%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET008+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 : n005.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 02:15:57 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 16 unt; 0 def)
% Number of atoms : 78 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 77 ( 33 ~; 26 |; 12 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 8 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_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(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(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(prove_intersection_difference_empty_set,conjecture,
! [X1,X2] : intersection(difference(X1,X2),X2) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_9,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])])])]) ).
fof(c_0_10,plain,
! [X15,X16,X17,X18,X19] :
( ( subset(X18,X19)
| ~ member(esk3_2(X18,X19),X19) )
& ( subset(X18,X19)
| member(esk3_2(X18,X19),X18) )
& ( member(X17,X16)
| ~ member(X17,X15)
| ~ subset(X15,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)],[subset_defn])])])])])])]) ).
fof(c_0_11,plain,
! [X6] : ~ member(X6,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])]) ).
fof(c_0_12,plain,
! [X12,X13,X14] :
( ( member(X14,difference(X12,X13))
| member(X14,X13)
| ~ member(X14,X12) )
& ( ~ member(X14,difference(X12,X13))
| ~ member(X14,X13) )
& ( ~ member(X14,difference(X12,X13))
| member(X14,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_13,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2] : intersection(difference(X1,X2),X2) = empty_set,
inference(assume_negation,[status(cth)],[prove_intersection_difference_empty_set]) ).
fof(c_0_16,plain,
! [X28,X29] :
( ( X28 = X29
| ~ subset(X29,X28)
| ~ subset(X28,X29) )
& ( X28 != X29
| subset(X29,X28) )
& ( X28 != X29
| subset(X28,X29) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_17,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( member(esk3_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_21,negated_conjecture,
intersection(difference(esk1_0,esk2_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_15])])])]) ).
fof(c_0_22,plain,
! [X10,X11] : intersection(X10,X11) = intersection(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_23,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_25,plain,
( ~ member(esk3_2(intersection(X1,difference(X2,X3)),X4),X3)
| subset(intersection(X1,difference(X2,X3)),X4) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
( member(esk3_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_27,negated_conjecture,
intersection(difference(esk1_0,esk2_0),esk2_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
subset(intersection(X1,difference(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
intersection(esk2_0,difference(esk1_0,esk2_0)) != empty_set,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
intersection(X1,difference(X2,X1)) = empty_set,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:41:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.15/0.44 % Version: 3.5.1
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % sh5l with pid 2570217 completed with status 0
% 0.15/0.44 % Result found by sh5l
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.15/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/0.44 % Search class: FGHSS-FFSF22-SFFFFFNN
% 0.15/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.44 % SubtermCWHack with pid 2570225 completed with status 0
% 0.15/0.44 % Result found by SubtermCWHack
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.15/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/0.44 % Search class: FGHSS-FFSF22-SFFFFFNN
% 0.15/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.44 % Preprocessing time : 0.001 s
% 0.15/0.44
% 0.15/0.44 % Proof found!
% 0.15/0.44 % SZS status Theorem
% 0.15/0.44 % SZS output start CNFRefutation
% See solution above
% 0.15/0.44 % Parsed axioms : 10
% 0.15/0.44 % Removed by relevancy pruning/SinE : 1
% 0.15/0.44 % Initial clauses : 20
% 0.15/0.44 % Removed in clause preprocessing : 2
% 0.15/0.44 % Initial clauses in saturation : 18
% 0.15/0.44 % Processed clauses : 101
% 0.15/0.44 % ...of these trivial : 6
% 0.15/0.44 % ...subsumed : 37
% 0.15/0.44 % ...remaining for further processing : 58
% 0.15/0.44 % Other redundant clauses eliminated : 2
% 0.15/0.44 % Clauses deleted for lack of memory : 0
% 0.15/0.44 % Backward-subsumed : 0
% 0.15/0.44 % Backward-rewritten : 6
% 0.15/0.44 % Generated clauses : 302
% 0.15/0.44 % ...of the previous two non-redundant : 200
% 0.15/0.44 % ...aggressively subsumed : 0
% 0.15/0.44 % Contextual simplify-reflections : 0
% 0.15/0.44 % Paramodulations : 298
% 0.15/0.44 % Factorizations : 2
% 0.15/0.44 % NegExts : 0
% 0.15/0.44 % Equation resolutions : 2
% 0.15/0.44 % Disequality decompositions : 0
% 0.15/0.44 % Total rewrite steps : 116
% 0.15/0.44 % ...of those cached : 93
% 0.15/0.44 % Propositional unsat checks : 0
% 0.15/0.44 % Propositional check models : 0
% 0.15/0.44 % Propositional check unsatisfiable : 0
% 0.15/0.44 % Propositional clauses : 0
% 0.15/0.44 % Propositional clauses after purity: 0
% 0.15/0.44 % Propositional unsat core size : 0
% 0.15/0.44 % Propositional preprocessing time : 0.000
% 0.15/0.44 % Propositional encoding time : 0.000
% 0.15/0.44 % Propositional solver time : 0.000
% 0.15/0.44 % Success case prop preproc time : 0.000
% 0.15/0.44 % Success case prop encoding time : 0.000
% 0.15/0.44 % Success case prop solver time : 0.000
% 0.15/0.44 % Current number of processed clauses : 50
% 0.15/0.44 % Positive orientable unit clauses : 13
% 0.15/0.44 % Positive unorientable unit clauses: 1
% 0.15/0.44 % Negative unit clauses : 1
% 0.15/0.44 % Non-unit-clauses : 35
% 0.15/0.44 % Current number of unprocessed clauses: 103
% 0.15/0.44 % ...number of literals in the above : 234
% 0.15/0.44 % Current number of archived formulas : 0
% 0.15/0.44 % Current number of archived clauses : 6
% 0.15/0.44 % Clause-clause subsumption calls (NU) : 154
% 0.15/0.44 % Rec. Clause-clause subsumption calls : 150
% 0.15/0.44 % Non-unit clause-clause subsumptions : 26
% 0.15/0.44 % Unit Clause-clause subsumption calls : 40
% 0.15/0.44 % Rewrite failures with RHS unbound : 0
% 0.15/0.44 % BW rewrite match attempts : 23
% 0.15/0.44 % BW rewrite match successes : 6
% 0.15/0.44 % Condensation attempts : 0
% 0.15/0.44 % Condensation successes : 0
% 0.15/0.44 % Termbank termtop insertions : 3979
% 0.15/0.44 % Search garbage collected termcells : 310
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.007 s
% 0.15/0.44 % System time : 0.003 s
% 0.15/0.44 % Total time : 0.010 s
% 0.15/0.44 % Maximum resident set size: 3636 pages
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.009 s
% 0.15/0.44 % System time : 0.007 s
% 0.15/0.44 % Total time : 0.016 s
% 0.15/0.44 % Maximum resident set size: 4864 pages
% 0.15/0.44 % E exiting
%------------------------------------------------------------------------------