%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET103+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 : n002.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 02:16:33 PM UTC 2026
% Result : Theorem 0.26s 0.59s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 60 ( 33 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 50 ( 15 ~; 21 |; 11 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(property_1_of_ordered_pair,conjecture,
! [X1,X2] :
( member(X2,universal_class)
| unordered_pair(singleton(X1),unordered_pair(X1,null_class)) = ordered_pair(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_1_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(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,
! [X1] :
( X1 != null_class
=> ? [X3] :
( disjoint(X3,X1)
& member(X3,X1)
& member(X3,universal_class) ) ),
inference(fof_simplification,[status(thm)],[regularity]) ).
fof(c_0_6,plain,
! [X19,X20,X21] :
( ( member(X19,unordered_pair(X20,X21))
| ~ member(X19,universal_class)
| X19 != X21 )
& ( member(X19,unordered_pair(X20,X21))
| ~ member(X19,universal_class)
| X19 != X20 )
& ( ~ member(X19,unordered_pair(X20,X21))
| X19 = X21
| X19 = X20 )
& ( ~ member(X19,unordered_pair(X20,X21))
| member(X19,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_7,plain,
! [X101] :
( ( X101 = null_class
| disjoint(esk6_1(X101),X101) )
& ( X101 = null_class
| member(esk6_1(X101),X101) )
& ( X101 = null_class
| member(esk6_1(X101),universal_class) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( member(X2,universal_class)
| unordered_pair(singleton(X1),unordered_pair(X1,null_class)) = ordered_pair(X1,X2) ),
inference(assume_negation,[status(cth)],[property_1_of_ordered_pair]) ).
fof(c_0_9,plain,
! [X25,X26] : ordered_pair(X25,X26) = unordered_pair(singleton(X25),unordered_pair(X25,singleton(X26))),
inference(variable_rename,[status(thm)],[ordered_pair_defn]) ).
fof(c_0_10,plain,
! [X24] : singleton(X24) = unordered_pair(X24,X24),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_11,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( X1 = null_class
| member(esk6_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,negated_conjecture,
( ~ member(esk9_0,universal_class)
& unordered_pair(singleton(esk8_0),unordered_pair(esk8_0,null_class)) != ordered_pair(esk8_0,esk9_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_14,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( unordered_pair(X1,X2) = null_class
| esk6_1(unordered_pair(X1,X2)) = X2
| esk6_1(unordered_pair(X1,X2)) = X1 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
unordered_pair(singleton(esk8_0),unordered_pair(esk8_0,null_class)) != ordered_pair(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]) ).
cnf(c_0_19,plain,
( X1 = null_class
| member(esk6_1(X1),universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,plain,
( unordered_pair(X1,X1) = null_class
| esk6_1(unordered_pair(X1,X1)) = X1 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_16])]) ).
cnf(c_0_21,negated_conjecture,
unordered_pair(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,null_class)) != unordered_pair(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_15]),c_0_18]) ).
cnf(c_0_22,plain,
( member(X1,universal_class)
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
~ member(esk9_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET103+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 04:55:31 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.49 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
% 0.26/0.59 % Version: 3.5.1
% 0.26/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.59 % Starting sh5l with 300s (1) cores
% 0.26/0.59 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2472693 completed with status 0
% 0.26/0.59 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.26/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.59 % No SInE strategy applied
% 0.26/0.59 % Search class: FGHSM-FFMS21-DFFFFFNN
% 0.26/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.26/0.59 % Starting sh3 with 271s (1) cores
% 0.26/0.59 % Starting ho_unfolding_3 with 271s (1) cores
% 0.26/0.59 % Starting new_ho_10_cnf2 with 271s (1) cores
% 0.26/0.59 % sh3 with pid 2472702 completed with status 0
% 0.26/0.59 % Result found by sh3
% 0.26/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.59 % No SInE strategy applied
% 0.26/0.59 % Search class: FGHSM-FFMS21-DFFFFFNN
% 0.26/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.26/0.59 % Starting sh3 with 271s (1) cores
% 0.26/0.59 % Preprocessing time : 0.004 s
% 0.26/0.59 % Presaturation interreduction done
% 0.26/0.59
% 0.26/0.59 % Proof found!
% 0.26/0.59 % SZS status Theorem
% 0.26/0.59 % SZS output start CNFRefutation
% See solution above
% 0.26/0.59 % Parsed axioms : 44
% 0.26/0.59 % Removed by relevancy pruning/SinE : 0
% 0.26/0.59 % Initial clauses : 91
% 0.26/0.59 % Removed in clause preprocessing : 8
% 0.26/0.59 % Initial clauses in saturation : 83
% 0.26/0.59 % Processed clauses : 419
% 0.26/0.59 % ...of these trivial : 17
% 0.26/0.59 % ...subsumed : 102
% 0.26/0.59 % ...remaining for further processing : 300
% 0.26/0.59 % Other redundant clauses eliminated : 8
% 0.26/0.59 % Clauses deleted for lack of memory : 0
% 0.26/0.59 % Backward-subsumed : 8
% 0.26/0.59 % Backward-rewritten : 28
% 0.26/0.59 % Generated clauses : 1099
% 0.26/0.59 % ...of the previous two non-redundant : 902
% 0.26/0.59 % ...aggressively subsumed : 0
% 0.26/0.59 % Contextual simplify-reflections : 2
% 0.26/0.59 % Paramodulations : 1089
% 0.26/0.59 % Factorizations : 2
% 0.26/0.59 % NegExts : 0
% 0.26/0.59 % Equation resolutions : 8
% 0.26/0.59 % Disequality decompositions : 0
% 0.26/0.59 % Total rewrite steps : 222
% 0.26/0.59 % ...of those cached : 183
% 0.26/0.59 % Propositional unsat checks : 0
% 0.26/0.59 % Propositional check models : 0
% 0.26/0.59 % Propositional check unsatisfiable : 0
% 0.26/0.59 % Propositional clauses : 0
% 0.26/0.59 % Propositional clauses after purity: 0
% 0.26/0.59 % Propositional unsat core size : 0
% 0.26/0.59 % Propositional preprocessing time : 0.000
% 0.26/0.59 % Propositional encoding time : 0.000
% 0.26/0.59 % Propositional solver time : 0.000
% 0.26/0.59 % Success case prop preproc time : 0.000
% 0.26/0.59 % Success case prop encoding time : 0.000
% 0.26/0.59 % Success case prop solver time : 0.000
% 0.26/0.59 % Current number of processed clauses : 176
% 0.26/0.59 % Positive orientable unit clauses : 35
% 0.26/0.59 % Positive unorientable unit clauses: 0
% 0.26/0.59 % Negative unit clauses : 5
% 0.26/0.59 % Non-unit-clauses : 136
% 0.26/0.59 % Current number of unprocessed clauses: 604
% 0.26/0.59 % ...number of literals in the above : 1696
% 0.26/0.59 % Current number of archived formulas : 0
% 0.26/0.59 % Current number of archived clauses : 126
% 0.26/0.59 % Clause-clause subsumption calls (NU) : 4582
% 0.26/0.59 % Rec. Clause-clause subsumption calls : 4171
% 0.26/0.59 % Non-unit clause-clause subsumptions : 85
% 0.26/0.59 % Unit Clause-clause subsumption calls : 414
% 0.26/0.59 % Rewrite failures with RHS unbound : 0
% 0.26/0.59 % BW rewrite match attempts : 8
% 0.26/0.59 % BW rewrite match successes : 3
% 0.26/0.59 % Condensation attempts : 0
% 0.26/0.59 % Condensation successes : 0
% 0.26/0.59 % Termbank termtop insertions : 24224
% 0.26/0.59 % Search garbage collected termcells : 979
% 0.26/0.59
% 0.26/0.59 % -------------------------------------------------
% 0.26/0.59 % User time : 0.066 s
% 0.26/0.59 % System time : 0.009 s
% 0.26/0.59 % Total time : 0.075 s
% 0.26/0.59 % Maximum resident set size: 3948 pages
% 0.26/0.59
% 0.26/0.59 % -------------------------------------------------
% 0.26/0.59 % User time : 0.293 s
% 0.26/0.59 % System time : 0.039 s
% 0.26/0.59 % Total time : 0.332 s
% 0.26/0.59 % Maximum resident set size: 4864 pages
% 0.26/0.59 % E exiting
%------------------------------------------------------------------------------