%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM404+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 : n004.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 01:48:59 PM UTC 2026
% Result : Theorem 0.25s 0.60s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 5 unt; 0 def)
% Number of atoms : 146 ( 9 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 162 ( 63 ~; 59 |; 23 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t37_ordinal1,conjecture,
! [X1] :
~ ! [X2] :
( in(X2,X1)
<=> ordinal(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).
fof(t23_ordinal1,axiom,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
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(d3_ordinal1,axiom,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( ~ in(X3,X2)
& X2 != X3
& ~ in(X2,X3)
& in(X3,X1)
& in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(t24_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_connected(X1)
& epsilon_transitive(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
~ ! [X2] :
( in(X2,X1)
<=> ordinal(X2) ),
inference(assume_negation,[status(cth)],[t37_ordinal1]) ).
fof(c_0_9,plain,
! [X47,X48] :
( ordinal(X47)
| ~ in(X47,X48)
| ~ ordinal(X48) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_ordinal1])])]) ).
fof(c_0_10,plain,
! [X22,X23,X24,X25,X26] :
( ( subset(X25,X26)
| ~ in(esk4_2(X25,X26),X26) )
& ( subset(X25,X26)
| in(esk4_2(X25,X26),X25) )
& ( in(X24,X23)
| ~ in(X24,X22)
| ~ subset(X22,X23) ) ),
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])])])])])])]) ).
fof(c_0_11,negated_conjecture,
! [X54] :
( ( in(X54,esk19_0)
| ~ ordinal(X54) )
& ( ordinal(X54)
| ~ in(X54,esk19_0) ) ),
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,
( ~ in(X2,X1)
| ~ ordinal(X1)
| ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| in(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( ~ in(X3,X2)
& X2 != X3
& ~ in(X2,X3)
& in(X3,X1)
& in(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[d3_ordinal1]) ).
fof(c_0_15,plain,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[t24_ordinal1]) ).
cnf(c_0_16,negated_conjecture,
( ~ ordinal(X1)
| in(X1,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ ordinal(X1)
| ordinal(esk4_2(X1,X2))
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,plain,
! [X12,X13,X14] :
( ( epsilon_transitive(X14)
| ~ subset(esk1_1(X14),X14) )
& ( epsilon_transitive(X14)
| in(esk1_1(X14),X14) )
& ( subset(X13,X12)
| ~ in(X13,X12)
| ~ epsilon_transitive(X12) ) ),
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)],[d2_ordinal1])])])])])])]) ).
fof(c_0_19,plain,
! [X16,X17,X18,X19] :
( ( epsilon_connected(X19)
| ~ in(esk3_1(X19),esk2_1(X19)) )
& ( epsilon_connected(X19)
| esk2_1(X19) != esk3_1(X19) )
& ( epsilon_connected(X19)
| ~ in(esk2_1(X19),esk3_1(X19)) )
& ( epsilon_connected(X19)
| in(esk3_1(X19),X19) )
& ( epsilon_connected(X19)
| in(esk2_1(X19),X19) )
& ( in(X18,X17)
| X17 = X18
| in(X17,X18)
| ~ in(X18,X16)
| ~ in(X17,X16)
| ~ epsilon_connected(X16) ) ),
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)],[c_0_14])])])])])])]) ).
fof(c_0_20,plain,
! [X49,X50] :
( in(X50,X49)
| X49 = X50
| in(X49,X50)
| ~ ordinal(X50)
| ~ ordinal(X49) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_21,plain,
( ~ in(esk4_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( ~ ordinal(X1)
| in(esk4_2(X1,X2),esk19_0)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(X1,esk19_0)
| ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,plain,
( epsilon_transitive(X1)
| in(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( ~ in(esk3_1(X1),esk2_1(X1))
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ~ ordinal(X2)
| ~ ordinal(X1)
| in(X2,X1)
| X1 = X2
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( ~ in(esk2_1(X1),esk3_1(X1))
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( esk2_1(X1) != esk3_1(X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( epsilon_connected(X1)
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( epsilon_connected(X1)
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_31,plain,
! [X10] :
( ordinal(X10)
| ~ epsilon_connected(X10)
| ~ epsilon_transitive(X10) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])])]) ).
cnf(c_0_32,plain,
( ~ subset(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_33,negated_conjecture,
( ~ ordinal(X1)
| subset(X1,esk19_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
( ordinal(esk1_1(esk19_0))
| epsilon_transitive(esk19_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_35,plain,
( ~ ordinal(esk3_1(X1))
| ~ ordinal(esk2_1(X1))
| epsilon_connected(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( ordinal(esk2_1(esk19_0))
| epsilon_connected(esk19_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( ordinal(esk3_1(esk19_0))
| epsilon_connected(esk19_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
fof(c_0_38,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_39,plain,
( ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1)
| ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,negated_conjecture,
epsilon_transitive(esk19_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,negated_conjecture,
epsilon_connected(esk19_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
fof(c_0_42,plain,
! [X4,X5] :
( ~ in(X5,X4)
| ~ in(X4,X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
cnf(c_0_43,negated_conjecture,
ordinal(esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_44,plain,
( ~ in(X2,X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_45,negated_conjecture,
in(esk19_0,esk19_0),
inference(spm,[status(thm)],[c_0_16,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 02:27:19 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.50 Running first-order theorem proving
% 0.25/0.51 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
% 0.25/0.60 % Version: 3.5.1
% 0.25/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.60 % Starting sh5l with 300s (1) cores
% 0.25/0.60 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2052990 completed with status 0
% 0.25/0.60 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.25/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.60 % No SInE strategy applied
% 0.25/0.60 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.25/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/0.60 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.25/0.60 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.60 % Starting new_bool_1 with 136s (1) cores
% 0.25/0.60 % new_bool_3 with pid 2052999 completed with status 0
% 0.25/0.60 % Result found by new_bool_3
% 0.25/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.60 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.60 % No SInE strategy applied
% 0.25/0.60 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.25/0.60 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.60 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/0.60 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.25/0.60 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.60 % Preprocessing time : 0.002 s
% 0.25/0.60 % Presaturation interreduction done
% 0.25/0.60
% 0.25/0.60 % Proof found!
% 0.25/0.60 % SZS status Theorem
% 0.25/0.60 % SZS output start CNFRefutation
% See solution above
% 0.25/0.60 % Parsed axioms : 41
% 0.25/0.60 % Removed by relevancy pruning/SinE : 0
% 0.25/0.60 % Initial clauses : 92
% 0.25/0.60 % Removed in clause preprocessing : 2
% 0.25/0.60 % Initial clauses in saturation : 90
% 0.25/0.60 % Processed clauses : 950
% 0.25/0.60 % ...of these trivial : 6
% 0.25/0.60 % ...subsumed : 499
% 0.25/0.60 % ...remaining for further processing : 445
% 0.25/0.60 % Other redundant clauses eliminated : 9
% 0.25/0.60 % Clauses deleted for lack of memory : 0
% 0.25/0.60 % Backward-subsumed : 20
% 0.25/0.60 % Backward-rewritten : 51
% 0.25/0.60 % Generated clauses : 2144
% 0.25/0.60 % ...of the previous two non-redundant : 1944
% 0.25/0.60 % ...aggressively subsumed : 0
% 0.25/0.60 % Contextual simplify-reflections : 13
% 0.25/0.60 % Paramodulations : 2127
% 0.25/0.60 % Factorizations : 8
% 0.25/0.60 % NegExts : 0
% 0.25/0.60 % Equation resolutions : 9
% 0.25/0.60 % Disequality decompositions : 0
% 0.25/0.60 % Total rewrite steps : 327
% 0.25/0.60 % ...of those cached : 290
% 0.25/0.60 % Propositional unsat checks : 0
% 0.25/0.60 % Propositional check models : 0
% 0.25/0.60 % Propositional check unsatisfiable : 0
% 0.25/0.60 % Propositional clauses : 0
% 0.25/0.60 % Propositional clauses after purity: 0
% 0.25/0.60 % Propositional unsat core size : 0
% 0.25/0.60 % Propositional preprocessing time : 0.000
% 0.25/0.60 % Propositional encoding time : 0.000
% 0.25/0.60 % Propositional solver time : 0.000
% 0.25/0.60 % Success case prop preproc time : 0.000
% 0.25/0.60 % Success case prop encoding time : 0.000
% 0.25/0.60 % Success case prop solver time : 0.000
% 0.25/0.60 % Current number of processed clauses : 293
% 0.25/0.60 % Positive orientable unit clauses : 48
% 0.25/0.60 % Positive unorientable unit clauses: 0
% 0.25/0.60 % Negative unit clauses : 8
% 0.25/0.60 % Non-unit-clauses : 237
% 0.25/0.60 % Current number of unprocessed clauses: 1137
% 0.25/0.60 % ...number of literals in the above : 5419
% 0.25/0.60 % Current number of archived formulas : 0
% 0.25/0.60 % Current number of archived clauses : 152
% 0.25/0.60 % Clause-clause subsumption calls (NU) : 15016
% 0.25/0.60 % Rec. Clause-clause subsumption calls : 7621
% 0.25/0.61 % Non-unit clause-clause subsumptions : 460
% 0.25/0.61 % Unit Clause-clause subsumption calls : 250
% 0.25/0.61 % Rewrite failures with RHS unbound : 0
% 0.25/0.61 % BW rewrite match attempts : 8
% 0.25/0.61 % BW rewrite match successes : 7
% 0.25/0.61 % Condensation attempts : 0
% 0.25/0.61 % Condensation successes : 0
% 0.25/0.61 % Termbank termtop insertions : 28913
% 0.25/0.61 % Search garbage collected termcells : 689
% 0.25/0.61
% 0.25/0.61 % -------------------------------------------------
% 0.25/0.61 % User time : 0.067 s
% 0.25/0.61 % System time : 0.004 s
% 0.25/0.61 % Total time : 0.071 s
% 0.25/0.61 % Maximum resident set size: 3660 pages
% 0.25/0.61
% 0.25/0.61 % -------------------------------------------------
% 0.25/0.61 % User time : 0.290 s
% 0.25/0.61 % System time : 0.021 s
% 0.25/0.61 % Total time : 0.311 s
% 0.25/0.61 % Maximum resident set size: 4608 pages
% 0.25/0.61 % E exiting
%------------------------------------------------------------------------------