%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET930+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 : n005.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 02:15:48 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 10 unt; 0 def)
% Number of atoms : 82 ( 46 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 105 ( 50 ~; 26 |; 24 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t74_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_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(t72_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X2,X3)
& ~ in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_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(t73_zfmisc_1,axiom,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = empty_set
<=> ( in(X2,X3)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != empty_set ),
inference(assume_negation,[status(cth)],[t74_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X2)
& set_difference(unordered_pair(X1,X2),X3) != singleton(X1)
& set_difference(unordered_pair(X1,X2),X3) != empty_set ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,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_8,plain,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X2,X3)
& ~ in(X1,X3) ) ),
inference(fof_simplification,[status(thm)],[t72_zfmisc_1]) ).
fof(c_0_9,negated_conjecture,
( set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != unordered_pair(esk1_0,esk2_0)
& set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk2_0)
& set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk1_0)
& set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,plain,
! [X9,X10,X11] :
( ( set_difference(unordered_pair(X9,X10),X11) = singleton(X9)
| in(X9,X11)
| X9 != X10 )
& ( set_difference(unordered_pair(X9,X10),X11) = singleton(X9)
| in(X9,X11)
| ~ in(X10,X11) )
& ( set_difference(unordered_pair(X9,X10),X11) != singleton(X9)
| X9 = X10
| in(X10,X11) )
& ( set_difference(unordered_pair(X9,X10),X11) != singleton(X9)
| ~ in(X9,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_11,plain,
! [X12,X13,X14] :
( ( set_difference(unordered_pair(X12,X13),X14) = unordered_pair(X12,X13)
| in(X13,X14)
| in(X12,X14) )
& ( set_difference(unordered_pair(X12,X13),X14) != unordered_pair(X12,X13)
| ~ in(X13,X14) )
& ( set_difference(unordered_pair(X12,X13),X14) != unordered_pair(X12,X13)
| ~ in(X12,X14) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_12,negated_conjecture,
set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
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_10]) ).
fof(c_0_14,plain,
! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_15,plain,
! [X15,X16,X17] :
( ( set_difference(unordered_pair(X15,X16),X17) = empty_set
| ~ in(X16,X17)
| ~ in(X15,X17) )
& ( set_difference(unordered_pair(X15,X16),X17) != empty_set
| in(X16,X17) )
& ( set_difference(unordered_pair(X15,X16),X17) != empty_set
| in(X15,X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t73_zfmisc_1])])])]) ).
cnf(c_0_16,negated_conjecture,
set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != unordered_pair(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( set_difference(unordered_pair(X1,X3),X2) = unordered_pair(X1,X3)
| in(X3,X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( ~ in(esk2_0,esk3_0)
| in(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,plain,
( ~ in(X3,X2)
| ~ in(X1,X2)
| set_difference(unordered_pair(X1,X3),X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
in(esk1_0,esk3_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_23,negated_conjecture,
set_difference(unordered_pair(esk1_0,esk2_0),esk3_0) != singleton(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,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_19]) ).
cnf(c_0_25,negated_conjecture,
~ in(esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_22])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:43:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.42 % Version: 3.5.1
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % sh5l with pid 2677076 completed with status 0
% 0.13/0.42 % Result found by sh5l
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.13/0.42 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.13/0.42 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.13/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.42 % SubtermCWHack with pid 2677077 completed with status 0
% 0.13/0.42 % Result found by SubtermCWHack
% 0.13/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.42 % Starting sh5l with 300s (1) cores
% 0.13/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.13/0.42 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.13/0.42 % Search class: FGHSF-FFSF21-SFFFFFNN
% 0.13/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.42 % Preprocessing time : 0.001 s
% 0.13/0.42
% 0.13/0.42 % Proof found!
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start CNFRefutation
% See solution above
% 0.13/0.42 % Parsed axioms : 9
% 0.13/0.42 % Removed by relevancy pruning/SinE : 0
% 0.13/0.42 % Initial clauses : 19
% 0.13/0.42 % Removed in clause preprocessing : 0
% 0.13/0.42 % Initial clauses in saturation : 19
% 0.13/0.42 % Processed clauses : 77
% 0.13/0.42 % ...of these trivial : 4
% 0.13/0.42 % ...subsumed : 33
% 0.13/0.42 % ...remaining for further processing : 40
% 0.13/0.42 % Other redundant clauses eliminated : 1
% 0.13/0.42 % Clauses deleted for lack of memory : 0
% 0.13/0.42 % Backward-subsumed : 3
% 0.13/0.42 % Backward-rewritten : 1
% 0.13/0.42 % Generated clauses : 128
% 0.13/0.42 % ...of the previous two non-redundant : 92
% 0.13/0.42 % ...aggressively subsumed : 0
% 0.13/0.42 % Contextual simplify-reflections : 2
% 0.13/0.42 % Paramodulations : 126
% 0.13/0.42 % Factorizations : 0
% 0.13/0.42 % NegExts : 0
% 0.13/0.42 % Equation resolutions : 2
% 0.13/0.42 % Disequality decompositions : 0
% 0.13/0.42 % Total rewrite steps : 14
% 0.13/0.42 % ...of those cached : 12
% 0.13/0.42 % Propositional unsat checks : 0
% 0.13/0.42 % Propositional check models : 0
% 0.13/0.42 % Propositional check unsatisfiable : 0
% 0.13/0.42 % Propositional clauses : 0
% 0.13/0.42 % Propositional clauses after purity: 0
% 0.13/0.42 % Propositional unsat core size : 0
% 0.13/0.42 % Propositional preprocessing time : 0.000
% 0.13/0.42 % Propositional encoding time : 0.000
% 0.13/0.42 % Propositional solver time : 0.000
% 0.13/0.42 % Success case prop preproc time : 0.000
% 0.13/0.42 % Success case prop encoding time : 0.000
% 0.13/0.42 % Success case prop solver time : 0.000
% 0.13/0.42 % Current number of processed clauses : 35
% 0.13/0.42 % Positive orientable unit clauses : 4
% 0.13/0.42 % Positive unorientable unit clauses: 1
% 0.13/0.42 % Negative unit clauses : 9
% 0.13/0.42 % Non-unit-clauses : 21
% 0.13/0.42 % Current number of unprocessed clauses: 28
% 0.13/0.42 % ...number of literals in the above : 80
% 0.13/0.42 % Current number of archived formulas : 0
% 0.13/0.42 % Current number of archived clauses : 4
% 0.13/0.42 % Clause-clause subsumption calls (NU) : 102
% 0.13/0.42 % Rec. Clause-clause subsumption calls : 91
% 0.13/0.42 % Non-unit clause-clause subsumptions : 25
% 0.13/0.42 % Unit Clause-clause subsumption calls : 15
% 0.13/0.42 % Rewrite failures with RHS unbound : 0
% 0.13/0.42 % BW rewrite match attempts : 1
% 0.13/0.42 % BW rewrite match successes : 1
% 0.13/0.42 % Condensation attempts : 0
% 0.13/0.42 % Condensation successes : 0
% 0.13/0.42 % Termbank termtop insertions : 1951
% 0.13/0.42 % Search garbage collected termcells : 176
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.004 s
% 0.13/0.42 % System time : 0.003 s
% 0.13/0.42 % Total time : 0.007 s
% 0.13/0.42 % Maximum resident set size: 3636 pages
% 0.13/0.42
% 0.13/0.42 % -------------------------------------------------
% 0.13/0.42 % User time : 0.007 s
% 0.13/0.42 % System time : 0.006 s
% 0.13/0.42 % Total time : 0.013 s
% 0.13/0.42 % Maximum resident set size: 4608 pages
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------