%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET611+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 : n018.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 02:14:43 PM UTC 2026
% Result : Theorem 0.60s 0.55s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 11 unt; 0 def)
% Number of atoms : 97 ( 32 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 93 ( 37 ~; 40 |; 9 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 6 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(member_equal,axiom,
! [X1,X2] :
( ! [X3] :
( member(X3,X1)
<=> member(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_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(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(prove_th84,conjecture,
! [X1,X2] :
( intersection(X1,X2) = empty_set
<=> difference(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th84) ).
fof(c_0_6,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_7,plain,
! [X9] : ~ member(X9,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
fof(c_0_8,plain,
! [X15,X16] :
( ( X15 = X16
| member(esk3_2(X15,X16),X16)
| member(esk3_2(X15,X16),X15) )
& ( X15 = X16
| ~ member(esk3_2(X15,X16),X16)
| ~ member(esk3_2(X15,X16),X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_equal])])])])]) ).
fof(c_0_9,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_10,plain,
! [X10,X11,X12] :
( ( member(X12,intersection(X10,X11))
| ~ member(X12,X11)
| ~ member(X12,X10) )
& ( ~ member(X12,intersection(X10,X11))
| member(X12,X11) )
& ( ~ member(X12,intersection(X10,X11))
| member(X12,X10) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_11,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
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_8]) ).
fof(c_0_13,plain,
! [X6,X7,X8] :
( ( member(X8,difference(X6,X7))
| member(X8,X7)
| ~ member(X8,X6) )
& ( ~ member(X8,difference(X6,X7))
| ~ member(X8,X7) )
& ( ~ member(X8,difference(X6,X7))
| member(X8,X6) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
cnf(c_0_14,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( member(esk3_2(X1,empty_set),X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( member(esk3_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_18,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_19,plain,
! [X13,X14] : intersection(X13,X14) = intersection(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1,X2] :
( intersection(X1,X2) = empty_set
<=> difference(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[prove_th84]) ).
cnf(c_0_21,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( ~ member(esk3_2(intersection(difference(X1,X2),X3),empty_set),X2)
| intersection(difference(X1,X2),X3) = empty_set ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( member(esk3_2(intersection(X1,X2),X3),X2)
| member(esk3_2(intersection(X1,X2),X3),X3)
| intersection(X1,X2) = X3 ),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_24,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,negated_conjecture,
( ( difference(esk1_0,esk2_0) = esk1_0
| intersection(esk1_0,esk2_0) = empty_set )
& ( difference(esk1_0,esk2_0) != esk1_0
| intersection(esk1_0,esk2_0) != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_26,plain,
( member(esk3_2(difference(X1,X2),X3),X1)
| member(esk3_2(difference(X1,X2),X3),X3)
| difference(X1,X2) = X3 ),
inference(spm,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_27,plain,
intersection(X1,difference(X2,X1)) = empty_set,
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_11]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( difference(esk1_0,esk2_0) = esk1_0
| intersection(esk1_0,esk2_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
( ~ member(esk3_2(X1,X2),X2)
| ~ member(esk3_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_30,plain,
( member(esk3_2(difference(X1,X2),X1),X1)
| difference(X1,X2) = X1 ),
inference(ef,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_32,negated_conjecture,
intersection(esk1_0,esk2_0) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24])]) ).
cnf(c_0_33,plain,
( ~ member(esk3_2(difference(X1,X2),X1),difference(X1,X2))
| difference(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(X1,esk1_0)
| ~ member(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_11]) ).
cnf(c_0_36,plain,
( member(esk3_2(difference(X1,X2),X1),X2)
| difference(X1,X2) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( difference(esk1_0,esk2_0) != esk1_0
| intersection(esk1_0,esk2_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,negated_conjecture,
( ~ member(esk3_2(difference(X1,esk2_0),X1),esk1_0)
| difference(X1,esk2_0) = X1 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
difference(esk1_0,esk2_0) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_32])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_30]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET611+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.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 05:30:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.60/0.55 % Version: 3.5.1
% 0.60/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.60/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.60/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.60/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.60/0.55 % Starting sh5l with 300s (1) cores
% 0.60/0.55 % new_bool_3 with pid 1057109 completed with status 0
% 0.60/0.55 % Result found by new_bool_3
% 0.60/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.60/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.60/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.60/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.60/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.60/0.55 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.60/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.60/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.60/0.55 % SubtermCWHack with pid 1057119 completed with status 0
% 0.60/0.55 % Result found by SubtermCWHack
% 0.60/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.60/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.60/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.60/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.60/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.60/0.55 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.60/0.55 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.60/0.55 % Starting SubtermCWHack with 31s (1) cores
% 0.60/0.55 % Preprocessing time : 0.001 s
% 0.60/0.55
% 0.60/0.55 % Proof found!
% 0.60/0.55 % SZS status Theorem
% 0.60/0.55 % SZS output start CNFRefutation
% See solution above
% 0.60/0.55 % Parsed axioms : 11
% 0.60/0.55 % Removed by relevancy pruning/SinE : 4
% 0.60/0.55 % Initial clauses : 16
% 0.60/0.55 % Removed in clause preprocessing : 2
% 0.60/0.55 % Initial clauses in saturation : 14
% 0.60/0.55 % Processed clauses : 1756
% 0.60/0.55 % ...of these trivial : 28
% 0.60/0.55 % ...subsumed : 1427
% 0.60/0.55 % ...remaining for further processing : 301
% 0.60/0.55 % Other redundant clauses eliminated : 0
% 0.60/0.55 % Clauses deleted for lack of memory : 0
% 0.60/0.55 % Backward-subsumed : 0
% 0.60/0.55 % Backward-rewritten : 15
% 0.60/0.55 % Generated clauses : 9250
% 0.60/0.55 % ...of the previous two non-redundant : 7327
% 0.60/0.55 % ...aggressively subsumed : 0
% 0.60/0.55 % Contextual simplify-reflections : 1
% 0.60/0.55 % Paramodulations : 9174
% 0.60/0.55 % Factorizations : 76
% 0.60/0.55 % NegExts : 0
% 0.60/0.55 % Equation resolutions : 0
% 0.60/0.55 % Disequality decompositions : 0
% 0.60/0.55 % Total rewrite steps : 5734
% 0.60/0.55 % ...of those cached : 5549
% 0.60/0.55 % Propositional unsat checks : 0
% 0.60/0.55 % Propositional check models : 0
% 0.60/0.55 % Propositional check unsatisfiable : 0
% 0.60/0.55 % Propositional clauses : 0
% 0.60/0.55 % Propositional clauses after purity: 0
% 0.60/0.55 % Propositional unsat core size : 0
% 0.60/0.55 % Propositional preprocessing time : 0.000
% 0.60/0.55 % Propositional encoding time : 0.000
% 0.60/0.55 % Propositional solver time : 0.000
% 0.60/0.55 % Success case prop preproc time : 0.000
% 0.60/0.55 % Success case prop encoding time : 0.000
% 0.60/0.55 % Success case prop solver time : 0.000
% 0.60/0.55 % Current number of processed clauses : 286
% 0.60/0.55 % Positive orientable unit clauses : 30
% 0.60/0.55 % Positive unorientable unit clauses: 1
% 0.60/0.55 % Negative unit clauses : 2
% 0.60/0.55 % Non-unit-clauses : 253
% 0.60/0.55 % Current number of unprocessed clauses: 5540
% 0.60/0.55 % ...number of literals in the above : 14888
% 0.60/0.55 % Current number of archived formulas : 0
% 0.60/0.55 % Current number of archived clauses : 15
% 0.60/0.55 % Clause-clause subsumption calls (NU) : 19204
% 0.60/0.55 % Rec. Clause-clause subsumption calls : 11175
% 0.60/0.55 % Non-unit clause-clause subsumptions : 1041
% 0.60/0.55 % Unit Clause-clause subsumption calls : 1240
% 0.60/0.55 % Rewrite failures with RHS unbound : 0
% 0.60/0.55 % BW rewrite match attempts : 20
% 0.60/0.55 % BW rewrite match successes : 1
% 0.60/0.55 % Condensation attempts : 0
% 0.60/0.55 % Condensation successes : 0
% 0.60/0.55 % Termbank termtop insertions : 121178
% 0.60/0.55 % Search garbage collected termcells : 297
% 0.60/0.55
% 0.60/0.55 % -------------------------------------------------
% 0.60/0.55 % User time : 0.107 s
% 0.60/0.55 % System time : 0.011 s
% 0.60/0.55 % Total time : 0.118 s
% 0.60/0.55 % Maximum resident set size: 3636 pages
% 0.60/0.55
% 0.60/0.55 % -------------------------------------------------
% 0.60/0.55 % User time : 0.109 s
% 0.60/0.55 % System time : 0.015 s
% 0.60/0.55 % Total time : 0.124 s
% 0.60/0.55 % Maximum resident set size: 4608 pages
% 0.60/0.55 % E exiting
%------------------------------------------------------------------------------