%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU144+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 02:23:57 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 15 unt; 0 def)
% Number of atoms : 84 ( 30 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 83 ( 36 ~; 32 |; 7 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 1 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l2_zfmisc_1,conjecture,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_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(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
inference(assume_negation,[status(cth)],[l2_zfmisc_1]) ).
fof(c_0_7,plain,
! [X17,X18,X19,X20,X21,X22] :
( ( X22 = singleton(X21)
| esk1_2(X21,X22) = X21
| in(esk1_2(X21,X22),X22) )
& ( X22 = singleton(X21)
| esk1_2(X21,X22) != X21
| ~ in(esk1_2(X21,X22),X22) )
& ( X18 != singleton(X17)
| in(X20,X18)
| X20 != X17 )
& ( X18 != singleton(X17)
| X19 = X17
| ~ in(X19,X18) ) ),
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_8,lemma,
! [X147] : unordered_pair(X147,X147) = singleton(X147),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_9,lemma,
! [X1] : singleton(X1) != empty_set,
inference(fof_simplification,[status(thm)],[l1_zfmisc_1]) ).
fof(c_0_10,negated_conjecture,
( ( in(esk8_0,esk9_0)
| subset(singleton(esk8_0),esk9_0) )
& ( ~ in(esk8_0,esk9_0)
| ~ subset(singleton(esk8_0),esk9_0) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_11,plain,
( X2 != singleton(X3)
| ~ in(X1,X2)
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_14,lemma,
! [X81] : singleton(X81) != empty_set,
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])]) ).
fof(c_0_15,plain,
! [X46,X47,X48,X49,X50] :
( ( subset(X49,X50)
| ~ in(esk5_2(X49,X50),X50) )
& ( subset(X49,X50)
| in(esk5_2(X49,X50),X49) )
& ( in(X48,X47)
| ~ in(X48,X46)
| ~ subset(X46,X47) ) ),
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)],[d3_tarski])])])])])])]) ).
cnf(c_0_16,negated_conjecture,
( in(esk8_0,esk9_0)
| subset(singleton(esk8_0),esk9_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ in(X1,X2)
| X2 != unordered_pair(X3,X3)
| X1 = X3 ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_18,plain,
! [X24,X25,X26] :
( ( X26 = empty_set
| in(esk2_1(X26),X26) )
& ( ~ in(X25,X24)
| X24 != empty_set ) ),
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)],[c_0_13])])])])])]) ).
cnf(c_0_19,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( subset(unordered_pair(esk8_0,esk8_0),esk9_0)
| in(esk8_0,esk9_0) ),
inference(rw,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_22,plain,
( ~ in(X1,unordered_pair(X2,X2))
| X1 = X2 ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( X1 = empty_set
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,lemma,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_25,negated_conjecture,
( ~ in(esk8_0,esk9_0)
| ~ subset(singleton(esk8_0),esk9_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
( ~ in(X1,unordered_pair(esk8_0,esk8_0))
| in(X1,esk9_0)
| in(esk8_0,esk9_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
esk2_1(unordered_pair(X1,X1)) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( ~ subset(unordered_pair(esk8_0,esk8_0),esk9_0)
| ~ in(esk8_0,esk9_0) ),
inference(rw,[status(thm)],[c_0_25,c_0_12]) ).
cnf(c_0_29,negated_conjecture,
in(esk8_0,esk9_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_27])]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
~ subset(unordered_pair(esk8_0,esk8_0),esk9_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_31,plain,
( subset(X1,X2)
| in(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,plain,
( ~ in(esk5_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_33,negated_conjecture,
in(esk5_2(unordered_pair(esk8_0,esk8_0),esk9_0),unordered_pair(esk8_0,esk8_0)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
~ in(esk5_2(unordered_pair(esk8_0,esk8_0),esk9_0),esk9_0),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
esk5_2(unordered_pair(esk8_0,esk8_0),esk9_0) = esk8_0,
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU144+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:57:07 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.46 % Version: 3.5.1
% 0.11/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % Starting sh5l with 300s (1) cores
% 0.11/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1702332 completed with status 0
% 0.11/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.11/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.46 % No SInE strategy applied
% 0.11/0.46 % Search class: FGHSM-FFMS32-SFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.11/0.46 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.11/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.46 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with pid 1702343 completed with status 0
% 0.11/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I
% 0.11/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.46 % No SInE strategy applied
% 0.11/0.46 % Search class: FGHSM-FFMS32-SFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.11/0.46 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.11/0.46 % Preprocessing time : 0.002 s
% 0.11/0.46 % Presaturation interreduction done
% 0.11/0.46
% 0.11/0.46 % Proof found!
% 0.11/0.46 % SZS status Theorem
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.11/0.47 % Parsed axioms : 65
% 0.11/0.47 % Removed by relevancy pruning/SinE : 0
% 0.11/0.47 % Initial clauses : 104
% 0.11/0.47 % Removed in clause preprocessing : 8
% 0.11/0.47 % Initial clauses in saturation : 96
% 0.11/0.47 % Processed clauses : 282
% 0.11/0.47 % ...of these trivial : 4
% 0.11/0.47 % ...subsumed : 91
% 0.11/0.47 % ...remaining for further processing : 187
% 0.11/0.47 % Other redundant clauses eliminated : 28
% 0.11/0.47 % Clauses deleted for lack of memory : 0
% 0.11/0.47 % Backward-subsumed : 0
% 0.11/0.47 % Backward-rewritten : 9
% 0.11/0.47 % Generated clauses : 309
% 0.11/0.47 % ...of the previous two non-redundant : 226
% 0.11/0.47 % ...aggressively subsumed : 0
% 0.11/0.47 % Contextual simplify-reflections : 0
% 0.11/0.47 % Paramodulations : 284
% 0.11/0.47 % Factorizations : 0
% 0.11/0.47 % NegExts : 0
% 0.11/0.47 % Equation resolutions : 28
% 0.11/0.47 % Disequality decompositions : 0
% 0.11/0.47 % Total rewrite steps : 140
% 0.11/0.47 % ...of those cached : 106
% 0.11/0.47 % Propositional unsat checks : 0
% 0.11/0.47 % Propositional check models : 0
% 0.11/0.47 % Propositional check unsatisfiable : 0
% 0.11/0.47 % Propositional clauses : 0
% 0.11/0.47 % Propositional clauses after purity: 0
% 0.11/0.47 % Propositional unsat core size : 0
% 0.11/0.47 % Propositional preprocessing time : 0.000
% 0.11/0.47 % Propositional encoding time : 0.000
% 0.11/0.47 % Propositional solver time : 0.000
% 0.11/0.47 % Success case prop preproc time : 0.000
% 0.11/0.47 % Success case prop encoding time : 0.000
% 0.11/0.47 % Success case prop solver time : 0.000
% 0.11/0.47 % Current number of processed clauses : 74
% 0.11/0.47 % Positive orientable unit clauses : 23
% 0.11/0.47 % Positive unorientable unit clauses: 3
% 0.11/0.47 % Negative unit clauses : 16
% 0.11/0.47 % Non-unit-clauses : 32
% 0.11/0.47 % Current number of unprocessed clauses: 121
% 0.11/0.47 % ...number of literals in the above : 235
% 0.11/0.47 % Current number of archived formulas : 0
% 0.11/0.47 % Current number of archived clauses : 97
% 0.11/0.47 % Clause-clause subsumption calls (NU) : 1401
% 0.11/0.47 % Rec. Clause-clause subsumption calls : 1119
% 0.11/0.47 % Non-unit clause-clause subsumptions : 27
% 0.11/0.47 % Unit Clause-clause subsumption calls : 155
% 0.11/0.47 % Rewrite failures with RHS unbound : 0
% 0.11/0.47 % BW rewrite match attempts : 58
% 0.11/0.47 % BW rewrite match successes : 40
% 0.11/0.47 % Condensation attempts : 0
% 0.11/0.47 % Condensation successes : 0
% 0.11/0.47 % Termbank termtop insertions : 8232
% 0.11/0.47 % Search garbage collected termcells : 1455
% 0.11/0.47
% 0.11/0.47 % -------------------------------------------------
% 0.11/0.47 % User time : 0.020 s
% 0.11/0.47 % System time : 0.003 s
% 0.11/0.47 % Total time : 0.023 s
% 0.11/0.47 % Maximum resident set size: 3936 pages
% 0.11/0.47
% 0.11/0.47 % -------------------------------------------------
% 0.11/0.47 % User time : 0.097 s
% 0.11/0.47 % System time : 0.016 s
% 0.11/0.47 % Total time : 0.114 s
% 0.11/0.47 % Maximum resident set size: 4608 pages
% 0.11/0.47 % E exiting
%------------------------------------------------------------------------------