%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET882+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 : n001.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 02:18:49 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 66 ( 42 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 71 ( 29 ~; 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 : 46 ( 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/sandbox/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/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_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,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_6,plain,
! [X8,X9,X10,X11,X12,X13] :
( ( X13 = singleton(X12)
| esk1_2(X12,X13) = X12
| in(esk1_2(X12,X13),X13) )
& ( X13 = singleton(X12)
| esk1_2(X12,X13) != X12
| ~ in(esk1_2(X12,X13),X13) )
& ( X9 != singleton(X8)
| in(X11,X9)
| X11 != X8 )
& ( X9 != singleton(X8)
| X10 = X8
| ~ in(X10,X9) ) ),
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])])])])])])]) ).
fof(c_0_7,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_8,plain,
! [X15,X16,X17] :
( ( set_difference(unordered_pair(X15,X16),X17) = singleton(X15)
| in(X15,X17)
| X15 != X16 )
& ( set_difference(unordered_pair(X15,X16),X17) = singleton(X15)
| in(X15,X17)
| ~ in(X16,X17) )
& ( set_difference(unordered_pair(X15,X16),X17) != singleton(X15)
| X15 = X16
| in(X16,X17) )
& ( set_difference(unordered_pair(X15,X16),X17) != singleton(X15)
| ~ in(X15,X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_9,plain,
( X3 != singleton(X2)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
( set_difference(unordered_pair(esk4_0,esk5_0),singleton(esk5_0)) != singleton(esk4_0)
& esk4_0 != esk5_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_11,plain,
! [X6,X7] : unordered_pair(X6,X7) = unordered_pair(X7,X6),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( ~ in(X1,X2)
| set_difference(unordered_pair(X3,X1),X2) = singleton(X3)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_14,negated_conjecture,
set_difference(unordered_pair(esk4_0,esk5_0),singleton(esk5_0)) != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( in(X1,singleton(X2))
| set_difference(unordered_pair(X1,X2),singleton(X2)) = singleton(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
set_difference(unordered_pair(esk5_0,esk4_0),singleton(esk5_0)) != singleton(esk4_0),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( in(X2,singleton(X1))
| set_difference(unordered_pair(X1,X2),singleton(X1)) = singleton(X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_20,plain,
( ~ in(X1,singleton(X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
in(esk4_0,singleton(esk5_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:48:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.42 % Version: 3.5.1
% 0.14/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % Starting sh5l with 300s (1) cores
% 0.14/0.42 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2311879 completed with status 0
% 0.14/0.42 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.14/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.42 % No SInE strategy applied
% 0.14/0.42 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.14/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.42 % new_bool_1 with pid 2311887 completed with status 0
% 0.14/0.42 % Result found by new_bool_1
% 0.14/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.42 % No SInE strategy applied
% 0.14/0.42 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.14/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.42 % Preprocessing time : 0.001 s
% 0.14/0.42 % Presaturation interreduction done
% 0.14/0.42
% 0.14/0.42 % Proof found!
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 % SZS output start CNFRefutation
% See solution above
% 0.14/0.42 % Parsed axioms : 7
% 0.14/0.42 % Removed by relevancy pruning/SinE : 0
% 0.14/0.42 % Initial clauses : 14
% 0.14/0.42 % Removed in clause preprocessing : 0
% 0.14/0.42 % Initial clauses in saturation : 14
% 0.14/0.42 % Processed clauses : 49
% 0.14/0.42 % ...of these trivial : 0
% 0.14/0.42 % ...subsumed : 9
% 0.14/0.42 % ...remaining for further processing : 40
% 0.14/0.42 % Other redundant clauses eliminated : 4
% 0.14/0.42 % Clauses deleted for lack of memory : 0
% 0.14/0.42 % Backward-subsumed : 0
% 0.14/0.42 % Backward-rewritten : 1
% 0.14/0.42 % Generated clauses : 37
% 0.14/0.42 % ...of the previous two non-redundant : 30
% 0.14/0.42 % ...aggressively subsumed : 0
% 0.14/0.42 % Contextual simplify-reflections : 0
% 0.14/0.42 % Paramodulations : 33
% 0.14/0.42 % Factorizations : 0
% 0.14/0.42 % NegExts : 0
% 0.14/0.42 % Equation resolutions : 5
% 0.14/0.42 % Disequality decompositions : 0
% 0.14/0.42 % Total rewrite steps : 6
% 0.14/0.42 % ...of those cached : 2
% 0.14/0.42 % Propositional unsat checks : 0
% 0.14/0.42 % Propositional check models : 0
% 0.14/0.42 % Propositional check unsatisfiable : 0
% 0.14/0.42 % Propositional clauses : 0
% 0.14/0.42 % Propositional clauses after purity: 0
% 0.14/0.42 % Propositional unsat core size : 0
% 0.14/0.42 % Propositional preprocessing time : 0.000
% 0.14/0.42 % Propositional encoding time : 0.000
% 0.14/0.42 % Propositional solver time : 0.000
% 0.14/0.42 % Success case prop preproc time : 0.000
% 0.14/0.42 % Success case prop encoding time : 0.000
% 0.14/0.42 % Success case prop solver time : 0.000
% 0.14/0.42 % Current number of processed clauses : 22
% 0.14/0.42 % Positive orientable unit clauses : 3
% 0.14/0.42 % Positive unorientable unit clauses: 1
% 0.14/0.42 % Negative unit clauses : 4
% 0.14/0.42 % Non-unit-clauses : 14
% 0.14/0.42 % Current number of unprocessed clauses: 7
% 0.14/0.42 % ...number of literals in the above : 18
% 0.14/0.42 % Current number of archived formulas : 0
% 0.14/0.42 % Current number of archived clauses : 15
% 0.14/0.42 % Clause-clause subsumption calls (NU) : 48
% 0.14/0.42 % Rec. Clause-clause subsumption calls : 43
% 0.14/0.42 % Non-unit clause-clause subsumptions : 9
% 0.14/0.42 % Unit Clause-clause subsumption calls : 6
% 0.14/0.42 % Rewrite failures with RHS unbound : 0
% 0.14/0.42 % BW rewrite match attempts : 4
% 0.14/0.42 % BW rewrite match successes : 4
% 0.14/0.42 % Condensation attempts : 0
% 0.14/0.42 % Condensation successes : 0
% 0.14/0.42 % Termbank termtop insertions : 1210
% 0.14/0.42 % Search garbage collected termcells : 215
% 0.14/0.42
% 0.14/0.42 % -------------------------------------------------
% 0.14/0.42 % User time : 0.004 s
% 0.14/0.42 % System time : 0.001 s
% 0.14/0.42 % Total time : 0.005 s
% 0.14/0.42 % Maximum resident set size: 3632 pages
% 0.14/0.42
% 0.14/0.42 % -------------------------------------------------
% 0.14/0.42 % User time : 0.014 s
% 0.14/0.42 % System time : 0.011 s
% 0.14/0.42 % Total time : 0.025 s
% 0.14/0.42 % Maximum resident set size: 4608 pages
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------