%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:19:00 PM UTC 2026
% Result : Theorem 0.17s 0.59s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 15 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t121_zfmisc_1,conjecture,
! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
fof(t120_zfmisc_1,axiom,
! [X1,X2,X3] :
( cartesian_product2(X3,set_union2(X1,X2)) = set_union2(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
& cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t4_xboole_1,axiom,
! [X1,X2,X3] : set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
inference(assume_negation,[status(cth)],[t121_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
cartesian_product2(set_union2(esk1_0,esk2_0),set_union2(esk3_0,esk4_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk1_0,esk4_0)),cartesian_product2(esk2_0,esk3_0)),cartesian_product2(esk2_0,esk4_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X15,X16,X17] :
( cartesian_product2(X17,set_union2(X15,X16)) = set_union2(cartesian_product2(X17,X15),cartesian_product2(X17,X16))
& cartesian_product2(set_union2(X15,X16),X17) = set_union2(cartesian_product2(X15,X17),cartesian_product2(X16,X17)) ),
inference(variable_rename,[status(thm)],[t120_zfmisc_1]) ).
fof(c_0_7,plain,
! [X9,X10] : set_union2(X9,X10) = set_union2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_8,plain,
! [X12,X13,X14] : set_union2(set_union2(X12,X13),X14) = set_union2(X12,set_union2(X13,X14)),
inference(variable_rename,[status(thm)],[t4_xboole_1]) ).
cnf(c_0_9,negated_conjecture,
cartesian_product2(set_union2(esk1_0,esk2_0),set_union2(esk3_0,esk4_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk1_0,esk4_0)),cartesian_product2(esk2_0,esk3_0)),cartesian_product2(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
cartesian_product2(X1,set_union2(X2,X3)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
set_union2(cartesian_product2(esk2_0,esk3_0),set_union2(cartesian_product2(esk2_0,esk4_0),cartesian_product2(esk1_0,set_union2(esk3_0,esk4_0)))) != cartesian_product2(set_union2(esk1_0,esk2_0),set_union2(esk3_0,esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),c_0_11]) ).
cnf(c_0_14,plain,
set_union2(cartesian_product2(X1,X2),set_union2(cartesian_product2(X1,X3),X4)) = set_union2(cartesian_product2(X1,set_union2(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_15,plain,
cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.52 % Computer : n006.cluster.edu
% 0.13/0.52 % Model : x86_64 x86_64
% 0.13/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.52 % Memory : 8046.5625MB
% 0.13/0.52 % OS : Linux 6.8.0-71-generic
% 0.13/0.52 % CPULimit : 300
% 0.13/0.52 % WCLimit : 300
% 0.13/0.52 % DateTime : Mon Sep 21 05:45:12 UTC 2026
% 0.13/0.53 % CPUTime :
% 0.13/0.53 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.57 Running first-order theorem proving
% 0.17/0.57 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
% 0.17/0.59 % Version: 3.5.1
% 0.17/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.59 % Starting sh5l with 300s (1) cores
% 0.17/0.59 % new_bool_3 with pid 2122088 completed with status 0
% 0.17/0.59 % Result found by new_bool_3
% 0.17/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.59 % Search class: FUUPM-FFSF22-MFFFFFNN
% 0.17/0.59 % Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.59 % Starting SubtermCWHack with 28s (1) cores
% 0.17/0.59 % SubtermCWHack with pid 2122091 completed with status 0
% 0.17/0.59 % Result found by SubtermCWHack
% 0.17/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/0.59 % Search class: FUUPM-FFSF22-MFFFFFNN
% 0.17/0.59 % Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 0.17/0.59 % Starting SubtermCWHack with 28s (1) cores
% 0.17/0.59 % Preprocessing time : 0.001 s
% 0.17/0.59
% 0.17/0.59 % Proof found!
% 0.17/0.59 % SZS status Theorem
% 0.17/0.59 % SZS output start CNFRefutation
% See solution above
% 0.17/0.59 % Parsed axioms : 9
% 0.17/0.59 % Removed by relevancy pruning/SinE : 4
% 0.17/0.59 % Initial clauses : 6
% 0.17/0.59 % Removed in clause preprocessing : 0
% 0.17/0.59 % Initial clauses in saturation : 6
% 0.17/0.59 % Processed clauses : 110
% 0.17/0.59 % ...of these trivial : 34
% 0.17/0.59 % ...subsumed : 60
% 0.17/0.59 % ...remaining for further processing : 16
% 0.17/0.59 % Other redundant clauses eliminated : 0
% 0.17/0.59 % Clauses deleted for lack of memory : 0
% 0.17/0.59 % Backward-subsumed : 0
% 0.17/0.59 % Backward-rewritten : 3
% 0.17/0.59 % Generated clauses : 422
% 0.17/0.59 % ...of the previous two non-redundant : 274
% 0.17/0.59 % ...aggressively subsumed : 0
% 0.17/0.59 % Contextual simplify-reflections : 0
% 0.17/0.59 % Paramodulations : 422
% 0.17/0.59 % Factorizations : 0
% 0.17/0.59 % NegExts : 0
% 0.17/0.59 % Equation resolutions : 0
% 0.17/0.59 % Disequality decompositions : 0
% 0.17/0.59 % Total rewrite steps : 436
% 0.17/0.59 % ...of those cached : 298
% 0.17/0.59 % Propositional unsat checks : 0
% 0.17/0.59 % Propositional check models : 0
% 0.17/0.59 % Propositional check unsatisfiable : 0
% 0.17/0.59 % Propositional clauses : 0
% 0.17/0.59 % Propositional clauses after purity: 0
% 0.17/0.59 % Propositional unsat core size : 0
% 0.17/0.59 % Propositional preprocessing time : 0.000
% 0.17/0.59 % Propositional encoding time : 0.000
% 0.17/0.59 % Propositional solver time : 0.000
% 0.17/0.59 % Success case prop preproc time : 0.000
% 0.17/0.59 % Success case prop encoding time : 0.000
% 0.17/0.59 % Success case prop solver time : 0.000
% 0.17/0.59 % Current number of processed clauses : 13
% 0.17/0.59 % Positive orientable unit clauses : 9
% 0.17/0.59 % Positive unorientable unit clauses: 4
% 0.17/0.59 % Negative unit clauses : 0
% 0.17/0.59 % Non-unit-clauses : 0
% 0.17/0.59 % Current number of unprocessed clauses: 148
% 0.17/0.59 % ...number of literals in the above : 148
% 0.17/0.59 % Current number of archived formulas : 0
% 0.17/0.59 % Current number of archived clauses : 3
% 0.17/0.59 % Clause-clause subsumption calls (NU) : 0
% 0.17/0.59 % Rec. Clause-clause subsumption calls : 0
% 0.17/0.59 % Non-unit clause-clause subsumptions : 0
% 0.17/0.59 % Unit Clause-clause subsumption calls : 6
% 0.17/0.59 % Rewrite failures with RHS unbound : 0
% 0.17/0.59 % BW rewrite match attempts : 40
% 0.17/0.59 % BW rewrite match successes : 30
% 0.17/0.59 % Condensation attempts : 0
% 0.17/0.59 % Condensation successes : 0
% 0.17/0.59 % Termbank termtop insertions : 3247
% 0.17/0.59 % Search garbage collected termcells : 48
% 0.17/0.59
% 0.17/0.59 % -------------------------------------------------
% 0.17/0.59 % User time : 0.007 s
% 0.17/0.59 % System time : 0.001 s
% 0.17/0.59 % Total time : 0.008 s
% 0.17/0.59 % Maximum resident set size: 3636 pages
% 0.17/0.59
% 0.17/0.59 % -------------------------------------------------
% 0.17/0.59 % User time : 0.011 s
% 0.17/0.59 % System time : 0.002 s
% 0.17/0.59 % Total time : 0.014 s
% 0.17/0.59 % Maximum resident set size: 4864 pages
% 0.17/0.59 % E exiting
%------------------------------------------------------------------------------