%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET636+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 : n014.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 0.16s 0.64s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 123 ( 22 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 127 ( 53 ~; 54 |; 11 &)
% ( 8 <=>; 1 =>; 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 : 92 ( 5 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(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(prove_th118,conjecture,
! [X1,X2] :
( disjoint(X1,X2)
<=> intersection(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th118) ).
fof(symmetry_of_intersect,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(c_0_7,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_8,plain,
! [X6] : ~ member(X6,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_9,plain,
! [X14,X15,X16,X17,X18,X19] :
( ( X18 = X19
| member(esk3_2(X18,X19),X19)
| member(esk3_2(X18,X19),X18) )
& ( X18 = X19
| ~ member(esk3_2(X18,X19),X19)
| ~ member(esk3_2(X18,X19),X18) )
& ( X14 != X15
| member(X17,X14)
| ~ member(X17,X15) )
& ( X14 != X15
| member(X16,X15)
| ~ member(X16,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)],[equal_member_defn])])])])])])]) ).
fof(c_0_10,plain,
! [X21,X22,X24,X25,X26] :
( ( intersect(X24,X25)
| ~ member(X26,X25)
| ~ member(X26,X24) )
& ( ~ intersect(X21,X22)
| member(esk4_2(X21,X22),X22) )
& ( ~ intersect(X21,X22)
| member(esk4_2(X21,X22),X21) ) ),
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,
! [X7,X8,X9] :
( ( member(X9,intersection(X7,X8))
| ~ member(X9,X8)
| ~ member(X9,X7) )
& ( ~ member(X9,intersection(X7,X8))
| member(X9,X8) )
& ( ~ member(X9,intersection(X7,X8))
| member(X9,X7) ) ),
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(esk3_2(X1,X2),X2)
| member(esk3_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(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( member(esk3_2(X1,empty_set),X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( ~ intersect(X1,X2)
| member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( ~ member(esk4_2(X2,X3),X1)
| ~ intersect(X2,X3)
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( ~ intersect(intersection(X1,X2),X3)
| member(esk4_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_22,plain,
( ~ member(esk3_2(X1,empty_set),X2)
| intersect(X2,X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
fof(c_0_23,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint_defn]) ).
fof(c_0_24,negated_conjecture,
~ ! [X1,X2] :
( disjoint(X1,X2)
<=> intersection(X1,X2) = empty_set ),
inference(assume_negation,[status(cth)],[prove_th118]) ).
cnf(c_0_25,plain,
( ~ intersect(X1,intersection(X2,X3))
| member(esk4_2(X1,intersection(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
( ~ intersect(intersection(X1,X2),X3)
| intersect(X1,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( intersect(X1,X1)
| X1 = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13]),c_0_12]) ).
fof(c_0_28,plain,
! [X12,X13] :
( ( disjoint(X12,X13)
| intersect(X12,X13) )
& ( ~ intersect(X12,X13)
| ~ disjoint(X12,X13) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_29,negated_conjecture,
( ( intersection(esk1_0,esk2_0) = empty_set
| disjoint(esk1_0,esk2_0) )
& ( intersection(esk1_0,esk2_0) != empty_set
| ~ disjoint(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_24])])])]) ).
fof(c_0_30,plain,
! [X27,X28] :
( intersect(X28,X27)
| ~ intersect(X27,X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])])]) ).
cnf(c_0_31,plain,
( ~ intersect(X2,intersection(X3,X1))
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_32,plain,
( intersect(X1,intersection(X1,X2))
| intersection(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( ~ intersect(X1,X2)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,negated_conjecture,
( intersection(esk1_0,esk2_0) = empty_set
| disjoint(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( ~ intersect(X1,X2)
| intersect(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
( intersect(X2,X1)
| intersection(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( ~ intersect(esk1_0,esk2_0)
| intersection(esk1_0,esk2_0) = empty_set ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( intersect(X1,X2)
| intersection(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( intersection(esk1_0,esk2_0) != empty_set
| ~ disjoint(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,plain,
( disjoint(X1,X2)
| intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_42,negated_conjecture,
intersection(esk1_0,esk2_0) = empty_set,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( intersection(esk1_0,esk2_0) != empty_set
| intersect(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( ~ member(X1,esk1_0)
| ~ member(X1,esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_12]) ).
cnf(c_0_45,negated_conjecture,
( intersection(esk1_0,esk2_0) != empty_set
| intersect(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
( ~ member(esk4_2(esk2_0,X1),esk1_0)
| ~ intersect(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_15]) ).
cnf(c_0_47,negated_conjecture,
intersect(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_42])]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_19]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.56 % Computer : n014.cluster.edu
% 0.12/0.56 % Model : x86_64 x86_64
% 0.12/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.56 % Memory : 8046.5625MB
% 0.12/0.56 % OS : Linux 6.8.0-71-generic
% 0.12/0.56 % CPULimit : 300
% 0.12/0.56 % WCLimit : 300
% 0.12/0.56 % DateTime : Mon Sep 21 05:30:50 UTC 2026
% 0.12/0.57 % CPUTime :
% 0.12/0.57 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.61 Running first-order theorem proving
% 0.12/0.61 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
% 0.16/0.64 % Version: 3.5.1
% 0.16/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.64 % Starting sh5l with 300s (1) cores
% 0.16/0.64 % new_bool_1 with pid 3232496 completed with status 0
% 0.16/0.64 % Result found by new_bool_1
% 0.16/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.64 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.16/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.64 % SubtermCWHack with pid 3232498 completed with status 0
% 0.16/0.64 % Result found by SubtermCWHack
% 0.16/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.64 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.16/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.64 % Preprocessing time : 0.001 s
% 0.16/0.64
% 0.16/0.64 % Proof found!
% 0.16/0.64 % SZS status Theorem
% 0.16/0.64 % SZS output start CNFRefutation
% See solution above
% 0.16/0.64 % Parsed axioms : 12
% 0.16/0.64 % Removed by relevancy pruning/SinE : 4
% 0.16/0.64 % Initial clauses : 17
% 0.16/0.64 % Removed in clause preprocessing : 2
% 0.16/0.64 % Initial clauses in saturation : 15
% 0.16/0.64 % Processed clauses : 202
% 0.16/0.64 % ...of these trivial : 3
% 0.16/0.64 % ...subsumed : 127
% 0.16/0.64 % ...remaining for further processing : 72
% 0.16/0.64 % Other redundant clauses eliminated : 0
% 0.16/0.64 % Clauses deleted for lack of memory : 0
% 0.16/0.64 % Backward-subsumed : 0
% 0.16/0.64 % Backward-rewritten : 11
% 0.16/0.64 % Generated clauses : 485
% 0.16/0.64 % ...of the previous two non-redundant : 449
% 0.16/0.64 % ...aggressively subsumed : 0
% 0.16/0.64 % Contextual simplify-reflections : 0
% 0.16/0.64 % Paramodulations : 475
% 0.16/0.64 % Factorizations : 10
% 0.16/0.64 % NegExts : 0
% 0.16/0.64 % Equation resolutions : 0
% 0.16/0.64 % Disequality decompositions : 0
% 0.16/0.64 % Total rewrite steps : 54
% 0.16/0.64 % ...of those cached : 45
% 0.16/0.64 % Propositional unsat checks : 0
% 0.16/0.64 % Propositional check models : 0
% 0.16/0.64 % Propositional check unsatisfiable : 0
% 0.16/0.64 % Propositional clauses : 0
% 0.16/0.64 % Propositional clauses after purity: 0
% 0.16/0.64 % Propositional unsat core size : 0
% 0.16/0.64 % Propositional preprocessing time : 0.000
% 0.16/0.64 % Propositional encoding time : 0.000
% 0.16/0.64 % Propositional solver time : 0.000
% 0.16/0.64 % Success case prop preproc time : 0.000
% 0.16/0.64 % Success case prop encoding time : 0.000
% 0.16/0.64 % Success case prop solver time : 0.000
% 0.16/0.64 % Current number of processed clauses : 61
% 0.16/0.64 % Positive orientable unit clauses : 7
% 0.16/0.64 % Positive unorientable unit clauses: 1
% 0.16/0.64 % Negative unit clauses : 4
% 0.16/0.64 % Non-unit-clauses : 49
% 0.16/0.64 % Current number of unprocessed clauses: 258
% 0.16/0.64 % ...number of literals in the above : 687
% 0.16/0.64 % Current number of archived formulas : 0
% 0.16/0.64 % Current number of archived clauses : 11
% 0.16/0.64 % Clause-clause subsumption calls (NU) : 527
% 0.16/0.64 % Rec. Clause-clause subsumption calls : 457
% 0.16/0.64 % Non-unit clause-clause subsumptions : 66
% 0.16/0.64 % Unit Clause-clause subsumption calls : 48
% 0.16/0.64 % Rewrite failures with RHS unbound : 0
% 0.16/0.64 % BW rewrite match attempts : 5
% 0.16/0.64 % BW rewrite match successes : 5
% 0.16/0.64 % Condensation attempts : 0
% 0.16/0.64 % Condensation successes : 0
% 0.16/0.64 % Termbank termtop insertions : 5406
% 0.16/0.64 % Search garbage collected termcells : 312
% 0.16/0.64
% 0.16/0.64 % -------------------------------------------------
% 0.16/0.64 % User time : 0.012 s
% 0.16/0.64 % System time : 0.002 s
% 0.16/0.64 % Total time : 0.014 s
% 0.16/0.64 % Maximum resident set size: 3636 pages
% 0.16/0.64
% 0.16/0.64 % -------------------------------------------------
% 0.16/0.64 % User time : 0.014 s
% 0.16/0.64 % System time : 0.005 s
% 0.16/0.64 % Total time : 0.020 s
% 0.16/0.64 % Maximum resident set size: 4608 pages
% 0.16/0.64 % E exiting
%------------------------------------------------------------------------------