%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 03:10:04 PM UTC 2026
% Result : Theorem 1.09s 0.79s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 24 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 4 |; 1 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 2 sgn 6 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
? [X23] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_odd__Suc__mult__two__ex,axiom,
! [X3] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
<=> ? [X23] : X3 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__Suc__mult__two__ex) ).
fof(fact_o,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o) ).
fof(fact_semiring__norm_I115_J,axiom,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(c_0_4,negated_conjecture,
~ ? [X23] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_5,plain,
! [X3] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
<=> ? [X23] : X3 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)) ),
inference(fof_simplification,[status(thm)],[fact_odd__Suc__mult__two__ex]) ).
fof(c_0_6,negated_conjecture,
! [X80] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X80)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X701,X703,X704] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X703)
| X703 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X704)) )
& ( X701 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk8_1(X701)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X701) ) ),
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_5])])])])])]) ).
fof(c_0_8,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(fof_simplification,[status(thm)],[fact_o]) ).
cnf(c_0_9,negated_conjecture,
v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).
cnf(c_0_11,plain,
( X1 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk8_1(X1)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) != v_na____,
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk8_1(X1))) = X1 ),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14])]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW198+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 09:40:35 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 1.09/0.79 % Version: 3.5.1
% 1.09/0.79 % Preprocessing class: FMLSSMSMSSSNFFN.
% 1.09/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 1.09/0.79 % Starting new_bool_3 with 600s (2) cores
% 1.09/0.79 % Starting new_bool_1 with 600s (2) cores
% 1.09/0.79 % Starting sh5l with 300s (1) cores
% 1.09/0.79 % new_bool_3 with pid 3755340 completed with status 0
% 1.09/0.79 % Result found by new_bool_3
% 1.09/0.79 % Preprocessing class: FMLSSMSMSSSNFFN.
% 1.09/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 1.09/0.79 % Starting new_bool_3 with 600s (2) cores
% 1.09/0.79 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.09/0.79 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.09/0.79 % Search class: FGHSM-FSLM31-DFFFFFNN
% 1.09/0.79 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 1.09/0.79 % Starting SubtermCWHack with 55s (1) cores
% 1.09/0.79 % Starting new_bool_3 with 61s (1) cores
% 1.09/0.79 % new_bool_3 with pid 3755359 completed with status 0
% 1.09/0.79 % Result found by new_bool_3
% 1.09/0.79 % Preprocessing class: FMLSSMSMSSSNFFN.
% 1.09/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 1.09/0.79 % Starting new_bool_3 with 600s (2) cores
% 1.09/0.79 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.09/0.79 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.09/0.79 % Search class: FGHSM-FSLM31-DFFFFFNN
% 1.09/0.79 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 1.09/0.79 % Starting SubtermCWHack with 55s (1) cores
% 1.09/0.79 % Starting new_bool_3 with 61s (1) cores
% 1.09/0.79 % Preprocessing time : 0.019 s
% 1.09/0.79 % Presaturation interreduction done
% 1.09/0.79
% 1.09/0.79 % Proof found!
% 1.09/0.79 % SZS status Theorem
% 1.09/0.79 % SZS output start CNFRefutation
% See solution above
% 1.09/0.79 % Parsed axioms : 1186
% 1.09/0.79 % Removed by relevancy pruning/SinE : 668
% 1.09/0.79 % Initial clauses : 779
% 1.09/0.79 % Removed in clause preprocessing : 22
% 1.09/0.79 % Initial clauses in saturation : 757
% 1.09/0.79 % Processed clauses : 2129
% 1.09/0.79 % ...of these trivial : 37
% 1.09/0.79 % ...subsumed : 951
% 1.09/0.79 % ...remaining for further processing : 1141
% 1.09/0.79 % Other redundant clauses eliminated : 98
% 1.09/0.79 % Clauses deleted for lack of memory : 0
% 1.09/0.79 % Backward-subsumed : 6
% 1.09/0.79 % Backward-rewritten : 38
% 1.09/0.79 % Generated clauses : 3348
% 1.09/0.79 % ...of the previous two non-redundant : 2883
% 1.09/0.79 % ...aggressively subsumed : 0
% 1.09/0.79 % Contextual simplify-reflections : 2
% 1.09/0.79 % Paramodulations : 3256
% 1.09/0.79 % Factorizations : 0
% 1.09/0.79 % NegExts : 0
% 1.09/0.79 % Equation resolutions : 108
% 1.09/0.79 % Disequality decompositions : 0
% 1.09/0.79 % Total rewrite steps : 2197
% 1.09/0.79 % ...of those cached : 1670
% 1.09/0.79 % Propositional unsat checks : 0
% 1.09/0.79 % Propositional check models : 0
% 1.09/0.79 % Propositional check unsatisfiable : 0
% 1.09/0.79 % Propositional clauses : 0
% 1.09/0.79 % Propositional clauses after purity: 0
% 1.09/0.79 % Propositional unsat core size : 0
% 1.09/0.79 % Propositional preprocessing time : 0.000
% 1.09/0.79 % Propositional encoding time : 0.000
% 1.09/0.79 % Propositional solver time : 0.000
% 1.09/0.79 % Success case prop preproc time : 0.000
% 1.09/0.79 % Success case prop encoding time : 0.000
% 1.09/0.79 % Success case prop solver time : 0.000
% 1.09/0.79 % Current number of processed clauses : 483
% 1.09/0.79 % Positive orientable unit clauses : 142
% 1.09/0.79 % Positive unorientable unit clauses: 10
% 1.09/0.79 % Negative unit clauses : 229
% 1.09/0.79 % Non-unit-clauses : 102
% 1.09/0.79 % Current number of unprocessed clauses: 1921
% 1.09/0.79 % ...number of literals in the above : 2910
% 1.09/0.79 % Current number of archived formulas : 0
% 1.09/0.79 % Current number of archived clauses : 584
% 1.09/0.79 % Clause-clause subsumption calls (NU) : 17439
% 1.09/0.79 % Rec. Clause-clause subsumption calls : 14410
% 1.09/0.79 % Non-unit clause-clause subsumptions : 180
% 1.09/0.79 % Unit Clause-clause subsumption calls : 14264
% 1.09/0.79 % Rewrite failures with RHS unbound : 0
% 1.09/0.79 % BW rewrite match attempts : 1497
% 1.09/0.79 % BW rewrite match successes : 339
% 1.09/0.79 % Condensation attempts : 0
% 1.09/0.79 % Condensation successes : 0
% 1.09/0.79 % Termbank termtop insertions : 111037
% 1.09/0.79 % Search garbage collected termcells : 12007
% 1.09/0.79
% 1.09/0.79 % -------------------------------------------------
% 1.09/0.79 % User time : 0.271 s
% 1.09/0.79 % System time : 0.022 s
% 1.09/0.79 % Total time : 0.293 s
% 1.09/0.79 % Maximum resident set size: 6456 pages
% 1.09/0.79
% 1.09/0.79 % -------------------------------------------------
% 1.09/0.79 % User time : 0.501 s
% 1.09/0.79 % System time : 0.044 s
% 1.09/0.79 % Total time : 0.545 s
% 1.09/0.79 % Maximum resident set size: 5888 pages
% 1.09/0.79 % E exiting
%------------------------------------------------------------------------------