%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET347+4 : 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 : n017.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 02:14:05 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 52 ( 24 ~; 16 |; 8 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI38,conjecture,
equal_set(sum(empty_set),empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI38) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X3,X5)
& member(X5,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',sum) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(c_0_5,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(assume_negation,[status(cth)],[thI38]) ).
fof(c_0_6,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(c_0_7,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X8] : ~ member(X8,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
fof(c_0_9,plain,
! [X15,X16,X17,X18,X19] :
( ( subset(X18,X19)
| ~ member(esk2_2(X18,X19),X19) )
& ( subset(X18,X19)
| member(esk2_2(X18,X19),X18) )
& ( member(X17,X16)
| ~ member(X17,X15)
| ~ subset(X15,X16) ) ),
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)],[subset])])])])])])]) ).
fof(c_0_10,plain,
! [X9,X10,X12,X13,X14] :
( ( member(X12,sum(X13))
| ~ member(X12,X14)
| ~ member(X14,X13) )
& ( ~ member(X9,sum(X10))
| member(X9,esk1_2(X9,X10)) )
& ( ~ member(X9,sum(X10))
| member(esk1_2(X9,X10),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)],[sum])])])])])])]) ).
fof(c_0_11,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X6,X7] :
( ( equal_set(X6,X7)
| ~ subset(X7,X6)
| ~ subset(X6,X7) )
& ( ~ equal_set(X6,X7)
| subset(X7,X6) )
& ( ~ equal_set(X6,X7)
| subset(X6,X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
cnf(c_0_13,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ member(X1,sum(X2))
| member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
~ member(X1,sum(empty_set)),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
~ subset(sum(empty_set),empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_21,plain,
subset(sum(empty_set),X1),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET347+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 05:05:43 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.43 % Version: 3.5.1
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.43 % Starting sh5l with 300s (1) cores
% 0.11/0.43 % new_bool_1 with pid 1491168 completed with status 0
% 0.11/0.43 % Result found by new_bool_1
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.43 % Search class: FGUNF-FFSF21-SFFFFFNN
% 0.11/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.43 % SubtermCWHack with pid 1491171 completed with status 0
% 0.11/0.43 % Result found by SubtermCWHack
% 0.11/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.43 % Search class: FGUNF-FFSF21-SFFFFFNN
% 0.11/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.43 % Preprocessing time : 0.001 s
% 0.11/0.43
% 0.11/0.43 % Proof found!
% 0.11/0.43 % SZS status Theorem
% 0.11/0.43 % SZS output start CNFRefutation
% See solution above
% 0.11/0.43 % Parsed axioms : 12
% 0.11/0.43 % Removed by relevancy pruning/SinE : 7
% 0.11/0.43 % Initial clauses : 11
% 0.11/0.43 % Removed in clause preprocessing : 0
% 0.11/0.43 % Initial clauses in saturation : 11
% 0.11/0.43 % Processed clauses : 16
% 0.11/0.43 % ...of these trivial : 0
% 0.11/0.43 % ...subsumed : 1
% 0.11/0.43 % ...remaining for further processing : 15
% 0.11/0.43 % Other redundant clauses eliminated : 0
% 0.11/0.43 % Clauses deleted for lack of memory : 0
% 0.11/0.43 % Backward-subsumed : 0
% 0.11/0.43 % Backward-rewritten : 1
% 0.11/0.43 % Generated clauses : 11
% 0.11/0.43 % ...of the previous two non-redundant : 7
% 0.11/0.43 % ...aggressively subsumed : 0
% 0.11/0.43 % Contextual simplify-reflections : 0
% 0.11/0.43 % Paramodulations : 11
% 0.11/0.43 % Factorizations : 0
% 0.11/0.43 % NegExts : 0
% 0.11/0.43 % Equation resolutions : 0
% 0.11/0.43 % Disequality decompositions : 0
% 0.11/0.43 % Total rewrite steps : 2
% 0.11/0.43 % ...of those cached : 0
% 0.11/0.43 % Propositional unsat checks : 0
% 0.11/0.43 % Propositional check models : 0
% 0.11/0.43 % Propositional check unsatisfiable : 0
% 0.11/0.43 % Propositional clauses : 0
% 0.11/0.43 % Propositional clauses after purity: 0
% 0.11/0.43 % Propositional unsat core size : 0
% 0.11/0.43 % Propositional preprocessing time : 0.000
% 0.11/0.43 % Propositional encoding time : 0.000
% 0.11/0.43 % Propositional solver time : 0.000
% 0.11/0.43 % Success case prop preproc time : 0.000
% 0.11/0.43 % Success case prop encoding time : 0.000
% 0.11/0.43 % Success case prop solver time : 0.000
% 0.11/0.43 % Current number of processed clauses : 14
% 0.11/0.43 % Positive orientable unit clauses : 3
% 0.11/0.43 % Positive unorientable unit clauses: 0
% 0.11/0.43 % Negative unit clauses : 3
% 0.11/0.43 % Non-unit-clauses : 8
% 0.11/0.43 % Current number of unprocessed clauses: 2
% 0.11/0.43 % ...number of literals in the above : 4
% 0.11/0.43 % Current number of archived formulas : 0
% 0.11/0.43 % Current number of archived clauses : 1
% 0.11/0.43 % Clause-clause subsumption calls (NU) : 5
% 0.11/0.43 % Rec. Clause-clause subsumption calls : 5
% 0.11/0.43 % Non-unit clause-clause subsumptions : 0
% 0.11/0.43 % Unit Clause-clause subsumption calls : 7
% 0.11/0.43 % Rewrite failures with RHS unbound : 0
% 0.11/0.43 % BW rewrite match attempts : 3
% 0.11/0.43 % BW rewrite match successes : 1
% 0.11/0.43 % Condensation attempts : 0
% 0.11/0.43 % Condensation successes : 0
% 0.11/0.43 % Termbank termtop insertions : 817
% 0.11/0.43 % Search garbage collected termcells : 241
% 0.11/0.43
% 0.11/0.43 % -------------------------------------------------
% 0.11/0.43 % User time : 0.003 s
% 0.11/0.43 % System time : 0.002 s
% 0.11/0.43 % Total time : 0.005 s
% 0.11/0.43 % Maximum resident set size: 3648 pages
% 0.11/0.43
% 0.11/0.43 % -------------------------------------------------
% 0.11/0.43 % User time : 0.006 s
% 0.11/0.43 % System time : 0.005 s
% 0.11/0.43 % Total time : 0.011 s
% 0.11/0.43 % Maximum resident set size: 4864 pages
% 0.11/0.43 % E exiting
%------------------------------------------------------------------------------