%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET630+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 : n026.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 0.14s 5.85s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 19 unt; 0 def)
% Number of atoms : 44 ( 6 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 11 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_and_symmetric_difference_disjoint,conjecture,
! [X1,X2] : disjoint(intersection(X1,X2),symmetric_difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_and_symmetric_difference_disjoint) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(intersection_and_union_disjoint,axiom,
! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_and_union_disjoint) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(intersect_with_union,axiom,
! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X3)
| intersect(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_with_union) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] : disjoint(intersection(X1,X2),symmetric_difference(X1,X2)),
inference(assume_negation,[status(cth)],[prove_intersection_and_symmetric_difference_disjoint]) ).
fof(c_0_7,negated_conjecture,
~ disjoint(intersection(esk3_0,esk4_0),symmetric_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_8,plain,
! [X4,X5] : symmetric_difference(X4,X5) = union(difference(X4,X5),difference(X5,X4)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
fof(c_0_9,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint_defn]) ).
fof(c_0_10,plain,
! [X9,X10] : disjoint(intersection(X9,X10),difference(X9,X10)),
inference(variable_rename,[status(thm)],[intersection_and_union_disjoint]) ).
fof(c_0_11,plain,
! [X24,X25] : intersection(X24,X25) = intersection(X25,X24),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_12,negated_conjecture,
~ disjoint(intersection(esk3_0,esk4_0),symmetric_difference(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X20,X21] :
( ( disjoint(X20,X21)
| intersect(X20,X21) )
& ( ~ intersect(X20,X21)
| ~ disjoint(X20,X21) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
disjoint(intersection(X1,X2),difference(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X6,X7,X8] :
( ( intersect(X6,union(X7,X8))
| ~ intersect(X6,X8) )
& ( intersect(X6,union(X7,X8))
| ~ intersect(X6,X7) )
& ( intersect(X6,X8)
| intersect(X6,X7)
| ~ intersect(X6,union(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersect_with_union])])])]) ).
cnf(c_0_18,negated_conjecture,
~ disjoint(intersection(esk3_0,esk4_0),union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( disjoint(X1,X2)
| intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ intersect(X1,X2)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
disjoint(intersection(X1,X2),difference(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( ~ intersect(X1,union(X2,X3))
| intersect(X1,X3)
| intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
intersect(intersection(esk3_0,esk4_0),union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
~ intersect(intersection(X1,X2),difference(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
~ intersect(intersection(X1,X2),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/5.78 % Computer : n026.cluster.edu
% 0.10/5.78 % Model : x86_64 x86_64
% 0.10/5.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.78 % Memory : 8046.5625MB
% 0.10/5.78 % OS : Linux 6.8.0-71-generic
% 0.10/5.78 % CPULimit : 300
% 0.10/5.78 % WCLimit : 300
% 0.10/5.78 % DateTime : Mon Sep 21 05:32:59 UTC 2026
% 0.10/5.78 % CPUTime :
% 0.10/5.78 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.82 Running first-order theorem proving
% 0.14/5.82 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
% 0.14/5.85 % Version: 3.5.1
% 0.14/5.85 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.85 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.85 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.85 % Starting sh5l with 300s (1) cores
% 0.14/5.85 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1464486 completed with status 0
% 0.14/5.85 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/5.85 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.85 % No SInE strategy applied
% 0.14/5.85 % Search class: FGHSM-FFSF22-SFFFFFNN
% 0.14/5.85 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.85 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/5.85 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/5.85 % Starting new_bool_3 with 136s (1) cores
% 0.14/5.85 % Starting new_bool_1 with 136s (1) cores
% 0.14/5.85 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1464493 completed with status 0
% 0.14/5.85 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/5.85 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/5.85 % No SInE strategy applied
% 0.14/5.85 % Search class: FGHSM-FFSF22-SFFFFFNN
% 0.14/5.85 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/5.85 % Starting SubtermCWHack with 136s (1) cores
% 0.14/5.85 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/5.85 % Preprocessing time : 0.001 s
% 0.14/5.85 % Presaturation interreduction done
% 0.14/5.85
% 0.14/5.85 % Proof found!
% 0.14/5.85 % SZS status Theorem
% 0.14/5.85 % SZS output start CNFRefutation
% See solution above
% 0.14/5.85 % Parsed axioms : 12
% 0.14/5.85 % Removed by relevancy pruning/SinE : 0
% 0.14/5.85 % Initial clauses : 22
% 0.14/5.85 % Removed in clause preprocessing : 3
% 0.14/5.85 % Initial clauses in saturation : 19
% 0.14/5.85 % Processed clauses : 41
% 0.14/5.85 % ...of these trivial : 2
% 0.14/5.85 % ...subsumed : 1
% 0.14/5.85 % ...remaining for further processing : 38
% 0.14/5.85 % Other redundant clauses eliminated : 0
% 0.14/5.85 % Clauses deleted for lack of memory : 0
% 0.14/5.85 % Backward-subsumed : 0
% 0.14/5.85 % Backward-rewritten : 0
% 0.14/5.85 % Generated clauses : 35
% 0.14/5.85 % ...of the previous two non-redundant : 28
% 0.14/5.85 % ...aggressively subsumed : 0
% 0.14/5.85 % Contextual simplify-reflections : 0
% 0.14/5.85 % Paramodulations : 35
% 0.14/5.85 % Factorizations : 0
% 0.14/5.85 % NegExts : 0
% 0.14/5.85 % Equation resolutions : 0
% 0.14/5.85 % Disequality decompositions : 0
% 0.14/5.85 % Total rewrite steps : 4
% 0.14/5.85 % ...of those cached : 1
% 0.14/5.85 % Propositional unsat checks : 0
% 0.14/5.85 % Propositional check models : 0
% 0.14/5.85 % Propositional check unsatisfiable : 0
% 0.14/5.85 % Propositional clauses : 0
% 0.14/5.85 % Propositional clauses after purity: 0
% 0.14/5.85 % Propositional unsat core size : 0
% 0.14/5.85 % Propositional preprocessing time : 0.000
% 0.14/5.85 % Propositional encoding time : 0.000
% 0.14/5.85 % Propositional solver time : 0.000
% 0.14/5.85 % Success case prop preproc time : 0.000
% 0.14/5.85 % Success case prop encoding time : 0.000
% 0.14/5.85 % Success case prop solver time : 0.000
% 0.14/5.85 % Current number of processed clauses : 20
% 0.14/5.85 % Positive orientable unit clauses : 4
% 0.14/5.85 % Positive unorientable unit clauses: 2
% 0.14/5.85 % Negative unit clauses : 3
% 0.14/5.85 % Non-unit-clauses : 11
% 0.14/5.85 % Current number of unprocessed clauses: 22
% 0.14/5.85 % ...number of literals in the above : 46
% 0.14/5.85 % Current number of archived formulas : 0
% 0.14/5.85 % Current number of archived clauses : 19
% 0.14/5.85 % Clause-clause subsumption calls (NU) : 55
% 0.14/5.85 % Rec. Clause-clause subsumption calls : 51
% 0.14/5.85 % Non-unit clause-clause subsumptions : 0
% 0.14/5.85 % Unit Clause-clause subsumption calls : 1
% 0.14/5.85 % Rewrite failures with RHS unbound : 0
% 0.14/5.85 % BW rewrite match attempts : 7
% 0.14/5.85 % BW rewrite match successes : 6
% 0.14/5.85 % Condensation attempts : 0
% 0.14/5.85 % Condensation successes : 0
% 0.14/5.85 % Termbank termtop insertions : 1658
% 0.14/5.85 % Search garbage collected termcells : 293
% 0.14/5.85
% 0.14/5.85 % -------------------------------------------------
% 0.14/5.85 % User time : 0.008 s
% 0.14/5.85 % System time : 0.003 s
% 0.14/5.85 % Total time : 0.010 s
% 0.14/5.85 % Maximum resident set size: 3636 pages
% 0.14/5.85
% 0.14/5.85 % -------------------------------------------------
% 0.14/5.85 % User time : 0.021 s
% 0.14/5.85 % System time : 0.014 s
% 0.14/5.85 % Total time : 0.034 s
% 0.14/5.85 % Maximum resident set size: 4608 pages
% 0.14/5.85 % E exiting
%------------------------------------------------------------------------------