%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:13:31 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 60 ( 26 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 53 ( 20 ~; 20 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( ( X3 = X2
| X3 = X1 )
& member(X3,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(member_of_singleton,conjecture,
! [X1,X3] :
( ( X1 = singleton(X3)
& member(X3,universal_class) )
=> member_of(X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_singleton) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(member_singleton_singleton,axiom,
! [X2] :
( member(X2,universal_class)
=> singleton(member_of(singleton(X2))) = singleton(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_singleton_singleton) ).
fof(member_singleton_universal,axiom,
! [X2] :
( member(X2,universal_class)
=> member(member_of(singleton(X2)),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_singleton_universal) ).
fof(c_0_5,plain,
! [X39,X40,X41] :
( ( member(X39,unordered_pair(X40,X41))
| ~ member(X39,universal_class)
| X39 != X41 )
& ( member(X39,unordered_pair(X40,X41))
| ~ member(X39,universal_class)
| X39 != X40 )
& ( ~ member(X39,unordered_pair(X40,X41))
| X39 = X41
| X39 = X40 )
& ( ~ member(X39,unordered_pair(X40,X41))
| member(X39,universal_class) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X3] :
( ( X1 = singleton(X3)
& member(X3,universal_class) )
=> member_of(X1) = X3 ),
inference(assume_negation,[status(cth)],[member_of_singleton]) ).
fof(c_0_7,plain,
! [X16] : singleton(X16) = unordered_pair(X16,X16),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_8,plain,
( ~ member(X1,universal_class)
| X1 != X2
| member(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X13] :
( singleton(member_of(singleton(X13))) = singleton(X13)
| ~ member(X13,universal_class) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_singleton_singleton])])]) ).
fof(c_0_10,negated_conjecture,
( member_of(esk1_0) != esk2_0
& esk1_0 = singleton(esk2_0)
& member(esk2_0,universal_class) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_11,plain,
! [X12] :
( member(member_of(singleton(X12)),universal_class)
| ~ member(X12,universal_class) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_singleton_universal])])]) ).
cnf(c_0_12,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( ~ member(X1,universal_class)
| singleton(member_of(singleton(X1))) = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
esk1_0 = singleton(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
member(esk2_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( ~ member(X1,universal_class)
| member(member_of(singleton(X1)),universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
( ~ member(X1,universal_class)
| member(X1,singleton(X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
singleton(member_of(esk1_0)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_22,negated_conjecture,
member(member_of(esk1_0),universal_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_17])]) ).
cnf(c_0_23,negated_conjecture,
( ~ member(X1,esk1_0)
| X1 = esk2_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_24,negated_conjecture,
member(member_of(esk1_0),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_25,negated_conjecture,
member_of(esk1_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:51:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % sh5l with pid 2284806 completed with status 0
% 0.14/0.44 % Result found by sh5l
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.44 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.14/0.44 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.44 % SubtermCWHack with pid 2284814 completed with status 0
% 0.14/0.44 % Result found by SubtermCWHack
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.44 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.14/0.44 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 48
% 0.14/0.44 % Removed by relevancy pruning/SinE : 3
% 0.14/0.44 % Initial clauses : 89
% 0.14/0.44 % Removed in clause preprocessing : 0
% 0.14/0.44 % Initial clauses in saturation : 89
% 0.14/0.44 % Processed clauses : 158
% 0.14/0.44 % ...of these trivial : 0
% 0.14/0.44 % ...subsumed : 40
% 0.14/0.44 % ...remaining for further processing : 118
% 0.14/0.44 % Other redundant clauses eliminated : 5
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 9
% 0.14/0.44 % Backward-rewritten : 4
% 0.14/0.44 % Generated clauses : 280
% 0.14/0.44 % ...of the previous two non-redundant : 246
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 0
% 0.14/0.44 % Paramodulations : 275
% 0.14/0.44 % Factorizations : 0
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 5
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 44
% 0.14/0.44 % ...of those cached : 27
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 100
% 0.14/0.44 % Positive orientable unit clauses : 34
% 0.14/0.44 % Positive unorientable unit clauses: 0
% 0.14/0.44 % Negative unit clauses : 2
% 0.14/0.44 % Non-unit-clauses : 64
% 0.14/0.44 % Current number of unprocessed clauses: 167
% 0.14/0.44 % ...number of literals in the above : 408
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 13
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 685
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 565
% 0.14/0.44 % Non-unit clause-clause subsumptions : 43
% 0.14/0.44 % Unit Clause-clause subsumption calls : 85
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 7
% 0.14/0.44 % BW rewrite match successes : 2
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 7877
% 0.14/0.44 % Search garbage collected termcells : 951
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.013 s
% 0.14/0.44 % System time : 0.001 s
% 0.14/0.44 % Total time : 0.014 s
% 0.14/0.44 % Maximum resident set size: 3948 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.018 s
% 0.14/0.44 % System time : 0.003 s
% 0.14/0.44 % Total time : 0.021 s
% 0.14/0.44 % Maximum resident set size: 4864 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------