%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM403+1 : 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 : n008.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 01:54:55 PM UTC 2026
% Result : Theorem 66.55s 10.50s
% Output : CNFRefutation 66.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 5 unt; 0 def)
% Number of atoms : 166 ( 17 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 203 ( 80 ~; 79 |; 25 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-3 aty)
% Number of variables : 88 ( 0 sgn 46 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t34_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,succ(X2))
<=> ordinal_subset(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t36_ordinal1,conjecture,
! [X1] :
~ ( ! [X2] :
( ordinal(X2)
=> ~ subset(X1,X2) )
& ! [X2] :
( in(X2,X1)
=> ordinal(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_ordinal1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X2)
& ordinal(X1) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(fc3_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( ordinal(succ(X1))
& epsilon_connected(succ(X1))
& epsilon_transitive(succ(X1))
& ~ empty(succ(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(t35_ordinal1,axiom,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ordinal(X2) )
=> ordinal(union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_ordinal1) ).
fof(c_0_8,plain,
! [X71,X72] :
( ( ~ ordinal(X71)
| ~ ordinal(X72)
| in(X71,succ(X72))
| ~ ordinal_subset(X71,X72) )
& ( ~ ordinal(X71)
| ~ ordinal(X72)
| ordinal_subset(X71,X72)
| ~ in(X71,succ(X72)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_ordinal1])])])])]) ).
fof(c_0_9,plain,
! [X17] : succ(X17) = set_union2(X17,singleton(X17)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_10,plain,
! [X24,X25,X26,X28,X29,X30,X31,X33] :
( ( X31 = union(X30)
| in(esk3_2(X30,X31),X31)
| in(esk4_2(X30,X31),X30) )
& ( X31 = union(X30)
| in(esk3_2(X30,X31),X31)
| in(esk3_2(X30,X31),esk4_2(X30,X31)) )
& ( X31 = union(X30)
| ~ in(X33,X30)
| ~ in(esk3_2(X30,X31),X33)
| ~ in(esk3_2(X30,X31),X31) )
& ( X25 != union(X24)
| in(X28,X25)
| ~ in(X29,X24)
| ~ in(X28,X29) )
& ( X25 != union(X24)
| ~ in(X26,X25)
| in(esk2_3(X24,X25,X26),X24) )
& ( X25 != union(X24)
| ~ in(X26,X25)
| in(X26,esk2_3(X24,X25,X26)) ) ),
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)],[d4_tarski])])])])])])]) ).
fof(c_0_11,plain,
! [X18,X19,X20,X21,X22] :
( ( subset(X21,X22)
| ~ in(esk1_2(X21,X22),X22) )
& ( subset(X21,X22)
| in(esk1_2(X21,X22),X21) )
& ( in(X20,X19)
| ~ in(X20,X18)
| ~ subset(X18,X19) ) ),
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)],[d3_tarski])])])])])])]) ).
cnf(c_0_12,plain,
( ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X1,X2)
| in(X1,succ(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( X4 != union(X3)
| ~ in(X2,X3)
| ~ in(X1,X2)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
~ ( ! [X2] :
( ordinal(X2)
=> ~ subset(X1,X2) )
& ! [X2] :
( in(X2,X1)
=> ordinal(X2) ) ),
inference(assume_negation,[status(cth)],[t36_ordinal1]) ).
cnf(c_0_17,plain,
( ~ in(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| in(X1,set_union2(X2,singleton(X2))) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_19,plain,
! [X60,X61] :
( ( ~ ordinal(X61)
| ~ ordinal(X60)
| ordinal_subset(X60,X61)
| ~ subset(X60,X61) )
& ( ~ ordinal(X61)
| ~ ordinal(X60)
| subset(X60,X61)
| ~ ordinal_subset(X60,X61) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])])]) ).
cnf(c_0_20,plain,
( ~ in(X3,esk1_2(X1,X2))
| X4 != union(X1)
| in(X3,X4)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
~ ( ! [X2] :
( ordinal(X2)
=> ~ subset(X1,X2) )
& ! [X2] :
( in(X2,X1)
=> ordinal(X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ ordinal(X2)
| ~ ordinal(esk1_2(X1,set_union2(X2,singleton(X2))))
| ~ ordinal_subset(esk1_2(X1,set_union2(X2,singleton(X2))),X2)
| subset(X1,set_union2(X2,singleton(X2))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( ~ ordinal(X2)
| ~ ordinal(X1)
| ~ subset(X1,X2)
| ordinal_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( X4 != union(X1)
| in(esk1_2(esk1_2(X1,X2),X3),X4)
| subset(X1,X2)
| subset(esk1_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
fof(c_0_25,negated_conjecture,
! [X76,X77] :
( ( ~ subset(esk20_0,X77)
| ~ ordinal(X77) )
& ( ordinal(X76)
| ~ in(X76,esk20_0) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).
fof(c_0_26,plain,
! [X1] :
( ordinal(X1)
=> ( ordinal(succ(X1))
& epsilon_connected(succ(X1))
& epsilon_transitive(succ(X1))
& ~ empty(succ(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc3_ordinal1]) ).
cnf(c_0_27,plain,
( ~ ordinal(X2)
| ~ ordinal(esk1_2(X1,set_union2(X2,singleton(X2))))
| ~ subset(esk1_2(X1,set_union2(X2,singleton(X2))),X2)
| subset(X1,set_union2(X2,singleton(X2))) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( X3 != union(X1)
| subset(X1,X2)
| subset(esk1_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( ~ in(X1,esk20_0)
| ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
! [X42] :
( ( ~ ordinal(X42)
| ordinal(succ(X42)) )
& ( ~ ordinal(X42)
| epsilon_connected(succ(X42)) )
& ( ~ ordinal(X42)
| epsilon_transitive(succ(X42)) )
& ( ~ ordinal(X42)
| ~ empty(succ(X42)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
cnf(c_0_31,plain,
( ~ ordinal(X2)
| ~ ordinal(esk1_2(X1,set_union2(X2,singleton(X2))))
| X2 != union(X1)
| subset(X1,set_union2(X2,singleton(X2))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( ordinal(esk1_2(esk20_0,X1))
| subset(esk20_0,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_33,plain,
( ~ ordinal(X1)
| ordinal(succ(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,plain,
! [X73] :
( ( ordinal(union(X73))
| ~ ordinal(esk19_1(X73)) )
& ( ordinal(union(X73))
| in(esk19_1(X73),X73) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t35_ordinal1])])])])]) ).
cnf(c_0_35,negated_conjecture,
( ~ subset(esk20_0,X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,negated_conjecture,
( ~ ordinal(X1)
| X1 != union(esk20_0)
| subset(esk20_0,set_union2(X1,singleton(X1))) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( ~ ordinal(X1)
| ordinal(set_union2(X1,singleton(X1))) ),
inference(rw,[status(thm)],[c_0_33,c_0_13]) ).
cnf(c_0_38,plain,
( ordinal(union(X1))
| in(esk19_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( ~ ordinal(esk19_1(X1))
| ordinal(union(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( ~ ordinal(X1)
| X1 != union(esk20_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_41,negated_conjecture,
ordinal(union(esk20_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM403+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n008.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 02:28:08 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.55 Running first-order theorem proving
% 0.26/0.55 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
% 66.55/10.50 % Version: 3.5.1
% 66.55/10.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 66.55/10.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.55/10.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 66.55/10.50 % Starting new_bool_3 with 300s (1) cores
% 66.55/10.50 % Starting new_bool_1 with 300s (1) cores
% 66.55/10.50 % Starting sh5l with 300s (1) cores
% 66.55/10.50 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4145137 completed with status 0
% 66.55/10.50 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 66.55/10.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 66.55/10.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.55/10.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 66.55/10.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 66.55/10.50 % No SInE strategy applied
% 66.55/10.50 % Search class: FGHSM-FFMM31-SFFFFFNN
% 66.55/10.50 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 66.55/10.50 % Starting SubtermCWHack with 136s (1) cores
% 66.55/10.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 66.55/10.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 66.55/10.50 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 66.55/10.50 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 66.55/10.50 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 4145147 completed with status 0
% 66.55/10.50 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 66.55/10.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 66.55/10.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.55/10.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 66.55/10.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 66.55/10.50 % No SInE strategy applied
% 66.55/10.50 % Search class: FGHSM-FFMM31-SFFFFFNN
% 66.55/10.50 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 66.55/10.50 % Starting SubtermCWHack with 136s (1) cores
% 66.55/10.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 66.55/10.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 66.55/10.50 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 66.55/10.50 % Preprocessing time : 0.004 s
% 66.55/10.50
% 66.55/10.50 % Proof found!
% 66.55/10.50 % SZS status Theorem
% 66.55/10.50 % SZS output start CNFRefutation
% See solution above
% 66.55/10.50 % Parsed axioms : 53
% 66.55/10.50 % Removed by relevancy pruning/SinE : 0
% 66.55/10.50 % Initial clauses : 108
% 66.55/10.50 % Removed in clause preprocessing : 3
% 66.55/10.50 % Initial clauses in saturation : 105
% 66.55/10.50 % Processed clauses : 8305
% 66.55/10.50 % ...of these trivial : 57
% 66.55/10.50 % ...subsumed : 5049
% 66.55/10.50 % ...remaining for further processing : 3199
% 66.55/10.50 % Other redundant clauses eliminated : 0
% 66.55/10.50 % Clauses deleted for lack of memory : 0
% 66.55/10.50 % Backward-subsumed : 134
% 66.55/10.50 % Backward-rewritten : 86
% 66.55/10.50 % Generated clauses : 243884
% 66.55/10.50 % ...of the previous two non-redundant : 238765
% 66.55/10.50 % ...aggressively subsumed : 0
% 66.55/10.50 % Contextual simplify-reflections : 111
% 66.55/10.50 % Paramodulations : 243392
% 66.55/10.50 % Factorizations : 4
% 66.55/10.50 % NegExts : 0
% 66.55/10.50 % Equation resolutions : 480
% 66.55/10.50 % Disequality decompositions : 0
% 66.55/10.50 % Total rewrite steps : 28219
% 66.55/10.50 % ...of those cached : 28106
% 66.55/10.50 % Propositional unsat checks : 0
% 66.55/10.50 % Propositional check models : 0
% 66.55/10.50 % Propositional check unsatisfiable : 0
% 66.55/10.50 % Propositional clauses : 0
% 66.55/10.50 % Propositional clauses after purity: 0
% 66.55/10.50 % Propositional unsat core size : 0
% 66.55/10.50 % Propositional preprocessing time : 0.000
% 66.55/10.50 % Propositional encoding time : 0.000
% 66.55/10.50 % Propositional solver time : 0.000
% 66.55/10.50 % Success case prop preproc time : 0.000
% 66.55/10.50 % Success case prop encoding time : 0.000
% 66.55/10.50 % Success case prop solver time : 0.000
% 66.55/10.50 % Current number of processed clauses : 2971
% 66.55/10.50 % Positive orientable unit clauses : 81
% 66.55/10.50 % Positive unorientable unit clauses: 1
% 66.55/10.50 % Negative unit clauses : 29
% 66.55/10.50 % Non-unit-clauses : 2860
% 66.55/10.50 % Current number of unprocessed clauses: 229961
% 66.55/10.50 % ...number of literals in the above : 1252361
% 66.55/10.50 % Current number of archived formulas : 0
% 66.55/10.50 % Current number of archived clauses : 229
% 66.55/10.50 % Clause-clause subsumption calls (NU) : 767790
% 66.55/10.50 % Rec. Clause-clause subsumption calls : 277231
% 66.55/10.50 % Non-unit clause-clause subsumptions : 3754
% 66.55/10.50 % Unit Clause-clause subsumption calls : 9940
% 66.55/10.50 % Rewrite failures with RHS unbound : 0
% 66.55/10.50 % BW rewrite match attempts : 455
% 66.55/10.50 % BW rewrite match successes : 31
% 66.55/10.50 % Condensation attempts : 0
% 66.55/10.50 % Condensation successes : 0
% 66.55/10.50 % Termbank termtop insertions : 5593728
% 66.55/10.50 % Search garbage collected termcells : 851
% 66.55/10.50
% 66.55/10.50 % -------------------------------------------------
% 66.55/10.50 % User time : 9.224 s
% 66.55/10.50 % System time : 0.251 s
% 66.55/10.50 % Total time : 9.475 s
% 66.55/10.50 % Maximum resident set size: 3932 pages
% 66.55/10.50
% 66.55/10.50 % -------------------------------------------------
% 66.55/10.50 % User time : 45.664 s
% 66.55/10.50 % System time : 1.883 s
% 66.55/10.50 % Total time : 47.547 s
% 66.55/10.50 % Maximum resident set size: 4608 pages
% 66.55/10.50 % E exiting
%------------------------------------------------------------------------------