%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET984+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 : 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 02:15:54 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 17 unt; 0 def)
% Number of atoms : 102 ( 80 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 84 ( 23 ~; 48 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 82 ( 12 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t138_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( ( subset(X2,X4)
& subset(X1,X3) )
| cartesian_product2(X1,X2) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(t134_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( cartesian_product2(X1,X2) = cartesian_product2(X3,X4)
=> ( ( X2 = X4
& X1 = X3 )
| X2 = empty_set
| X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(t123_zfmisc_1,axiom,
! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(t28_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(t17_xboole_1,axiom,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t113_zfmisc_1,axiom,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X2 = empty_set
| X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( ( subset(X2,X4)
& subset(X1,X3) )
| cartesian_product2(X1,X2) = empty_set ) ),
inference(assume_negation,[status(cth)],[t138_zfmisc_1]) ).
fof(c_0_8,plain,
! [X17,X18,X19,X20] :
( ( cartesian_product2(X17,X18) != cartesian_product2(X19,X20)
| X18 = empty_set
| X17 = empty_set
| X18 = X20 )
& ( cartesian_product2(X17,X18) != cartesian_product2(X19,X20)
| X18 = empty_set
| X17 = empty_set
| X17 = X19 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t134_zfmisc_1])])])]) ).
fof(c_0_9,plain,
! [X13,X14,X15,X16] : cartesian_product2(set_intersection2(X13,X14),set_intersection2(X15,X16)) = set_intersection2(cartesian_product2(X13,X15),cartesian_product2(X14,X16)),
inference(variable_rename,[status(thm)],[t123_zfmisc_1]) ).
fof(c_0_10,plain,
! [X27,X28] :
( set_intersection2(X27,X28) = X27
| ~ subset(X27,X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])])]) ).
fof(c_0_11,negated_conjecture,
( ( ~ subset(esk4_0,esk6_0)
| ~ subset(esk3_0,esk5_0) )
& cartesian_product2(esk3_0,esk4_0) != empty_set
& subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_12,plain,
( cartesian_product2(X3,X1) != cartesian_product2(X4,X2)
| X1 = empty_set
| X3 = empty_set
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ subset(X1,X2)
| set_intersection2(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X25,X26] : subset(set_intersection2(X25,X26),X25),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(c_0_17,plain,
! [X5,X6] : set_intersection2(X5,X6) = set_intersection2(X6,X5),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_18,plain,
( cartesian_product2(X4,X1) != set_intersection2(cartesian_product2(X5,X2),cartesian_product2(X6,X3))
| X4 = empty_set
| X1 = empty_set
| X1 = set_intersection2(X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
set_intersection2(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) = cartesian_product2(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( cartesian_product2(X1,X3) != cartesian_product2(X2,X4)
| X3 = empty_set
| X1 = empty_set
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( cartesian_product2(X2,X1) != cartesian_product2(esk3_0,esk4_0)
| X1 = empty_set
| X2 = empty_set
| X1 = set_intersection2(esk4_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( cartesian_product2(X1,X4) != set_intersection2(cartesian_product2(X2,X5),cartesian_product2(X3,X6))
| X4 = empty_set
| X1 = empty_set
| X1 = set_intersection2(X2,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_25,plain,
subset(set_intersection2(X1,X2),X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( esk3_0 = empty_set
| esk4_0 = empty_set
| set_intersection2(esk4_0,esk6_0) = esk4_0 ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( cartesian_product2(X1,X2) != cartesian_product2(esk3_0,esk4_0)
| X1 = empty_set
| X2 = empty_set
| X1 = set_intersection2(esk3_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( ~ subset(esk4_0,esk6_0)
| ~ subset(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( subset(esk4_0,esk6_0)
| esk4_0 = empty_set
| esk3_0 = empty_set ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_30,plain,
! [X11,X12] :
( ( cartesian_product2(X11,X12) = empty_set
| X12 != empty_set )
& ( cartesian_product2(X11,X12) = empty_set
| X11 != empty_set )
& ( X12 = empty_set
| X11 = empty_set
| cartesian_product2(X11,X12) != empty_set ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t113_zfmisc_1])])])]) ).
cnf(c_0_31,negated_conjecture,
( esk4_0 = empty_set
| esk3_0 = empty_set
| set_intersection2(esk3_0,esk5_0) = esk3_0 ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( ~ subset(esk3_0,esk5_0)
| esk3_0 = empty_set
| esk4_0 = empty_set ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( X1 != empty_set
| cartesian_product2(X2,X1) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
cartesian_product2(esk3_0,esk4_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_35,negated_conjecture,
( esk3_0 = empty_set
| esk4_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_31]),c_0_32]) ).
cnf(c_0_36,plain,
cartesian_product2(X1,empty_set) = empty_set,
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( X1 != empty_set
| cartesian_product2(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,negated_conjecture,
esk3_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,plain,
cartesian_product2(empty_set,X1) = empty_set,
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_38]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET984+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:45:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2680602 completed with status 0
% 0.14/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FGHSM-FFSS22-SFFFFFNN
% 0.14/0.44 % partial match(1): FGHSF-FFSS22-SFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2680609 completed with status 0
% 0.14/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FGHSM-FFSS22-SFFFFFNN
% 0.14/0.44 % partial match(1): FGHSF-FFSS22-SFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44 % Presaturation interreduction done
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 12
% 0.14/0.44 % Removed by relevancy pruning/SinE : 0
% 0.14/0.44 % Initial clauses : 17
% 0.14/0.44 % Removed in clause preprocessing : 0
% 0.14/0.44 % Initial clauses in saturation : 17
% 0.14/0.44 % Processed clauses : 194
% 0.14/0.44 % ...of these trivial : 23
% 0.14/0.44 % ...subsumed : 65
% 0.14/0.44 % ...remaining for further processing : 106
% 0.14/0.44 % Other redundant clauses eliminated : 2
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 9
% 0.14/0.44 % Backward-rewritten : 23
% 0.14/0.44 % Generated clauses : 956
% 0.14/0.44 % ...of the previous two non-redundant : 661
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 1
% 0.14/0.44 % Paramodulations : 946
% 0.14/0.44 % Factorizations : 3
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 7
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 959
% 0.14/0.44 % ...of those cached : 774
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 55
% 0.14/0.44 % Positive orientable unit clauses : 34
% 0.14/0.44 % Positive unorientable unit clauses: 3
% 0.14/0.44 % Negative unit clauses : 2
% 0.14/0.44 % Non-unit-clauses : 16
% 0.14/0.44 % Current number of unprocessed clauses: 461
% 0.14/0.44 % ...number of literals in the above : 1155
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 49
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 294
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 231
% 0.14/0.44 % Non-unit clause-clause subsumptions : 65
% 0.14/0.44 % Unit Clause-clause subsumption calls : 20
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 90
% 0.14/0.44 % BW rewrite match successes : 46
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 11380
% 0.14/0.44 % Search garbage collected termcells : 135
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.014 s
% 0.14/0.44 % System time : 0.003 s
% 0.14/0.44 % Total time : 0.016 s
% 0.14/0.44 % Maximum resident set size: 3328 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.056 s
% 0.14/0.44 % System time : 0.010 s
% 0.14/0.44 % Total time : 0.066 s
% 0.14/0.44 % Maximum resident set size: 4864 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------