%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET600+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 : n010.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 02:14:39 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 77 ( 37 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 73 ( 26 ~; 33 |; 9 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 5 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(prove_th59,conjecture,
! [X1,X2] :
( union(X1,X2) = empty_set
<=> ( X2 = empty_set
& X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th59) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_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(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,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( union(X1,X2) = empty_set
<=> ( X2 = empty_set
& X1 = empty_set ) ),
inference(assume_negation,[status(cth)],[prove_th59]) ).
fof(c_0_7,plain,
! [X6] : ~ member(X6,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
fof(c_0_8,plain,
! [X12,X13,X14,X15,X16,X17] :
( ( X16 = X17
| member(esk3_2(X16,X17),X17)
| member(esk3_2(X16,X17),X16) )
& ( X16 = X17
| ~ member(esk3_2(X16,X17),X17)
| ~ member(esk3_2(X16,X17),X16) )
& ( X12 != X13
| member(X15,X12)
| ~ member(X15,X13) )
& ( X12 != X13
| member(X14,X13)
| ~ member(X14,X12) ) ),
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)],[equal_member_defn])])])])])])]) ).
fof(c_0_9,plain,
! [X7,X8,X9] :
( ( member(X9,union(X7,X8))
| ~ member(X9,X8) )
& ( member(X9,union(X7,X8))
| ~ member(X9,X7) )
& ( member(X9,X8)
| member(X9,X7)
| ~ member(X9,union(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])])]) ).
fof(c_0_10,negated_conjecture,
( ( union(esk1_0,esk2_0) = empty_set
| esk2_0 = empty_set )
& ( union(esk1_0,esk2_0) = empty_set
| esk1_0 = empty_set )
& ( esk2_0 != empty_set
| esk1_0 != empty_set
| union(esk1_0,esk2_0) != empty_set ) ),
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_6])])])])]) ).
cnf(c_0_11,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( union(esk1_0,esk2_0) = empty_set
| esk2_0 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( union(esk1_0,esk2_0) = empty_set
| esk1_0 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( member(esk3_2(X1,empty_set),X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X1,esk2_0)
| esk2_0 = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).
fof(c_0_20,plain,
! [X10,X11] : union(X10,X11) = union(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X1,esk1_0)
| esk1_0 = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_11]) ).
cnf(c_0_22,plain,
( member(esk3_2(union(X1,X2),empty_set),X1)
| member(esk3_2(union(X1,X2),empty_set),X2)
| union(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( esk2_0 != empty_set
| esk1_0 != empty_set
| union(esk1_0,esk2_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
esk2_0 = empty_set,
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_25,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
esk1_0 = empty_set,
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_27,plain,
( member(esk3_2(union(X1,X1),empty_set),X1)
| union(X1,X1) = empty_set ),
inference(ef,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
union(empty_set,empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_24])]),c_0_26]),c_0_26])]) ).
cnf(c_0_29,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:28:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.42 % Version: 3.5.1
% 0.14/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % Starting sh5l with 300s (1) cores
% 0.14/0.42 % new_bool_1 with pid 106870 completed with status 0
% 0.14/0.42 % Result found by new_bool_1
% 0.14/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.42 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.14/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.42 % SubtermCWHack with pid 106874 completed with status 0
% 0.14/0.42 % Result found by SubtermCWHack
% 0.14/0.42 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.42 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.42 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.42 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.42 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.42 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.14/0.42 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.42 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.42 % Preprocessing time : 0.001 s
% 0.14/0.42
% 0.14/0.42 % Proof found!
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 % SZS output start CNFRefutation
% See solution above
% 0.14/0.42 % Parsed axioms : 9
% 0.14/0.42 % Removed by relevancy pruning/SinE : 4
% 0.14/0.42 % Initial clauses : 12
% 0.14/0.42 % Removed in clause preprocessing : 2
% 0.14/0.42 % Initial clauses in saturation : 10
% 0.14/0.42 % Processed clauses : 37
% 0.14/0.42 % ...of these trivial : 2
% 0.14/0.42 % ...subsumed : 11
% 0.14/0.42 % ...remaining for further processing : 24
% 0.14/0.42 % Other redundant clauses eliminated : 0
% 0.14/0.42 % Clauses deleted for lack of memory : 0
% 0.14/0.42 % Backward-subsumed : 0
% 0.14/0.42 % Backward-rewritten : 7
% 0.14/0.42 % Generated clauses : 89
% 0.14/0.42 % ...of the previous two non-redundant : 78
% 0.14/0.42 % ...aggressively subsumed : 0
% 0.14/0.42 % Contextual simplify-reflections : 0
% 0.14/0.42 % Paramodulations : 79
% 0.14/0.42 % Factorizations : 10
% 0.14/0.42 % NegExts : 0
% 0.14/0.42 % Equation resolutions : 0
% 0.14/0.42 % Disequality decompositions : 0
% 0.14/0.42 % Total rewrite steps : 19
% 0.14/0.42 % ...of those cached : 16
% 0.14/0.42 % Propositional unsat checks : 0
% 0.14/0.42 % Propositional check models : 0
% 0.14/0.42 % Propositional check unsatisfiable : 0
% 0.14/0.42 % Propositional clauses : 0
% 0.14/0.42 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 17
% 0.14/0.43 % Positive orientable unit clauses : 2
% 0.14/0.43 % Positive unorientable unit clauses: 1
% 0.14/0.43 % Negative unit clauses : 2
% 0.14/0.43 % Non-unit-clauses : 12
% 0.14/0.43 % Current number of unprocessed clauses: 41
% 0.14/0.43 % ...number of literals in the above : 135
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 7
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 54
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 36
% 0.14/0.43 % Non-unit clause-clause subsumptions : 6
% 0.14/0.43 % Unit Clause-clause subsumption calls : 0
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 2
% 0.14/0.43 % BW rewrite match successes : 2
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 1750
% 0.14/0.43 % Search garbage collected termcells : 233
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.005 s
% 0.14/0.43 % System time : 0.001 s
% 0.14/0.43 % Total time : 0.007 s
% 0.14/0.43 % Maximum resident set size: 3636 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.006 s
% 0.14/0.43 % System time : 0.006 s
% 0.14/0.43 % Total time : 0.012 s
% 0.14/0.43 % Maximum resident set size: 4864 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------