%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET811+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:15:26 PM UTC 2026
% Result : Theorem 1.68s 0.67s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 8 unt; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 144 ( 57 ~; 59 |; 17 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 94 ( 7 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(thV5,conjecture,
! [X1] :
( member(X1,on)
=> ! [X3] :
( member(X3,X1)
=> equal_set(X3,initial_segment(X3,member_predicate,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV5) ).
fof(initial_segment,axiom,
! [X3,X6,X1,X5] :
( member(X5,initial_segment(X3,X6,X1))
<=> ( apply(X6,X5,X3)
& member(X5,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',initial_segment) ).
fof(rel_member,axiom,
! [X3,X5] :
( apply(member_predicate,X3,X5)
<=> member(X3,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',rel_member) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(c_0_6,plain,
! [X23,X24,X25,X26,X27] :
( ( subset(X26,X27)
| ~ member(esk4_2(X26,X27),X27) )
& ( subset(X26,X27)
| member(esk4_2(X26,X27),X26) )
& ( member(X25,X24)
| ~ member(X25,X23)
| ~ subset(X23,X24) ) ),
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_7,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_8,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> ! [X3] :
( member(X3,X1)
=> equal_set(X3,initial_segment(X3,member_predicate,X1)) ) ),
inference(assume_negation,[status(cth)],[thV5]) ).
cnf(c_0_9,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ member(X2,on)
| ~ member(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( ~ equal_set(esk2_0,initial_segment(esk2_0,member_predicate,esk1_0))
& member(esk2_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_8])])])]) ).
cnf(c_0_12,plain,
( ~ member(X3,X2)
| ~ member(X1,X3)
| ~ member(X2,on)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
member(esk1_0,on),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X13,X14,X15,X16] :
( ( member(X16,initial_segment(X13,X14,X15))
| ~ apply(X14,X16,X13)
| ~ member(X16,X15) )
& ( ~ member(X16,initial_segment(X13,X14,X15))
| apply(X14,X16,X13) )
& ( ~ member(X16,initial_segment(X13,X14,X15))
| member(X16,X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[initial_segment])])])]) ).
cnf(c_0_15,negated_conjecture,
( ~ member(X1,X2)
| ~ member(X2,esk1_0)
| member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
member(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X21,X22] :
( ( apply(member_predicate,X21,X22)
| ~ member(X21,X22) )
& ( member(X21,X22)
| ~ apply(member_predicate,X21,X22) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rel_member])])]) ).
cnf(c_0_18,plain,
( ~ member(X2,initial_segment(X3,X1,X4))
| apply(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,plain,
( ~ member(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X1,esk2_0)
| member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( ~ apply(member_predicate,X1,X2)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( subset(initial_segment(X2,X1,X3),X4)
| apply(X1,esk4_2(initial_segment(X2,X1,X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(esk4_2(X1,esk1_0),esk2_0)
| subset(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( subset(initial_segment(X1,member_predicate,X2),X3)
| member(esk4_2(initial_segment(X1,member_predicate,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( ~ apply(X3,X1,X4)
| ~ member(X1,X2)
| member(X1,initial_segment(X4,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,negated_conjecture,
subset(initial_segment(esk2_0,member_predicate,X1),esk1_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( ~ member(esk4_2(X1,initial_segment(X2,X3,X4)),X4)
| ~ apply(X3,esk4_2(X1,initial_segment(X2,X3,X4)),X2)
| subset(X1,initial_segment(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( ~ member(X1,initial_segment(esk2_0,member_predicate,X2))
| member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_27]) ).
cnf(c_0_30,plain,
( ~ member(esk4_2(initial_segment(X1,X2,X3),initial_segment(X1,X2,X4)),X4)
| subset(initial_segment(X1,X2,X3),initial_segment(X1,X2,X4)) ),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( subset(initial_segment(esk2_0,member_predicate,X1),X2)
| member(esk4_2(initial_segment(esk2_0,member_predicate,X1),X2),esk1_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_32,negated_conjecture,
subset(initial_segment(esk2_0,member_predicate,X1),initial_segment(esk2_0,member_predicate,esk1_0)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(X1,initial_segment(esk2_0,member_predicate,X2))
| member(X1,initial_segment(esk2_0,member_predicate,esk1_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( ~ member(X1,X2)
| ~ apply(member_predicate,X1,esk2_0)
| member(X1,initial_segment(esk2_0,member_predicate,esk1_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
fof(c_0_35,plain,
! [X11,X12] :
( ( equal_set(X11,X12)
| ~ subset(X12,X11)
| ~ subset(X11,X12) )
& ( ~ equal_set(X11,X12)
| subset(X12,X11) )
& ( ~ equal_set(X11,X12)
| subset(X11,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
cnf(c_0_36,negated_conjecture,
( ~ apply(member_predicate,esk4_2(X1,X2),esk2_0)
| subset(X1,X2)
| member(esk4_2(X1,X2),initial_segment(esk2_0,member_predicate,esk1_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_37,negated_conjecture,
~ equal_set(esk2_0,initial_segment(esk2_0,member_predicate,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_38,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( ~ apply(member_predicate,esk4_2(X1,initial_segment(esk2_0,member_predicate,esk1_0)),esk2_0)
| subset(X1,initial_segment(esk2_0,member_predicate,esk1_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
cnf(c_0_40,plain,
( ~ member(X1,X2)
| apply(member_predicate,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_41,negated_conjecture,
( ~ subset(esk2_0,initial_segment(esk2_0,member_predicate,esk1_0))
| ~ subset(initial_segment(esk2_0,member_predicate,esk1_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
subset(initial_segment(X1,member_predicate,X2),X1),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_43,negated_conjecture,
( ~ member(esk4_2(X1,initial_segment(esk2_0,member_predicate,esk1_0)),esk2_0)
| subset(X1,initial_segment(esk2_0,member_predicate,esk1_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
~ subset(esk2_0,initial_segment(esk2_0,member_predicate,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_19]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET811+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:41:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 1.68/0.67 % Version: 3.5.1
% 1.68/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.68/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.68/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.68/0.67 % Starting new_bool_3 with 300s (1) cores
% 1.68/0.67 % Starting new_bool_1 with 300s (1) cores
% 1.68/0.67 % Starting sh5l with 300s (1) cores
% 1.68/0.67 % new_bool_1 with pid 1080520 completed with status 0
% 1.68/0.67 % Result found by new_bool_1
% 1.68/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.68/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.68/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.68/0.67 % Starting new_bool_3 with 300s (1) cores
% 1.68/0.67 % Starting new_bool_1 with 300s (1) cores
% 1.68/0.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.68/0.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.68/0.67 % Search class: FGHSF-FFMF32-SFFFFFNN
% 1.68/0.67 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.68/0.67 % Starting SubtermCWHack with 31s (1) cores
% 1.68/0.67 % SubtermCWHack with pid 1080526 completed with status 0
% 1.68/0.67 % Result found by SubtermCWHack
% 1.68/0.67 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.68/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.68/0.67 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.68/0.67 % Starting new_bool_3 with 300s (1) cores
% 1.68/0.67 % Starting new_bool_1 with 300s (1) cores
% 1.68/0.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.68/0.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.68/0.67 % Search class: FGHSF-FFMF32-SFFFFFNN
% 1.68/0.67 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.68/0.67 % Starting SubtermCWHack with 31s (1) cores
% 1.68/0.67 % Preprocessing time : 0.001 s
% 1.68/0.67
% 1.68/0.67 % Proof found!
% 1.68/0.67 % SZS status Theorem
% 1.68/0.67 % SZS output start CNFRefutation
% See solution above
% 1.68/0.67 % Parsed axioms : 20
% 1.68/0.67 % Removed by relevancy pruning/SinE : 10
% 1.68/0.67 % Initial clauses : 56
% 1.68/0.67 % Removed in clause preprocessing : 0
% 1.68/0.67 % Initial clauses in saturation : 56
% 1.68/0.67 % Processed clauses : 2114
% 1.68/0.67 % ...of these trivial : 4
% 1.68/0.67 % ...subsumed : 900
% 1.68/0.67 % ...remaining for further processing : 1210
% 1.68/0.67 % Other redundant clauses eliminated : 0
% 1.68/0.67 % Clauses deleted for lack of memory : 0
% 1.68/0.67 % Backward-subsumed : 130
% 1.68/0.67 % Backward-rewritten : 87
% 1.68/0.67 % Generated clauses : 17764
% 1.68/0.67 % ...of the previous two non-redundant : 17210
% 1.68/0.67 % ...aggressively subsumed : 0
% 1.68/0.67 % Contextual simplify-reflections : 30
% 1.68/0.67 % Paramodulations : 17763
% 1.68/0.67 % Factorizations : 1
% 1.68/0.67 % NegExts : 0
% 1.68/0.67 % Equation resolutions : 0
% 1.68/0.67 % Disequality decompositions : 0
% 1.68/0.67 % Total rewrite steps : 790
% 1.68/0.67 % ...of those cached : 743
% 1.68/0.67 % Propositional unsat checks : 0
% 1.68/0.67 % Propositional check models : 0
% 1.68/0.67 % Propositional check unsatisfiable : 0
% 1.68/0.67 % Propositional clauses : 0
% 1.68/0.67 % Propositional clauses after purity: 0
% 1.68/0.67 % Propositional unsat core size : 0
% 1.68/0.67 % Propositional preprocessing time : 0.000
% 1.68/0.67 % Propositional encoding time : 0.000
% 1.68/0.67 % Propositional solver time : 0.000
% 1.68/0.67 % Success case prop preproc time : 0.000
% 1.68/0.67 % Success case prop encoding time : 0.000
% 1.68/0.67 % Success case prop solver time : 0.000
% 1.68/0.67 % Current number of processed clauses : 993
% 1.68/0.67 % Positive orientable unit clauses : 57
% 1.68/0.67 % Positive unorientable unit clauses: 0
% 1.68/0.67 % Negative unit clauses : 14
% 1.68/0.67 % Non-unit-clauses : 922
% 1.68/0.67 % Current number of unprocessed clauses: 14722
% 1.68/0.67 % ...number of literals in the above : 66837
% 1.68/0.67 % Current number of archived formulas : 0
% 1.68/0.67 % Current number of archived clauses : 217
% 1.68/0.67 % Clause-clause subsumption calls (NU) : 63062
% 1.68/0.67 % Rec. Clause-clause subsumption calls : 28709
% 1.68/0.67 % Non-unit clause-clause subsumptions : 922
% 1.68/0.67 % Unit Clause-clause subsumption calls : 5007
% 1.68/0.67 % Rewrite failures with RHS unbound : 0
% 1.68/0.67 % BW rewrite match attempts : 377
% 1.68/0.67 % BW rewrite match successes : 18
% 1.68/0.67 % Condensation attempts : 0
% 1.68/0.67 % Condensation successes : 0
% 1.68/0.67 % Termbank termtop insertions : 392984
% 1.68/0.67 % Search garbage collected termcells : 978
% 1.68/0.67
% 1.68/0.67 % -------------------------------------------------
% 1.68/0.67 % User time : 0.219 s
% 1.68/0.67 % System time : 0.011 s
% 1.68/0.67 % Total time : 0.231 s
% 1.68/0.67 % Maximum resident set size: 3616 pages
% 1.68/0.67
% 1.68/0.67 % -------------------------------------------------
% 1.68/0.67 % User time : 0.221 s
% 1.68/0.67 % System time : 0.017 s
% 1.68/0.67 % Total time : 0.237 s
% 1.68/0.67 % Maximum resident set size: 4608 pages
% 1.68/0.67 % E exiting
%------------------------------------------------------------------------------