%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET702+4 : 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 : n017.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 02:15:01 PM UTC 2026
% Result : Theorem 9.44s 1.78s
% Output : CNFRefutation 9.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 24 ~; 30 |; 7 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 69 ( 6 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(product,axiom,
! [X3,X1] :
( member(X3,product(X1))
<=> ! [X5] :
( member(X5,X1)
=> member(X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',product) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(thI36,conjecture,
! [X1,X2] : subset(intersection(product(X1),product(X2)),product(intersection(X1,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI36) ).
fof(c_0_4,plain,
! [X14,X15,X16,X17,X18] :
( ( member(X17,product(X18))
| ~ member(X17,esk4_2(X17,X18)) )
& ( member(X17,product(X18))
| member(esk4_2(X17,X18),X18) )
& ( member(X14,X16)
| ~ member(X16,X15)
| ~ member(X14,product(X15)) ) ),
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)],[product])])])])])])]) ).
fof(c_0_5,plain,
! [X8,X9,X10,X11,X12] :
( ( subset(X11,X12)
| ~ member(esk3_2(X11,X12),X12) )
& ( subset(X11,X12)
| member(esk3_2(X11,X12),X11) )
& ( member(X10,X9)
| ~ member(X10,X8)
| ~ subset(X8,X9) ) ),
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])])])])])])]) ).
cnf(c_0_6,plain,
( ~ member(X3,X2)
| ~ member(X1,product(X2))
| member(X1,X3) ),
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,plain,
! [X20,X21,X22] :
( ( member(X20,intersection(X21,X22))
| ~ member(X20,X22)
| ~ member(X20,X21) )
& ( ~ member(X20,intersection(X21,X22))
| member(X20,X22) )
& ( ~ member(X20,intersection(X21,X22))
| member(X20,X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])])]) ).
cnf(c_0_9,plain,
( ~ member(X1,esk4_2(X1,X2))
| member(X1,product(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,plain,
( ~ member(X3,X1)
| subset(product(X1),X2)
| member(esk3_2(product(X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(X1,product(X2))
| member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,plain,
( ~ member(esk4_2(esk3_2(product(X1),X2),X3),X1)
| subset(product(X1),X2)
| member(esk3_2(product(X1),X2),product(X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( member(X1,product(intersection(X2,X3)))
| member(esk4_2(X1,intersection(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( ~ member(esk3_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,plain,
( subset(product(X1),X2)
| member(esk3_2(product(X1),X2),product(intersection(X3,X1))) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
subset(product(X1),product(intersection(X2,X1))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2] : subset(intersection(product(X1),product(X2)),product(intersection(X1,X2))),
inference(assume_negation,[status(cth)],[thI36]) ).
cnf(c_0_20,plain,
( ~ member(X1,product(X3))
| member(X1,product(intersection(X2,X3))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_21,negated_conjecture,
~ subset(intersection(product(esk1_0),product(esk2_0)),product(intersection(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_19])])])]) ).
cnf(c_0_22,plain,
( ~ member(esk3_2(X1,product(intersection(X2,X3))),product(X3))
| subset(X1,product(intersection(X2,X3))) ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_23,plain,
( subset(intersection(X1,X2),X3)
| member(esk3_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_24,negated_conjecture,
~ subset(intersection(product(esk1_0),product(esk2_0)),product(intersection(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
subset(intersection(X1,product(X2)),product(intersection(X3,X2))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET702+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n017.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:28:42 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 9.44/1.78 % Version: 3.5.1
% 9.44/1.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 9.44/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.44/1.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.44/1.78 % Starting new_bool_3 with 300s (1) cores
% 9.44/1.78 % Starting new_bool_1 with 300s (1) cores
% 9.44/1.78 % Starting sh5l with 300s (1) cores
% 9.44/1.78 % new_bool_3 with pid 1527868 completed with status 0
% 9.44/1.78 % Result found by new_bool_3
% 9.44/1.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 9.44/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.44/1.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.44/1.78 % Starting new_bool_3 with 300s (1) cores
% 9.44/1.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.44/1.78 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.44/1.78 % Search class: FGUNF-FFSF21-SFFFFFNN
% 9.44/1.78 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 9.44/1.78 % Starting SubtermCWHack with 31s (1) cores
% 9.44/1.78 % SubtermCWHack with pid 1527871 completed with status 0
% 9.44/1.78 % Result found by SubtermCWHack
% 9.44/1.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 9.44/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.44/1.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.44/1.78 % Starting new_bool_3 with 300s (1) cores
% 9.44/1.78 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.44/1.78 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.44/1.78 % Search class: FGUNF-FFSF21-SFFFFFNN
% 9.44/1.78 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 9.44/1.78 % Starting SubtermCWHack with 31s (1) cores
% 9.44/1.78 % Preprocessing time : 0.002 s
% 9.44/1.78
% 9.44/1.78 % Proof found!
% 9.44/1.78 % SZS status Theorem
% 9.44/1.78 % SZS output start CNFRefutation
% See solution above
% 9.44/1.78 % Parsed axioms : 12
% 9.44/1.78 % Removed by relevancy pruning/SinE : 8
% 9.44/1.78 % Initial clauses : 10
% 9.44/1.78 % Removed in clause preprocessing : 0
% 9.44/1.78 % Initial clauses in saturation : 10
% 9.44/1.78 % Processed clauses : 5227
% 9.44/1.78 % ...of these trivial : 7
% 9.44/1.78 % ...subsumed : 4186
% 9.44/1.78 % ...remaining for further processing : 1034
% 9.44/1.78 % Other redundant clauses eliminated : 0
% 9.44/1.78 % Clauses deleted for lack of memory : 0
% 9.44/1.78 % Backward-subsumed : 0
% 9.44/1.78 % Backward-rewritten : 1
% 9.44/1.78 % Generated clauses : 53207
% 9.44/1.78 % ...of the previous two non-redundant : 53010
% 9.44/1.78 % ...aggressively subsumed : 0
% 9.44/1.78 % Contextual simplify-reflections : 0
% 9.44/1.78 % Paramodulations : 53207
% 9.44/1.78 % Factorizations : 0
% 9.44/1.78 % NegExts : 0
% 9.44/1.78 % Equation resolutions : 0
% 9.44/1.78 % Disequality decompositions : 0
% 9.44/1.78 % Total rewrite steps : 91
% 9.44/1.78 % ...of those cached : 10
% 9.44/1.78 % Propositional unsat checks : 0
% 9.44/1.78 % Propositional check models : 0
% 9.44/1.78 % Propositional check unsatisfiable : 0
% 9.44/1.78 % Propositional clauses : 0
% 9.44/1.78 % Propositional clauses after purity: 0
% 9.44/1.78 % Propositional unsat core size : 0
% 9.44/1.78 % Propositional preprocessing time : 0.000
% 9.44/1.78 % Propositional encoding time : 0.000
% 9.44/1.78 % Propositional solver time : 0.000
% 9.44/1.78 % Success case prop preproc time : 0.000
% 9.44/1.78 % Success case prop encoding time : 0.000
% 9.44/1.78 % Success case prop solver time : 0.000
% 9.44/1.78 % Current number of processed clauses : 1033
% 9.44/1.78 % Positive orientable unit clauses : 302
% 9.44/1.78 % Positive unorientable unit clauses: 0
% 9.44/1.78 % Negative unit clauses : 2
% 9.44/1.78 % Non-unit-clauses : 729
% 9.44/1.78 % Current number of unprocessed clauses: 47793
% 9.44/1.78 % ...number of literals in the above : 129422
% 9.44/1.78 % Current number of archived formulas : 0
% 9.44/1.78 % Current number of archived clauses : 1
% 9.44/1.78 % Clause-clause subsumption calls (NU) : 161168
% 9.44/1.78 % Rec. Clause-clause subsumption calls : 146988
% 9.44/1.78 % Non-unit clause-clause subsumptions : 4186
% 9.44/1.78 % Unit Clause-clause subsumption calls : 9241
% 9.44/1.78 % Rewrite failures with RHS unbound : 0
% 9.44/1.78 % BW rewrite match attempts : 9297
% 9.44/1.78 % BW rewrite match successes : 1
% 9.44/1.78 % Condensation attempts : 0
% 9.44/1.78 % Condensation successes : 0
% 9.44/1.78 % Termbank termtop insertions : 981944
% 9.44/1.78 % Search garbage collected termcells : 270
% 9.44/1.78
% 9.44/1.78 % -------------------------------------------------
% 9.44/1.78 % User time : 1.154 s
% 9.44/1.78 % System time : 0.046 s
% 9.44/1.78 % Total time : 1.200 s
% 9.44/1.78 % Maximum resident set size: 3648 pages
% 9.44/1.78
% 9.44/1.78 % -------------------------------------------------
% 9.44/1.78 % User time : 1.156 s
% 9.44/1.78 % System time : 0.053 s
% 9.44/1.78 % Total time : 1.209 s
% 9.44/1.78 % Maximum resident set size: 4864 pages
% 9.44/1.78 % E exiting
%------------------------------------------------------------------------------