%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET096+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 : n020.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 02:13:33 PM UTC 2026
% Result : Theorem 0.25s 0.67s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 93 ( 34 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 91 ( 31 ~; 35 |; 17 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(two_subsets_of_singleton,conjecture,
! [X1,X2] :
( subclass(X1,singleton(X2))
=> ( singleton(X2) = X1
| X1 = null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
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(subclass_defn,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_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(extensionality,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subclass(X2,X1)
& subclass(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',extensionality) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subclass(X1,singleton(X2))
=> ( singleton(X2) = X1
| X1 = null_class ) ),
inference(assume_negation,[status(cth)],[two_subsets_of_singleton]) ).
fof(c_0_7,plain,
! [X42,X43,X44] :
( ( member(X42,unordered_pair(X43,X44))
| ~ member(X42,universal_class)
| X42 != X44 )
& ( member(X42,unordered_pair(X43,X44))
| ~ member(X42,universal_class)
| X42 != X43 )
& ( ~ member(X42,unordered_pair(X43,X44))
| X42 = X44
| X42 = X43 )
& ( ~ member(X42,unordered_pair(X43,X44))
| member(X42,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_8,plain,
! [X12] : singleton(X12) = unordered_pair(X12,X12),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_9,plain,
! [X30,X31,X32,X33,X34] :
( ( subclass(X33,X34)
| ~ member(esk5_2(X33,X34),X34) )
& ( subclass(X33,X34)
| member(esk5_2(X33,X34),X33) )
& ( member(X32,X31)
| ~ member(X32,X30)
| ~ subclass(X30,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)],[subclass_defn])])])])])])]) ).
fof(c_0_10,negated_conjecture,
( singleton(esk2_0) != esk1_0
& esk1_0 != null_class
& subclass(esk1_0,singleton(esk2_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_11,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
subclass(esk1_0,singleton(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X1] :
( X1 != null_class
=> ? [X3] :
( disjoint(X3,X1)
& member(X3,X1)
& member(X3,universal_class) ) ),
inference(fof_simplification,[status(thm)],[regularity]) ).
cnf(c_0_16,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(X1,esk1_0)
| member(X1,singleton(esk2_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,plain,
! [X26] :
( ( X26 = null_class
| disjoint(esk3_1(X26),X26) )
& ( X26 = null_class
| member(esk3_1(X26),X26) )
& ( X26 = null_class
| member(esk3_1(X26),universal_class) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_19,plain,
! [X37,X38] :
( ( X37 = X38
| ~ subclass(X38,X37)
| ~ subclass(X37,X38) )
& ( X37 != X38
| subclass(X38,X37) )
& ( X37 != X38
| subclass(X37,X38) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[extensionality])])])]) ).
cnf(c_0_20,plain,
( subclass(X1,X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X1,esk1_0)
| X1 = esk2_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( X1 = null_class
| member(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
esk1_0 != null_class,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
singleton(esk2_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,plain,
( ~ member(esk5_2(X1,X2),X2)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,plain,
( subclass(singleton(X1),X2)
| esk5_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
esk3_1(esk1_0) = esk2_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_29,negated_conjecture,
~ subclass(singleton(esk2_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_14]),c_0_25]) ).
cnf(c_0_30,plain,
( ~ member(X1,X2)
| subclass(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
member(esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_23]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET096+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 % Computer : n020.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 04:53:02 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.52 Running first-order theorem proving
% 0.15/0.52 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
% 0.25/0.67 % Version: 3.5.1
% 0.25/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.67 % Starting sh5l with 300s (1) cores
% 0.25/0.67 % sh5l with pid 2044793 completed with status 0
% 0.25/0.67 % Result found by sh5l
% 0.25/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.67 % Starting sh5l with 300s (1) cores
% 0.25/0.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.25/0.67 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.25/0.67 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.25/0.67 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.67 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.67 % SubtermCWHack with pid 2044796 completed with status 0
% 0.25/0.67 % Result found by SubtermCWHack
% 0.25/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.67 % Starting sh5l with 300s (1) cores
% 0.25/0.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.25/0.67 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.25/0.67 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.25/0.67 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.67 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.67 % Preprocessing time : 0.003 s
% 0.25/0.67
% 0.25/0.67 % Proof found!
% 0.25/0.67 % SZS status Theorem
% 0.25/0.67 % SZS output start CNFRefutation
% See solution above
% 0.25/0.67 % Parsed axioms : 44
% 0.25/0.67 % Removed by relevancy pruning/SinE : 3
% 0.25/0.67 % Initial clauses : 85
% 0.25/0.67 % Removed in clause preprocessing : 0
% 0.25/0.67 % Initial clauses in saturation : 85
% 0.25/0.67 % Processed clauses : 338
% 0.25/0.67 % ...of these trivial : 5
% 0.25/0.67 % ...subsumed : 91
% 0.25/0.67 % ...remaining for further processing : 242
% 0.25/0.67 % Other redundant clauses eliminated : 6
% 0.25/0.67 % Clauses deleted for lack of memory : 0
% 0.25/0.67 % Backward-subsumed : 6
% 0.25/0.67 % Backward-rewritten : 32
% 0.25/0.67 % Generated clauses : 872
% 0.25/0.67 % ...of the previous two non-redundant : 694
% 0.25/0.67 % ...aggressively subsumed : 0
% 0.25/0.67 % Contextual simplify-reflections : 1
% 0.25/0.67 % Paramodulations : 866
% 0.25/0.67 % Factorizations : 0
% 0.25/0.67 % NegExts : 0
% 0.25/0.67 % Equation resolutions : 6
% 0.25/0.67 % Disequality decompositions : 0
% 0.25/0.67 % Total rewrite steps : 242
% 0.25/0.67 % ...of those cached : 179
% 0.25/0.67 % Propositional unsat checks : 0
% 0.25/0.67 % Propositional check models : 0
% 0.25/0.67 % Propositional check unsatisfiable : 0
% 0.25/0.67 % Propositional clauses : 0
% 0.25/0.67 % Propositional clauses after purity: 0
% 0.25/0.67 % Propositional unsat core size : 0
% 0.25/0.67 % Propositional preprocessing time : 0.000
% 0.25/0.67 % Propositional encoding time : 0.000
% 0.25/0.67 % Propositional solver time : 0.000
% 0.25/0.67 % Success case prop preproc time : 0.000
% 0.25/0.67 % Success case prop encoding time : 0.000
% 0.25/0.67 % Success case prop solver time : 0.000
% 0.25/0.67 % Current number of processed clauses : 198
% 0.25/0.67 % Positive orientable unit clauses : 44
% 0.25/0.67 % Positive unorientable unit clauses: 1
% 0.25/0.67 % Negative unit clauses : 5
% 0.25/0.67 % Non-unit-clauses : 148
% 0.25/0.67 % Current number of unprocessed clauses: 405
% 0.25/0.67 % ...number of literals in the above : 1017
% 0.25/0.67 % Current number of archived formulas : 0
% 0.25/0.67 % Current number of archived clauses : 38
% 0.25/0.67 % Clause-clause subsumption calls (NU) : 3288
% 0.25/0.67 % Rec. Clause-clause subsumption calls : 2760
% 0.25/0.67 % Non-unit clause-clause subsumptions : 87
% 0.25/0.67 % Unit Clause-clause subsumption calls : 302
% 0.25/0.67 % Rewrite failures with RHS unbound : 0
% 0.25/0.67 % BW rewrite match attempts : 17
% 0.25/0.67 % BW rewrite match successes : 9
% 0.25/0.67 % Condensation attempts : 0
% 0.25/0.67 % Condensation successes : 0
% 0.25/0.67 % Termbank termtop insertions : 14018
% 0.25/0.67 % Search garbage collected termcells : 940
% 0.25/0.67
% 0.25/0.67 % -------------------------------------------------
% 0.25/0.67 % User time : 0.045 s
% 0.25/0.67 % System time : 0.008 s
% 0.25/0.67 % Total time : 0.053 s
% 0.25/0.67 % Maximum resident set size: 3904 pages
% 0.25/0.67
% 0.25/0.67 % -------------------------------------------------
% 0.25/0.67 % User time : 0.052 s
% 0.25/0.67 % System time : 0.012 s
% 0.25/0.67 % Total time : 0.064 s
% 0.25/0.67 % Maximum resident set size: 4608 pages
% 0.25/0.67 % E exiting
%------------------------------------------------------------------------------