%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM390+1 : 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 : 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 01:48:58 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 103 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 108 ( 40 ~; 34 |; 17 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 50 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t22_ordinal1,conjecture,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ! [X3] :
( ordinal(X3)
=> ( ( in(X2,X3)
& subset(X1,X2) )
=> in(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ordinal1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_connected(X1)
& epsilon_transitive(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_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(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( X1 != X2
& subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X2,X3)
& subset(X1,X2) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t21_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(t7_ordinal1,axiom,
! [X1,X2] :
~ ( subset(X2,X1)
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ! [X3] :
( ordinal(X3)
=> ( ( in(X2,X3)
& subset(X1,X2) )
=> in(X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t22_ordinal1]) ).
fof(c_0_8,plain,
! [X37] :
( ( ~ ordinal(X37)
| epsilon_connected(X37) )
& ( ~ ordinal(X37)
| epsilon_transitive(X37) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])])]) ).
fof(c_0_9,negated_conjecture,
( ~ in(esk1_0,esk3_0)
& in(esk2_0,esk3_0)
& subset(esk1_0,esk2_0)
& ordinal(esk3_0)
& ordinal(esk2_0)
& epsilon_transitive(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_10,plain,
! [X9,X10,X11] :
( ( epsilon_transitive(X11)
| ~ subset(esk4_1(X11),X11) )
& ( epsilon_transitive(X11)
| in(esk4_1(X11),X11) )
& ( subset(X10,X9)
| ~ in(X10,X9)
| ~ epsilon_transitive(X9) ) ),
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])])])])])])]) ).
cnf(c_0_11,plain,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
ordinal(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( X1 != X2
& subset(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d8_xboole_0]) ).
fof(c_0_14,plain,
! [X32,X33,X34] :
( subset(X32,X34)
| ~ subset(X33,X34)
| ~ subset(X32,X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])]) ).
cnf(c_0_15,plain,
( ~ in(X2,X1)
| ~ epsilon_transitive(X1)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
epsilon_transitive(esk3_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_17,plain,
! [X15,X16] :
( in(X15,X16)
| ~ proper_subset(X15,X16)
| ~ ordinal(X16)
| ~ epsilon_transitive(X15) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_ordinal1])])])]) ).
fof(c_0_18,plain,
! [X29,X30] :
( ( proper_subset(X29,X30)
| X29 = X30
| ~ subset(X29,X30) )
& ( ~ proper_subset(X29,X30)
| X29 != X30 )
& ( ~ proper_subset(X29,X30)
| subset(X29,X30) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
cnf(c_0_19,plain,
( ~ subset(X2,X3)
| ~ subset(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( ~ in(X1,esk3_0)
| subset(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_21,plain,
! [X27,X28] :
( ~ subset(X28,X27)
| ~ in(X27,X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_ordinal1])])]) ).
cnf(c_0_22,plain,
( ~ proper_subset(X1,X2)
| ~ ordinal(X2)
| ~ epsilon_transitive(X1)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( ~ subset(X1,X2)
| proper_subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(X2,esk3_0)
| ~ subset(X1,X2)
| subset(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,negated_conjecture,
in(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,plain,
( ~ subset(X2,X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( ~ ordinal(X2)
| ~ epsilon_transitive(X1)
| ~ subset(X1,X2)
| in(X1,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
subset(esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_30,negated_conjecture,
epsilon_transitive(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,negated_conjecture,
~ in(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
esk1_0 = esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_12])]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 02:27:39 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.45 % Version: 3.5.1
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % sh5l with pid 4143886 completed with status 0
% 0.10/0.45 % Result found by sh5l
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.45 % Search class: FGHSS-FFMM11-SFFFFFNN
% 0.10/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.45 % SubtermCWHack with pid 4143887 completed with status 0
% 0.10/0.45 % Result found by SubtermCWHack
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.45 % Search class: FGHSS-FFMM11-SFFFFFNN
% 0.10/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.45 % Preprocessing time : 0.002 s
% 0.10/0.45
% 0.10/0.45 % Proof found!
% 0.10/0.45 % SZS status Theorem
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 38
% 0.10/0.45 % Removed by relevancy pruning/SinE : 1
% 0.10/0.45 % Initial clauses : 65
% 0.10/0.45 % Removed in clause preprocessing : 2
% 0.10/0.45 % Initial clauses in saturation : 63
% 0.10/0.45 % Processed clauses : 179
% 0.10/0.45 % ...of these trivial : 3
% 0.10/0.45 % ...subsumed : 35
% 0.10/0.45 % ...remaining for further processing : 141
% 0.10/0.45 % Other redundant clauses eliminated : 1
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 2
% 0.10/0.45 % Backward-rewritten : 29
% 0.10/0.45 % Generated clauses : 279
% 0.10/0.45 % ...of the previous two non-redundant : 252
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 3
% 0.10/0.45 % Paramodulations : 278
% 0.10/0.45 % Factorizations : 0
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 1
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 97
% 0.10/0.45 % ...of those cached : 76
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 109
% 0.10/0.45 % Positive orientable unit clauses : 34
% 0.10/0.45 % Positive unorientable unit clauses: 0
% 0.10/0.45 % Negative unit clauses : 11
% 0.10/0.45 % Non-unit-clauses : 64
% 0.10/0.45 % Current number of unprocessed clauses: 118
% 0.10/0.45 % ...number of literals in the above : 321
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 31
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 842
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 694
% 0.10/0.45 % Non-unit clause-clause subsumptions : 37
% 0.10/0.45 % Unit Clause-clause subsumption calls : 157
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 9
% 0.10/0.45 % BW rewrite match successes : 5
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 5644
% 0.10/0.45 % Search garbage collected termcells : 545
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.010 s
% 0.10/0.45 % System time : 0.005 s
% 0.10/0.45 % Total time : 0.015 s
% 0.10/0.45 % Maximum resident set size: 3656 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.013 s
% 0.10/0.45 % System time : 0.008 s
% 0.10/0.45 % Total time : 0.022 s
% 0.10/0.45 % Maximum resident set size: 4608 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------