%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 0.23s 5.56s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 65 ( 41 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 72 ( 30 ~; 26 |; 9 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t23_zfmisc_1,conjecture,
! [X1,X2] :
( X1 != X2
=> set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).
fof(l39_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ( X1 = X2
| in(X2,X3) )
& ~ in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( X1 != X2
=> set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1) ),
inference(assume_negation,[status(cth)],[t23_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( X1 != X2
=> set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ( X1 = X2
| in(X2,X3) )
& ~ in(X1,X3) ) ),
inference(fof_simplification,[status(thm)],[l39_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
( set_difference(unordered_pair(esk1_0,esk2_0),singleton(esk2_0)) != singleton(esk1_0)
& 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_5])])])]) ).
fof(c_0_8,plain,
! [X16,X17] : unordered_pair(X16,X17) = unordered_pair(X17,X16),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_9,plain,
! [X13,X14,X15] :
( ( set_difference(unordered_pair(X13,X14),X15) = singleton(X13)
| in(X13,X15)
| X13 != X14 )
& ( set_difference(unordered_pair(X13,X14),X15) = singleton(X13)
| in(X13,X15)
| ~ in(X14,X15) )
& ( set_difference(unordered_pair(X13,X14),X15) != singleton(X13)
| X13 = X14
| in(X14,X15) )
& ( set_difference(unordered_pair(X13,X14),X15) != singleton(X13)
| ~ in(X13,X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,plain,
! [X6,X7,X8,X9,X10,X11] :
( ( X11 = singleton(X10)
| esk3_2(X10,X11) = X10
| in(esk3_2(X10,X11),X11) )
& ( X11 = singleton(X10)
| esk3_2(X10,X11) != X10
| ~ in(esk3_2(X10,X11),X11) )
& ( X7 != singleton(X6)
| in(X9,X7)
| X9 != X6 )
& ( X7 != singleton(X6)
| X8 = X6
| ~ in(X8,X7) ) ),
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)],[d1_tarski])])])])])])]) ).
cnf(c_0_11,negated_conjecture,
set_difference(unordered_pair(esk1_0,esk2_0),singleton(esk2_0)) != singleton(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ in(X1,X2)
| set_difference(unordered_pair(X3,X1),X2) = singleton(X3)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
set_difference(unordered_pair(esk2_0,esk1_0),singleton(esk2_0)) != singleton(esk1_0),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( ~ in(X1,X3)
| in(X2,X3)
| set_difference(unordered_pair(X1,X2),X3) = singleton(X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).
cnf(c_0_19,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
in(esk1_0,singleton(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_21,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/5.46 % Computer : n018.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Mon Sep 21 05:44:34 UTC 2026
% 0.19/5.46 % CPUTime :
% 0.19/5.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/5.53 Running first-order theorem proving
% 0.23/5.54 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.23/5.56 % Version: 3.5.1
% 0.23/5.56 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.23/5.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.56 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.23/5.56 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.56 % Starting new_bool_1 with 300s (1) cores
% 0.23/5.56 % Starting sh5l with 300s (1) cores
% 0.23/5.56 % sh5l with pid 1090782 completed with status 0
% 0.23/5.56 % Result found by sh5l
% 0.23/5.56 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.23/5.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.56 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.23/5.56 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.56 % Starting new_bool_1 with 300s (1) cores
% 0.23/5.56 % Starting sh5l with 300s (1) cores
% 0.23/5.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/5.56 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/5.56 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.23/5.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/5.56 % Starting SubtermCWHack with 31s (1) cores
% 0.23/5.56 % SubtermCWHack with pid 1090785 completed with status 0
% 0.23/5.56 % Result found by SubtermCWHack
% 0.23/5.56 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.23/5.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/5.56 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.23/5.56 % Starting new_bool_3 with 300s (1) cores
% 0.23/5.56 % Starting new_bool_1 with 300s (1) cores
% 0.23/5.56 % Starting sh5l with 300s (1) cores
% 0.23/5.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/5.56 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/5.56 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.23/5.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/5.56 % Starting SubtermCWHack with 31s (1) cores
% 0.23/5.56 % Preprocessing time : 0.002 s
% 0.23/5.56
% 0.23/5.56 % Proof found!
% 0.23/5.56 % SZS status Theorem
% 0.23/5.56 % SZS output start CNFRefutation
% See solution above
% 0.23/5.56 % Parsed axioms : 7
% 0.23/5.56 % Removed by relevancy pruning/SinE : 2
% 0.23/5.56 % Initial clauses : 12
% 0.23/5.56 % Removed in clause preprocessing : 0
% 0.23/5.56 % Initial clauses in saturation : 12
% 0.23/5.56 % Processed clauses : 34
% 0.23/5.56 % ...of these trivial : 0
% 0.23/5.56 % ...subsumed : 7
% 0.23/5.56 % ...remaining for further processing : 27
% 0.23/5.56 % Other redundant clauses eliminated : 7
% 0.23/5.56 % Clauses deleted for lack of memory : 0
% 0.23/5.56 % Backward-subsumed : 0
% 0.23/5.56 % Backward-rewritten : 0
% 0.23/5.56 % Generated clauses : 53
% 0.23/5.56 % ...of the previous two non-redundant : 36
% 0.23/5.56 % ...aggressively subsumed : 0
% 0.23/5.56 % Contextual simplify-reflections : 0
% 0.23/5.56 % Paramodulations : 43
% 0.23/5.56 % Factorizations : 2
% 0.23/5.56 % NegExts : 0
% 0.23/5.56 % Equation resolutions : 9
% 0.23/5.56 % Disequality decompositions : 0
% 0.23/5.56 % Total rewrite steps : 5
% 0.23/5.56 % ...of those cached : 1
% 0.23/5.56 % Propositional unsat checks : 0
% 0.23/5.56 % Propositional check models : 0
% 0.23/5.56 % Propositional check unsatisfiable : 0
% 0.23/5.56 % Propositional clauses : 0
% 0.23/5.56 % Propositional clauses after purity: 0
% 0.23/5.56 % Propositional unsat core size : 0
% 0.23/5.56 % Propositional preprocessing time : 0.000
% 0.23/5.56 % Propositional encoding time : 0.000
% 0.23/5.56 % Propositional solver time : 0.000
% 0.23/5.56 % Success case prop preproc time : 0.000
% 0.23/5.56 % Success case prop encoding time : 0.000
% 0.23/5.56 % Success case prop solver time : 0.000
% 0.23/5.56 % Current number of processed clauses : 24
% 0.23/5.56 % Positive orientable unit clauses : 2
% 0.23/5.56 % Positive unorientable unit clauses: 1
% 0.23/5.56 % Negative unit clauses : 4
% 0.23/5.56 % Non-unit-clauses : 17
% 0.23/5.56 % Current number of unprocessed clauses: 12
% 0.23/5.56 % ...number of literals in the above : 39
% 0.23/5.56 % Current number of archived formulas : 0
% 0.23/5.56 % Current number of archived clauses : 0
% 0.23/5.56 % Clause-clause subsumption calls (NU) : 40
% 0.23/5.56 % Rec. Clause-clause subsumption calls : 36
% 0.23/5.56 % Non-unit clause-clause subsumptions : 5
% 0.23/5.56 % Unit Clause-clause subsumption calls : 5
% 0.23/5.56 % Rewrite failures with RHS unbound : 0
% 0.23/5.56 % BW rewrite match attempts : 0
% 0.23/5.56 % BW rewrite match successes : 0
% 0.23/5.56 % Condensation attempts : 0
% 0.23/5.56 % Condensation successes : 0
% 0.23/5.56 % Termbank termtop insertions : 1223
% 0.23/5.56 % Search garbage collected termcells : 212
% 0.23/5.56
% 0.23/5.56 % -------------------------------------------------
% 0.23/5.56 % User time : 0.010 s
% 0.23/5.56 % System time : 0.001 s
% 0.23/5.56 % Total time : 0.011 s
% 0.23/5.56 % Maximum resident set size: 3632 pages
% 0.23/5.56
% 0.23/5.56 % -------------------------------------------------
% 0.23/5.56 % User time : 0.012 s
% 0.23/5.56 % System time : 0.007 s
% 0.23/5.56 % Total time : 0.019 s
% 0.23/5.56 % Maximum resident set size: 4608 pages
% 0.23/5.56 % E exiting
%------------------------------------------------------------------------------