%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET814+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 02:15:27 PM UTC 2026
% Result : Theorem 0.14s 5.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 3 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 88 ( 34 ~; 35 |; 12 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(ordinal_number,axiom,
! [X1] :
( member(X1,on)
<=> ( ! [X3] :
( member(X3,X1)
=> subset(X3,X1) )
& strict_well_order(member_predicate,X1)
& set(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(thV14,conjecture,
! [X1] :
( member(X1,on)
=> subset(sum(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV14) ).
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(c_0_4,plain,
! [X11,X12,X13,X14,X15] :
( ( subset(X14,X15)
| ~ member(esk2_2(X14,X15),X15) )
& ( subset(X14,X15)
| member(esk2_2(X14,X15),X14) )
& ( member(X13,X12)
| ~ member(X13,X11)
| ~ subset(X11,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)],[subset])])])])])])]) ).
fof(c_0_5,plain,
! [X17,X18,X19] :
( ( member(X19,on)
| ~ strict_well_order(member_predicate,X19)
| ~ set(X19)
| ~ subset(esk3_1(X19),X19) )
& ( member(X19,on)
| ~ strict_well_order(member_predicate,X19)
| ~ set(X19)
| member(esk3_1(X19),X19) )
& ( ~ member(X17,on)
| subset(X18,X17)
| ~ member(X18,X17) )
& ( ~ member(X17,on)
| strict_well_order(member_predicate,X17) )
& ( ~ member(X17,on)
| set(X17) ) ),
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)],[ordinal_number])])])])])])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> subset(sum(X1),X1) ),
inference(assume_negation,[status(cth)],[thV14]) ).
cnf(c_0_7,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( ~ member(X2,on)
| ~ member(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,negated_conjecture,
( ~ subset(sum(esk1_0),esk1_0)
& member(esk1_0,on) ),
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_10,plain,
( ~ member(X3,X2)
| ~ member(X1,X3)
| ~ member(X2,on)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
member(esk1_0,on),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X34,X35,X37,X38,X39] :
( ( member(X37,sum(X38))
| ~ member(X37,X39)
| ~ member(X39,X38) )
& ( ~ member(X34,sum(X35))
| member(X34,esk7_2(X34,X35)) )
& ( ~ member(X34,sum(X35))
| member(esk7_2(X34,X35),X35) ) ),
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])])])])])])]) ).
cnf(c_0_13,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X2,esk1_0)
| member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( ~ member(X1,sum(X2))
| member(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( ~ member(X2,sum(esk1_0))
| ~ member(X1,esk7_2(X2,esk1_0))
| member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( ~ member(X1,sum(X2))
| member(X1,esk7_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(X1,sum(esk1_0))
| member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_19,plain,
( ~ member(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_20,negated_conjecture,
( subset(sum(esk1_0),X1)
| member(esk2_2(sum(esk1_0),X1),esk1_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ subset(sum(esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET814+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.54 % Computer : n018.cluster.edu
% 0.11/5.54 % Model : x86_64 x86_64
% 0.11/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.54 % Memory : 8046.5625MB
% 0.11/5.54 % OS : Linux 6.8.0-71-generic
% 0.11/5.54 % CPULimit : 300
% 0.11/5.54 % WCLimit : 300
% 0.11/5.54 % DateTime : Mon Sep 21 05:41:49 UTC 2026
% 0.11/5.54 % CPUTime :
% 0.11/5.54 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.58 Running first-order theorem proving
% 0.11/5.58 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
% 0.14/5.61 % Version: 3.5.1
% 0.14/5.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.61 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.61 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.61 % Starting sh5l with 300s (1) cores
% 0.14/5.61 % sh5l with pid 1082316 completed with status 0
% 0.14/5.61 % Result found by sh5l
% 0.14/5.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.61 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.61 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.61 % Starting sh5l with 300s (1) cores
% 0.14/5.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/5.61 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/5.61 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.14/5.61 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.61 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.61 % SubtermCWHack with pid 1082317 completed with status 0
% 0.14/5.61 % Result found by SubtermCWHack
% 0.14/5.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.61 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.61 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.61 % Starting sh5l with 300s (1) cores
% 0.14/5.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/5.61 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/5.61 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.14/5.61 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.61 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.61 % Preprocessing time : 0.002 s
% 0.14/5.61
% 0.14/5.61 % Proof found!
% 0.14/5.61 % SZS status Theorem
% 0.14/5.61 % SZS output start CNFRefutation
% See solution above
% 0.14/5.61 % Parsed axioms : 21
% 0.14/5.61 % Removed by relevancy pruning/SinE : 10
% 0.14/5.61 % Initial clauses : 56
% 0.14/5.61 % Removed in clause preprocessing : 0
% 0.14/5.61 % Initial clauses in saturation : 56
% 0.14/5.61 % Processed clauses : 140
% 0.14/5.61 % ...of these trivial : 1
% 0.14/5.61 % ...subsumed : 24
% 0.14/5.61 % ...remaining for further processing : 115
% 0.14/5.61 % Other redundant clauses eliminated : 0
% 0.14/5.61 % Clauses deleted for lack of memory : 0
% 0.14/5.61 % Backward-subsumed : 0
% 0.14/5.61 % Backward-rewritten : 0
% 0.14/5.61 % Generated clauses : 374
% 0.14/5.61 % ...of the previous two non-redundant : 357
% 0.14/5.61 % ...aggressively subsumed : 0
% 0.14/5.61 % Contextual simplify-reflections : 0
% 0.14/5.61 % Paramodulations : 374
% 0.14/5.61 % Factorizations : 0
% 0.14/5.61 % NegExts : 0
% 0.14/5.61 % Equation resolutions : 0
% 0.14/5.61 % Disequality decompositions : 0
% 0.14/5.61 % Total rewrite steps : 13
% 0.14/5.61 % ...of those cached : 11
% 0.14/5.61 % Propositional unsat checks : 0
% 0.14/5.61 % Propositional check models : 0
% 0.14/5.61 % Propositional check unsatisfiable : 0
% 0.14/5.61 % Propositional clauses : 0
% 0.14/5.61 % Propositional clauses after purity: 0
% 0.14/5.61 % Propositional unsat core size : 0
% 0.14/5.61 % Propositional preprocessing time : 0.000
% 0.14/5.61 % Propositional encoding time : 0.000
% 0.14/5.61 % Propositional solver time : 0.000
% 0.14/5.61 % Success case prop preproc time : 0.000
% 0.14/5.61 % Success case prop encoding time : 0.000
% 0.14/5.61 % Success case prop solver time : 0.000
% 0.14/5.61 % Current number of processed clauses : 115
% 0.14/5.61 % Positive orientable unit clauses : 3
% 0.14/5.61 % Positive unorientable unit clauses: 0
% 0.14/5.61 % Negative unit clauses : 2
% 0.14/5.61 % Non-unit-clauses : 110
% 0.14/5.61 % Current number of unprocessed clauses: 266
% 0.14/5.61 % ...number of literals in the above : 970
% 0.14/5.61 % Current number of archived formulas : 0
% 0.14/5.61 % Current number of archived clauses : 0
% 0.14/5.61 % Clause-clause subsumption calls (NU) : 1233
% 0.14/5.61 % Rec. Clause-clause subsumption calls : 1106
% 0.14/5.61 % Non-unit clause-clause subsumptions : 24
% 0.14/5.61 % Unit Clause-clause subsumption calls : 11
% 0.14/5.61 % Rewrite failures with RHS unbound : 0
% 0.14/5.61 % BW rewrite match attempts : 2
% 0.14/5.61 % BW rewrite match successes : 0
% 0.14/5.61 % Condensation attempts : 0
% 0.14/5.61 % Condensation successes : 0
% 0.14/5.61 % Termbank termtop insertions : 8712
% 0.14/5.61 % Search garbage collected termcells : 1016
% 0.14/5.61
% 0.14/5.61 % -------------------------------------------------
% 0.14/5.61 % User time : 0.015 s
% 0.14/5.61 % System time : 0.003 s
% 0.14/5.61 % Total time : 0.018 s
% 0.14/5.61 % Maximum resident set size: 3668 pages
% 0.14/5.61
% 0.14/5.61 % -------------------------------------------------
% 0.14/5.61 % User time : 0.017 s
% 0.14/5.61 % System time : 0.007 s
% 0.14/5.61 % Total time : 0.024 s
% 0.14/5.61 % Maximum resident set size: 4864 pages
% 0.14/5.61 % E exiting
%------------------------------------------------------------------------------