%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 02:15:41 PM UTC 2026
% Result : Theorem 0.24s 0.55s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 42 ( 27 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 48 ( 19 ~; 20 |; 6 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t22_zfmisc_1,conjecture,
! [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).
fof(l36_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),X2) = empty_set
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] : set_difference(singleton(X1),unordered_pair(X1,X2)) = empty_set,
inference(assume_negation,[status(cth)],[t22_zfmisc_1]) ).
fof(c_0_4,negated_conjecture,
set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != empty_set,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_5,plain,
! [X18,X19] :
( ( set_difference(singleton(X18),X19) = empty_set
| ~ in(X18,X19) )
& ( in(X18,X19)
| set_difference(singleton(X18),X19) != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l36_zfmisc_1])])]) ).
fof(c_0_6,plain,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( X16 = unordered_pair(X14,X15)
| esk1_3(X14,X15,X16) = X15
| esk1_3(X14,X15,X16) = X14
| in(esk1_3(X14,X15,X16),X16) )
& ( X16 = unordered_pair(X14,X15)
| ~ in(esk1_3(X14,X15,X16),X16)
| esk1_3(X14,X15,X16) != X15 )
& ( X16 = unordered_pair(X14,X15)
| ~ in(esk1_3(X14,X15,X16),X16)
| esk1_3(X14,X15,X16) != X14 )
& ( X11 != unordered_pair(X9,X10)
| in(X13,X11)
| X13 != X10 )
& ( X11 != unordered_pair(X9,X10)
| in(X13,X11)
| X13 != X9 )
& ( X11 != unordered_pair(X9,X10)
| X12 = X10
| X12 = X9
| ~ in(X12,X11) ) ),
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)],[d2_tarski])])])])])])]) ).
cnf(c_0_7,negated_conjecture,
set_difference(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( ~ in(X1,X2)
| set_difference(singleton(X1),X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( X3 != unordered_pair(X2,X4)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
~ in(esk4_0,unordered_pair(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n026.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 05:44:51 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 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
% 0.24/0.55 % Version: 3.5.1
% 0.24/0.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.55 % Starting sh5l with 300s (1) cores
% 0.24/0.55 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1486601 completed with status 0
% 0.24/0.55 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.24/0.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.55 % No SInE strategy applied
% 0.24/0.55 % Search class: FGHSF-FFSF32-SFFFFFNN
% 0.24/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.24/0.55 % Starting new_bool_3 with 136s (1) cores
% 0.24/0.55 % Starting new_bool_1 with 136s (1) cores
% 0.24/0.55 % SubtermCWHack with pid 1486605 completed with status 0
% 0.24/0.55 % Result found by SubtermCWHack
% 0.24/0.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.55 % No SInE strategy applied
% 0.24/0.55 % Search class: FGHSF-FFSF32-SFFFFFNN
% 0.24/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.55 % Preprocessing time : 0.001 s
% 0.24/0.55
% 0.24/0.55 % Proof found!
% 0.24/0.55 % SZS status Theorem
% 0.24/0.55 % SZS output start CNFRefutation
% See solution above
% 0.24/0.56 % Parsed axioms : 8
% 0.24/0.56 % Removed by relevancy pruning/SinE : 0
% 0.24/0.56 % Initial clauses : 14
% 0.24/0.56 % Removed in clause preprocessing : 0
% 0.24/0.56 % Initial clauses in saturation : 14
% 0.24/0.56 % Processed clauses : 13
% 0.24/0.56 % ...of these trivial : 0
% 0.24/0.56 % ...subsumed : 0
% 0.24/0.56 % ...remaining for further processing : 13
% 0.24/0.56 % Other redundant clauses eliminated : 4
% 0.24/0.56 % Clauses deleted for lack of memory : 0
% 0.24/0.56 % Backward-subsumed : 0
% 0.24/0.56 % Backward-rewritten : 1
% 0.24/0.56 % Generated clauses : 10
% 0.24/0.56 % ...of the previous two non-redundant : 6
% 0.24/0.56 % ...aggressively subsumed : 0
% 0.24/0.56 % Contextual simplify-reflections : 0
% 0.24/0.56 % Paramodulations : 8
% 0.24/0.56 % Factorizations : 0
% 0.24/0.56 % NegExts : 0
% 0.24/0.56 % Equation resolutions : 4
% 0.24/0.56 % Disequality decompositions : 0
% 0.24/0.56 % Total rewrite steps : 1
% 0.24/0.56 % ...of those cached : 0
% 0.24/0.56 % Propositional unsat checks : 0
% 0.24/0.56 % Propositional check models : 0
% 0.24/0.56 % Propositional check unsatisfiable : 0
% 0.24/0.56 % Propositional clauses : 0
% 0.24/0.56 % Propositional clauses after purity: 0
% 0.24/0.56 % Propositional unsat core size : 0
% 0.24/0.56 % Propositional preprocessing time : 0.000
% 0.24/0.56 % Propositional encoding time : 0.000
% 0.24/0.56 % Propositional solver time : 0.000
% 0.24/0.56 % Success case prop preproc time : 0.000
% 0.24/0.56 % Success case prop encoding time : 0.000
% 0.24/0.56 % Success case prop solver time : 0.000
% 0.24/0.56 % Current number of processed clauses : 10
% 0.24/0.56 % Positive orientable unit clauses : 4
% 0.24/0.56 % Positive unorientable unit clauses: 1
% 0.24/0.56 % Negative unit clauses : 2
% 0.24/0.56 % Non-unit-clauses : 3
% 0.24/0.56 % Current number of unprocessed clauses: 7
% 0.24/0.56 % ...number of literals in the above : 17
% 0.24/0.56 % Current number of archived formulas : 0
% 0.24/0.56 % Current number of archived clauses : 1
% 0.24/0.56 % Clause-clause subsumption calls (NU) : 0
% 0.24/0.56 % Rec. Clause-clause subsumption calls : 0
% 0.24/0.56 % Non-unit clause-clause subsumptions : 0
% 0.24/0.56 % Unit Clause-clause subsumption calls : 0
% 0.24/0.56 % Rewrite failures with RHS unbound : 0
% 0.24/0.56 % BW rewrite match attempts : 3
% 0.24/0.56 % BW rewrite match successes : 1
% 0.24/0.56 % Condensation attempts : 0
% 0.24/0.56 % Condensation successes : 0
% 0.24/0.56 % Termbank termtop insertions : 770
% 0.24/0.56 % Search garbage collected termcells : 213
% 0.24/0.56
% 0.24/0.56 % -------------------------------------------------
% 0.24/0.56 % User time : 0.006 s
% 0.24/0.56 % System time : 0.003 s
% 0.24/0.56 % Total time : 0.009 s
% 0.24/0.56 % Maximum resident set size: 3632 pages
% 0.24/0.56
% 0.24/0.56 % -------------------------------------------------
% 0.24/0.56 % User time : 0.013 s
% 0.24/0.56 % System time : 0.013 s
% 0.24/0.56 % Total time : 0.026 s
% 0.24/0.56 % Maximum resident set size: 4864 pages
% 0.24/0.56 % E exiting
%------------------------------------------------------------------------------