%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:14:48 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 75 ( 17 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 78 ( 33 ~; 30 |; 8 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 3 sgn 27 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(prove_th110,conjecture,
! [X1] :
( intersect(X1,X1)
<=> not_equal(X1,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th110) ).
fof(not_equal_defn,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(c_0_5,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_6,plain,
! [X7] : ~ member(X7,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
fof(c_0_7,plain,
! [X16,X17,X18,X19,X20,X21] :
( ( X20 = X21
| member(esk3_2(X20,X21),X21)
| member(esk3_2(X20,X21),X20) )
& ( X20 = X21
| ~ member(esk3_2(X20,X21),X21)
| ~ member(esk3_2(X20,X21),X20) )
& ( X16 != X17
| member(X19,X16)
| ~ member(X19,X17) )
& ( X16 != X17
| member(X18,X17)
| ~ member(X18,X16) ) ),
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)],[equal_member_defn])])])])])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( intersect(X1,X1)
<=> not_equal(X1,empty_set) ),
inference(assume_negation,[status(cth)],[prove_th110]) ).
fof(c_0_9,plain,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
inference(fof_simplification,[status(thm)],[not_equal_defn]) ).
fof(c_0_10,plain,
! [X8,X9,X11,X12,X13] :
( ( intersect(X11,X12)
| ~ member(X13,X12)
| ~ member(X13,X11) )
& ( ~ intersect(X8,X9)
| member(esk2_2(X8,X9),X9) )
& ( ~ intersect(X8,X9)
| member(esk2_2(X8,X9),X8) ) ),
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)],[intersect_defn])])])])])])]) ).
cnf(c_0_11,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,negated_conjecture,
( ( not_equal(esk1_0,empty_set)
| intersect(esk1_0,esk1_0) )
& ( ~ not_equal(esk1_0,empty_set)
| ~ intersect(esk1_0,esk1_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_14,plain,
! [X5,X6] :
( ( not_equal(X5,X6)
| X5 = X6 )
& ( X5 != X6
| ~ not_equal(X5,X6) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| intersect(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(esk3_2(X1,empty_set),X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ not_equal(esk1_0,empty_set)
| ~ intersect(esk1_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( not_equal(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( ~ member(esk3_2(X1,empty_set),X2)
| intersect(X2,X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( ~ intersect(X1,X2)
| member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
( ~ intersect(esk1_0,esk1_0)
| empty_set = esk1_0 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( intersect(X1,X1)
| X1 = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_11]) ).
cnf(c_0_23,plain,
( X1 != X2
| ~ not_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
~ intersect(X1,empty_set),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
empty_set = esk1_0,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( not_equal(esk1_0,empty_set)
| intersect(esk1_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,plain,
~ not_equal(X1,X1),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
~ intersect(X1,esk1_0),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_25]),c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.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 05:30:36 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 0.11/0.45 % Version: 3.5.1
% 0.11/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.45 % Starting sh5l with 300s (1) cores
% 0.11/0.45 % new_bool_3 with pid 1776427 completed with status 0
% 0.11/0.45 % Result found by new_bool_3
% 0.11/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % SubtermCWHack with pid 1776433 completed with status 0
% 0.11/0.45 % Result found by SubtermCWHack
% 0.11/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.45 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.11/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.45 % Preprocessing time : 0.001 s
% 0.11/0.45
% 0.11/0.45 % Proof found!
% 0.11/0.45 % SZS status Theorem
% 0.11/0.45 % SZS output start CNFRefutation
% See solution above
% 0.11/0.45 % Parsed axioms : 7
% 0.11/0.45 % Removed by relevancy pruning/SinE : 1
% 0.11/0.45 % Initial clauses : 13
% 0.11/0.45 % Removed in clause preprocessing : 2
% 0.11/0.45 % Initial clauses in saturation : 11
% 0.11/0.45 % Processed clauses : 29
% 0.11/0.45 % ...of these trivial : 0
% 0.11/0.45 % ...subsumed : 2
% 0.11/0.45 % ...remaining for further processing : 26
% 0.11/0.45 % Other redundant clauses eliminated : 1
% 0.11/0.45 % Clauses deleted for lack of memory : 0
% 0.11/0.45 % Backward-subsumed : 0
% 0.11/0.45 % Backward-rewritten : 10
% 0.11/0.45 % Generated clauses : 28
% 0.11/0.45 % ...of the previous two non-redundant : 32
% 0.11/0.45 % ...aggressively subsumed : 0
% 0.11/0.45 % Contextual simplify-reflections : 0
% 0.11/0.45 % Paramodulations : 25
% 0.11/0.45 % Factorizations : 2
% 0.11/0.45 % NegExts : 0
% 0.11/0.45 % Equation resolutions : 1
% 0.11/0.45 % Disequality decompositions : 0
% 0.11/0.45 % Total rewrite steps : 13
% 0.11/0.45 % ...of those cached : 12
% 0.11/0.45 % Propositional unsat checks : 0
% 0.11/0.45 % Propositional check models : 0
% 0.11/0.45 % Propositional check unsatisfiable : 0
% 0.11/0.45 % Propositional clauses : 0
% 0.11/0.45 % Propositional clauses after purity: 0
% 0.11/0.45 % Propositional unsat core size : 0
% 0.11/0.45 % Propositional preprocessing time : 0.000
% 0.11/0.45 % Propositional encoding time : 0.000
% 0.11/0.45 % Propositional solver time : 0.000
% 0.11/0.45 % Success case prop preproc time : 0.000
% 0.11/0.45 % Success case prop encoding time : 0.000
% 0.11/0.45 % Success case prop solver time : 0.000
% 0.11/0.45 % Current number of processed clauses : 15
% 0.11/0.45 % Positive orientable unit clauses : 1
% 0.11/0.45 % Positive unorientable unit clauses: 0
% 0.11/0.45 % Negative unit clauses : 3
% 0.11/0.45 % Non-unit-clauses : 11
% 0.11/0.45 % Current number of unprocessed clauses: 14
% 0.11/0.45 % ...number of literals in the above : 33
% 0.11/0.45 % Current number of archived formulas : 0
% 0.11/0.45 % Current number of archived clauses : 10
% 0.11/0.45 % Clause-clause subsumption calls (NU) : 32
% 0.11/0.45 % Rec. Clause-clause subsumption calls : 30
% 0.11/0.45 % Non-unit clause-clause subsumptions : 1
% 0.11/0.45 % Unit Clause-clause subsumption calls : 4
% 0.11/0.45 % Rewrite failures with RHS unbound : 0
% 0.11/0.45 % BW rewrite match attempts : 1
% 0.11/0.45 % BW rewrite match successes : 1
% 0.11/0.45 % Condensation attempts : 0
% 0.11/0.45 % Condensation successes : 0
% 0.11/0.45 % Termbank termtop insertions : 1115
% 0.11/0.45 % Search garbage collected termcells : 263
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.004 s
% 0.11/0.45 % System time : 0.002 s
% 0.11/0.45 % Total time : 0.007 s
% 0.11/0.45 % Maximum resident set size: 3632 pages
% 0.11/0.45
% 0.11/0.45 % -------------------------------------------------
% 0.11/0.45 % User time : 0.005 s
% 0.11/0.45 % System time : 0.007 s
% 0.11/0.45 % Total time : 0.013 s
% 0.11/0.45 % Maximum resident set size: 4608 pages
% 0.11/0.45 % E exiting
%------------------------------------------------------------------------------