%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET629+3 : 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 : 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 02:14:48 PM UTC 2026
% Result : Theorem 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 68 ( 29 ~; 21 |; 11 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 3 sgn 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_and_difference_disjoint,conjecture,
! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_and_difference_disjoint) ).
fof(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(symmetry_of_intersect,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
inference(assume_negation,[status(cth)],[prove_intersection_and_difference_disjoint]) ).
fof(c_0_7,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint_defn]) ).
fof(c_0_8,negated_conjecture,
~ disjoint(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,plain,
! [X16,X17] :
( ( disjoint(X16,X17)
| intersect(X16,X17) )
& ( ~ intersect(X16,X17)
| ~ disjoint(X16,X17) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X20,X21] :
( intersect(X21,X20)
| ~ intersect(X20,X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])])]) ).
cnf(c_0_11,negated_conjecture,
~ disjoint(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( disjoint(X1,X2)
| intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X10,X11,X13,X14,X15] :
( ( intersect(X13,X14)
| ~ member(X15,X14)
| ~ member(X15,X13) )
& ( ~ intersect(X10,X11)
| member(esk1_2(X10,X11),X11) )
& ( ~ intersect(X10,X11)
| member(esk1_2(X10,X11),X10) ) ),
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)],[intersect_defn])])])])])])]) ).
cnf(c_0_14,plain,
( ~ intersect(X1,X2)
| intersect(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
intersect(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_16,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_17,plain,
! [X4,X5,X6] :
( ( member(X6,intersection(X4,X5))
| ~ member(X6,X5)
| ~ member(X6,X4) )
& ( ~ member(X6,intersection(X4,X5))
| member(X6,X5) )
& ( ~ member(X6,intersection(X4,X5))
| member(X6,X4) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_18,plain,
( ~ intersect(X1,X2)
| member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
intersect(difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_20,plain,
! [X7,X8,X9] :
( ( member(X9,difference(X7,X8))
| member(X9,X8)
| ~ member(X9,X7) )
& ( ~ member(X9,difference(X7,X8))
| ~ member(X9,X8) )
& ( ~ member(X9,difference(X7,X8))
| member(X9,X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_21,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
member(esk1_2(difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),intersection(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
member(esk1_2(difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),esk4_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( ~ intersect(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
~ member(esk1_2(difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),difference(X1,esk4_0)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET629+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:30:15 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42 % Version: 3.5.1
% 0.10/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.42 % Starting sh5l with 300s (1) cores
% 0.10/0.42 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2092920 completed with status 0
% 0.10/0.42 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.42 % No SInE strategy applied
% 0.10/0.42 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.10/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.10/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.42 % new_bool_1 with pid 2092928 completed with status 0
% 0.10/0.42 % Result found by new_bool_1
% 0.10/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.42 % No SInE strategy applied
% 0.10/0.42 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.10/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.42 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.42 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.10/0.42 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.42 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.42 % Preprocessing time : 0.001 s
% 0.10/0.42 % Presaturation interreduction done
% 0.10/0.42
% 0.10/0.42 % Proof found!
% 0.10/0.42 % SZS status Theorem
% 0.10/0.42 % SZS output start CNFRefutation
% See solution above
% 0.10/0.42 % Parsed axioms : 8
% 0.10/0.42 % Removed by relevancy pruning/SinE : 0
% 0.10/0.42 % Initial clauses : 18
% 0.10/0.42 % Removed in clause preprocessing : 2
% 0.10/0.42 % Initial clauses in saturation : 16
% 0.10/0.42 % Processed clauses : 94
% 0.10/0.42 % ...of these trivial : 2
% 0.10/0.42 % ...subsumed : 4
% 0.10/0.42 % ...remaining for further processing : 87
% 0.10/0.42 % Other redundant clauses eliminated : 0
% 0.10/0.42 % Clauses deleted for lack of memory : 0
% 0.10/0.42 % Backward-subsumed : 0
% 0.10/0.42 % Backward-rewritten : 0
% 0.10/0.42 % Generated clauses : 158
% 0.10/0.42 % ...of the previous two non-redundant : 129
% 0.10/0.42 % ...aggressively subsumed : 0
% 0.10/0.42 % Contextual simplify-reflections : 0
% 0.10/0.42 % Paramodulations : 156
% 0.10/0.42 % Factorizations : 2
% 0.10/0.42 % NegExts : 0
% 0.10/0.42 % Equation resolutions : 0
% 0.10/0.42 % Disequality decompositions : 0
% 0.10/0.42 % Total rewrite steps : 27
% 0.10/0.42 % ...of those cached : 16
% 0.10/0.42 % Propositional unsat checks : 0
% 0.10/0.42 % Propositional check models : 0
% 0.10/0.42 % Propositional check unsatisfiable : 0
% 0.10/0.42 % Propositional clauses : 0
% 0.10/0.42 % Propositional clauses after purity: 0
% 0.10/0.42 % Propositional unsat core size : 0
% 0.10/0.42 % Propositional preprocessing time : 0.000
% 0.10/0.42 % Propositional encoding time : 0.000
% 0.10/0.42 % Propositional solver time : 0.000
% 0.10/0.42 % Success case prop preproc time : 0.000
% 0.10/0.42 % Success case prop encoding time : 0.000
% 0.10/0.42 % Success case prop solver time : 0.000
% 0.10/0.42 % Current number of processed clauses : 71
% 0.10/0.42 % Positive orientable unit clauses : 29
% 0.10/0.42 % Positive unorientable unit clauses: 1
% 0.10/0.42 % Negative unit clauses : 17
% 0.10/0.42 % Non-unit-clauses : 24
% 0.10/0.42 % Current number of unprocessed clauses: 67
% 0.10/0.42 % ...number of literals in the above : 148
% 0.10/0.42 % Current number of archived formulas : 0
% 0.10/0.42 % Current number of archived clauses : 16
% 0.10/0.42 % Clause-clause subsumption calls (NU) : 82
% 0.10/0.42 % Rec. Clause-clause subsumption calls : 82
% 0.10/0.42 % Non-unit clause-clause subsumptions : 4
% 0.10/0.42 % Unit Clause-clause subsumption calls : 77
% 0.10/0.42 % Rewrite failures with RHS unbound : 0
% 0.10/0.42 % BW rewrite match attempts : 2
% 0.10/0.42 % BW rewrite match successes : 2
% 0.10/0.42 % Condensation attempts : 0
% 0.10/0.42 % Condensation successes : 0
% 0.10/0.42 % Termbank termtop insertions : 3395
% 0.10/0.42 % Search garbage collected termcells : 289
% 0.10/0.42
% 0.10/0.42 % -------------------------------------------------
% 0.10/0.42 % User time : 0.005 s
% 0.10/0.42 % System time : 0.002 s
% 0.10/0.42 % Total time : 0.007 s
% 0.10/0.42 % Maximum resident set size: 3580 pages
% 0.10/0.42
% 0.10/0.42 % -------------------------------------------------
% 0.10/0.42 % User time : 0.022 s
% 0.10/0.42 % System time : 0.013 s
% 0.10/0.42 % Total time : 0.035 s
% 0.10/0.42 % Maximum resident set size: 4864 pages
% 0.10/0.42 % E exiting
%------------------------------------------------------------------------------