%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET067+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 : n015.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 02:13:24 PM UTC 2026
% Result : Theorem 0.17s 0.57s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 69 ( 14 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 63 ( 25 ~; 29 |; 6 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 55 ( 6 sgn 22 !; 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(class_elements_are_sets,axiom,
! [X1] : subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(pair_contains_other,conjecture,
! [X1,X2] : subclass(unordered_pair(X1,X1),unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pair_contains_other) ).
fof(c_0_5,plain,
! [X21,X22,X23] :
( ( member(X21,unordered_pair(X22,X23))
| ~ member(X21,universal_class)
| X21 != X23 )
& ( member(X21,unordered_pair(X22,X23))
| ~ member(X21,universal_class)
| X21 != X22 )
& ( ~ member(X21,unordered_pair(X22,X23))
| X21 = X23
| X21 = X22 )
& ( ~ member(X21,unordered_pair(X22,X23))
| member(X21,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,plain,
! [X26] : singleton(X26) = unordered_pair(X26,X26),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_7,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,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_10,plain,
! [X18] : subclass(X18,universal_class),
inference(variable_rename,[status(thm)],[class_elements_are_sets]) ).
cnf(c_0_11,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( subclass(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
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,plain,
subclass(X1,universal_class),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2] : subclass(unordered_pair(X1,X1),unordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[pair_contains_other]) ).
cnf(c_0_16,plain,
( ~ member(esk3_2(X1,X2),X2)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( subclass(singleton(X1),X2)
| esk3_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_19,negated_conjecture,
~ subclass(unordered_pair(esk1_0,esk1_0),unordered_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_15])])])]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| subclass(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( subclass(X1,X2)
| member(esk3_2(X1,X2),universal_class) ),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_22,negated_conjecture,
~ subclass(unordered_pair(esk1_0,esk1_0),unordered_pair(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( ~ member(X1,X2)
| subclass(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_8]) ).
cnf(c_0_24,plain,
( ~ member(X1,universal_class)
| X1 != X2
| member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_25,plain,
( subclass(singleton(X1),X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
~ member(esk1_0,unordered_pair(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
( subclass(unordered_pair(X1,X1),X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_25,c_0_8]) ).
cnf(c_0_29,negated_conjecture,
~ member(esk1_0,universal_class),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET067+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.49 % Computer : n015.cluster.edu
% 0.11/0.49 % Model : x86_64 x86_64
% 0.11/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.49 % Memory : 8046.5625MB
% 0.11/0.49 % OS : Linux 6.8.0-71-generic
% 0.11/0.50 % CPULimit : 300
% 0.11/0.50 % WCLimit : 300
% 0.11/0.50 % DateTime : Mon Sep 21 04:52:22 UTC 2026
% 0.11/0.50 % CPUTime :
% 0.11/0.50 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.54 Running first-order theorem proving
% 0.11/0.54 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
% 0.17/0.57 % Version: 3.5.1
% 0.17/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.57 % Starting sh5l with 300s (1) cores
% 0.17/0.57 % new_bool_3 with pid 597154 completed with status 0
% 0.17/0.57 % Result found by new_bool_3
% 0.17/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.57 % Search class: FGUSM-FFSF21-MFFFFFNN
% 0.17/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.57 % SubtermCWHack with pid 597157 completed with status 0
% 0.17/0.57 % Result found by SubtermCWHack
% 0.17/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.57 % Search class: FGUSM-FFSF21-MFFFFFNN
% 0.17/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.17/0.57 % Preprocessing time : 0.002 s
% 0.17/0.57
% 0.17/0.57 % Proof found!
% 0.17/0.57 % SZS status Theorem
% 0.17/0.57 % SZS output start CNFRefutation
% See solution above
% 0.17/0.57 % Parsed axioms : 44
% 0.17/0.57 % Removed by relevancy pruning/SinE : 35
% 0.17/0.57 % Initial clauses : 18
% 0.17/0.57 % Removed in clause preprocessing : 0
% 0.17/0.57 % Initial clauses in saturation : 18
% 0.17/0.57 % Processed clauses : 49
% 0.17/0.57 % ...of these trivial : 0
% 0.17/0.57 % ...subsumed : 7
% 0.17/0.57 % ...remaining for further processing : 42
% 0.17/0.57 % Other redundant clauses eliminated : 4
% 0.17/0.57 % Clauses deleted for lack of memory : 0
% 0.17/0.57 % Backward-subsumed : 2
% 0.17/0.57 % Backward-rewritten : 0
% 0.17/0.57 % Generated clauses : 77
% 0.17/0.57 % ...of the previous two non-redundant : 53
% 0.17/0.57 % ...aggressively subsumed : 0
% 0.17/0.57 % Contextual simplify-reflections : 0
% 0.17/0.57 % Paramodulations : 73
% 0.17/0.57 % Factorizations : 0
% 0.17/0.57 % NegExts : 0
% 0.17/0.57 % Equation resolutions : 4
% 0.17/0.57 % Disequality decompositions : 0
% 0.17/0.57 % Total rewrite steps : 18
% 0.17/0.57 % ...of those cached : 6
% 0.17/0.57 % Propositional unsat checks : 0
% 0.17/0.57 % Propositional check models : 0
% 0.17/0.57 % Propositional check unsatisfiable : 0
% 0.17/0.57 % Propositional clauses : 0
% 0.17/0.57 % Propositional clauses after purity: 0
% 0.17/0.57 % Propositional unsat core size : 0
% 0.17/0.57 % Propositional preprocessing time : 0.000
% 0.17/0.57 % Propositional encoding time : 0.000
% 0.17/0.57 % Propositional solver time : 0.000
% 0.17/0.57 % Success case prop preproc time : 0.000
% 0.17/0.57 % Success case prop encoding time : 0.000
% 0.17/0.57 % Success case prop solver time : 0.000
% 0.17/0.57 % Current number of processed clauses : 36
% 0.17/0.57 % Positive orientable unit clauses : 10
% 0.17/0.57 % Positive unorientable unit clauses: 1
% 0.17/0.57 % Negative unit clauses : 3
% 0.17/0.57 % Non-unit-clauses : 22
% 0.17/0.57 % Current number of unprocessed clauses: 19
% 0.17/0.57 % ...number of literals in the above : 44
% 0.17/0.57 % Current number of archived formulas : 0
% 0.17/0.57 % Current number of archived clauses : 2
% 0.17/0.57 % Clause-clause subsumption calls (NU) : 63
% 0.17/0.57 % Rec. Clause-clause subsumption calls : 57
% 0.17/0.57 % Non-unit clause-clause subsumptions : 9
% 0.17/0.57 % Unit Clause-clause subsumption calls : 0
% 0.17/0.57 % Rewrite failures with RHS unbound : 0
% 0.17/0.57 % BW rewrite match attempts : 2
% 0.17/0.57 % BW rewrite match successes : 0
% 0.17/0.57 % Condensation attempts : 0
% 0.17/0.57 % Condensation successes : 0
% 0.17/0.57 % Termbank termtop insertions : 2040
% 0.17/0.57 % Search garbage collected termcells : 481
% 0.17/0.57
% 0.17/0.57 % -------------------------------------------------
% 0.17/0.57 % User time : 0.004 s
% 0.17/0.57 % System time : 0.005 s
% 0.17/0.57 % Total time : 0.009 s
% 0.17/0.57 % Maximum resident set size: 3692 pages
% 0.17/0.57
% 0.17/0.57 % -------------------------------------------------
% 0.17/0.57 % User time : 0.006 s
% 0.17/0.57 % System time : 0.010 s
% 0.17/0.57 % Total time : 0.016 s
% 0.17/0.57 % Maximum resident set size: 4608 pages
% 0.17/0.57 % E exiting
%------------------------------------------------------------------------------