%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU162+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 : n015.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 02:24:04 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 22 unt; 0 def)
% Number of atoms : 78 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 27 ~; 19 |; 3 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 2 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l28_zfmisc_1,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(t65_zfmisc_1,conjecture,
! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(l1_zfmisc_1,lemma,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
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(c_0_11,lemma,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[l28_zfmisc_1]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(assume_negation,[status(cth)],[t65_zfmisc_1]) ).
fof(c_0_13,plain,
! [X140,X141] :
( disjoint(X141,X140)
| ~ disjoint(X140,X141) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])]) ).
fof(c_0_14,lemma,
! [X138,X139] :
( disjoint(singleton(X138),X139)
| in(X138,X139) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,singleton(X2)) = X1
<=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_16,lemma,
! [X151,X152] :
( ( disjoint(X151,X152)
| set_difference(X151,X152) != X151 )
& ( set_difference(X151,X152) = X151
| ~ disjoint(X151,X152) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])])]) ).
cnf(c_0_17,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,lemma,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,negated_conjecture,
( ( ~ in(esk2_0,esk1_0)
| set_difference(esk1_0,singleton(esk2_0)) = esk1_0 )
& ( in(esk2_0,esk1_0)
| set_difference(esk1_0,singleton(esk2_0)) != esk1_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_20,lemma,
( ~ disjoint(X1,X2)
| set_difference(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,lemma,
( in(X2,X1)
| disjoint(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( set_difference(esk1_0,singleton(esk2_0)) != esk1_0
| in(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,lemma,
( in(X2,X1)
| set_difference(X1,singleton(X2)) = X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_24,lemma,
! [X59,X60] : set_difference(X59,set_difference(X59,X60)) = set_intersection2(X59,X60),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_25,plain,
! [X54] : set_difference(X54,empty_set) = X54,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(c_0_26,plain,
! [X84] : set_intersection2(X84,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(c_0_27,plain,
! [X106,X107] : set_intersection2(X106,X107) = set_intersection2(X107,X106),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_28,lemma,
! [X128,X129] :
( set_intersection2(X128,X129) = X128
| ~ subset(X128,X129) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])])]) ).
cnf(c_0_29,negated_conjecture,
( ~ in(esk2_0,esk1_0)
| set_difference(esk1_0,singleton(esk2_0)) = esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,negated_conjecture,
in(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_34,lemma,
! [X1] : singleton(X1) != empty_set,
inference(fof_simplification,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_0_35,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,lemma,
( ~ subset(X1,X2)
| set_intersection2(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,negated_conjecture,
set_difference(esk1_0,singleton(esk2_0)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_38,lemma,
set_difference(X1,X1) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
fof(c_0_39,lemma,
! [X62] : singleton(X62) != empty_set,
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
cnf(c_0_40,lemma,
( ~ subset(X2,X1)
| set_intersection2(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,lemma,
set_intersection2(esk1_0,singleton(esk2_0)) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_37]),c_0_38]) ).
cnf(c_0_42,lemma,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_43,lemma,
! [X24,X25] :
( ( subset(singleton(X24),X25)
| ~ in(X24,X25) )
& ( in(X24,X25)
| ~ subset(singleton(X24),X25) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])])]) ).
cnf(c_0_44,lemma,
~ subset(singleton(esk2_0),esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_45,lemma,
( ~ in(X1,X2)
| subset(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_46,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:57:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % new_bool_3 with pid 709053 completed with status 0
% 0.14/0.44 % Result found by new_bool_3
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FGHSM-FFMF32-SFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.44 % SubtermCWHack with pid 709056 completed with status 0
% 0.14/0.44 % Result found by SubtermCWHack
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FGHSM-FFMF32-SFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 92
% 0.14/0.44 % Removed by relevancy pruning/SinE : 38
% 0.14/0.44 % Initial clauses : 92
% 0.14/0.44 % Removed in clause preprocessing : 0
% 0.14/0.44 % Initial clauses in saturation : 92
% 0.14/0.44 % Processed clauses : 634
% 0.14/0.44 % ...of these trivial : 20
% 0.14/0.44 % ...subsumed : 397
% 0.14/0.44 % ...remaining for further processing : 217
% 0.14/0.44 % Other redundant clauses eliminated : 40
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 1
% 0.14/0.44 % Backward-rewritten : 5
% 0.14/0.44 % Generated clauses : 2025
% 0.14/0.44 % ...of the previous two non-redundant : 1442
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 0
% 0.14/0.44 % Paramodulations : 1972
% 0.14/0.44 % Factorizations : 14
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 40
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 695
% 0.14/0.44 % ...of those cached : 587
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 187
% 0.14/0.44 % Positive orientable unit clauses : 42
% 0.14/0.44 % Positive unorientable unit clauses: 2
% 0.14/0.44 % Negative unit clauses : 25
% 0.14/0.44 % Non-unit-clauses : 118
% 0.14/0.44 % Current number of unprocessed clauses: 900
% 0.14/0.44 % ...number of literals in the above : 2136
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 6
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 4790
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 4239
% 0.14/0.44 % Non-unit clause-clause subsumptions : 188
% 0.14/0.44 % Unit Clause-clause subsumption calls : 55
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 31
% 0.14/0.44 % BW rewrite match successes : 16
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 19442
% 0.14/0.44 % Search garbage collected termcells : 1478
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.022 s
% 0.14/0.44 % System time : 0.001 s
% 0.14/0.44 % Total time : 0.023 s
% 0.14/0.44 % Maximum resident set size: 3964 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.025 s
% 0.14/0.44 % System time : 0.004 s
% 0.14/0.44 % Total time : 0.029 s
% 0.14/0.44 % Maximum resident set size: 4608 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------