%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET102+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 02:13:35 PM UTC 2026
% Result : Theorem 0.23s 0.55s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 17 unt; 0 def)
% Number of atoms : 37 ( 13 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 11 |; 4 &)
% ( 1 <=>; 0 =>; 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 : 34 ( 4 sgn 20 !; 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(unordered_pair_member_of_ordered_pair,conjecture,
! [X1,X2] : member(unordered_pair(X1,singleton(X2)),ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member_of_ordered_pair) ).
fof(ordered_pair_defn,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(unordered_pair,axiom,
! [X1,X2] : member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
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(c_0_5,plain,
! [X16,X17,X18] :
( ( member(X16,unordered_pair(X17,X18))
| ~ member(X16,universal_class)
| X16 != X18 )
& ( member(X16,unordered_pair(X17,X18))
| ~ member(X16,universal_class)
| X16 != X17 )
& ( ~ member(X16,unordered_pair(X17,X18))
| X16 = X18
| X16 = X17 )
& ( ~ member(X16,unordered_pair(X17,X18))
| member(X16,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,X2] : member(unordered_pair(X1,singleton(X2)),ordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[unordered_pair_member_of_ordered_pair]) ).
cnf(c_0_7,plain,
( ~ member(X1,universal_class)
| X1 != X2
| member(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X22,X23] : ordered_pair(X22,X23) = unordered_pair(singleton(X22),unordered_pair(X22,singleton(X23))),
inference(variable_rename,[status(thm)],[ordered_pair_defn]) ).
fof(c_0_9,plain,
! [X19,X20] : member(unordered_pair(X19,X20),universal_class),
inference(variable_rename,[status(thm)],[unordered_pair]) ).
fof(c_0_10,negated_conjecture,
~ member(unordered_pair(esk1_0,singleton(esk2_0)),ordered_pair(esk1_0,esk2_0)),
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,
! [X21] : singleton(X21) = unordered_pair(X21,X21),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_12,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
member(unordered_pair(X1,X2),universal_class),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
~ member(unordered_pair(esk1_0,singleton(esk2_0)),ordered_pair(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
member(unordered_pair(X1,singleton(X2)),ordered_pair(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_18,negated_conjecture,
~ member(unordered_pair(esk1_0,unordered_pair(esk2_0,esk2_0)),ordered_pair(esk1_0,esk2_0)),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
member(unordered_pair(X1,unordered_pair(X2,X2)),ordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET102+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n006.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 04:52:57 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 0.23/0.55 % Version: 3.5.1
% 0.23/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.55 % Starting sh5l with 300s (1) cores
% 0.23/0.55 % new_bool_3 with pid 2042166 completed with status 0
% 0.23/0.55 % Result found by new_bool_3
% 0.23/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.55 % Search class: FGUSS-FFSF21-MFFFFFNN
% 0.23/0.55 % partial match(1): FGUSS-FFSF22-MFFFFFNN
% 0.23/0.55 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.55 % SubtermCWHack with pid 2042169 completed with status 0
% 0.23/0.55 % Result found by SubtermCWHack
% 0.23/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.55 % Search class: FGUSS-FFSF21-MFFFFFNN
% 0.23/0.55 % partial match(1): FGUSS-FFSF22-MFFFFFNN
% 0.23/0.55 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.55 % Preprocessing time : 0.002 s
% 0.23/0.55
% 0.23/0.55 % Proof found!
% 0.23/0.55 % SZS status Theorem
% 0.23/0.55 % SZS output start CNFRefutation
% See solution above
% 0.23/0.55 % Parsed axioms : 44
% 0.23/0.55 % Removed by relevancy pruning/SinE : 38
% 0.23/0.55 % Initial clauses : 11
% 0.23/0.55 % Removed in clause preprocessing : 0
% 0.23/0.55 % Initial clauses in saturation : 11
% 0.23/0.55 % Processed clauses : 28
% 0.23/0.55 % ...of these trivial : 0
% 0.23/0.55 % ...subsumed : 4
% 0.23/0.55 % ...remaining for further processing : 24
% 0.23/0.55 % Other redundant clauses eliminated : 2
% 0.23/0.55 % Clauses deleted for lack of memory : 0
% 0.23/0.55 % Backward-subsumed : 0
% 0.23/0.55 % Backward-rewritten : 1
% 0.23/0.55 % Generated clauses : 36
% 0.23/0.55 % ...of the previous two non-redundant : 21
% 0.23/0.55 % ...aggressively subsumed : 0
% 0.23/0.55 % Contextual simplify-reflections : 0
% 0.23/0.55 % Paramodulations : 34
% 0.23/0.55 % Factorizations : 0
% 0.23/0.55 % NegExts : 0
% 0.23/0.55 % Equation resolutions : 2
% 0.23/0.55 % Disequality decompositions : 0
% 0.23/0.55 % Total rewrite steps : 10
% 0.23/0.55 % ...of those cached : 3
% 0.23/0.55 % Propositional unsat checks : 0
% 0.23/0.55 % Propositional check models : 0
% 0.23/0.55 % Propositional check unsatisfiable : 0
% 0.23/0.55 % Propositional clauses : 0
% 0.23/0.55 % Propositional clauses after purity: 0
% 0.23/0.55 % Propositional unsat core size : 0
% 0.23/0.55 % Propositional preprocessing time : 0.000
% 0.23/0.55 % Propositional encoding time : 0.000
% 0.23/0.55 % Propositional solver time : 0.000
% 0.23/0.55 % Success case prop preproc time : 0.000
% 0.23/0.55 % Success case prop encoding time : 0.000
% 0.23/0.55 % Success case prop solver time : 0.000
% 0.23/0.55 % Current number of processed clauses : 21
% 0.23/0.55 % Positive orientable unit clauses : 8
% 0.23/0.55 % Positive unorientable unit clauses: 1
% 0.23/0.55 % Negative unit clauses : 0
% 0.23/0.55 % Non-unit-clauses : 12
% 0.23/0.55 % Current number of unprocessed clauses: 4
% 0.23/0.55 % ...number of literals in the above : 6
% 0.23/0.55 % Current number of archived formulas : 0
% 0.23/0.55 % Current number of archived clauses : 1
% 0.23/0.55 % Clause-clause subsumption calls (NU) : 26
% 0.23/0.55 % Rec. Clause-clause subsumption calls : 26
% 0.23/0.55 % Non-unit clause-clause subsumptions : 4
% 0.23/0.55 % Unit Clause-clause subsumption calls : 0
% 0.23/0.55 % Rewrite failures with RHS unbound : 0
% 0.23/0.55 % BW rewrite match attempts : 3
% 0.23/0.55 % BW rewrite match successes : 1
% 0.23/0.55 % Condensation attempts : 0
% 0.23/0.55 % Condensation successes : 0
% 0.23/0.55 % Termbank termtop insertions : 1353
% 0.23/0.55 % Search garbage collected termcells : 393
% 0.23/0.55
% 0.23/0.55 % -------------------------------------------------
% 0.23/0.55 % User time : 0.007 s
% 0.23/0.55 % System time : 0.003 s
% 0.23/0.55 % Total time : 0.010 s
% 0.23/0.55 % Maximum resident set size: 3692 pages
% 0.23/0.55
% 0.23/0.55 % -------------------------------------------------
% 0.23/0.55 % User time : 0.012 s
% 0.23/0.55 % System time : 0.009 s
% 0.23/0.55 % Total time : 0.020 s
% 0.23/0.55 % Maximum resident set size: 4608 pages
% 0.23/0.55 % E exiting
%------------------------------------------------------------------------------