%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET809+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 : n010.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 02:18:34 PM UTC 2026
% Result : Theorem 0.17s 0.60s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 3 unt; 0 def)
% Number of atoms : 186 ( 0 equ)
% Maximal formula atoms : 84 ( 7 avg)
% Number of connectives : 231 ( 70 ~; 104 |; 45 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 62 ( 0 sgn 38 !; 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/sandbox/benchmark/Axioms/SET006+4.ax',strict_order) ).
fof(rel_member,axiom,
! [X3,X5] :
( apply(member_predicate,X3,X5)
<=> member(X3,X5) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(thV2,conjecture,
! [X1] :
( member(X1,on)
=> ~ member(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV2) ).
fof(c_0_5,plain,
! [X70,X71,X72,X73,X74,X75,X76,X77,X78] :
( ( strict_order(X77,X78)
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| ~ apply(X77,esk11_2(X77,X78),esk13_2(X77,X78)) )
& ( strict_order(X77,X78)
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| apply(X77,esk12_2(X77,X78),esk13_2(X77,X78)) )
& ( strict_order(X77,X78)
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| apply(X77,esk11_2(X77,X78),esk12_2(X77,X78)) )
& ( strict_order(X77,X78)
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| member(esk13_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| member(esk12_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| member(esk11_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| ~ apply(X77,esk11_2(X77,X78),esk13_2(X77,X78)) )
& ( strict_order(X77,X78)
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| apply(X77,esk12_2(X77,X78),esk13_2(X77,X78)) )
& ( strict_order(X77,X78)
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| apply(X77,esk11_2(X77,X78),esk12_2(X77,X78)) )
& ( strict_order(X77,X78)
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| member(esk13_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| member(esk12_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| member(esk11_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| member(esk10_2(X77,X78),X78)
| ~ apply(X77,esk11_2(X77,X78),esk13_2(X77,X78)) )
& ( strict_order(X77,X78)
| member(esk10_2(X77,X78),X78)
| apply(X77,esk12_2(X77,X78),esk13_2(X77,X78)) )
& ( strict_order(X77,X78)
| member(esk10_2(X77,X78),X78)
| apply(X77,esk11_2(X77,X78),esk12_2(X77,X78)) )
& ( strict_order(X77,X78)
| member(esk10_2(X77,X78),X78)
| member(esk13_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| member(esk10_2(X77,X78),X78)
| member(esk12_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| member(esk10_2(X77,X78),X78)
| member(esk11_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| member(esk9_2(X77,X78),X78)
| ~ apply(X77,esk11_2(X77,X78),esk13_2(X77,X78)) )
& ( strict_order(X77,X78)
| member(esk9_2(X77,X78),X78)
| apply(X77,esk12_2(X77,X78),esk13_2(X77,X78)) )
& ( strict_order(X77,X78)
| member(esk9_2(X77,X78),X78)
| apply(X77,esk11_2(X77,X78),esk12_2(X77,X78)) )
& ( strict_order(X77,X78)
| member(esk9_2(X77,X78),X78)
| member(esk13_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| member(esk9_2(X77,X78),X78)
| member(esk12_2(X77,X78),X78) )
& ( strict_order(X77,X78)
| member(esk9_2(X77,X78),X78)
| member(esk11_2(X77,X78),X78) )
& ( ~ strict_order(X70,X71)
| apply(X70,X74,X76)
| ~ apply(X70,X75,X76)
| ~ apply(X70,X74,X75)
| ~ member(X76,X71)
| ~ member(X75,X71)
| ~ member(X74,X71) )
& ( ~ strict_order(X70,X71)
| ~ apply(X70,X73,X72)
| ~ apply(X70,X72,X73)
| ~ member(X73,X71)
| ~ member(X72,X71) ) ),
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_6,plain,
! [X68,X69] :
( ( apply(member_predicate,X68,X69)
| ~ member(X68,X69) )
& ( member(X68,X69)
| ~ apply(member_predicate,X68,X69) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rel_member])])]) ).
cnf(c_0_7,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_5]) ).
cnf(c_0_8,plain,
( ~ member(X1,X2)
| apply(member_predicate,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X50,X51,X52,X53,X55,X56,X59] :
( ( strict_well_order(X55,X56)
| ~ strict_order(X55,X56)
| ~ least(X59,X55,esk6_2(X55,X56)) )
& ( strict_well_order(X55,X56)
| ~ strict_order(X55,X56)
| member(esk7_2(X55,X56),esk6_2(X55,X56)) )
& ( strict_well_order(X55,X56)
| ~ strict_order(X55,X56)
| subset(esk6_2(X55,X56),X56) )
& ( ~ strict_well_order(X50,X51)
| least(esk5_3(X50,X51,X52),X50,X52)
| ~ member(X53,X52)
| ~ subset(X52,X51) )
& ( ~ strict_well_order(X50,X51)
| strict_order(X50,X51) ) ),
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_10,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_11,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> ~ member(X1,X1) ),
inference(assume_negation,[status(cth)],[thV2]) ).
cnf(c_0_12,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_7,c_0_8]) ).
cnf(c_0_13,plain,
( ~ strict_well_order(X1,X2)
| strict_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ member(X1,on)
| strict_well_order(member_predicate,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> ~ member(X1,X1) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ member(X3,X2)
| ~ member(X2,X3)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ strict_order(member_predicate,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_17,plain,
( ~ member(X1,on)
| strict_order(member_predicate,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,negated_conjecture,
( member(esk14_0,esk14_0)
& member(esk14_0,on) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_19,plain,
( ~ member(X3,X2)
| ~ member(X2,X3)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ member(X1,on) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
member(esk14_0,on),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X2,X1)
| ~ member(X1,X2)
| ~ member(X2,esk14_0)
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
member(esk14_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ member(esk14_0,X1)
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET809+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.52 % Computer : n010.cluster.edu
% 0.11/0.52 % Model : x86_64 x86_64
% 0.11/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.52 % Memory : 8046.5625MB
% 0.11/0.52 % OS : Linux 6.8.0-71-generic
% 0.11/0.52 % CPULimit : 300
% 0.11/0.52 % WCLimit : 300
% 0.11/0.52 % DateTime : Mon Sep 21 05:39:27 UTC 2026
% 0.11/0.52 % CPUTime :
% 0.11/0.52 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.56 Running first-order theorem proving
% 0.11/0.56 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
% 0.17/0.60 % Version: 3.5.1
% 0.17/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.60 % Starting sh5l with 300s (1) cores
% 0.17/0.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 130037 completed with status 0
% 0.17/0.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.60 % No SInE strategy applied
% 0.17/0.60 % Search class: FGHSF-FFMF31-SFFFFFNN
% 0.17/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.17/0.60 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 166s (1) cores
% 0.17/0.60 % Starting new_bool_3 with 162s (1) cores
% 0.17/0.60 % Starting new_bool_1 with 158s (1) cores
% 0.17/0.60 % G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 130046 completed with status 0
% 0.17/0.60 % Result found by G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.17/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.60 % No SInE strategy applied
% 0.17/0.60 % Search class: FGHSF-FFMF31-SFFFFFNN
% 0.17/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.17/0.60 % Starting G-E--_208_B07----S_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 166s (1) cores
% 0.17/0.60 % Preprocessing time : 0.001 s
% 0.17/0.60 % Presaturation interreduction done
% 0.17/0.60
% 0.17/0.60 % Proof found!
% 0.17/0.60 % SZS status Theorem
% 0.17/0.60 % SZS output start CNFRefutation
% See solution above
% 0.17/0.60 % Parsed axioms : 20
% 0.17/0.60 % Removed by relevancy pruning/SinE : 0
% 0.17/0.60 % Initial clauses : 80
% 0.17/0.60 % Removed in clause preprocessing : 0
% 0.17/0.60 % Initial clauses in saturation : 80
% 0.17/0.60 % Processed clauses : 253
% 0.17/0.60 % ...of these trivial : 1
% 0.17/0.60 % ...subsumed : 6
% 0.17/0.60 % ...remaining for further processing : 246
% 0.17/0.60 % Other redundant clauses eliminated : 3
% 0.17/0.60 % Clauses deleted for lack of memory : 0
% 0.17/0.60 % Backward-subsumed : 6
% 0.17/0.60 % Backward-rewritten : 6
% 0.17/0.60 % Generated clauses : 446
% 0.17/0.60 % ...of the previous two non-redundant : 378
% 0.17/0.60 % ...aggressively subsumed : 0
% 0.17/0.60 % Contextual simplify-reflections : 1
% 0.17/0.60 % Paramodulations : 443
% 0.17/0.60 % Factorizations : 0
% 0.17/0.60 % NegExts : 0
% 0.17/0.60 % Equation resolutions : 3
% 0.17/0.60 % Disequality decompositions : 0
% 0.17/0.60 % Total rewrite steps : 62
% 0.17/0.60 % ...of those cached : 38
% 0.17/0.60 % Propositional unsat checks : 0
% 0.17/0.60 % Propositional check models : 0
% 0.17/0.60 % Propositional check unsatisfiable : 0
% 0.17/0.60 % Propositional clauses : 0
% 0.17/0.60 % Propositional clauses after purity: 0
% 0.17/0.60 % Propositional unsat core size : 0
% 0.17/0.60 % Propositional preprocessing time : 0.000
% 0.17/0.60 % Propositional encoding time : 0.000
% 0.17/0.60 % Propositional solver time : 0.000
% 0.17/0.60 % Success case prop preproc time : 0.000
% 0.17/0.60 % Success case prop encoding time : 0.000
% 0.17/0.60 % Success case prop solver time : 0.000
% 0.17/0.60 % Current number of processed clauses : 151
% 0.17/0.60 % Positive orientable unit clauses : 20
% 0.17/0.60 % Positive unorientable unit clauses: 0
% 0.17/0.60 % Negative unit clauses : 1
% 0.17/0.60 % Non-unit-clauses : 130
% 0.17/0.60 % Current number of unprocessed clauses: 284
% 0.17/0.60 % ...number of literals in the above : 680
% 0.17/0.60 % Current number of archived formulas : 0
% 0.17/0.60 % Current number of archived clauses : 92
% 0.17/0.60 % Clause-clause subsumption calls (NU) : 5562
% 0.17/0.60 % Rec. Clause-clause subsumption calls : 4107
% 0.17/0.60 % Non-unit clause-clause subsumptions : 12
% 0.17/0.60 % Unit Clause-clause subsumption calls : 229
% 0.17/0.60 % Rewrite failures with RHS unbound : 0
% 0.17/0.60 % BW rewrite match attempts : 10
% 0.17/0.60 % BW rewrite match successes : 3
% 0.17/0.60 % Condensation attempts : 0
% 0.17/0.60 % Condensation successes : 0
% 0.17/0.60 % Termbank termtop insertions : 10644
% 0.17/0.60 % Search garbage collected termcells : 1219
% 0.17/0.60
% 0.17/0.60 % -------------------------------------------------
% 0.17/0.60 % User time : 0.016 s
% 0.17/0.60 % System time : 0.004 s
% 0.17/0.60 % Total time : 0.021 s
% 0.17/0.60 % Maximum resident set size: 3412 pages
% 0.17/0.60
% 0.17/0.60 % -------------------------------------------------
% 0.17/0.60 % User time : 0.066 s
% 0.17/0.60 % System time : 0.013 s
% 0.17/0.60 % Total time : 0.080 s
% 0.17/0.60 % Maximum resident set size: 4608 pages
% 0.17/0.60 % E exiting
%------------------------------------------------------------------------------