%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET629+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 : n002.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 02:17:46 PM UTC 2026
% Result : Theorem 0.23s 0.56s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 83 ( 37 ~; 28 |; 11 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 4 sgn 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_and_difference_disjoint,conjecture,
! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_and_difference_disjoint) ).
fof(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_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(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(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_6,negated_conjecture,
~ ! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
inference(assume_negation,[status(cth)],[prove_intersection_and_difference_disjoint]) ).
fof(c_0_7,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint_defn]) ).
fof(c_0_8,plain,
! [X16,X17,X19,X20,X21] :
( ( intersect(X19,X20)
| ~ member(X21,X20)
| ~ member(X21,X19) )
& ( ~ intersect(X16,X17)
| member(esk3_2(X16,X17),X17) )
& ( ~ intersect(X16,X17)
| member(esk3_2(X16,X17),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)],[intersect_defn])])])])])])]) ).
fof(c_0_9,plain,
! [X11,X12,X13] :
( ( member(X13,intersection(X11,X12))
| ~ member(X13,X12)
| ~ member(X13,X11) )
& ( ~ member(X13,intersection(X11,X12))
| member(X13,X12) )
& ( ~ member(X13,intersection(X11,X12))
| member(X13,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
fof(c_0_10,negated_conjecture,
~ disjoint(intersection(esk1_0,esk2_0),difference(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_6])])])]) ).
fof(c_0_11,plain,
! [X6,X7] :
( ( disjoint(X6,X7)
| intersect(X6,X7) )
& ( ~ intersect(X6,X7)
| ~ disjoint(X6,X7) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_12,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
cnf(c_0_13,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| intersect(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ intersect(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ intersect(X1,X2)
| member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_17,plain,
! [X22,X23] :
( intersect(X23,X22)
| ~ intersect(X22,X23) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])])]) ).
cnf(c_0_18,negated_conjecture,
~ disjoint(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( disjoint(X1,X2)
| intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_20,plain,
! [X8,X9,X10] :
( ( member(X10,difference(X8,X9))
| member(X10,X9)
| ~ member(X10,X8) )
& ( ~ member(X10,difference(X8,X9))
| ~ member(X10,X9) )
& ( ~ member(X10,difference(X8,X9))
| member(X10,X8) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
cnf(c_0_21,plain,
( ~ member(esk3_2(X2,X3),X1)
| ~ intersect(X2,X3)
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,plain,
( ~ intersect(X1,intersection(X2,X3))
| member(esk3_2(X1,intersection(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,plain,
( ~ intersect(X1,X2)
| intersect(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
intersect(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( ~ intersect(X2,intersection(X3,X1))
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
intersect(difference(esk1_0,esk2_0),intersection(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( ~ member(esk3_2(X1,difference(X2,X3)),X3)
| ~ intersect(X1,difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_29,negated_conjecture,
intersect(esk2_0,difference(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
~ intersect(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_14]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_29,c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET629+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.45 % Computer : n002.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Mon Sep 21 05:33:02 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.51 Running first-order theorem proving
% 0.21/0.51 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
% 0.23/0.56 % Version: 3.5.1
% 0.23/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.56 % Starting sh5l with 300s (1) cores
% 0.23/0.56 % new_bool_3 with pid 2526880 completed with status 0
% 0.23/0.56 % Result found by new_bool_3
% 0.23/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.56 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.23/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.56 % SubtermCWHack with pid 2526886 completed with status 0
% 0.23/0.56 % Result found by SubtermCWHack
% 0.23/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.56 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.23/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.56 % Preprocessing time : 0.002 s
% 0.23/0.56
% 0.23/0.56 % Proof found!
% 0.23/0.56 % SZS status Theorem
% 0.23/0.56 % SZS output start CNFRefutation
% See solution above
% 0.23/0.56 % Parsed axioms : 8
% 0.23/0.56 % Removed by relevancy pruning/SinE : 0
% 0.23/0.56 % Initial clauses : 18
% 0.23/0.56 % Removed in clause preprocessing : 2
% 0.23/0.56 % Initial clauses in saturation : 16
% 0.23/0.56 % Processed clauses : 78
% 0.23/0.56 % ...of these trivial : 0
% 0.23/0.56 % ...subsumed : 23
% 0.23/0.56 % ...remaining for further processing : 55
% 0.23/0.56 % Other redundant clauses eliminated : 0
% 0.23/0.56 % Clauses deleted for lack of memory : 0
% 0.23/0.56 % Backward-subsumed : 0
% 0.23/0.56 % Backward-rewritten : 0
% 0.23/0.56 % Generated clauses : 213
% 0.23/0.56 % ...of the previous two non-redundant : 126
% 0.23/0.56 % ...aggressively subsumed : 0
% 0.23/0.56 % Contextual simplify-reflections : 0
% 0.23/0.56 % Paramodulations : 210
% 0.23/0.56 % Factorizations : 2
% 0.23/0.56 % NegExts : 0
% 0.23/0.56 % Equation resolutions : 0
% 0.23/0.56 % Disequality decompositions : 0
% 0.23/0.56 % Total rewrite steps : 77
% 0.23/0.56 % ...of those cached : 66
% 0.23/0.56 % Propositional unsat checks : 0
% 0.23/0.56 % Propositional check models : 0
% 0.23/0.56 % Propositional check unsatisfiable : 0
% 0.23/0.56 % Propositional clauses : 0
% 0.23/0.56 % Propositional clauses after purity: 0
% 0.23/0.56 % Propositional unsat core size : 0
% 0.23/0.56 % Propositional preprocessing time : 0.000
% 0.23/0.56 % Propositional encoding time : 0.000
% 0.23/0.56 % Propositional solver time : 0.000
% 0.23/0.56 % Success case prop preproc time : 0.000
% 0.23/0.56 % Success case prop encoding time : 0.000
% 0.23/0.56 % Success case prop solver time : 0.000
% 0.23/0.56 % Current number of processed clauses : 54
% 0.23/0.56 % Positive orientable unit clauses : 15
% 0.23/0.56 % Positive unorientable unit clauses: 1
% 0.23/0.56 % Negative unit clauses : 2
% 0.23/0.56 % Non-unit-clauses : 36
% 0.23/0.56 % Current number of unprocessed clauses: 64
% 0.23/0.56 % ...number of literals in the above : 160
% 0.23/0.56 % Current number of archived formulas : 0
% 0.23/0.56 % Current number of archived clauses : 1
% 0.23/0.56 % Clause-clause subsumption calls (NU) : 293
% 0.23/0.56 % Rec. Clause-clause subsumption calls : 291
% 0.23/0.56 % Non-unit clause-clause subsumptions : 23
% 0.23/0.56 % Unit Clause-clause subsumption calls : 80
% 0.23/0.56 % Rewrite failures with RHS unbound : 0
% 0.23/0.56 % BW rewrite match attempts : 0
% 0.23/0.56 % BW rewrite match successes : 0
% 0.23/0.56 % Condensation attempts : 0
% 0.23/0.56 % Condensation successes : 0
% 0.23/0.56 % Termbank termtop insertions : 3083
% 0.23/0.56 % Search garbage collected termcells : 289
% 0.23/0.56
% 0.23/0.56 % -------------------------------------------------
% 0.23/0.56 % User time : 0.014 s
% 0.23/0.56 % System time : 0.004 s
% 0.23/0.56 % Total time : 0.018 s
% 0.23/0.56 % Maximum resident set size: 3632 pages
% 0.23/0.56
% 0.23/0.56 % -------------------------------------------------
% 0.23/0.56 % User time : 0.015 s
% 0.23/0.56 % System time : 0.008 s
% 0.23/0.56 % Total time : 0.023 s
% 0.23/0.56 % Maximum resident set size: 4608 pages
% 0.23/0.56 % E exiting
%------------------------------------------------------------------------------