%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET095+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 : n016.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 0.17s 10.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 50 ( 13 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 47 ( 16 ~; 19 |; 7 &)
% ( 2 <=>; 3 =>; 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 : 34 ( 0 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(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(property_of_singletons2,conjecture,
! [X1,X2] :
( member(X1,X2)
=> subclass(singleton(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_singletons2) ).
fof(c_0_4,plain,
! [X49,X50,X51] :
( ( member(X49,unordered_pair(X50,X51))
| ~ member(X49,universal_class)
| X49 != X51 )
& ( member(X49,unordered_pair(X50,X51))
| ~ member(X49,universal_class)
| X49 != X50 )
& ( ~ member(X49,unordered_pair(X50,X51))
| X49 = X51
| X49 = X50 )
& ( ~ member(X49,unordered_pair(X50,X51))
| member(X49,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,
! [X24] : singleton(X24) = unordered_pair(X24,X24),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_6,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X12,X13,X14,X15,X16] :
( ( subclass(X15,X16)
| ~ member(esk3_2(X15,X16),X16) )
& ( subclass(X15,X16)
| member(esk3_2(X15,X16),X15) )
& ( member(X14,X13)
| ~ member(X14,X12)
| ~ subclass(X12,X13) ) ),
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_9,negated_conjecture,
~ ! [X1,X2] :
( member(X1,X2)
=> subclass(singleton(X1),X2) ),
inference(assume_negation,[status(cth)],[property_of_singletons2]) ).
cnf(c_0_10,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
( subclass(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,negated_conjecture,
( ~ subclass(singleton(esk1_0),esk2_0)
& member(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_9])])])]) ).
cnf(c_0_13,plain,
( ~ member(esk3_2(X1,X2),X2)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( subclass(singleton(X1),X2)
| esk3_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
~ subclass(singleton(esk1_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| subclass(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
member(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET095+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/10.39 % Computer : n016.cluster.edu
% 0.14/10.39 % Model : x86_64 x86_64
% 0.14/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.39 % Memory : 8046.5625MB
% 0.14/10.39 % OS : Linux 6.8.0-71-generic
% 0.14/10.39 % CPULimit : 300
% 0.14/10.39 % WCLimit : 300
% 0.14/10.39 % DateTime : Mon Sep 21 04:57:18 UTC 2026
% 0.14/10.39 % CPUTime :
% 0.14/10.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/10.44 Running first-order theorem proving
% 0.17/10.44 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
% 0.17/10.50 % Version: 3.5.1
% 0.17/10.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/10.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/10.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/10.50 % Starting new_bool_3 with 300s (1) cores
% 0.17/10.50 % Starting new_bool_1 with 300s (1) cores
% 0.17/10.50 % Starting sh5l with 300s (1) cores
% 0.17/10.50 % sh5l with pid 1600828 completed with status 0
% 0.17/10.50 % Result found by sh5l
% 0.17/10.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/10.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/10.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/10.50 % Starting new_bool_3 with 300s (1) cores
% 0.17/10.50 % Starting new_bool_1 with 300s (1) cores
% 0.17/10.50 % Starting sh5l with 300s (1) cores
% 0.17/10.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.17/10.50 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.17/10.50 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.17/10.50 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.17/10.50 % Starting SubtermCWHack with 28s (1) cores
% 0.17/10.50 % SubtermCWHack with pid 1600840 completed with status 0
% 0.17/10.51 % Result found by SubtermCWHack
% 0.17/10.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/10.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/10.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/10.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/10.51 % Starting new_bool_1 with 300s (1) cores
% 0.17/10.51 % Starting sh5l with 300s (1) cores
% 0.17/10.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.17/10.51 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.17/10.51 % Search class: FGHSM-FFMM31-MFFFFFNN
% 0.17/10.51 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.17/10.51 % Starting SubtermCWHack with 28s (1) cores
% 0.17/10.51 % Preprocessing time : 0.002 s
% 0.17/10.51
% 0.17/10.51 % Proof found!
% 0.17/10.51 % SZS status Theorem
% 0.17/10.51 % SZS output start CNFRefutation
% See solution above
% 0.17/10.51 % Parsed axioms : 44
% 0.17/10.51 % Removed by relevancy pruning/SinE : 3
% 0.17/10.51 % Initial clauses : 84
% 0.17/10.51 % Removed in clause preprocessing : 0
% 0.17/10.51 % Initial clauses in saturation : 84
% 0.17/10.51 % Processed clauses : 276
% 0.17/10.51 % ...of these trivial : 2
% 0.17/10.51 % ...subsumed : 78
% 0.17/10.51 % ...remaining for further processing : 196
% 0.17/10.51 % Other redundant clauses eliminated : 6
% 0.17/10.51 % Clauses deleted for lack of memory : 0
% 0.17/10.51 % Backward-subsumed : 5
% 0.17/10.51 % Backward-rewritten : 28
% 0.17/10.51 % Generated clauses : 664
% 0.17/10.51 % ...of the previous two non-redundant : 529
% 0.17/10.51 % ...aggressively subsumed : 0
% 0.17/10.51 % Contextual simplify-reflections : 1
% 0.17/10.51 % Paramodulations : 658
% 0.17/10.51 % Factorizations : 0
% 0.17/10.51 % NegExts : 0
% 0.17/10.51 % Equation resolutions : 6
% 0.17/10.51 % Disequality decompositions : 0
% 0.17/10.51 % Total rewrite steps : 189
% 0.17/10.51 % ...of those cached : 140
% 0.17/10.51 % Propositional unsat checks : 0
% 0.17/10.51 % Propositional check models : 0
% 0.17/10.51 % Propositional check unsatisfiable : 0
% 0.17/10.51 % Propositional clauses : 0
% 0.17/10.51 % Propositional clauses after purity: 0
% 0.17/10.51 % Propositional unsat core size : 0
% 0.17/10.51 % Propositional preprocessing time : 0.000
% 0.17/10.51 % Propositional encoding time : 0.000
% 0.17/10.51 % Propositional solver time : 0.000
% 0.17/10.51 % Success case prop preproc time : 0.000
% 0.17/10.51 % Success case prop encoding time : 0.000
% 0.17/10.51 % Success case prop solver time : 0.000
% 0.17/10.51 % Current number of processed clauses : 157
% 0.17/10.51 % Positive orientable unit clauses : 41
% 0.17/10.51 % Positive unorientable unit clauses: 1
% 0.17/10.51 % Negative unit clauses : 3
% 0.17/10.51 % Non-unit-clauses : 112
% 0.17/10.51 % Current number of unprocessed clauses: 304
% 0.17/10.51 % ...number of literals in the above : 740
% 0.17/10.51 % Current number of archived formulas : 0
% 0.17/10.51 % Current number of archived clauses : 33
% 0.17/10.51 % Clause-clause subsumption calls (NU) : 1954
% 0.17/10.51 % Rec. Clause-clause subsumption calls : 1637
% 0.17/10.51 % Non-unit clause-clause subsumptions : 76
% 0.17/10.51 % Unit Clause-clause subsumption calls : 173
% 0.17/10.51 % Rewrite failures with RHS unbound : 0
% 0.17/10.51 % BW rewrite match attempts : 16
% 0.17/10.51 % BW rewrite match successes : 8
% 0.17/10.51 % Condensation attempts : 0
% 0.17/10.51 % Condensation successes : 0
% 0.17/10.51 % Termbank termtop insertions : 11814
% 0.17/10.51 % Search garbage collected termcells : 936
% 0.17/10.51
% 0.17/10.51 % -------------------------------------------------
% 0.17/10.51 % User time : 0.024 s
% 0.17/10.51 % System time : 0.003 s
% 0.17/10.51 % Total time : 0.027 s
% 0.17/10.51 % Maximum resident set size: 3948 pages
% 0.17/10.51
% 0.17/10.51 % -------------------------------------------------
% 0.17/10.51 % User time : 0.029 s
% 0.17/10.51 % System time : 0.005 s
% 0.17/10.51 % Total time : 0.035 s
% 0.17/10.51 % Maximum resident set size: 4608 pages
% 0.17/10.51 % E exiting
%------------------------------------------------------------------------------