%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 02:15:52 PM UTC 2026
% Result : Theorem 0.33s 0.53s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% 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 : 5 ( 3 ~; 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 : 40 ( 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/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',t4_xboole_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/sandbox/benchmark/theBenchmark.p',t120_zfmisc_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,plain,
! [X5,X6] : set_union2(X5,X6) = set_union2(X6,X5),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_6,plain,
! [X21,X22,X23] : set_union2(set_union2(X21,X22),X23) = set_union2(X21,set_union2(X22,X23)),
inference(variable_rename,[status(thm)],[t4_xboole_1]) ).
fof(c_0_7,negated_conjecture,
cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk3_0,esk6_0)),cartesian_product2(esk4_0,esk5_0)),cartesian_product2(esk4_0,esk6_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_8,plain,
! [X14,X15,X16] :
( cartesian_product2(X16,set_union2(X14,X15)) = set_union2(cartesian_product2(X16,X14),cartesian_product2(X16,X15))
& cartesian_product2(set_union2(X14,X15),X16) = set_union2(cartesian_product2(X14,X16),cartesian_product2(X15,X16)) ),
inference(variable_rename,[status(thm)],[t120_zfmisc_1]) ).
cnf(c_0_9,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
cartesian_product2(set_union2(esk3_0,esk4_0),set_union2(esk5_0,esk6_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk3_0,esk6_0)),cartesian_product2(esk4_0,esk5_0)),cartesian_product2(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,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_8]) ).
cnf(c_0_13,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_8]) ).
cnf(c_0_14,plain,
set_union2(X1,X2) = set_union2(X2,X1),
c_0_9 ).
cnf(c_0_15,plain,
set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
c_0_10 ).
cnf(c_0_16,negated_conjecture,
$false,
inference(ar,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_10]),c_0_12]),c_0_13]),c_0_13]),c_0_10]),c_0_14,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n003.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 21 05:47:00 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 0.33/0.53 % Version: 3.5.1
% 0.33/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.33/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.33/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.33/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.33/0.53 % Starting sh5l with 300s (1) cores
% 0.33/0.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3536407 completed with status 0
% 0.33/0.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.33/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.33/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.33/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.53 % No SInE strategy applied
% 0.33/0.53 % Search class: FHUSM-FFSF22-MFFFFFNN
% 0.33/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.33/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.33/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.33/0.53 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.33/0.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.33/0.53 % Starting new_bool_3 with 136s (1) cores
% 0.33/0.53 % U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3536415 completed with status 0
% 0.33/0.53 % Result found by U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.33/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.33/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.33/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.33/0.53 % No SInE strategy applied
% 0.33/0.53 % Search class: FHUSM-FFSF22-MFFFFFNN
% 0.33/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.33/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.33/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.33/0.53 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.33/0.53 % Preprocessing time : 0.002 s
% 0.33/0.53 % Presaturation interreduction done
% 0.33/0.53
% 0.33/0.53 % Proof found!
% 0.33/0.53 % SZS status Theorem
% 0.33/0.53 % SZS output start CNFRefutation
% See solution above
% 0.33/0.53 % Parsed axioms : 9
% 0.33/0.53 % Removed by relevancy pruning/SinE : 0
% 0.33/0.53 % Initial clauses : 10
% 0.33/0.53 % Removed in clause preprocessing : 0
% 0.33/0.53 % Initial clauses in saturation : 10
% 0.33/0.53 % Processed clauses : 11
% 0.33/0.53 % ...of these trivial : 0
% 0.33/0.53 % ...subsumed : 0
% 0.33/0.53 % ...remaining for further processing : 10
% 0.33/0.53 % Other redundant clauses eliminated : 0
% 0.33/0.53 % Clauses deleted for lack of memory : 0
% 0.33/0.53 % Backward-subsumed : 0
% 0.33/0.53 % Backward-rewritten : 1
% 0.33/0.53 % Generated clauses : 0
% 0.33/0.53 % ...of the previous two non-redundant : 1
% 0.33/0.53 % ...aggressively subsumed : 0
% 0.33/0.53 % Contextual simplify-reflections : 0
% 0.33/0.53 % Paramodulations : 0
% 0.33/0.53 % Factorizations : 0
% 0.33/0.53 % NegExts : 0
% 0.33/0.53 % Equation resolutions : 0
% 0.33/0.53 % Disequality decompositions : 0
% 0.33/0.53 % Total rewrite steps : 6
% 0.33/0.53 % ...of those cached : 0
% 0.33/0.53 % Propositional unsat checks : 0
% 0.33/0.53 % Propositional check models : 0
% 0.33/0.53 % Propositional check unsatisfiable : 0
% 0.33/0.53 % Propositional clauses : 0
% 0.33/0.53 % Propositional clauses after purity: 0
% 0.33/0.53 % Propositional unsat core size : 0
% 0.33/0.53 % Propositional preprocessing time : 0.000
% 0.33/0.53 % Propositional encoding time : 0.000
% 0.33/0.53 % Propositional solver time : 0.000
% 0.33/0.53 % Success case prop preproc time : 0.000
% 0.33/0.53 % Success case prop encoding time : 0.000
% 0.33/0.53 % Success case prop solver time : 0.000
% 0.33/0.53 % Current number of processed clauses : 9
% 0.33/0.53 % Positive orientable unit clauses : 5
% 0.33/0.53 % Positive unorientable unit clauses: 1
% 0.33/0.53 % Negative unit clauses : 1
% 0.33/0.53 % Non-unit-clauses : 2
% 0.33/0.53 % Current number of unprocessed clauses: 0
% 0.33/0.53 % ...number of literals in the above : 0
% 0.33/0.53 % Current number of archived formulas : 0
% 0.33/0.53 % Current number of archived clauses : 1
% 0.33/0.53 % Clause-clause subsumption calls (NU) : 2
% 0.33/0.53 % Rec. Clause-clause subsumption calls : 2
% 0.33/0.53 % Non-unit clause-clause subsumptions : 0
% 0.33/0.53 % Unit Clause-clause subsumption calls : 0
% 0.33/0.53 % Rewrite failures with RHS unbound : 0
% 0.33/0.53 % BW rewrite match attempts : 16
% 0.33/0.53 % BW rewrite match successes : 12
% 0.33/0.53 % Condensation attempts : 0
% 0.33/0.53 % Condensation successes : 0
% 0.33/0.53 % Termbank termtop insertions : 557
% 0.33/0.53 % Search garbage collected termcells : 59
% 0.33/0.53
% 0.33/0.53 % -------------------------------------------------
% 0.33/0.53 % User time : 0.008 s
% 0.33/0.53 % System time : 0.003 s
% 0.33/0.53 % Total time : 0.010 s
% 0.33/0.53 % Maximum resident set size: 3636 pages
% 0.33/0.53
% 0.33/0.53 % -------------------------------------------------
% 0.33/0.53 % User time : 0.023 s
% 0.33/0.53 % System time : 0.015 s
% 0.33/0.53 % Total time : 0.038 s
% 0.33/0.53 % Maximum resident set size: 4864 pages
% 0.33/0.53 % E exiting
%------------------------------------------------------------------------------