%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET927+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 : n013.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 02:18:56 PM UTC 2026
% Result : Theorem 0.24s 0.57s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 77 ( 42 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 87 ( 34 ~; 37 |; 11 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 3 con; 0-2 aty)
% Number of variables : 32 ( 1 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t70_zfmisc_1,conjecture,
! [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',t70_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(c_0_2,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
<=> ( ( X1 = X2
| in(X2,X3) )
& ~ in(X1,X3) ) ),
inference(assume_negation,[status(cth)],[t70_zfmisc_1]) ).
fof(c_0_3,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_4,negated_conjecture,
~ ! [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)],[c_0_2]) ).
fof(c_0_5,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_3])])])]) ).
fof(c_0_6,negated_conjecture,
( ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0)
| esk3_0 = esk4_0
| in(esk4_0,esk5_0) )
& ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0)
| ~ in(esk3_0,esk5_0) )
& ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0)
| in(esk3_0,esk5_0)
| esk3_0 != esk4_0 )
& ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0)
| in(esk3_0,esk5_0)
| ~ in(esk4_0,esk5_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
cnf(c_0_7,plain,
( set_difference(unordered_pair(X1,X3),X2) != singleton(X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( ~ in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0)
| ~ in(esk4_0,esk5_0)
| in(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
~ in(esk3_0,esk5_0),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( ~ in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0) ),
inference(sr,[status(thm)],[c_0_9,c_0_10]) ).
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_5]) ).
cnf(c_0_13,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0)
| esk3_0 = esk4_0
| in(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
~ in(esk4_0,esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0)
| esk3_0 != esk4_0
| in(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( set_difference(unordered_pair(X3,X1),X2) != singleton(X3)
| X3 = X1
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
( esk4_0 = esk3_0
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = singleton(esk3_0) ),
inference(sr,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( esk4_0 != esk3_0
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != singleton(esk3_0) ),
inference(sr,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_19,negated_conjecture,
esk4_0 = esk3_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]) ).
cnf(c_0_20,plain,
( X1 != X2
| set_difference(unordered_pair(X1,X2),X3) = singleton(X1)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
set_difference(unordered_pair(esk3_0,esk3_0),esk5_0) != singleton(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19])]) ).
cnf(c_0_22,plain,
( in(X1,X2)
| set_difference(unordered_pair(X1,X1),X2) = singleton(X1) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET927+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 : n013.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
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 05:43:36 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.52 Running first-order theorem proving
% 0.19/0.52 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
% 0.24/0.57 % Version: 3.5.1
% 0.24/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.57 % Starting sh5l with 300s (1) cores
% 0.24/0.57 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 54371 completed with status 0
% 0.24/0.57 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.24/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.57 % No SInE strategy applied
% 0.24/0.57 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.24/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.24/0.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.24/0.57 % Starting new_bool_3 with 136s (1) cores
% 0.24/0.57 % Starting new_bool_1 with 136s (1) cores
% 0.24/0.57 % SubtermCWHack with pid 54375 completed with status 0
% 0.24/0.57 % Result found by SubtermCWHack
% 0.24/0.57 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.24/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.57 % No SInE strategy applied
% 0.24/0.57 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.24/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.57 % Preprocessing time : 0.001 s
% 0.24/0.57
% 0.24/0.57 % Proof found!
% 0.24/0.57 % SZS status Theorem
% 0.24/0.57 % SZS output start CNFRefutation
% See solution above
% 0.24/0.57 % Parsed axioms : 6
% 0.24/0.57 % Removed by relevancy pruning/SinE : 0
% 0.24/0.57 % Initial clauses : 12
% 0.24/0.57 % Removed in clause preprocessing : 0
% 0.24/0.57 % Initial clauses in saturation : 12
% 0.24/0.57 % Processed clauses : 30
% 0.24/0.57 % ...of these trivial : 0
% 0.24/0.57 % ...subsumed : 9
% 0.24/0.57 % ...remaining for further processing : 21
% 0.24/0.57 % Other redundant clauses eliminated : 1
% 0.24/0.57 % Clauses deleted for lack of memory : 0
% 0.24/0.57 % Backward-subsumed : 3
% 0.24/0.57 % Backward-rewritten : 3
% 0.24/0.57 % Generated clauses : 32
% 0.24/0.57 % ...of the previous two non-redundant : 24
% 0.24/0.57 % ...aggressively subsumed : 0
% 0.24/0.57 % Contextual simplify-reflections : 0
% 0.24/0.57 % Paramodulations : 30
% 0.24/0.57 % Factorizations : 0
% 0.24/0.57 % NegExts : 0
% 0.24/0.57 % Equation resolutions : 1
% 0.24/0.57 % Disequality decompositions : 0
% 0.24/0.57 % Total rewrite steps : 5
% 0.24/0.57 % ...of those cached : 4
% 0.24/0.57 % Propositional unsat checks : 0
% 0.24/0.57 % Propositional check models : 0
% 0.24/0.57 % Propositional check unsatisfiable : 0
% 0.24/0.57 % Propositional clauses : 0
% 0.24/0.57 % Propositional clauses after purity: 0
% 0.24/0.57 % Propositional unsat core size : 0
% 0.24/0.57 % Propositional preprocessing time : 0.000
% 0.24/0.57 % Propositional encoding time : 0.000
% 0.24/0.57 % Propositional solver time : 0.000
% 0.24/0.57 % Success case prop preproc time : 0.000
% 0.24/0.57 % Success case prop encoding time : 0.000
% 0.24/0.57 % Success case prop solver time : 0.000
% 0.24/0.57 % Current number of processed clauses : 13
% 0.24/0.57 % Positive orientable unit clauses : 2
% 0.24/0.57 % Positive unorientable unit clauses: 1
% 0.24/0.57 % Negative unit clauses : 3
% 0.24/0.57 % Non-unit-clauses : 7
% 0.24/0.57 % Current number of unprocessed clauses: 4
% 0.24/0.57 % ...number of literals in the above : 12
% 0.24/0.57 % Current number of archived formulas : 0
% 0.24/0.57 % Current number of archived clauses : 7
% 0.24/0.57 % Clause-clause subsumption calls (NU) : 22
% 0.24/0.57 % Rec. Clause-clause subsumption calls : 19
% 0.24/0.57 % Non-unit clause-clause subsumptions : 5
% 0.24/0.57 % Unit Clause-clause subsumption calls : 3
% 0.24/0.57 % Rewrite failures with RHS unbound : 0
% 0.24/0.57 % BW rewrite match attempts : 1
% 0.24/0.57 % BW rewrite match successes : 1
% 0.24/0.57 % Condensation attempts : 0
% 0.24/0.57 % Condensation successes : 0
% 0.24/0.57 % Termbank termtop insertions : 1032
% 0.24/0.57 % Search garbage collected termcells : 153
% 0.24/0.57
% 0.24/0.57 % -------------------------------------------------
% 0.24/0.57 % User time : 0.006 s
% 0.24/0.57 % System time : 0.004 s
% 0.24/0.57 % Total time : 0.010 s
% 0.24/0.57 % Maximum resident set size: 3376 pages
% 0.24/0.57
% 0.24/0.57 % -------------------------------------------------
% 0.24/0.57 % User time : 0.016 s
% 0.24/0.57 % System time : 0.014 s
% 0.24/0.57 % Total time : 0.030 s
% 0.24/0.57 % Maximum resident set size: 4608 pages
% 0.24/0.57 % E exiting
%------------------------------------------------------------------------------