%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 02:13:23 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 42 ( 16 ~; 13 |; 9 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(null_class_is_a_set,conjecture,
member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(subclass_defn,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(class_elements_are_sets,axiom,
! [X1] : subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(inductive_defn,axiom,
! [X1] :
( inductive(X1)
<=> ( subclass(image(successor_relation,X1),X1)
& member(null_class,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',inductive_defn) ).
fof(infinity,axiom,
? [X1] :
( ! [X2] :
( inductive(X2)
=> subclass(X1,X2) )
& inductive(X1)
& member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',infinity) ).
fof(c_0_5,negated_conjecture,
~ member(null_class,universal_class),
inference(assume_negation,[status(cth)],[null_class_is_a_set]) ).
fof(c_0_6,plain,
! [X10,X11,X12,X13,X14] :
( ( subclass(X13,X14)
| ~ member(esk1_2(X13,X14),X14) )
& ( subclass(X13,X14)
| member(esk1_2(X13,X14),X13) )
& ( member(X12,X11)
| ~ member(X12,X10)
| ~ subclass(X10,X11) ) ),
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)],[subclass_defn])])])])])])]) ).
fof(c_0_7,plain,
! [X21] : subclass(X21,universal_class),
inference(variable_rename,[status(thm)],[class_elements_are_sets]) ).
fof(c_0_8,plain,
! [X24] :
( ( inductive(X24)
| ~ subclass(image(successor_relation,X24),X24)
| ~ member(null_class,X24) )
& ( ~ inductive(X24)
| subclass(image(successor_relation,X24),X24) )
& ( ~ inductive(X24)
| member(null_class,X24) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inductive_defn])])])]) ).
fof(c_0_9,plain,
! [X75] :
( ( subclass(esk5_0,X75)
| ~ inductive(X75) )
& inductive(esk5_0)
& member(esk5_0,universal_class) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infinity])])])])]) ).
fof(c_0_10,negated_conjecture,
~ member(null_class,universal_class),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
subclass(X1,universal_class),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( ~ inductive(X1)
| member(null_class,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
inductive(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,negated_conjecture,
~ member(null_class,universal_class),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
member(null_class,esk5_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
~ member(null_class,universal_class),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:46:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % sh5l with pid 205039 completed with status 0
% 0.10/0.44 % Result found by sh5l
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.44 % Search class: FGHSM-FFMS31-MFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.44 % SubtermCWHack with pid 205046 completed with status 0
% 0.10/0.44 % Result found by SubtermCWHack
% 0.10/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.44 % Search class: FGHSM-FFMS31-MFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.44 % Preprocessing time : 0.002 s
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 44
% 0.10/0.44 % Removed by relevancy pruning/SinE : 3
% 0.10/0.44 % Initial clauses : 83
% 0.10/0.44 % Removed in clause preprocessing : 0
% 0.10/0.44 % Initial clauses in saturation : 83
% 0.10/0.44 % Processed clauses : 64
% 0.10/0.44 % ...of these trivial : 0
% 0.10/0.44 % ...subsumed : 1
% 0.10/0.44 % ...remaining for further processing : 63
% 0.10/0.44 % Other redundant clauses eliminated : 2
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 5
% 0.10/0.44 % Backward-rewritten : 1
% 0.10/0.44 % Generated clauses : 89
% 0.10/0.44 % ...of the previous two non-redundant : 78
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 0
% 0.10/0.44 % Paramodulations : 87
% 0.10/0.44 % Factorizations : 0
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 2
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 4
% 0.10/0.44 % ...of those cached : 1
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 55
% 0.10/0.44 % Positive orientable unit clauses : 22
% 0.10/0.44 % Positive unorientable unit clauses: 0
% 0.10/0.44 % Negative unit clauses : 2
% 0.10/0.44 % Non-unit-clauses : 31
% 0.10/0.44 % Current number of unprocessed clauses: 90
% 0.10/0.44 % ...number of literals in the above : 207
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 6
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 126
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 112
% 0.10/0.44 % Non-unit clause-clause subsumptions : 5
% 0.10/0.44 % Unit Clause-clause subsumption calls : 6
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 6
% 0.10/0.44 % BW rewrite match successes : 1
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 5716
% 0.10/0.44 % Search garbage collected termcells : 902
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.011 s
% 0.10/0.44 % System time : 0.002 s
% 0.10/0.44 % Total time : 0.014 s
% 0.10/0.44 % Maximum resident set size: 3948 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.015 s
% 0.10/0.44 % System time : 0.005 s
% 0.10/0.44 % Total time : 0.021 s
% 0.10/0.44 % Maximum resident set size: 4864 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------