%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET637+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 : n020.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 02:14:50 PM UTC 2026
% Result : Theorem 0.26s 0.55s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 111 ( 22 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 114 ( 48 ~; 47 |; 11 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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 : 85 ( 4 sgn 39 !; 1 ?)
% 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(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
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(prove_th119,conjecture,
! [X1,X2] :
( intersect(X1,X2)
<=> not_equal(intersection(X1,X2),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th119) ).
fof(not_equal_defn,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_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_7,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_8,plain,
! [X8] : ~ member(X8,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_9,plain,
! [X22,X23,X24,X25,X26,X27] :
( ( X26 = X27
| member(esk4_2(X26,X27),X27)
| member(esk4_2(X26,X27),X26) )
& ( X26 = X27
| ~ member(esk4_2(X26,X27),X27)
| ~ member(esk4_2(X26,X27),X26) )
& ( X22 != X23
| member(X25,X22)
| ~ member(X25,X23) )
& ( X22 != X23
| member(X24,X23)
| ~ member(X24,X22) ) ),
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_10,plain,
! [X14,X15,X17,X18,X19] :
( ( intersect(X17,X18)
| ~ member(X19,X18)
| ~ member(X19,X17) )
& ( ~ intersect(X14,X15)
| member(esk3_2(X14,X15),X15) )
& ( ~ intersect(X14,X15)
| member(esk3_2(X14,X15),X14) ) ),
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])])])])])])]) ).
fof(c_0_11,plain,
! [X9,X10,X11] :
( ( member(X11,intersection(X9,X10))
| ~ member(X11,X10)
| ~ member(X11,X9) )
& ( ~ member(X11,intersection(X9,X10))
| member(X11,X10) )
& ( ~ member(X11,intersection(X9,X10))
| member(X11,X9) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_12,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( X1 = X2
| member(esk4_2(X1,X2),X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| intersect(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( ~ intersect(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ intersect(X1,X2)
| member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( member(esk4_2(X1,empty_set),X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2] :
( intersect(X1,X2)
<=> not_equal(intersection(X1,X2),empty_set) ),
inference(assume_negation,[status(cth)],[prove_th119]) ).
fof(c_0_20,plain,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
inference(fof_simplification,[status(thm)],[not_equal_defn]) ).
cnf(c_0_21,plain,
( ~ member(esk3_2(X2,X3),X1)
| ~ intersect(X2,X3)
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( ~ intersect(X1,intersection(X2,X3))
| member(esk3_2(X1,intersection(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_23,plain,
! [X12,X13] : intersection(X12,X13) = intersection(X13,X12),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_24,plain,
( ~ member(esk4_2(X1,empty_set),X2)
| intersect(X2,X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
fof(c_0_25,negated_conjecture,
( ( not_equal(intersection(esk1_0,esk2_0),empty_set)
| intersect(esk1_0,esk2_0) )
& ( ~ not_equal(intersection(esk1_0,esk2_0),empty_set)
| ~ intersect(esk1_0,esk2_0) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
fof(c_0_26,plain,
! [X6,X7] :
( ( not_equal(X6,X7)
| X6 = X7 )
& ( X6 != X7
| ~ not_equal(X6,X7) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_27,plain,
( ~ intersect(X2,intersection(X3,X1))
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( intersect(X1,X1)
| X1 = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_13]),c_0_12]) ).
cnf(c_0_30,negated_conjecture,
( ~ not_equal(intersection(esk1_0,esk2_0),empty_set)
| ~ intersect(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( not_equal(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( ~ intersect(X2,intersection(X1,X3))
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( intersect(X2,intersection(X1,X2))
| intersection(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_27,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( ~ intersect(esk1_0,esk2_0)
| intersection(esk1_0,esk2_0) = empty_set ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( intersect(X1,X2)
| intersection(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_37,negated_conjecture,
intersection(esk1_0,esk2_0) = empty_set,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
( X1 != X2
| ~ not_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,negated_conjecture,
( ~ member(X1,esk1_0)
| ~ member(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_12]) ).
cnf(c_0_40,negated_conjecture,
( not_equal(intersection(esk1_0,esk2_0),empty_set)
| intersect(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_41,plain,
~ not_equal(X1,X1),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( ~ member(esk3_2(X1,esk2_0),esk1_0)
| ~ intersect(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_17]) ).
cnf(c_0_43,negated_conjecture,
intersect(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_37]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_15]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET637+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:31:47 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.52 Running first-order theorem proving
% 0.26/0.52 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
% 0.26/0.55 % Version: 3.5.1
% 0.26/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.55 % Starting sh5l with 300s (1) cores
% 0.26/0.55 % new_bool_1 with pid 2101662 completed with status 0
% 0.26/0.55 % Result found by new_bool_1
% 0.26/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.55 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.26/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.55 % SubtermCWHack with pid 2101667 completed with status 0
% 0.26/0.55 % Result found by SubtermCWHack
% 0.26/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.55 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.26/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.55 % Preprocessing time : 0.001 s
% 0.26/0.55
% 0.26/0.55 % Proof found!
% 0.26/0.55 % SZS status Theorem
% 0.26/0.55 % SZS output start CNFRefutation
% See solution above
% 0.26/0.55 % Parsed axioms : 9
% 0.26/0.55 % Removed by relevancy pruning/SinE : 1
% 0.26/0.55 % Initial clauses : 17
% 0.26/0.55 % Removed in clause preprocessing : 2
% 0.26/0.55 % Initial clauses in saturation : 15
% 0.26/0.55 % Processed clauses : 149
% 0.26/0.55 % ...of these trivial : 3
% 0.26/0.55 % ...subsumed : 84
% 0.26/0.55 % ...remaining for further processing : 62
% 0.26/0.55 % Other redundant clauses eliminated : 1
% 0.26/0.55 % Clauses deleted for lack of memory : 0
% 0.26/0.55 % Backward-subsumed : 0
% 0.26/0.55 % Backward-rewritten : 5
% 0.26/0.55 % Generated clauses : 410
% 0.26/0.55 % ...of the previous two non-redundant : 381
% 0.26/0.55 % ...aggressively subsumed : 0
% 0.26/0.55 % Contextual simplify-reflections : 0
% 0.26/0.55 % Paramodulations : 399
% 0.26/0.55 % Factorizations : 10
% 0.26/0.55 % NegExts : 0
% 0.26/0.55 % Equation resolutions : 1
% 0.26/0.55 % Disequality decompositions : 0
% 0.26/0.55 % Total rewrite steps : 42
% 0.26/0.55 % ...of those cached : 34
% 0.26/0.55 % Propositional unsat checks : 0
% 0.26/0.55 % Propositional check models : 0
% 0.26/0.55 % Propositional check unsatisfiable : 0
% 0.26/0.55 % Propositional clauses : 0
% 0.26/0.55 % Propositional clauses after purity: 0
% 0.26/0.55 % Propositional unsat core size : 0
% 0.26/0.55 % Propositional preprocessing time : 0.000
% 0.26/0.55 % Propositional encoding time : 0.000
% 0.26/0.55 % Propositional solver time : 0.000
% 0.26/0.55 % Success case prop preproc time : 0.000
% 0.26/0.55 % Success case prop encoding time : 0.000
% 0.26/0.55 % Success case prop solver time : 0.000
% 0.26/0.55 % Current number of processed clauses : 56
% 0.26/0.55 % Positive orientable unit clauses : 7
% 0.26/0.55 % Positive unorientable unit clauses: 1
% 0.26/0.55 % Negative unit clauses : 4
% 0.26/0.55 % Non-unit-clauses : 44
% 0.26/0.55 % Current number of unprocessed clauses: 245
% 0.26/0.55 % ...number of literals in the above : 698
% 0.26/0.55 % Current number of archived formulas : 0
% 0.26/0.55 % Current number of archived clauses : 5
% 0.26/0.55 % Clause-clause subsumption calls (NU) : 336
% 0.26/0.55 % Rec. Clause-clause subsumption calls : 296
% 0.26/0.55 % Non-unit clause-clause subsumptions : 37
% 0.26/0.55 % Unit Clause-clause subsumption calls : 20
% 0.26/0.55 % Rewrite failures with RHS unbound : 0
% 0.26/0.55 % BW rewrite match attempts : 3
% 0.26/0.55 % BW rewrite match successes : 3
% 0.26/0.55 % Condensation attempts : 0
% 0.26/0.55 % Condensation successes : 0
% 0.26/0.55 % Termbank termtop insertions : 4708
% 0.26/0.55 % Search garbage collected termcells : 304
% 0.26/0.55
% 0.26/0.55 % -------------------------------------------------
% 0.26/0.55 % User time : 0.009 s
% 0.26/0.55 % System time : 0.006 s
% 0.26/0.55 % Total time : 0.015 s
% 0.26/0.55 % Maximum resident set size: 3636 pages
% 0.26/0.55
% 0.26/0.55 % -------------------------------------------------
% 0.26/0.55 % User time : 0.011 s
% 0.26/0.55 % System time : 0.012 s
% 0.26/0.55 % Total time : 0.023 s
% 0.26/0.55 % Maximum resident set size: 4864 pages
% 0.26/0.55 % E exiting
%------------------------------------------------------------------------------