%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU245+2 : TPTP v9.3.1. Released v3.3.0.
% 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 02:24:26 PM UTC 2026
% Result : Theorem 7.55s 1.57s
% Output : CNFRefutation 7.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 118 ( 27 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 137 ( 52 ~; 56 |; 18 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 77 ( 3 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(t16_wellord1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,cartesian_product2(X2,X2))
& in(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(d6_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_6,plain,
! [X235,X236,X237,X238,X239,X240,X241,X242] :
( ( X242 = set_intersection2(X240,X241)
| in(esk47_3(X240,X241,X242),X242)
| in(esk47_3(X240,X241,X242),X241) )
& ( X242 = set_intersection2(X240,X241)
| in(esk47_3(X240,X241,X242),X242)
| in(esk47_3(X240,X241,X242),X240) )
& ( X242 = set_intersection2(X240,X241)
| ~ in(esk47_3(X240,X241,X242),X241)
| ~ in(esk47_3(X240,X241,X242),X240)
| ~ in(esk47_3(X240,X241,X242),X242) )
& ( X237 != set_intersection2(X235,X236)
| in(X239,X237)
| ~ in(X239,X236)
| ~ in(X239,X235) )
& ( X237 != set_intersection2(X235,X236)
| ~ in(X238,X237)
| in(X238,X236) )
& ( X237 != set_intersection2(X235,X236)
| ~ in(X238,X237)
| in(X238,X235) ) ),
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)],[d3_xboole_0])])])])])])]) ).
fof(c_0_7,lemma,
! [X717,X718] : set_difference(X717,set_difference(X717,X718)) = set_intersection2(X717,X718),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,cartesian_product2(X2,X2))
& in(X1,X3) ) ) ),
inference(assume_negation,[status(cth)],[t16_wellord1]) ).
fof(c_0_9,plain,
! [X322,X323] :
( relation_restriction(X322,X323) = set_intersection2(X322,cartesian_product2(X323,X323))
| ~ relation(X322) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_wellord1])])])]) ).
fof(c_0_10,plain,
! [X278,X279,X280,X281,X282,X283,X284,X285] :
( ( X285 = set_difference(X283,X284)
| in(esk56_3(X283,X284,X285),X285)
| ~ in(esk56_3(X283,X284,X285),X284) )
& ( X285 = set_difference(X283,X284)
| in(esk56_3(X283,X284,X285),X285)
| in(esk56_3(X283,X284,X285),X283) )
& ( X285 = set_difference(X283,X284)
| in(esk56_3(X283,X284,X285),X284)
| ~ in(esk56_3(X283,X284,X285),X283)
| ~ in(esk56_3(X283,X284,X285),X285) )
& ( X280 != set_difference(X278,X279)
| in(X282,X280)
| in(X282,X279)
| ~ in(X282,X278) )
& ( X280 != set_difference(X278,X279)
| ~ in(X281,X280)
| ~ in(X281,X279) )
& ( X280 != set_difference(X278,X279)
| ~ in(X281,X280)
| in(X281,X278) ) ),
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)],[c_0_5])])])])])])]) ).
cnf(c_0_11,plain,
( X3 != set_intersection2(X4,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,negated_conjecture,
( ( in(esk104_0,relation_restriction(esk106_0,esk105_0))
| in(esk104_0,cartesian_product2(esk105_0,esk105_0)) )
& ( in(esk104_0,relation_restriction(esk106_0,esk105_0))
| in(esk104_0,esk106_0) )
& ( ~ in(esk104_0,cartesian_product2(esk105_0,esk105_0))
| ~ in(esk104_0,esk106_0)
| ~ in(esk104_0,relation_restriction(esk106_0,esk105_0)) )
& relation(esk106_0) ),
inference(distribute,[status(thm)],[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_14,plain,
( ~ relation(X1)
| relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( X3 != set_difference(X2,X4)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ in(X1,X3)
| X3 != set_difference(X4,set_difference(X4,X2))
| in(X1,X2) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( X4 != set_intersection2(X2,X3)
| ~ in(X1,X3)
| ~ in(X1,X2)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
( ~ in(esk104_0,cartesian_product2(esk105_0,esk105_0))
| ~ in(esk104_0,esk106_0)
| ~ in(esk104_0,relation_restriction(esk106_0,esk105_0)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ relation(X1)
| relation_restriction(X1,X2) = set_difference(X1,set_difference(X1,cartesian_product2(X2,X2))) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_20,negated_conjecture,
relation(esk106_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ in(X1,set_difference(X2,X3))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( ~ in(X1,set_difference(X3,set_difference(X3,X2)))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_difference(X2,set_difference(X2,X3))
| in(X1,X4) ),
inference(rw,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_24,negated_conjecture,
~ in(esk104_0,set_difference(esk106_0,set_difference(esk106_0,cartesian_product2(esk105_0,esk105_0)))),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_21]),c_0_22]) ).
cnf(c_0_25,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( in(esk104_0,relation_restriction(esk106_0,esk105_0))
| in(esk104_0,esk106_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(esk104_0,esk106_0)
| ~ in(esk104_0,cartesian_product2(esk105_0,esk105_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
in(esk104_0,esk106_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_20])]),c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( in(esk104_0,relation_restriction(esk106_0,esk105_0))
| in(esk104_0,cartesian_product2(esk105_0,esk105_0)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,negated_conjecture,
~ in(esk104_0,cartesian_product2(esk105_0,esk105_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
in(esk104_0,relation_restriction(esk106_0,esk105_0)),
inference(sr,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_19]),c_0_20])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU245+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n006.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Mon Sep 21 06:02:43 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 7.55/1.57 % Version: 3.5.1
% 7.55/1.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.55/1.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.55/1.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.55/1.57 % Starting new_bool_3 with 300s (1) cores
% 7.55/1.57 % Starting new_bool_1 with 300s (1) cores
% 7.55/1.57 % Starting sh5l with 300s (1) cores
% 7.55/1.57 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2149188 completed with status 0
% 7.55/1.57 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 7.55/1.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.55/1.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.55/1.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.55/1.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.55/1.57 % No SInE strategy applied
% 7.55/1.57 % Search class: FGHSM-FSLM32-MFFFFFNN
% 7.55/1.57 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 7.55/1.57 % Starting SubtermCWHack with 136s (1) cores
% 7.55/1.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 7.55/1.57 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 7.55/1.57 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 7.55/1.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 7.55/1.57 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 2149199 completed with status 0
% 7.55/1.57 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 7.55/1.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 7.55/1.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.55/1.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 7.55/1.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.55/1.57 % No SInE strategy applied
% 7.55/1.57 % Search class: FGHSM-FSLM32-MFFFFFNN
% 7.55/1.57 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 7.55/1.57 % Starting SubtermCWHack with 136s (1) cores
% 7.55/1.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 7.55/1.57 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 123s (1) cores
% 7.55/1.57 % Starting U----_100_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_ND_S04AN with 123s (1) cores
% 7.55/1.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 123s (1) cores
% 7.55/1.57 % Preprocessing time : 0.017 s
% 7.55/1.57 % Presaturation interreduction done
% 7.55/1.57
% 7.55/1.57 % Proof found!
% 7.55/1.57 % SZS status Theorem
% 7.55/1.57 % SZS output start CNFRefutation
% See solution above
% 7.55/1.57 % Parsed axioms : 302
% 7.55/1.57 % Removed by relevancy pruning/SinE : 0
% 7.55/1.57 % Initial clauses : 651
% 7.55/1.57 % Removed in clause preprocessing : 30
% 7.55/1.57 % Initial clauses in saturation : 621
% 7.55/1.57 % Processed clauses : 2207
% 7.55/1.57 % ...of these trivial : 48
% 7.55/1.57 % ...subsumed : 589
% 7.55/1.57 % ...remaining for further processing : 1570
% 7.55/1.57 % Other redundant clauses eliminated : 169
% 7.55/1.57 % Clauses deleted for lack of memory : 0
% 7.55/1.57 % Backward-subsumed : 11
% 7.55/1.57 % Backward-rewritten : 80
% 7.55/1.57 % Generated clauses : 14754
% 7.55/1.57 % ...of the previous two non-redundant : 14118
% 7.55/1.57 % ...aggressively subsumed : 0
% 7.55/1.57 % Contextual simplify-reflections : 36
% 7.55/1.57 % Paramodulations : 14580
% 7.55/1.57 % Factorizations : 14
% 7.55/1.57 % NegExts : 0
% 7.55/1.57 % Equation resolutions : 175
% 7.55/1.57 % Disequality decompositions : 0
% 7.55/1.57 % Total rewrite steps : 1870
% 7.55/1.57 % ...of those cached : 1639
% 7.55/1.57 % Propositional unsat checks : 0
% 7.55/1.57 % Propositional check models : 0
% 7.55/1.57 % Propositional check unsatisfiable : 0
% 7.55/1.57 % Propositional clauses : 0
% 7.55/1.57 % Propositional clauses after purity: 0
% 7.55/1.57 % Propositional unsat core size : 0
% 7.55/1.57 % Propositional preprocessing time : 0.000
% 7.55/1.57 % Propositional encoding time : 0.000
% 7.55/1.57 % Propositional solver time : 0.000
% 7.55/1.57 % Success case prop preproc time : 0.000
% 7.55/1.57 % Success case prop encoding time : 0.000
% 7.55/1.57 % Success case prop solver time : 0.000
% 7.55/1.57 % Current number of processed clauses : 828
% 7.55/1.57 % Positive orientable unit clauses : 101
% 7.55/1.57 % Positive unorientable unit clauses: 3
% 7.55/1.57 % Negative unit clauses : 86
% 7.55/1.57 % Non-unit-clauses : 638
% 7.55/1.57 % Current number of unprocessed clauses: 12987
% 7.55/1.57 % ...number of literals in the above : 55049
% 7.55/1.57 % Current number of archived formulas : 0
% 7.55/1.57 % Current number of archived clauses : 655
% 7.55/1.57 % Clause-clause subsumption calls (NU) : 209598
% 7.55/1.57 % Rec. Clause-clause subsumption calls : 87210
% 7.55/1.57 % Non-unit clause-clause subsumptions : 315
% 7.55/1.57 % Unit Clause-clause subsumption calls : 24722
% 7.55/1.57 % Rewrite failures with RHS unbound : 0
% 7.55/1.57 % BW rewrite match attempts : 91
% 7.55/1.57 % BW rewrite match successes : 66
% 7.55/1.57 % Condensation attempts : 0
% 7.55/1.57 % Condensation successes : 0
% 7.55/1.57 % Termbank termtop insertions : 284579
% 7.55/1.57 % Search garbage collected termcells : 11225
% 7.55/1.57
% 7.55/1.57 % -------------------------------------------------
% 7.55/1.57 % User time : 0.872 s
% 7.55/1.57 % System time : 0.038 s
% 7.55/1.57 % Total time : 0.910 s
% 7.55/1.57 % Maximum resident set size: 5752 pages
% 7.55/1.57
% 7.55/1.57 % -------------------------------------------------
% 7.55/1.57 % User time : 4.500 s
% 7.55/1.57 % System time : 0.179 s
% 7.55/1.57 % Total time : 4.679 s
% 7.55/1.57 % Maximum resident set size: 5120 pages
% 7.55/1.57 % E exiting
%------------------------------------------------------------------------------