%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET146+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 02:13:44 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 48 ( 17 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 45 ( 19 ~; 17 |; 6 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(prove_th61,conjecture,
! [X1] : intersection(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th61) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_5,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_6,plain,
! [X5] : ~ member(X5,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
fof(c_0_7,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( X15 = X16
| member(esk2_2(X15,X16),X16)
| member(esk2_2(X15,X16),X15) )
& ( X15 = X16
| ~ member(esk2_2(X15,X16),X16)
| ~ member(esk2_2(X15,X16),X15) )
& ( X11 != X12
| member(X14,X11)
| ~ member(X14,X12) )
& ( X11 != X12
| member(X13,X12)
| ~ member(X13,X11) ) ),
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] : intersection(X1,empty_set) = empty_set,
inference(assume_negation,[status(cth)],[prove_th61]) ).
fof(c_0_9,plain,
! [X6,X7,X8] :
( ( member(X8,intersection(X6,X7))
| ~ member(X8,X7)
| ~ member(X8,X6) )
& ( ~ member(X8,intersection(X6,X7))
| member(X8,X7) )
& ( ~ member(X8,intersection(X6,X7))
| member(X8,X6) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_10,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( X1 = X2
| member(esk2_2(X1,X2),X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,negated_conjecture,
intersection(esk1_0,empty_set) != empty_set,
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_13,plain,
! [X9,X10] : intersection(X9,X10) = intersection(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_14,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(esk2_2(X1,empty_set),X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
intersection(esk1_0,empty_set) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( member(esk2_2(intersection(X1,X2),empty_set),X1)
| intersection(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
intersection(empty_set,esk1_0) != empty_set,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
intersection(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET146+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n006.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 04:56:27 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.13/0.45 % Version: 3.5.1
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.45 % Starting sh5l with 300s (1) cores
% 0.13/0.45 % new_bool_3 with pid 2047924 completed with status 0
% 0.13/0.45 % Result found by new_bool_3
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.45 % Search class: FGUSF-FFSF22-SFFFFFNN
% 0.13/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.45 % SubtermCWHack with pid 2047927 completed with status 0
% 0.13/0.45 % Result found by SubtermCWHack
% 0.13/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.45 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.45 % Search class: FGUSF-FFSF22-SFFFFFNN
% 0.13/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.45 % Preprocessing time : 0.001 s
% 0.13/0.45
% 0.13/0.45 % Proof found!
% 0.13/0.45 % SZS status Theorem
% 0.13/0.45 % SZS output start CNFRefutation
% See solution above
% 0.13/0.45 % Parsed axioms : 9
% 0.13/0.45 % Removed by relevancy pruning/SinE : 4
% 0.13/0.45 % Initial clauses : 10
% 0.13/0.45 % Removed in clause preprocessing : 2
% 0.13/0.45 % Initial clauses in saturation : 8
% 0.13/0.45 % Processed clauses : 18
% 0.13/0.45 % ...of these trivial : 0
% 0.13/0.45 % ...subsumed : 6
% 0.13/0.45 % ...remaining for further processing : 12
% 0.13/0.45 % Other redundant clauses eliminated : 0
% 0.13/0.45 % Clauses deleted for lack of memory : 0
% 0.13/0.45 % Backward-subsumed : 0
% 0.13/0.45 % Backward-rewritten : 2
% 0.13/0.45 % Generated clauses : 30
% 0.13/0.45 % ...of the previous two non-redundant : 22
% 0.13/0.45 % ...aggressively subsumed : 0
% 0.13/0.45 % Contextual simplify-reflections : 0
% 0.13/0.45 % Paramodulations : 28
% 0.13/0.45 % Factorizations : 2
% 0.13/0.45 % NegExts : 0
% 0.13/0.45 % Equation resolutions : 0
% 0.13/0.45 % Disequality decompositions : 0
% 0.13/0.45 % Total rewrite steps : 2
% 0.13/0.45 % ...of those cached : 0
% 0.13/0.45 % Propositional unsat checks : 0
% 0.13/0.45 % Propositional check models : 0
% 0.13/0.45 % Propositional check unsatisfiable : 0
% 0.13/0.45 % Propositional clauses : 0
% 0.13/0.45 % Propositional clauses after purity: 0
% 0.13/0.45 % Propositional unsat core size : 0
% 0.13/0.45 % Propositional preprocessing time : 0.000
% 0.13/0.45 % Propositional encoding time : 0.000
% 0.13/0.45 % Propositional solver time : 0.000
% 0.13/0.45 % Success case prop preproc time : 0.000
% 0.13/0.45 % Success case prop encoding time : 0.000
% 0.13/0.45 % Success case prop solver time : 0.000
% 0.13/0.45 % Current number of processed clauses : 10
% 0.13/0.45 % Positive orientable unit clauses : 1
% 0.13/0.45 % Positive unorientable unit clauses: 1
% 0.13/0.45 % Negative unit clauses : 1
% 0.13/0.45 % Non-unit-clauses : 7
% 0.13/0.45 % Current number of unprocessed clauses: 12
% 0.13/0.45 % ...number of literals in the above : 29
% 0.13/0.45 % Current number of archived formulas : 0
% 0.13/0.45 % Current number of archived clauses : 2
% 0.13/0.45 % Clause-clause subsumption calls (NU) : 16
% 0.13/0.45 % Rec. Clause-clause subsumption calls : 14
% 0.13/0.45 % Non-unit clause-clause subsumptions : 6
% 0.13/0.45 % Unit Clause-clause subsumption calls : 2
% 0.13/0.45 % Rewrite failures with RHS unbound : 0
% 0.13/0.45 % BW rewrite match attempts : 3
% 0.13/0.45 % BW rewrite match successes : 3
% 0.13/0.45 % Condensation attempts : 0
% 0.13/0.45 % Condensation successes : 0
% 0.13/0.45 % Termbank termtop insertions : 855
% 0.13/0.45 % Search garbage collected termcells : 185
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.004 s
% 0.13/0.45 % System time : 0.003 s
% 0.13/0.45 % Total time : 0.006 s
% 0.13/0.45 % Maximum resident set size: 3636 pages
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.006 s
% 0.13/0.45 % System time : 0.006 s
% 0.13/0.45 % Total time : 0.012 s
% 0.13/0.45 % Maximum resident set size: 4608 pages
% 0.13/0.45 % E exiting
%------------------------------------------------------------------------------