%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET812+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 : n012.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 0.03s 15.37s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 7 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 114 ( 47 ~; 42 |; 16 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 1 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thV10,conjecture,
! [X1] :
( member(X1,on)
=> equal_set(X1,intersection(X1,power_set(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV10) ).
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(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(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> equal_set(X1,intersection(X1,power_set(X1))) ),
inference(assume_negation,[status(cth)],[thV10]) ).
fof(c_0_7,negated_conjecture,
( ~ equal_set(esk14_0,intersection(esk14_0,power_set(esk14_0)))
& member(esk14_0,on) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_8,plain,
! [X15,X16] :
( ( equal_set(X15,X16)
| ~ subset(X16,X15)
| ~ subset(X15,X16) )
& ( ~ equal_set(X15,X16)
| subset(X16,X15) )
& ( ~ equal_set(X15,X16)
| subset(X15,X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
cnf(c_0_9,negated_conjecture,
~ equal_set(esk14_0,intersection(esk14_0,power_set(esk14_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X9,X10,X11,X12,X13] :
( ( subset(X12,X13)
| ~ member(esk1_2(X12,X13),X13) )
& ( subset(X12,X13)
| member(esk1_2(X12,X13),X12) )
& ( member(X11,X10)
| ~ member(X11,X9)
| ~ subset(X9,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)],[subset])])])])])])]) ).
cnf(c_0_12,negated_conjecture,
( ~ subset(esk14_0,intersection(esk14_0,power_set(esk14_0)))
| ~ subset(intersection(esk14_0,power_set(esk14_0)),esk14_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X46,X47,X48] :
( ( member(X48,on)
| ~ strict_well_order(member_predicate,X48)
| ~ set(X48)
| ~ subset(esk4_1(X48),X48) )
& ( member(X48,on)
| ~ strict_well_order(member_predicate,X48)
| ~ set(X48)
| member(esk4_1(X48),X48) )
& ( ~ member(X46,on)
| subset(X47,X46)
| ~ member(X47,X46) )
& ( ~ member(X46,on)
| strict_well_order(member_predicate,X46) )
& ( ~ member(X46,on)
| set(X46) ) ),
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_16,plain,
! [X19,X20,X21] :
( ( member(X19,intersection(X20,X21))
| ~ member(X19,X21)
| ~ member(X19,X20) )
& ( ~ member(X19,intersection(X20,X21))
| member(X19,X21) )
& ( ~ member(X19,intersection(X20,X21))
| member(X19,X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ subset(esk14_0,intersection(esk14_0,power_set(esk14_0)))
| member(esk1_2(intersection(esk14_0,power_set(esk14_0)),esk14_0),intersection(esk14_0,power_set(esk14_0))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( ~ subset(esk14_0,intersection(esk14_0,power_set(esk14_0)))
| ~ member(esk1_2(intersection(esk14_0,power_set(esk14_0)),esk14_0),esk14_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
fof(c_0_19,plain,
! [X17,X18] :
( ( member(X17,power_set(X18))
| ~ subset(X17,X18) )
& ( subset(X17,X18)
| ~ member(X17,power_set(X18)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])])]) ).
cnf(c_0_20,plain,
( ~ member(X2,on)
| ~ member(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
member(esk14_0,on),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( ~ member(esk1_2(esk14_0,intersection(esk14_0,power_set(esk14_0))),intersection(esk14_0,power_set(esk14_0)))
| member(esk1_2(intersection(esk14_0,power_set(esk14_0)),esk14_0),intersection(esk14_0,power_set(esk14_0))) ),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(esk1_2(intersection(esk14_0,power_set(esk14_0)),esk14_0),esk14_0)
| ~ member(esk1_2(esk14_0,intersection(esk14_0,power_set(esk14_0))),intersection(esk14_0,power_set(esk14_0))) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_25,plain,
( ~ subset(X1,X2)
| member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( ~ member(X1,esk14_0)
| subset(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
~ member(esk1_2(esk14_0,intersection(esk14_0,power_set(esk14_0))),intersection(esk14_0,power_set(esk14_0))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,negated_conjecture,
( ~ member(X1,esk14_0)
| member(X1,power_set(esk14_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
~ member(esk1_2(esk14_0,intersection(esk14_0,power_set(esk14_0))),esk14_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
member(esk1_2(intersection(esk14_0,power_set(esk14_0)),esk14_0),intersection(esk14_0,power_set(esk14_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_13]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( ~ member(esk1_2(intersection(esk14_0,power_set(esk14_0)),esk14_0),esk14_0)
| member(esk1_2(esk14_0,intersection(esk14_0,power_set(esk14_0))),esk14_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_33,negated_conjecture,
member(esk1_2(intersection(esk14_0,power_set(esk14_0)),esk14_0),esk14_0),
inference(spm,[status(thm)],[c_0_22,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET812+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/15.32 % Computer : n012.cluster.edu
% 0.03/15.32 % Model : x86_64 x86_64
% 0.03/15.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/15.32 % Memory : 8046.5625MB
% 0.03/15.32 % OS : Linux 6.8.0-71-generic
% 0.03/15.32 % CPULimit : 300
% 0.03/15.32 % WCLimit : 300
% 0.03/15.32 % DateTime : Mon Sep 21 05:39:07 UTC 2026
% 0.03/15.32 % CPUTime :
% 0.03/15.32 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/15.34 Running first-order theorem proving
% 0.03/15.34 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
% 0.03/15.37 % Version: 3.5.1
% 0.03/15.37 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.03/15.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.03/15.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.03/15.37 % Starting new_bool_3 with 300s (1) cores
% 0.03/15.37 % Starting new_bool_1 with 300s (1) cores
% 0.03/15.37 % Starting sh5l with 300s (1) cores
% 0.03/15.37 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1659874 completed with status 0
% 0.03/15.37 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.03/15.37 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.03/15.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.03/15.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.03/15.37 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.03/15.37 % No SInE strategy applied
% 0.03/15.37 % Search class: FGHSF-FFMF31-SFFFFFNN
% 0.03/15.37 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.03/15.37 % Starting SubtermCWHack with 136s (1) cores
% 0.03/15.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.03/15.37 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 166s (1) cores
% 0.03/15.37 % Starting new_bool_3 with 162s (1) cores
% 0.03/15.37 % Starting new_bool_1 with 158s (1) cores
% 0.03/15.37 % G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1659883 completed with status 0
% 0.03/15.37 % Result found by G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.03/15.37 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.03/15.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.03/15.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.03/15.37 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.03/15.37 % No SInE strategy applied
% 0.03/15.37 % Search class: FGHSF-FFMF31-SFFFFFNN
% 0.03/15.37 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.03/15.37 % Starting SubtermCWHack with 136s (1) cores
% 0.03/15.37 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.03/15.37 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 166s (1) cores
% 0.03/15.37 % Preprocessing time : 0.001 s
% 0.03/15.37 % Presaturation interreduction done
% 0.03/15.37
% 0.03/15.37 % Proof found!
% 0.03/15.37 % SZS status Theorem
% 0.03/15.37 % SZS output start CNFRefutation
% See solution above
% 0.03/15.37 % Parsed axioms : 20
% 0.03/15.37 % Removed by relevancy pruning/SinE : 0
% 0.03/15.37 % Initial clauses : 80
% 0.03/15.37 % Removed in clause preprocessing : 0
% 0.03/15.37 % Initial clauses in saturation : 80
% 0.03/15.37 % Processed clauses : 177
% 0.03/15.37 % ...of these trivial : 0
% 0.03/15.37 % ...subsumed : 2
% 0.03/15.37 % ...remaining for further processing : 175
% 0.03/15.37 % Other redundant clauses eliminated : 3
% 0.03/15.37 % Clauses deleted for lack of memory : 0
% 0.03/15.37 % Backward-subsumed : 7
% 0.03/15.37 % Backward-rewritten : 3
% 0.03/15.37 % Generated clauses : 177
% 0.03/15.37 % ...of the previous two non-redundant : 151
% 0.03/15.37 % ...aggressively subsumed : 0
% 0.03/15.37 % Contextual simplify-reflections : 4
% 0.03/15.37 % Paramodulations : 174
% 0.03/15.37 % Factorizations : 0
% 0.03/15.37 % NegExts : 0
% 0.03/15.37 % Equation resolutions : 3
% 0.03/15.37 % Disequality decompositions : 0
% 0.03/15.37 % Total rewrite steps : 11
% 0.03/15.37 % ...of those cached : 2
% 0.03/15.37 % Propositional unsat checks : 0
% 0.03/15.37 % Propositional check models : 0
% 0.03/15.37 % Propositional check unsatisfiable : 0
% 0.03/15.37 % Propositional clauses : 0
% 0.03/15.37 % Propositional clauses after purity: 0
% 0.03/15.37 % Propositional unsat core size : 0
% 0.03/15.37 % Propositional preprocessing time : 0.000
% 0.03/15.37 % Propositional encoding time : 0.000
% 0.03/15.37 % Propositional solver time : 0.000
% 0.03/15.37 % Success case prop preproc time : 0.000
% 0.03/15.37 % Success case prop encoding time : 0.000
% 0.03/15.37 % Success case prop solver time : 0.000
% 0.03/15.37 % Current number of processed clauses : 82
% 0.03/15.37 % Positive orientable unit clauses : 8
% 0.03/15.37 % Positive unorientable unit clauses: 0
% 0.03/15.37 % Negative unit clauses : 5
% 0.03/15.37 % Non-unit-clauses : 69
% 0.03/15.37 % Current number of unprocessed clauses: 132
% 0.03/15.37 % ...number of literals in the above : 360
% 0.03/15.37 % Current number of archived formulas : 0
% 0.03/15.37 % Current number of archived clauses : 90
% 0.03/15.37 % Clause-clause subsumption calls (NU) : 2280
% 0.03/15.37 % Rec. Clause-clause subsumption calls : 1743
% 0.03/15.37 % Non-unit clause-clause subsumptions : 5
% 0.03/15.37 % Unit Clause-clause subsumption calls : 78
% 0.03/15.37 % Rewrite failures with RHS unbound : 0
% 0.03/15.37 % BW rewrite match attempts : 5
% 0.03/15.37 % BW rewrite match successes : 2
% 0.03/15.37 % Condensation attempts : 0
% 0.03/15.37 % Condensation successes : 0
% 0.03/15.37 % Termbank termtop insertions : 7501
% 0.03/15.37 % Search garbage collected termcells : 1225
% 0.03/15.37
% 0.03/15.37 % -------------------------------------------------
% 0.03/15.37 % User time : 0.010 s
% 0.03/15.37 % System time : 0.003 s
% 0.03/15.37 % Total time : 0.013 s
% 0.03/15.37 % Maximum resident set size: 3668 pages
% 0.03/15.37
% 0.03/15.37 % -------------------------------------------------
% 0.03/15.37 % User time : 0.034 s
% 0.03/15.37 % System time : 0.013 s
% 0.03/15.37 % Total time : 0.046 s
% 0.03/15.37 % Maximum resident set size: 4864 pages
% 0.03/15.37 % E exiting
%------------------------------------------------------------------------------