%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU234+3 : 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 : n002.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 02:24:23 PM UTC 2026
% Result : Theorem 0.28s 0.64s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 5 unt; 0 def)
% Number of atoms : 123 ( 15 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 138 ( 50 ~; 51 |; 24 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 44 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t31_ordinal1,conjecture,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( subset(X2,X1)
& ordinal(X2) ) )
=> ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(t24_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
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/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_connected(X1)
& epsilon_transitive(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ! [X2] :
( in(X2,X1)
=> ( subset(X2,X1)
& ordinal(X2) ) )
=> ordinal(X1) ),
inference(assume_negation,[status(cth)],[t31_ordinal1]) ).
fof(c_0_6,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_7,negated_conjecture,
! [X46] :
( ~ ordinal(esk18_0)
& ( ~ in(X46,esk18_0)
| subset(X46,esk18_0) )
& ( ~ in(X46,esk18_0)
| ordinal(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(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).
fof(c_0_8,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_9,plain,
( ~ subset(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( ~ in(X1,esk18_0)
| subset(X1,esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X41,X42] :
( in(X42,X41)
| X41 = X42
| in(X41,X42)
| ~ ordinal(X42)
| ~ ordinal(X41) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_12,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_13,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_14,negated_conjecture,
( ~ in(esk1_1(esk18_0),esk18_0)
| epsilon_transitive(esk18_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( epsilon_transitive(X1)
| in(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( ~ ordinal(X2)
| ~ ordinal(X1)
| in(X2,X1)
| X1 = X2
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(X1,esk18_0)
| ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_18,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_12])])])])])])]) ).
cnf(c_0_19,plain,
( ~ epsilon_connected(X1)
| ~ epsilon_transitive(X1)
| ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
epsilon_transitive(esk18_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
~ ordinal(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(X2,esk18_0)
| ~ ordinal(X1)
| in(X2,X1)
| in(X1,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( epsilon_connected(X1)
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
~ epsilon_connected(esk18_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( ~ ordinal(X1)
| in(X1,esk3_1(esk18_0))
| in(esk3_1(esk18_0),X1)
| X1 = esk3_1(esk18_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( ~ in(X1,esk18_0)
| in(esk3_1(esk18_0),X1)
| in(X1,esk3_1(esk18_0))
| X1 = esk3_1(esk18_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_27,plain,
( epsilon_connected(X1)
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
( ~ in(esk3_1(X1),esk2_1(X1))
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,negated_conjecture,
( in(esk2_1(esk18_0),esk3_1(esk18_0))
| in(esk3_1(esk18_0),esk2_1(esk18_0))
| esk3_1(esk18_0) = esk2_1(esk18_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24]) ).
cnf(c_0_30,plain,
( ~ in(esk2_1(X1),esk3_1(X1))
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,negated_conjecture,
( in(esk2_1(esk18_0),esk3_1(esk18_0))
| esk3_1(esk18_0) = esk2_1(esk18_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24]) ).
cnf(c_0_32,plain,
( esk2_1(X1) != esk3_1(X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_33,negated_conjecture,
esk3_1(esk18_0) = esk2_1(esk18_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_24]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU234+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n002.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 06:04:32 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.53 Running first-order theorem proving
% 0.28/0.53 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
% 0.28/0.64 % Version: 3.5.1
% 0.28/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.64 % Starting sh5l with 300s (1) cores
% 0.28/0.64 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2590582 completed with status 0
% 0.28/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.28/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.64 % No SInE strategy applied
% 0.28/0.64 % Search class: FGHSS-FFMM11-SFFFFFNN
% 0.28/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.28/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.28/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.28/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.28/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.28/0.64 % Starting new_bool_1 with 136s (1) cores
% 0.28/0.64 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 2590588 completed with status 0
% 0.28/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.28/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.64 % No SInE strategy applied
% 0.28/0.64 % Search class: FGHSS-FFMM11-SFFFFFNN
% 0.28/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.28/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.28/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.28/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.28/0.64 % Preprocessing time : 0.003 s
% 0.28/0.64 % Presaturation interreduction done
% 0.28/0.64
% 0.28/0.64 % Proof found!
% 0.28/0.64 % SZS status Theorem
% 0.28/0.64 % SZS output start CNFRefutation
% See solution above
% 0.28/0.65 % Parsed axioms : 39
% 0.28/0.65 % Removed by relevancy pruning/SinE : 0
% 0.28/0.65 % Initial clauses : 89
% 0.28/0.65 % Removed in clause preprocessing : 2
% 0.28/0.65 % Initial clauses in saturation : 87
% 0.28/0.65 % Processed clauses : 542
% 0.28/0.65 % ...of these trivial : 6
% 0.28/0.65 % ...subsumed : 180
% 0.28/0.65 % ...remaining for further processing : 356
% 0.28/0.65 % Other redundant clauses eliminated : 0
% 0.28/0.65 % Clauses deleted for lack of memory : 0
% 0.28/0.65 % Backward-subsumed : 15
% 0.28/0.65 % Backward-rewritten : 44
% 0.28/0.65 % Generated clauses : 894
% 0.28/0.65 % ...of the previous two non-redundant : 784
% 0.28/0.65 % ...aggressively subsumed : 0
% 0.28/0.65 % Contextual simplify-reflections : 9
% 0.28/0.65 % Paramodulations : 894
% 0.28/0.65 % Factorizations : 0
% 0.28/0.65 % NegExts : 0
% 0.28/0.65 % Equation resolutions : 0
% 0.28/0.65 % Disequality decompositions : 0
% 0.28/0.65 % Total rewrite steps : 240
% 0.28/0.65 % ...of those cached : 216
% 0.28/0.65 % Propositional unsat checks : 0
% 0.28/0.65 % Propositional check models : 0
% 0.28/0.65 % Propositional check unsatisfiable : 0
% 0.28/0.65 % Propositional clauses : 0
% 0.28/0.65 % Propositional clauses after purity: 0
% 0.28/0.65 % Propositional unsat core size : 0
% 0.28/0.65 % Propositional preprocessing time : 0.000
% 0.28/0.65 % Propositional encoding time : 0.000
% 0.28/0.65 % Propositional solver time : 0.000
% 0.28/0.65 % Success case prop preproc time : 0.000
% 0.28/0.65 % Success case prop encoding time : 0.000
% 0.28/0.65 % Success case prop solver time : 0.000
% 0.28/0.65 % Current number of processed clauses : 219
% 0.28/0.65 % Positive orientable unit clauses : 39
% 0.28/0.65 % Positive unorientable unit clauses: 0
% 0.28/0.65 % Negative unit clauses : 8
% 0.28/0.65 % Non-unit-clauses : 172
% 0.28/0.65 % Current number of unprocessed clauses: 362
% 0.28/0.65 % ...number of literals in the above : 1590
% 0.28/0.65 % Current number of archived formulas : 0
% 0.28/0.65 % Current number of archived clauses : 137
% 0.28/0.65 % Clause-clause subsumption calls (NU) : 5950
% 0.28/0.65 % Rec. Clause-clause subsumption calls : 3919
% 0.28/0.65 % Non-unit clause-clause subsumptions : 165
% 0.28/0.65 % Unit Clause-clause subsumption calls : 281
% 0.28/0.65 % Rewrite failures with RHS unbound : 0
% 0.28/0.65 % BW rewrite match attempts : 9
% 0.28/0.65 % BW rewrite match successes : 7
% 0.28/0.65 % Condensation attempts : 0
% 0.28/0.65 % Condensation successes : 0
% 0.28/0.65 % Termbank termtop insertions : 16502
% 0.28/0.65 % Search garbage collected termcells : 631
% 0.28/0.65
% 0.28/0.65 % -------------------------------------------------
% 0.28/0.65 % User time : 0.055 s
% 0.28/0.65 % System time : 0.009 s
% 0.28/0.65 % Total time : 0.065 s
% 0.28/0.65 % Maximum resident set size: 3628 pages
% 0.28/0.65
% 0.28/0.65 % -------------------------------------------------
% 0.28/0.65 % User time : 0.114 s
% 0.28/0.65 % System time : 0.027 s
% 0.28/0.65 % Total time : 0.141 s
% 0.28/0.65 % Maximum resident set size: 4864 pages
% 0.28/0.65 % E exiting
%------------------------------------------------------------------------------