 % Generated clauses : 144
% 0.12/0.45 % ...of the previous two non-redundant : 120
% 0.12/0.45 % ...aggressively subsumed : 0
% 0.12/0.45 % Contextual simplify-reflections : 0
% 0.12/0.45 % Paramodulations : 136
% 0.12/0.45 % Factorizations : 3
% 0.12/0.45 % NegExts : 0
% 0.12/0.45 % Equation resolutions : 5
% 0.12/0.45 % Disequality decompositions : 0
% 0.12/0.45 % Total rewrite steps : 28
% 0.12/0.45 % ...of those cached : 19
% 0.12/0.45 % Propositional unsat checks : 0
% 0.12/0.45 % Propositional check models : 0
% 0.12/0.45 % Propositional check unsatisfiable : 0
% 0.12/0.45 % Propositional clauses : 0
% 0.12/0.45 % Propositional clauses after purity: 0
% 0.12/0.45 % Propositional unsat core size : 0
% 0.12/0.45 % Propositional preprocessing time : 0.000
% 0.12/0.45 % Propositional encoding time : 0.000
% 0.12/0.45 % Propositional solver time : 0.000
% 0.12/0.45 % Success case prop preproc time : 0.000
% 0.12/0.45 % Success case prop encoding time : 0.000
% 0.12/0.45 % Success case prop solver time : 0.000
% 0.12/0.45 % Current number of processed clauses : 40
% 0.12/0.45 % Positive orientable unit clauses : 11
% 0.12/0.45 % Positive unorientable unit clauses: 0
% 0.12/0.45 % Negative unit clauses : 1
% 0.12/0.45 % Non-unit-clauses : 28
% 0.12/0.45 % Current number of unprocessed clauses: 75
% 0.12/0.45 % ...number of literals in the above : 223
% 0.12/0.45 % Current number of archived formulas : 0
% 0.12/0.45 % Current number of archived clauses : 4
% 0.12/0.45 % Clause-clause subsumption calls (NU) : 196
% 0.12/0.45 % Rec. Clause-clause subsumption calls : 157
% 0.12/0.45 % Non-unit clause-clause subsumptions : 6
% 0.12/0.45 % Unit Clause-clause subsumption calls : 5
% 0.12/0.45 % Rewrite failures with RHS unbound : 0
% 0.12/0.45 % BW rewrite match attempts : 5
% 0.12/0.45 % BW rewrite match successes : 2
% 0.12/0.45 % Condensation attempts : 0
% 0.12/0.45 % Condensation successes : 0
% 0.12/0.45 % Termbank termtop insertions : 2730
% 0.12/0.45 % Search garbage collected termcells : 266
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.005 s
% 0.12/0.45 % System time : 0.003 s
% 0.12/0.45 % Total time : 0.008 s
% 0.12/0.45 % Maximum resident set size: 3648 pages
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.007 s
% 0.12/0.45 % System time : 0.007 s
% 0.12/0.45 % Total time : 0.014 s
% 0.12/0.45 % Maximum resident set size: 4608 pages
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------