%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM388+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 : n019.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 01:54:54 PM UTC 2026
% Result : Theorem 0.14s 5.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 91 ( 33 ~; 30 |; 14 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 50 ( 1 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X3))
& in(X1,X2) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
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(t19_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ! [X3] :
( epsilon_transitive(X3)
=> ( ( in(X1,X2)
& in(X3,X1) )
=> in(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_ordinal1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_connected(X1)
& epsilon_transitive(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(c_0_7,plain,
! [X17,X18,X19] :
( element(X17,X19)
| ~ element(X18,powerset(X19))
| ~ in(X17,X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
fof(c_0_8,plain,
! [X29,X30] :
( ( element(X29,powerset(X30))
| ~ subset(X29,X30) )
& ( subset(X29,X30)
| ~ element(X29,powerset(X30)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
cnf(c_0_9,plain,
( ~ element(X2,powerset(X3))
| ~ in(X1,X2)
| element(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,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])])])])])])]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ! [X3] :
( epsilon_transitive(X3)
=> ( ( in(X1,X2)
& in(X3,X1) )
=> in(X3,X2) ) ) ) ),
inference(assume_negation,[status(cth)],[t19_ordinal1]) ).
cnf(c_0_13,plain,
( ~ in(X1,X3)
| ~ subset(X3,X2)
| element(X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( ~ in(X2,X1)
| ~ epsilon_transitive(X1)
| subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,negated_conjecture,
( ~ in(esk3_0,esk2_0)
& in(esk1_0,esk2_0)
& in(esk3_0,esk1_0)
& epsilon_transitive(esk3_0)
& ordinal(esk2_0)
& ordinal(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_16,plain,
! [X25] :
( ( ~ ordinal(X25)
| epsilon_connected(X25) )
& ( ~ ordinal(X25)
| epsilon_transitive(X25) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])])]) ).
cnf(c_0_17,plain,
( ~ in(X3,X2)
| ~ in(X1,X3)
| ~ epsilon_transitive(X2)
| element(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
in(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
ordinal(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X23,X24] :
( ~ empty(X24)
| ~ in(X23,X24) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_22,plain,
! [X15,X16] :
( in(X15,X16)
| empty(X16)
| ~ element(X15,X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(esk1_0,X1)
| ~ epsilon_transitive(X1)
| element(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
epsilon_transitive(esk2_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
in(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( ~ empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
element(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
~ empty(esk2_0),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
~ in(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM388+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.37 % Computer : n019.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 02:27:10 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.45 % Version: 3.5.1
% 0.14/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.45 % Starting sh5l with 300s (1) cores
% 0.14/5.45 % sh5l with pid 1489266 completed with status 0
% 0.14/5.45 % Result found by sh5l
% 0.14/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.45 % Starting sh5l with 300s (1) cores
% 0.14/5.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/5.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/5.45 % Search class: FGHSS-FFSM11-SFFFFFNN
% 0.14/5.45 % partial match(1): FGHSS-FFMM11-SFFFFFNN
% 0.14/5.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.45 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.45 % SubtermCWHack with pid 1489267 completed with status 0
% 0.14/5.45 % Result found by SubtermCWHack
% 0.14/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.45 % Starting sh5l with 300s (1) cores
% 0.14/5.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/5.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/5.45 % Search class: FGHSS-FFSM11-SFFFFFNN
% 0.14/5.45 % partial match(1): FGHSS-FFMM11-SFFFFFNN
% 0.14/5.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.45 % Starting SubtermCWHack with 31s (1) cores
% 0.14/5.45 % Preprocessing time : 0.002 s
% 0.14/5.45
% 0.14/5.45 % Proof found!
% 0.14/5.45 % SZS status Theorem
% 0.14/5.45 % SZS output start CNFRefutation
% See solution above
% 0.14/5.45 % Parsed axioms : 32
% 0.14/5.45 % Removed by relevancy pruning/SinE : 1
% 0.14/5.45 % Initial clauses : 57
% 0.14/5.45 % Removed in clause preprocessing : 2
% 0.14/5.45 % Initial clauses in saturation : 55
% 0.14/5.45 % Processed clauses : 145
% 0.14/5.45 % ...of these trivial : 3
% 0.14/5.45 % ...subsumed : 40
% 0.14/5.45 % ...remaining for further processing : 102
% 0.14/5.45 % Other redundant clauses eliminated : 0
% 0.14/5.45 % Clauses deleted for lack of memory : 0
% 0.14/5.45 % Backward-subsumed : 0
% 0.14/5.45 % Backward-rewritten : 7
% 0.14/5.45 % Generated clauses : 162
% 0.14/5.45 % ...of the previous two non-redundant : 143
% 0.14/5.45 % ...aggressively subsumed : 0
% 0.14/5.45 % Contextual simplify-reflections : 2
% 0.14/5.45 % Paramodulations : 162
% 0.14/5.45 % Factorizations : 0
% 0.14/5.45 % NegExts : 0
% 0.14/5.45 % Equation resolutions : 0
% 0.14/5.45 % Disequality decompositions : 0
% 0.14/5.45 % Total rewrite steps : 27
% 0.14/5.45 % ...of those cached : 17
% 0.14/5.45 % Propositional unsat checks : 0
% 0.14/5.45 % Propositional check models : 0
% 0.14/5.45 % Propositional check unsatisfiable : 0
% 0.14/5.45 % Propositional clauses : 0
% 0.14/5.45 % Propositional clauses after purity: 0
% 0.14/5.45 % Propositional unsat core size : 0
% 0.14/5.45 % Propositional preprocessing time : 0.000
% 0.14/5.45 % Propositional encoding time : 0.000
% 0.14/5.45 % Propositional solver time : 0.000
% 0.14/5.45 % Success case prop preproc time : 0.000
% 0.14/5.45 % Success case prop encoding time : 0.000
% 0.14/5.45 % Success case prop solver time : 0.000
% 0.14/5.45 % Current number of processed clauses : 95
% 0.14/5.45 % Positive orientable unit clauses : 33
% 0.14/5.45 % Positive unorientable unit clauses: 0
% 0.14/5.45 % Negative unit clauses : 7
% 0.14/5.45 % Non-unit-clauses : 55
% 0.14/5.45 % Current number of unprocessed clauses: 52
% 0.14/5.45 % ...number of literals in the above : 185
% 0.14/5.45 % Current number of archived formulas : 0
% 0.14/5.45 % Current number of archived clauses : 7
% 0.14/5.45 % Clause-clause subsumption calls (NU) : 498
% 0.14/5.45 % Rec. Clause-clause subsumption calls : 446
% 0.14/5.45 % Non-unit clause-clause subsumptions : 42
% 0.14/5.45 % Unit Clause-clause subsumption calls : 40
% 0.14/5.45 % Rewrite failures with RHS unbound : 0
% 0.14/5.45 % BW rewrite match attempts : 4
% 0.14/5.45 % BW rewrite match successes : 4
% 0.14/5.45 % Condensation attempts : 0
% 0.14/5.45 % Condensation successes : 0
% 0.14/5.45 % Termbank termtop insertions : 4121
% 0.14/5.45 % Search garbage collected termcells : 430
% 0.14/5.45
% 0.14/5.45 % -------------------------------------------------
% 0.14/5.45 % User time : 0.008 s
% 0.14/5.45 % System time : 0.003 s
% 0.14/5.45 % Total time : 0.012 s
% 0.14/5.45 % Maximum resident set size: 3652 pages
% 0.14/5.45
% 0.14/5.45 % -------------------------------------------------
% 0.14/5.45 % User time : 0.009 s
% 0.14/5.45 % System time : 0.009 s
% 0.14/5.45 % Total time : 0.018 s
% 0.14/5.45 % Maximum resident set size: 4608 pages
% 0.14/5.45 % E exiting
%------------------------------------------------------------------------------