%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET624+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 02:14:47 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 8 unt; 0 def)
% Number of atoms : 94 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 93 ( 36 ~; 45 |; 7 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 5 sgn 27 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X2)
| member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(prove_intersect_with_union,conjecture,
! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X3)
| intersect(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersect_with_union) ).
fof(symmetry_of_intersect,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_5,plain,
! [X7,X8,X10,X11,X12] :
( ( intersect(X10,X11)
| ~ member(X12,X11)
| ~ member(X12,X10) )
& ( ~ intersect(X7,X8)
| member(esk1_2(X7,X8),X8) )
& ( ~ intersect(X7,X8)
| member(esk1_2(X7,X8),X7) ) ),
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_6,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| intersect(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_7,plain,
( ~ intersect(X1,X2)
| member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X4,X5,X6] :
( ( member(X6,union(X4,X5))
| ~ member(X6,X5) )
& ( member(X6,union(X4,X5))
| ~ member(X6,X4) )
& ( member(X6,X5)
| member(X6,X4)
| ~ member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
cnf(c_0_9,plain,
( ~ member(esk1_2(X3,X2),X1)
| ~ intersect(X3,X2)
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X3)
| intersect(X1,X2) ) ),
inference(assume_negation,[status(cth)],[prove_intersect_with_union]) ).
fof(c_0_12,plain,
! [X15,X16] :
( intersect(X16,X15)
| ~ intersect(X15,X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])])]) ).
cnf(c_0_13,plain,
( ~ member(esk1_2(X4,X3),X2)
| ~ intersect(X4,X3)
| intersect(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( ~ intersect(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_15,negated_conjecture,
( ( intersect(esk3_0,esk5_0)
| intersect(esk3_0,esk4_0)
| intersect(esk3_0,union(esk4_0,esk5_0)) )
& ( ~ intersect(esk3_0,union(esk4_0,esk5_0))
| ~ intersect(esk3_0,esk5_0) )
& ( ~ intersect(esk3_0,union(esk4_0,esk5_0))
| ~ intersect(esk3_0,esk4_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_11])])])])]) ).
cnf(c_0_16,plain,
( ~ intersect(X1,X2)
| intersect(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ~ intersect(X2,X3)
| intersect(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( ~ intersect(esk3_0,union(esk4_0,esk5_0))
| ~ intersect(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ intersect(X3,X1)
| intersect(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( intersect(esk3_0,esk5_0)
| intersect(esk3_0,esk4_0)
| intersect(esk3_0,union(esk4_0,esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
~ intersect(esk3_0,esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_16]) ).
cnf(c_0_23,plain,
( ~ intersect(X1,union(X2,X3))
| member(esk1_2(X1,union(X2,X3)),X3)
| member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_7]) ).
cnf(c_0_24,negated_conjecture,
( intersect(esk3_0,esk4_0)
| intersect(esk3_0,union(esk4_0,esk5_0)) ),
inference(sr,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( ~ member(esk1_2(X2,X3),X1)
| ~ intersect(X2,X3)
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_6,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0)
| member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk5_0)
| intersect(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
( member(esk1_2(esk3_0,union(esk4_0,esk5_0)),esk4_0)
| intersect(esk5_0,esk3_0)
| intersect(esk3_0,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( intersect(esk4_0,esk3_0)
| intersect(esk5_0,esk3_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_24]),c_0_16]) ).
cnf(c_0_29,negated_conjecture,
intersect(esk4_0,esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_28]),c_0_22]) ).
fof(c_0_30,plain,
! [X13,X14] : union(X13,X14) = union(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_31,negated_conjecture,
( ~ intersect(esk3_0,union(esk4_0,esk5_0))
| ~ intersect(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,negated_conjecture,
intersect(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_16,c_0_29]) ).
cnf(c_0_33,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
~ intersect(esk3_0,union(esk4_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_35,plain,
( ~ intersect(X2,X1)
| intersect(X1,union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:29:58 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.43 % Version: 3.5.1
% 0.13/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.43 % Starting sh5l with 300s (1) cores
% 0.13/0.43 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 940036 completed with status 0
% 0.13/0.43 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.13/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.43 % No SInE strategy applied
% 0.13/0.43 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.13/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.43 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 940044 completed with status 0
% 0.13/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.13/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.13/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.43 % No SInE strategy applied
% 0.13/0.43 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.13/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.43 % Preprocessing time : 0.001 s
% 0.13/0.43 % Presaturation interreduction done
% 0.13/0.43
% 0.13/0.43 % Proof found!
% 0.13/0.43 % SZS status Theorem
% 0.13/0.43 % SZS output start CNFRefutation
% See solution above
% 0.13/0.43 % Parsed axioms : 6
% 0.13/0.43 % Removed by relevancy pruning/SinE : 0
% 0.13/0.43 % Initial clauses : 15
% 0.13/0.43 % Removed in clause preprocessing : 2
% 0.13/0.43 % Initial clauses in saturation : 13
% 0.13/0.43 % Processed clauses : 238
% 0.13/0.43 % ...of these trivial : 60
% 0.13/0.43 % ...subsumed : 66
% 0.13/0.43 % ...remaining for further processing : 112
% 0.13/0.43 % Other redundant clauses eliminated : 0
% 0.13/0.43 % Clauses deleted for lack of memory : 0
% 0.13/0.43 % Backward-subsumed : 2
% 0.13/0.43 % Backward-rewritten : 15
% 0.13/0.43 % Generated clauses : 824
% 0.13/0.43 % ...of the previous two non-redundant : 579
% 0.13/0.43 % ...aggressively subsumed : 0
% 0.13/0.43 % Contextual simplify-reflections : 6
% 0.13/0.43 % Paramodulations : 807
% 0.13/0.43 % Factorizations : 14
% 0.13/0.43 % NegExts : 0
% 0.13/0.43 % Equation resolutions : 0
% 0.13/0.43 % Disequality decompositions : 0
% 0.13/0.43 % Total rewrite steps : 298
% 0.13/0.43 % ...of those cached : 260
% 0.13/0.43 % Propositional unsat checks : 0
% 0.13/0.43 % Propositional check models : 0
% 0.13/0.43 % Propositional check unsatisfiable : 0
% 0.13/0.43 % Propositional clauses : 0
% 0.13/0.43 % Propositional clauses after purity: 0
% 0.13/0.43 % Propositional unsat core size : 0
% 0.13/0.43 % Propositional preprocessing time : 0.000
% 0.13/0.43 % Propositional encoding time : 0.000
% 0.13/0.43 % Propositional solver time : 0.000
% 0.13/0.43 % Success case prop preproc time : 0.000
% 0.13/0.43 % Success case prop encoding time : 0.000
% 0.13/0.43 % Success case prop solver time : 0.000
% 0.13/0.43 % Current number of processed clauses : 79
% 0.13/0.43 % Positive orientable unit clauses : 31
% 0.13/0.43 % Positive unorientable unit clauses: 1
% 0.13/0.43 % Negative unit clauses : 3
% 0.13/0.43 % Non-unit-clauses : 44
% 0.13/0.43 % Current number of unprocessed clauses: 355
% 0.13/0.43 % ...number of literals in the above : 964
% 0.13/0.43 % Current number of archived formulas : 0
% 0.13/0.43 % Current number of archived clauses : 33
% 0.13/0.43 % Clause-clause subsumption calls (NU) : 927
% 0.13/0.43 % Rec. Clause-clause subsumption calls : 856
% 0.13/0.43 % Non-unit clause-clause subsumptions : 72
% 0.13/0.43 % Unit Clause-clause subsumption calls : 41
% 0.13/0.43 % Rewrite failures with RHS unbound : 0
% 0.13/0.43 % BW rewrite match attempts : 7
% 0.13/0.43 % BW rewrite match successes : 7
% 0.13/0.43 % Condensation attempts : 0
% 0.13/0.43 % Condensation successes : 0
% 0.13/0.43 % Termbank termtop insertions : 10096
% 0.13/0.43 % Search garbage collected termcells : 292
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.018 s
% 0.13/0.43 % System time : 0.002 s
% 0.13/0.43 % Total time : 0.021 s
% 0.13/0.43 % Maximum resident set size: 3632 pages
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.078 s
% 0.13/0.43 % System time : 0.017 s
% 0.13/0.43 % Total time : 0.095 s
% 0.13/0.43 % Maximum resident set size: 4864 pages
% 0.13/0.43 % E exiting
%------------------------------------------------------------------------------