%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET809+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 : n020.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 0.22s 5.82s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 3 unt; 0 def)
% Number of atoms : 204 ( 0 equ)
% Maximal formula atoms : 84 ( 6 avg)
% Number of connectives : 252 ( 78 ~; 113 |; 47 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(strict_order,axiom,
! [X6,X4] :
( strict_order(X6,X4)
<=> ( ! [X3,X5,X8] :
( ( member(X8,X4)
& member(X5,X4)
& member(X3,X4) )
=> ( ( apply(X6,X5,X8)
& apply(X6,X3,X5) )
=> apply(X6,X3,X8) ) )
& ! [X3,X5] :
( ( member(X5,X4)
& member(X3,X4) )
=> ~ ( apply(X6,X5,X3)
& apply(X6,X3,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',strict_order) ).
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(strict_well_order,axiom,
! [X6,X4] :
( strict_well_order(X6,X4)
<=> ( ! [X1] :
( ( ? [X3] : member(X3,X1)
& subset(X1,X4) )
=> ? [X5] : least(X5,X6,X1) )
& strict_order(X6,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',strict_well_order) ).
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(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(thV2,conjecture,
! [X1] :
( member(X1,on)
=> ~ member(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV2) ).
fof(c_0_6,plain,
! [X42,X43,X44,X45,X46,X47,X48,X49,X50] :
( ( strict_order(X49,X50)
| apply(X49,esk9_2(X49,X50),esk8_2(X49,X50))
| ~ apply(X49,esk10_2(X49,X50),esk12_2(X49,X50)) )
& ( strict_order(X49,X50)
| apply(X49,esk9_2(X49,X50),esk8_2(X49,X50))
| apply(X49,esk11_2(X49,X50),esk12_2(X49,X50)) )
& ( strict_order(X49,X50)
| apply(X49,esk9_2(X49,X50),esk8_2(X49,X50))
| apply(X49,esk10_2(X49,X50),esk11_2(X49,X50)) )
& ( strict_order(X49,X50)
| apply(X49,esk9_2(X49,X50),esk8_2(X49,X50))
| member(esk12_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| apply(X49,esk9_2(X49,X50),esk8_2(X49,X50))
| member(esk11_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| apply(X49,esk9_2(X49,X50),esk8_2(X49,X50))
| member(esk10_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| apply(X49,esk8_2(X49,X50),esk9_2(X49,X50))
| ~ apply(X49,esk10_2(X49,X50),esk12_2(X49,X50)) )
& ( strict_order(X49,X50)
| apply(X49,esk8_2(X49,X50),esk9_2(X49,X50))
| apply(X49,esk11_2(X49,X50),esk12_2(X49,X50)) )
& ( strict_order(X49,X50)
| apply(X49,esk8_2(X49,X50),esk9_2(X49,X50))
| apply(X49,esk10_2(X49,X50),esk11_2(X49,X50)) )
& ( strict_order(X49,X50)
| apply(X49,esk8_2(X49,X50),esk9_2(X49,X50))
| member(esk12_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| apply(X49,esk8_2(X49,X50),esk9_2(X49,X50))
| member(esk11_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| apply(X49,esk8_2(X49,X50),esk9_2(X49,X50))
| member(esk10_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| member(esk9_2(X49,X50),X50)
| ~ apply(X49,esk10_2(X49,X50),esk12_2(X49,X50)) )
& ( strict_order(X49,X50)
| member(esk9_2(X49,X50),X50)
| apply(X49,esk11_2(X49,X50),esk12_2(X49,X50)) )
& ( strict_order(X49,X50)
| member(esk9_2(X49,X50),X50)
| apply(X49,esk10_2(X49,X50),esk11_2(X49,X50)) )
& ( strict_order(X49,X50)
| member(esk9_2(X49,X50),X50)
| member(esk12_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| member(esk9_2(X49,X50),X50)
| member(esk11_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| member(esk9_2(X49,X50),X50)
| member(esk10_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| member(esk8_2(X49,X50),X50)
| ~ apply(X49,esk10_2(X49,X50),esk12_2(X49,X50)) )
& ( strict_order(X49,X50)
| member(esk8_2(X49,X50),X50)
| apply(X49,esk11_2(X49,X50),esk12_2(X49,X50)) )
& ( strict_order(X49,X50)
| member(esk8_2(X49,X50),X50)
| apply(X49,esk10_2(X49,X50),esk11_2(X49,X50)) )
& ( strict_order(X49,X50)
| member(esk8_2(X49,X50),X50)
| member(esk12_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| member(esk8_2(X49,X50),X50)
| member(esk11_2(X49,X50),X50) )
& ( strict_order(X49,X50)
| member(esk8_2(X49,X50),X50)
| member(esk10_2(X49,X50),X50) )
& ( ~ strict_order(X42,X43)
| apply(X42,X46,X48)
| ~ apply(X42,X47,X48)
| ~ apply(X42,X46,X47)
| ~ member(X48,X43)
| ~ member(X47,X43)
| ~ member(X46,X43) )
& ( ~ strict_order(X42,X43)
| ~ apply(X42,X45,X44)
| ~ apply(X42,X44,X45)
| ~ member(X45,X43)
| ~ member(X44,X43) ) ),
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)],[strict_order])])])])])])]) ).
fof(c_0_7,plain,
! [X30,X31] :
( ( apply(member_predicate,X30,X31)
| ~ member(X30,X31) )
& ( member(X30,X31)
| ~ apply(member_predicate,X30,X31) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rel_member])])]) ).
cnf(c_0_8,plain,
( ~ strict_order(X4,X2)
| ~ apply(X4,X3,X1)
| ~ apply(X4,X1,X3)
| ~ member(X3,X2)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( ~ member(X1,X2)
| apply(member_predicate,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X20,X21,X22,X23,X25,X26,X29] :
( ( strict_well_order(X25,X26)
| ~ strict_order(X25,X26)
| ~ least(X29,X25,esk5_2(X25,X26)) )
& ( strict_well_order(X25,X26)
| ~ strict_order(X25,X26)
| member(esk6_2(X25,X26),esk5_2(X25,X26)) )
& ( strict_well_order(X25,X26)
| ~ strict_order(X25,X26)
| subset(esk5_2(X25,X26),X26) )
& ( ~ strict_well_order(X20,X21)
| least(esk4_3(X20,X21,X22),X20,X22)
| ~ member(X23,X22)
| ~ subset(X22,X21) )
& ( ~ strict_well_order(X20,X21)
| strict_order(X20,X21) ) ),
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)],[strict_well_order])])])])])])]) ).
fof(c_0_11,plain,
! [X10,X11,X12] :
( ( member(X12,on)
| ~ strict_well_order(member_predicate,X12)
| ~ set(X12)
| ~ subset(esk2_1(X12),X12) )
& ( member(X12,on)
| ~ strict_well_order(member_predicate,X12)
| ~ set(X12)
| member(esk2_1(X12),X12) )
& ( ~ member(X10,on)
| subset(X11,X10)
| ~ member(X11,X10) )
& ( ~ member(X10,on)
| strict_well_order(member_predicate,X10) )
& ( ~ member(X10,on)
| set(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)],[ordinal_number])])])])])])]) ).
fof(c_0_12,plain,
! [X14,X15,X16,X17,X18] :
( ( subset(X17,X18)
| ~ member(esk3_2(X17,X18),X18) )
& ( subset(X17,X18)
| member(esk3_2(X17,X18),X17) )
& ( member(X16,X15)
| ~ member(X16,X14)
| ~ subset(X14,X15) ) ),
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_13,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> ~ member(X1,X1) ),
inference(assume_negation,[status(cth)],[thV2]) ).
cnf(c_0_14,plain,
( ~ member(X2,X1)
| ~ member(X1,X3)
| ~ member(X2,X3)
| ~ strict_order(member_predicate,X3)
| ~ apply(member_predicate,X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,plain,
( ~ strict_well_order(X1,X2)
| strict_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ member(X1,on)
| strict_well_order(member_predicate,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ member(X2,on)
| ~ member(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> ~ member(X1,X1) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ member(X3,X2)
| ~ member(X2,X3)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ strict_order(member_predicate,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_21,plain,
( ~ member(X1,on)
| strict_order(member_predicate,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( ~ member(X3,X2)
| ~ member(X1,X3)
| ~ member(X2,on)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_23,negated_conjecture,
( member(esk1_0,esk1_0)
& member(esk1_0,on) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_24,plain,
( ~ member(X3,X2)
| ~ member(X2,X3)
| ~ member(X2,X1)
| ~ member(X1,on) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,negated_conjecture,
member(esk1_0,on),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X1,X2)
| ~ member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
member(esk1_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( ~ member(X1,esk1_0)
| ~ member(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET809+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/5.65 % Computer : n020.cluster.edu
% 0.18/5.65 % Model : x86_64 x86_64
% 0.18/5.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.65 % Memory : 8046.5625MB
% 0.18/5.65 % OS : Linux 6.8.0-71-generic
% 0.18/5.66 % CPULimit : 300
% 0.18/5.66 % WCLimit : 300
% 0.18/5.66 % DateTime : Mon Sep 21 05:40:08 UTC 2026
% 0.18/5.66 % CPUTime :
% 0.18/5.66 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.73 Running first-order theorem proving
% 0.22/5.73 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
% 0.22/5.82 % Version: 3.5.1
% 0.22/5.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.82 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.82 % Starting new_bool_1 with 300s (1) cores
% 0.22/5.82 % Starting sh5l with 300s (1) cores
% 0.22/5.82 % new_bool_3 with pid 2114874 completed with status 0
% 0.22/5.82 % Result found by new_bool_3
% 0.22/5.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.82 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.82 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/5.82 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/5.82 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.22/5.82 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/5.82 % Starting SubtermCWHack with 31s (1) cores
% 0.22/5.82 % SubtermCWHack with pid 2114877 completed with status 0
% 0.22/5.82 % Result found by SubtermCWHack
% 0.22/5.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.82 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.82 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/5.82 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/5.82 % Search class: FGHSF-FFMF32-SFFFFFNN
% 0.22/5.82 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/5.82 % Starting SubtermCWHack with 31s (1) cores
% 0.22/5.82 % Preprocessing time : 0.002 s
% 0.22/5.82
% 0.22/5.82 % Proof found!
% 0.22/5.82 % SZS status Theorem
% 0.22/5.82 % SZS output start CNFRefutation
% See solution above
% 0.22/5.82 % Parsed axioms : 20
% 0.22/5.82 % Removed by relevancy pruning/SinE : 12
% 0.22/5.82 % Initial clauses : 49
% 0.22/5.82 % Removed in clause preprocessing : 0
% 0.22/5.82 % Initial clauses in saturation : 49
% 0.22/5.82 % Processed clauses : 218
% 0.22/5.82 % ...of these trivial : 0
% 0.22/5.82 % ...subsumed : 45
% 0.22/5.82 % ...remaining for further processing : 173
% 0.22/5.82 % Other redundant clauses eliminated : 0
% 0.22/5.82 % Clauses deleted for lack of memory : 0
% 0.22/5.82 % Backward-subsumed : 13
% 0.22/5.82 % Backward-rewritten : 0
% 0.22/5.82 % Generated clauses : 963
% 0.22/5.82 % ...of the previous two non-redundant : 910
% 0.22/5.82 % ...aggressively subsumed : 0
% 0.22/5.82 % Contextual simplify-reflections : 4
% 0.22/5.82 % Paramodulations : 963
% 0.22/5.82 % Factorizations : 0
% 0.22/5.82 % NegExts : 0
% 0.22/5.82 % Equation resolutions : 0
% 0.22/5.82 % Disequality decompositions : 0
% 0.22/5.82 % Total rewrite steps : 40
% 0.22/5.82 % ...of those cached : 38
% 0.22/5.82 % Propositional unsat checks : 0
% 0.22/5.82 % Propositional check models : 0
% 0.22/5.82 % Propositional check unsatisfiable : 0
% 0.22/5.82 % Propositional clauses : 0
% 0.22/5.82 % Propositional clauses after purity: 0
% 0.22/5.82 % Propositional unsat core size : 0
% 0.22/5.82 % Propositional preprocessing time : 0.000
% 0.22/5.82 % Propositional encoding time : 0.000
% 0.22/5.82 % Propositional solver time : 0.000
% 0.22/5.82 % Success case prop preproc time : 0.000
% 0.22/5.82 % Success case prop encoding time : 0.000
% 0.22/5.82 % Success case prop solver time : 0.000
% 0.22/5.82 % Current number of processed clauses : 160
% 0.22/5.82 % Positive orientable unit clauses : 3
% 0.22/5.82 % Positive unorientable unit clauses: 0
% 0.22/5.82 % Negative unit clauses : 0
% 0.22/5.82 % Non-unit-clauses : 157
% 0.22/5.82 % Current number of unprocessed clauses: 707
% 0.22/5.82 % ...number of literals in the above : 3508
% 0.22/5.82 % Current number of archived formulas : 0
% 0.22/5.82 % Current number of archived clauses : 13
% 0.22/5.82 % Clause-clause subsumption calls (NU) : 1376
% 0.22/5.82 % Rec. Clause-clause subsumption calls : 804
% 0.22/5.82 % Non-unit clause-clause subsumptions : 62
% 0.22/5.82 % Unit Clause-clause subsumption calls : 2
% 0.22/5.82 % Rewrite failures with RHS unbound : 0
% 0.22/5.82 % BW rewrite match attempts : 1
% 0.22/5.82 % BW rewrite match successes : 0
% 0.22/5.82 % Condensation attempts : 0
% 0.22/5.82 % Condensation successes : 0
% 0.22/5.82 % Termbank termtop insertions : 21908
% 0.22/5.82 % Search garbage collected termcells : 898
% 0.22/5.82
% 0.22/5.82 % -------------------------------------------------
% 0.22/5.82 % User time : 0.029 s
% 0.22/5.82 % System time : 0.003 s
% 0.22/5.82 % Total time : 0.032 s
% 0.22/5.82 % Maximum resident set size: 3668 pages
% 0.22/5.82
% 0.22/5.82 % -------------------------------------------------
% 0.22/5.82 % User time : 0.031 s
% 0.22/5.82 % System time : 0.010 s
% 0.22/5.82 % Total time : 0.042 s
% 0.22/5.82 % Maximum resident set size: 4608 pages
% 0.22/5.82 % E exiting
%------------------------------------------------------------------------------