%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET082+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 : n005.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 02:13:29 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 56 ( 27 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 54 ( 19 ~; 18 |; 11 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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; 0-2 aty)
% Number of variables : 26 ( 0 sgn 14 !; 2 ?)
% 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(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(regularity,axiom,
! [X1] :
( X1 != null_class
=> ? [X3] :
( disjoint(X3,X1)
& member(X3,X1)
& member(X3,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(singleton_is_null_class,conjecture,
! [X1] :
( ~ member(X1,universal_class)
=> singleton(X1) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(c_0_4,plain,
! [X65,X66,X67] :
( ( member(X65,unordered_pair(X66,X67))
| ~ member(X65,universal_class)
| X65 != X67 )
& ( member(X65,unordered_pair(X66,X67))
| ~ member(X65,universal_class)
| X65 != X66 )
& ( ~ member(X65,unordered_pair(X66,X67))
| X65 = X67
| X65 = X66 )
& ( ~ member(X65,unordered_pair(X66,X67))
| member(X65,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_5,plain,
! [X19] : singleton(X19) = unordered_pair(X19,X19),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_6,plain,
! [X1] :
( X1 != null_class
=> ? [X3] :
( disjoint(X3,X1)
& member(X3,X1)
& member(X3,universal_class) ) ),
inference(fof_simplification,[status(thm)],[regularity]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ~ member(X1,universal_class)
=> singleton(X1) = null_class ),
inference(assume_negation,[status(cth)],[singleton_is_null_class]) ).
cnf(c_0_8,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,plain,
! [X15] :
( ( X15 = null_class
| disjoint(esk2_1(X15),X15) )
& ( X15 = null_class
| member(esk2_1(X15),X15) )
& ( X15 = null_class
| member(esk2_1(X15),universal_class) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ~ member(X1,universal_class)
=> singleton(X1) = null_class ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( X1 = null_class
| member(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,negated_conjecture,
( singleton(esk1_0) != null_class
& ~ member(esk1_0,universal_class) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_15,plain,
( X1 = null_class
| member(esk2_1(X1),universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( singleton(X1) = null_class
| esk2_1(singleton(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
singleton(esk1_0) != null_class,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( member(X1,universal_class)
| singleton(X1) = null_class ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
~ member(esk1_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET082+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:50:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.42 % Version: 3.5.1
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % sh5l with pid 2590556 completed with status 0
% 0.13/0.42 % Result found by sh5l
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.13/0.42 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.13/0.42 % Search class: FGHSM-FFMS31-MFFFFFNN
% 0.13/0.42 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.42 % Starting SubtermCWHack with 28s (1) cores
% 0.13/0.42 % SubtermCWHack with pid 2590563 completed with status 0
% 0.13/0.42 % Result found by SubtermCWHack
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.13/0.42 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.13/0.42 % Search class: FGHSM-FFMS31-MFFFFFNN
% 0.13/0.42 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.42 % Starting SubtermCWHack with 28s (1) cores
% 0.13/0.42 % Preprocessing time : 0.002 s
% 0.13/0.42
% 0.13/0.42 % Proof found!
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start CNFRefutation
% See solution above
% 0.13/0.42 % Parsed axioms : 44
% 0.13/0.42 % Removed by relevancy pruning/SinE : 3
% 0.13/0.42 % Initial clauses : 84
% 0.13/0.42 % Removed in clause preprocessing : 0
% 0.13/0.42 % Initial clauses in saturation : 84
% 0.13/0.42 % Processed clauses : 135
% 0.13/0.42 % ...of these trivial : 0
% 0.13/0.42 % ...subsumed : 29
% 0.13/0.42 % ...remaining for further processing : 106
% 0.13/0.42 % Other redundant clauses eliminated : 5
% 0.13/0.42 % Clauses deleted for lack of memory : 0
% 0.13/0.42 % Backward-subsumed : 5
% 0.13/0.42 % Backward-rewritten : 5
% 0.13/0.42 % Generated clauses : 227
% 0.13/0.42 % ...of the previous two non-redundant : 204
% 0.13/0.42 % ...aggressively subsumed : 0
% 0.13/0.42 % Contextual simplify-reflections : 0
% 0.13/0.42 % Paramodulations : 222
% 0.13/0.42 % Factorizations : 0
% 0.13/0.42 % NegExts : 0
% 0.13/0.42 % Equation resolutions : 5
% 0.13/0.42 % Disequality decompositions : 0
% 0.13/0.42 % Total rewrite steps : 24
% 0.13/0.42 % ...of those cached : 12
% 0.13/0.42 % Propositional unsat checks : 0
% 0.13/0.42 % Propositional check models : 0
% 0.13/0.42 % Propositional check unsatisfiable : 0
% 0.13/0.42 % Propositional clauses : 0
% 0.13/0.42 % Propositional clauses after purity: 0
% 0.13/0.42 % Propositional unsat core size : 0
% 0.13/0.42 % Propositional preprocessing time : 0.000
% 0.13/0.42 % Propositional encoding time : 0.000
% 0.13/0.42 % Propositional solver time : 0.000
% 0.13/0.42 % Success case prop preproc time : 0.000
% 0.13/0.42 % Success case prop encoding time : 0.000
% 0.13/0.42 % Success case prop solver time : 0.000
% 0.13/0.42 % Current number of processed clauses : 91
% 0.13/0.42 % Positive orientable unit clauses : 27
% 0.13/0.42 % Positive unorientable unit clauses: 0
% 0.13/0.42 % Negative unit clauses : 3
% 0.13/0.42 % Non-unit-clauses : 61
% 0.13/0.42 % Current number of unprocessed clauses: 142
% 0.13/0.42 % ...number of literals in the above : 347
% 0.13/0.42 % Current number of archived formulas : 0
% 0.13/0.42 % Current number of archived clauses : 10
% 0.13/0.42 % Clause-clause subsumption calls (NU) : 429
% 0.13/0.42 % Rec. Clause-clause subsumption calls : 371
% 0.13/0.42 % Non-unit clause-clause subsumptions : 28
% 0.13/0.42 % Unit Clause-clause subsumption calls : 53
% 0.13/0.42 % Rewrite failures with RHS unbound : 0
% 0.13/0.42 % BW rewrite match attempts : 7
% 0.13/0.42 % BW rewrite match successes : 2
% 0.13/0.42 % Condensation attempts : 0
% 0.13/0.42 % Condensation successes : 0
% 0.13/0.42 % Termbank termtop insertions : 7180
% 0.13/0.42 % Search garbage collected termcells : 921
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.013 s
% 0.13/0.42 % System time : 0.004 s
% 0.13/0.42 % Total time : 0.017 s
% 0.13/0.42 % Maximum resident set size: 3948 pages
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.015 s
% 0.13/0.42 % System time : 0.007 s
% 0.13/0.42 % Total time : 0.022 s
% 0.13/0.42 % Maximum resident set size: 4864 pages
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------