%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET902+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 : n019.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 02:15:43 PM UTC 2026
% Result : Theorem 0.24s 0.55s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 20 unt; 0 def)
% Number of atoms : 72 ( 60 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 70 ( 33 ~; 19 |; 17 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 4 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t43_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( ~ ( X3 = empty_set
& X2 = singleton(X1) )
& ~ ( X3 = singleton(X1)
& X2 = empty_set )
& ~ ( X3 = singleton(X1)
& X2 = singleton(X1) )
& singleton(X1) = set_union2(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(l4_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = singleton(X2)
| X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(l1_zfmisc_1,axiom,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(c_0_6,plain,
! [X20,X21] : subset(X20,set_union2(X20,X21)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_7,plain,
! [X10,X11] : set_union2(X10,X11) = set_union2(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( ~ ( X3 = empty_set
& X2 = singleton(X1) )
& ~ ( X3 = singleton(X1)
& X2 = empty_set )
& ~ ( X3 = singleton(X1)
& X2 = singleton(X1) )
& singleton(X1) = set_union2(X2,X3) ),
inference(assume_negation,[status(cth)],[t43_zfmisc_1]) ).
cnf(c_0_9,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( ( esk3_0 != empty_set
| esk2_0 != singleton(esk1_0) )
& ( esk3_0 != singleton(esk1_0)
| esk2_0 != empty_set )
& ( esk3_0 != singleton(esk1_0)
| esk2_0 != singleton(esk1_0) )
& singleton(esk1_0) = set_union2(esk2_0,esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_12,plain,
! [X8,X9] :
( ( subset(X8,singleton(X9))
| X8 != singleton(X9) )
& ( subset(X8,singleton(X9))
| X8 != empty_set )
& ( X8 = singleton(X9)
| X8 = empty_set
| ~ subset(X8,singleton(X9)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])])]) ).
cnf(c_0_13,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
singleton(esk1_0) = set_union2(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ subset(X1,singleton(X2))
| X1 = singleton(X2)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
subset(esk3_0,singleton(esk1_0)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
subset(esk2_0,singleton(esk1_0)),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( esk3_0 != singleton(esk1_0)
| esk2_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( esk3_0 = empty_set
| singleton(esk1_0) = esk3_0 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( esk3_0 != singleton(esk1_0)
| esk2_0 != singleton(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( esk3_0 != empty_set
| esk2_0 != singleton(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,negated_conjecture,
( esk2_0 = empty_set
| singleton(esk1_0) = esk2_0 ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( esk2_0 != empty_set
| esk3_0 = empty_set ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( esk3_0 != esk2_0
| esk3_0 = empty_set ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
fof(c_0_25,plain,
! [X1] : singleton(X1) != empty_set,
inference(fof_simplification,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_0_26,negated_conjecture,
( esk3_0 != empty_set
| esk2_0 = empty_set ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
esk3_0 = empty_set,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_23]),c_0_24]) ).
fof(c_0_28,plain,
! [X16] : set_union2(X16,X16) = X16,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(c_0_29,plain,
! [X7] : singleton(X7) != empty_set,
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_25])]) ).
cnf(c_0_30,negated_conjecture,
( esk2_0 != empty_set
| set_union2(empty_set,esk2_0) = singleton(esk1_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_10]) ).
cnf(c_0_31,negated_conjecture,
esk2_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_32,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_31])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n019.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 05:43:34 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.55 % Version: 3.5.1
% 0.24/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN 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 % new_bool_1 with pid 1804679 completed with status 0
% 0.24/0.55 % Result found by new_bool_1
% 0.24/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN 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 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.55 % Search class: FGHSM-FFSS21-SFFFFFNN
% 0.24/0.55 % partial match(1): FGHSF-FFSS21-SFFFFFNN
% 0.24/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.55 % SubtermCWHack with pid 1804681 completed with status 0
% 0.24/0.55 % Result found by SubtermCWHack
% 0.24/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN 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 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.55 % Search class: FGHSM-FFSS21-SFFFFFNN
% 0.24/0.55 % partial match(1): FGHSF-FFSS21-SFFFFFNN
% 0.24/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.55 % Preprocessing time : 0.002 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
% 0.24/0.55 % Parsed axioms : 12
% 0.24/0.55 % Removed by relevancy pruning/SinE : 0
% 0.24/0.55 % Initial clauses : 17
% 0.24/0.55 % Removed in clause preprocessing : 0
% 0.24/0.55 % Initial clauses in saturation : 17
% 0.24/0.55 % Processed clauses : 45
% 0.24/0.55 % ...of these trivial : 1
% 0.24/0.55 % ...subsumed : 5
% 0.24/0.55 % ...remaining for further processing : 39
% 0.24/0.55 % Other redundant clauses eliminated : 2
% 0.24/0.55 % Clauses deleted for lack of memory : 0
% 0.24/0.55 % Backward-subsumed : 1
% 0.24/0.55 % Backward-rewritten : 21
% 0.24/0.55 % Generated clauses : 54
% 0.24/0.55 % ...of the previous two non-redundant : 34
% 0.24/0.55 % ...aggressively subsumed : 0
% 0.24/0.55 % Contextual simplify-reflections : 2
% 0.24/0.55 % Paramodulations : 52
% 0.24/0.55 % Factorizations : 0
% 0.24/0.55 % NegExts : 0
% 0.24/0.55 % Equation resolutions : 2
% 0.24/0.55 % Disequality decompositions : 0
% 0.24/0.55 % Total rewrite steps : 45
% 0.24/0.55 % ...of those cached : 30
% 0.24/0.55 % Propositional unsat checks : 0
% 0.24/0.55 % Propositional check models : 0
% 0.24/0.55 % Propositional check unsatisfiable : 0
% 0.24/0.55 % Propositional clauses : 0
% 0.24/0.55 % Propositional clauses after purity: 0
% 0.24/0.55 % Propositional unsat core size : 0
% 0.24/0.55 % Propositional preprocessing time : 0.000
% 0.24/0.55 % Propositional encoding time : 0.000
% 0.24/0.55 % Propositional solver time : 0.000
% 0.24/0.55 % Success case prop preproc time : 0.000
% 0.24/0.55 % Success case prop encoding time : 0.000
% 0.24/0.55 % Success case prop solver time : 0.000
% 0.24/0.55 % Current number of processed clauses : 15
% 0.24/0.55 % Positive orientable unit clauses : 9
% 0.24/0.55 % Positive unorientable unit clauses: 1
% 0.24/0.55 % Negative unit clauses : 2
% 0.24/0.55 % Non-unit-clauses : 3
% 0.24/0.55 % Current number of unprocessed clauses: 5
% 0.24/0.55 % ...number of literals in the above : 8
% 0.24/0.55 % Current number of archived formulas : 0
% 0.24/0.55 % Current number of archived clauses : 22
% 0.24/0.55 % Clause-clause subsumption calls (NU) : 41
% 0.24/0.55 % Rec. Clause-clause subsumption calls : 40
% 0.24/0.55 % Non-unit clause-clause subsumptions : 7
% 0.24/0.55 % Unit Clause-clause subsumption calls : 6
% 0.24/0.55 % Rewrite failures with RHS unbound : 0
% 0.24/0.55 % BW rewrite match attempts : 11
% 0.24/0.55 % BW rewrite match successes : 10
% 0.24/0.55 % Condensation attempts : 0
% 0.24/0.55 % Condensation successes : 0
% 0.24/0.55 % Termbank termtop insertions : 1089
% 0.24/0.55 % Search garbage collected termcells : 124
% 0.24/0.55
% 0.24/0.55 % -------------------------------------------------
% 0.24/0.55 % User time : 0.007 s
% 0.24/0.55 % System time : 0.003 s
% 0.24/0.55 % Total time : 0.010 s
% 0.24/0.55 % Maximum resident set size: 3636 pages
% 0.24/0.55
% 0.24/0.55 % -------------------------------------------------
% 0.24/0.55 % User time : 0.011 s
% 0.24/0.55 % System time : 0.007 s
% 0.24/0.55 % Total time : 0.018 s
% 0.24/0.55 % Maximum resident set size: 4608 pages
% 0.24/0.55 % E exiting
%------------------------------------------------------------------------------