%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU146+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 : n026.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 02:28:14 PM UTC 2026
% Result : Theorem 0.17s 0.54s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 11 unt; 0 def)
% Number of atoms : 135 ( 66 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 136 ( 48 ~; 66 |; 13 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 70 ( 2 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l4_zfmisc_1,conjecture,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = singleton(X2)
| X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_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(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X2,X3)
& subset(X1,X2) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = singleton(X2)
| X1 = empty_set ) ),
inference(assume_negation,[status(cth)],[l4_zfmisc_1]) ).
fof(c_0_10,negated_conjecture,
( ( esk8_0 = singleton(esk9_0)
| esk8_0 = empty_set
| subset(esk8_0,singleton(esk9_0)) )
& ( ~ subset(esk8_0,singleton(esk9_0))
| esk8_0 != singleton(esk9_0) )
& ( ~ subset(esk8_0,singleton(esk9_0))
| esk8_0 != empty_set ) ),
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_9])])])])]) ).
fof(c_0_11,lemma,
! [X152] : unordered_pair(X152,X152) = singleton(X152),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_12,lemma,
! [X82,X83] :
( ( subset(singleton(X82),X83)
| ~ in(X82,X83) )
& ( in(X82,X83)
| ~ subset(singleton(X82),X83) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])])]) ).
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,
! [X104,X105,X106] :
( subset(X104,X106)
| ~ subset(X105,X106)
| ~ subset(X104,X105) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])]) ).
cnf(c_0_15,negated_conjecture,
( esk8_0 = singleton(esk9_0)
| esk8_0 = empty_set
| subset(esk8_0,singleton(esk9_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,lemma,
( ~ in(X1,X2)
| subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[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,
( ~ subset(X2,X3)
| ~ subset(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( subset(esk8_0,unordered_pair(esk9_0,esk9_0))
| esk8_0 = unordered_pair(esk9_0,esk9_0)
| esk8_0 = empty_set ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_21,lemma,
( ~ in(X1,X2)
| subset(unordered_pair(X1,X1),X2) ),
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_22,plain,
( X1 = empty_set
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X28,X29,X30,X31,X32,X33,X34,X35] :
( ( X35 = unordered_pair(X33,X34)
| esk3_3(X33,X34,X35) = X34
| esk3_3(X33,X34,X35) = X33
| in(esk3_3(X33,X34,X35),X35) )
& ( X35 = unordered_pair(X33,X34)
| ~ in(esk3_3(X33,X34,X35),X35)
| esk3_3(X33,X34,X35) != X34 )
& ( X35 = unordered_pair(X33,X34)
| ~ in(esk3_3(X33,X34,X35),X35)
| esk3_3(X33,X34,X35) != X33 )
& ( X30 != unordered_pair(X28,X29)
| in(X32,X30)
| X32 != X29 )
& ( X30 != unordered_pair(X28,X29)
| in(X32,X30)
| X32 != X28 )
& ( X30 != unordered_pair(X28,X29)
| X31 = X29
| X31 = X28
| ~ in(X31,X30) ) ),
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)],[d2_tarski])])])])])])]) ).
cnf(c_0_24,lemma,
( ~ subset(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
( ~ subset(X1,esk8_0)
| subset(X1,unordered_pair(esk9_0,esk9_0))
| esk8_0 = empty_set
| unordered_pair(esk9_0,esk9_0) = esk8_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,lemma,
( subset(unordered_pair(esk2_1(X1),esk2_1(X1)),X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( X2 != unordered_pair(X3,X4)
| ~ in(X1,X2)
| X1 = X4
| X1 = X3 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,lemma,
( ~ subset(unordered_pair(X1,X1),X2)
| in(X1,X2) ),
inference(rw,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_29,negated_conjecture,
( subset(unordered_pair(esk2_1(esk8_0),esk2_1(esk8_0)),unordered_pair(esk9_0,esk9_0))
| esk8_0 = empty_set
| unordered_pair(esk9_0,esk9_0) = esk8_0 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_30,plain,
! [X15,X16] :
( ( X15 = X16
| ~ subset(X16,X15)
| ~ subset(X15,X16) )
& ( X15 != X16
| subset(X16,X15) )
& ( X15 != X16
| subset(X15,X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])]) ).
cnf(c_0_31,plain,
( ~ in(X1,unordered_pair(X3,X2))
| X1 = X3
| X1 = X2 ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,lemma,
( in(esk2_1(esk8_0),unordered_pair(esk9_0,esk9_0))
| esk8_0 = empty_set
| unordered_pair(esk9_0,esk9_0) = esk8_0 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( ~ subset(esk8_0,singleton(esk9_0))
| esk8_0 != singleton(esk9_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,lemma,
( esk8_0 = empty_set
| esk2_1(esk8_0) = esk9_0
| unordered_pair(esk9_0,esk9_0) = esk8_0 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( ~ subset(unordered_pair(esk9_0,esk9_0),esk8_0)
| esk8_0 = empty_set
| unordered_pair(esk9_0,esk9_0) = esk8_0 ),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
fof(c_0_37,plain,
! [X93] : subset(X93,X93),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_38,negated_conjecture,
( ~ subset(esk8_0,singleton(esk9_0))
| esk8_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_39,negated_conjecture,
( ~ subset(esk8_0,unordered_pair(esk9_0,esk9_0))
| esk8_0 != unordered_pair(esk9_0,esk9_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_16]),c_0_16]) ).
cnf(c_0_40,lemma,
( esk8_0 = empty_set
| unordered_pair(esk9_0,esk9_0) = esk8_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_35]),c_0_36]) ).
cnf(c_0_41,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_42,lemma,
! [X116] : subset(empty_set,X116),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_43,negated_conjecture,
( ~ subset(esk8_0,unordered_pair(esk9_0,esk9_0))
| esk8_0 != empty_set ),
inference(rw,[status(thm)],[c_0_38,c_0_16]) ).
cnf(c_0_44,negated_conjecture,
esk8_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_45,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 05:55:38 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.17/0.54 % Version: 3.5.1
% 0.17/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.54 % Starting sh5l with 300s (1) cores
% 0.17/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1506755 completed with status 0
% 0.17/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.17/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.54 % No SInE strategy applied
% 0.17/0.54 % Search class: FGHSM-FFMS32-SFFFFFNN
% 0.17/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.17/0.54 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.17/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.17/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.17/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1506764 completed with status 0
% 0.17/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.17/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.54 % No SInE strategy applied
% 0.17/0.54 % Search class: FGHSM-FFMS32-SFFFFFNN
% 0.17/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.17/0.54 % Preprocessing time : 0.003 s
% 0.17/0.54 % Presaturation interreduction done
% 0.17/0.54
% 0.17/0.54 % Proof found!
% 0.17/0.54 % SZS status Theorem
% 0.17/0.54 % SZS output start CNFRefutation
% See solution above
% 0.17/0.54 % Parsed axioms : 67
% 0.17/0.54 % Removed by relevancy pruning/SinE : 0
% 0.17/0.54 % Initial clauses : 108
% 0.17/0.54 % Removed in clause preprocessing : 8
% 0.17/0.54 % Initial clauses in saturation : 100
% 0.17/0.54 % Processed clauses : 993
% 0.17/0.54 % ...of these trivial : 29
% 0.17/0.54 % ...subsumed : 644
% 0.17/0.54 % ...remaining for further processing : 320
% 0.17/0.54 % Other redundant clauses eliminated : 77
% 0.17/0.54 % Clauses deleted for lack of memory : 0
% 0.17/0.54 % Backward-subsumed : 30
% 0.17/0.54 % Backward-rewritten : 8
% 0.17/0.54 % Generated clauses : 3058
% 0.17/0.54 % ...of the previous two non-redundant : 2636
% 0.17/0.54 % ...aggressively subsumed : 0
% 0.17/0.54 % Contextual simplify-reflections : 2
% 0.17/0.54 % Paramodulations : 2970
% 0.17/0.54 % Factorizations : 14
% 0.17/0.54 % NegExts : 0
% 0.17/0.54 % Equation resolutions : 77
% 0.17/0.54 % Disequality decompositions : 0
% 0.17/0.54 % Total rewrite steps : 903
% 0.17/0.54 % ...of those cached : 771
% 0.17/0.54 % Propositional unsat checks : 0
% 0.17/0.54 % Propositional check models : 0
% 0.17/0.54 % Propositional check unsatisfiable : 0
% 0.17/0.54 % Propositional clauses : 0
% 0.17/0.54 % Propositional clauses after purity: 0
% 0.17/0.54 % Propositional unsat core size : 0
% 0.17/0.54 % Propositional preprocessing time : 0.000
% 0.17/0.54 % Propositional encoding time : 0.000
% 0.17/0.54 % Propositional solver time : 0.000
% 0.17/0.54 % Success case prop preproc time : 0.000
% 0.17/0.54 % Success case prop encoding time : 0.000
% 0.17/0.54 % Success case prop solver time : 0.000
% 0.17/0.54 % Current number of processed clauses : 174
% 0.17/0.54 % Positive orientable unit clauses : 38
% 0.17/0.54 % Positive unorientable unit clauses: 3
% 0.17/0.54 % Negative unit clauses : 20
% 0.17/0.54 % Non-unit-clauses : 113
% 0.17/0.54 % Current number of unprocessed clauses: 1816
% 0.17/0.54 % ...number of literals in the above : 5779
% 0.17/0.54 % Current number of archived formulas : 0
% 0.17/0.54 % Current number of archived clauses : 130
% 0.17/0.54 % Clause-clause subsumption calls (NU) : 5009
% 0.17/0.54 % Rec. Clause-clause subsumption calls : 3762
% 0.17/0.54 % Non-unit clause-clause subsumptions : 383
% 0.17/0.54 % Unit Clause-clause subsumption calls : 902
% 0.17/0.54 % Rewrite failures with RHS unbound : 0
% 0.17/0.54 % BW rewrite match attempts : 73
% 0.17/0.54 % BW rewrite match successes : 41
% 0.17/0.54 % Condensation attempts : 0
% 0.17/0.54 % Condensation successes : 0
% 0.17/0.54 % Termbank termtop insertions : 33626
% 0.17/0.54 % Search garbage collected termcells : 1501
% 0.17/0.54
% 0.17/0.54 % -------------------------------------------------
% 0.17/0.54 % User time : 0.082 s
% 0.17/0.54 % System time : 0.008 s
% 0.17/0.54 % Total time : 0.090 s
% 0.17/0.54 % Maximum resident set size: 3684 pages
% 0.17/0.54
% 0.17/0.54 % -------------------------------------------------
% 0.17/0.54 % User time : 0.300 s
% 0.17/0.54 % System time : 0.034 s
% 0.17/0.54 % Total time : 0.334 s
% 0.17/0.54 % Maximum resident set size: 4608 pages
% 0.17/0.54 % E exiting
%------------------------------------------------------------------------------