%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET196+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 02:13:53 PM UTC 2026
% Result : Theorem 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 38 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 32 ( 12 ~; 12 |; 5 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(prove_intersection_is_subset,conjecture,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_is_subset) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_4,plain,
! [X13,X14,X15] :
( ( member(X15,intersection(X13,X14))
| ~ member(X15,X14)
| ~ member(X15,X13) )
& ( ~ member(X15,intersection(X13,X14))
| member(X15,X14) )
& ( ~ member(X15,intersection(X13,X14))
| member(X15,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
fof(c_0_5,plain,
! [X6,X7,X8,X9,X10] :
( ( subset(X9,X10)
| ~ member(esk3_2(X9,X10),X10) )
& ( subset(X9,X10)
| member(esk3_2(X9,X10),X9) )
& ( member(X8,X7)
| ~ member(X8,X6)
| ~ subset(X6,X7) ) ),
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])])])])])])]) ).
cnf(c_0_6,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] : subset(intersection(X1,X2),X1),
inference(assume_negation,[status(cth)],[prove_intersection_is_subset]) ).
cnf(c_0_9,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( member(esk3_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
fof(c_0_11,plain,
! [X16,X17] : intersection(X16,X17) = intersection(X17,X16),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_12,negated_conjecture,
~ subset(intersection(esk1_0,esk2_0),esk1_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_13,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
~ subset(intersection(esk1_0,esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET196+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:59:42 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Version: 3.5.1
% 0.15/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.42 % Starting sh5l with 300s (1) cores
% 0.15/0.42 % new_bool_3 with pid 2054020 completed with status 0
% 0.15/0.42 % Result found by new_bool_3
% 0.15/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.42 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.15/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.42 % SubtermCWHack with pid 2054023 completed with status 0
% 0.15/0.42 % Result found by SubtermCWHack
% 0.15/0.42 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.42 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.42 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.15/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.42 % Preprocessing time : 0.001 s
% 0.15/0.42
% 0.15/0.42 % Proof found!
% 0.15/0.42 % SZS status Theorem
% 0.15/0.42 % SZS output start CNFRefutation
% See solution above
% 0.15/0.42 % Parsed axioms : 6
% 0.15/0.42 % Removed by relevancy pruning/SinE : 0
% 0.15/0.42 % Initial clauses : 13
% 0.15/0.42 % Removed in clause preprocessing : 2
% 0.15/0.42 % Initial clauses in saturation : 11
% 0.15/0.42 % Processed clauses : 18
% 0.15/0.42 % ...of these trivial : 0
% 0.15/0.42 % ...subsumed : 6
% 0.15/0.42 % ...remaining for further processing : 12
% 0.15/0.42 % Other redundant clauses eliminated : 0
% 0.15/0.42 % Clauses deleted for lack of memory : 0
% 0.15/0.42 % Backward-subsumed : 0
% 0.15/0.42 % Backward-rewritten : 1
% 0.15/0.42 % Generated clauses : 24
% 0.15/0.42 % ...of the previous two non-redundant : 17
% 0.15/0.42 % ...aggressively subsumed : 0
% 0.15/0.42 % Contextual simplify-reflections : 0
% 0.15/0.42 % Paramodulations : 24
% 0.15/0.42 % Factorizations : 0
% 0.15/0.42 % NegExts : 0
% 0.15/0.42 % Equation resolutions : 0
% 0.15/0.42 % Disequality decompositions : 0
% 0.15/0.42 % Total rewrite steps : 2
% 0.15/0.42 % ...of those cached : 0
% 0.15/0.42 % Propositional unsat checks : 0
% 0.15/0.42 % Propositional check models : 0
% 0.15/0.42 % Propositional check unsatisfiable : 0
% 0.15/0.42 % Propositional clauses : 0
% 0.15/0.42 % Propositional clauses after purity: 0
% 0.15/0.42 % Propositional unsat core size : 0
% 0.15/0.42 % Propositional preprocessing time : 0.000
% 0.15/0.42 % Propositional encoding time : 0.000
% 0.15/0.42 % Propositional solver time : 0.000
% 0.15/0.42 % Success case prop preproc time : 0.000
% 0.15/0.42 % Success case prop encoding time : 0.000
% 0.15/0.42 % Success case prop solver time : 0.000
% 0.15/0.42 % Current number of processed clauses : 11
% 0.15/0.42 % Positive orientable unit clauses : 3
% 0.15/0.42 % Positive unorientable unit clauses: 1
% 0.15/0.42 % Negative unit clauses : 0
% 0.15/0.42 % Non-unit-clauses : 7
% 0.15/0.42 % Current number of unprocessed clauses: 10
% 0.15/0.42 % ...number of literals in the above : 22
% 0.15/0.42 % Current number of archived formulas : 0
% 0.15/0.42 % Current number of archived clauses : 1
% 0.15/0.42 % Clause-clause subsumption calls (NU) : 13
% 0.15/0.42 % Rec. Clause-clause subsumption calls : 13
% 0.15/0.42 % Non-unit clause-clause subsumptions : 6
% 0.15/0.42 % Unit Clause-clause subsumption calls : 2
% 0.15/0.42 % Rewrite failures with RHS unbound : 0
% 0.15/0.42 % BW rewrite match attempts : 7
% 0.15/0.42 % BW rewrite match successes : 3
% 0.15/0.42 % Condensation attempts : 0
% 0.15/0.42 % Condensation successes : 0
% 0.15/0.42 % Termbank termtop insertions : 968
% 0.15/0.42 % Search garbage collected termcells : 237
% 0.15/0.42
% 0.15/0.42 % -------------------------------------------------
% 0.15/0.42 % User time : 0.002 s
% 0.15/0.42 % System time : 0.004 s
% 0.15/0.42 % Total time : 0.006 s
% 0.15/0.42 % Maximum resident set size: 3632 pages
% 0.15/0.42
% 0.15/0.42 % -------------------------------------------------
% 0.15/0.42 % User time : 0.005 s
% 0.15/0.42 % System time : 0.008 s
% 0.15/0.42 % Total time : 0.013 s
% 0.15/0.42 % Maximum resident set size: 4608 pages
% 0.15/0.42 % E exiting
%------------------------------------------------------------------------------