%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW196+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 0.20s 5.67s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 25 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 5 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 10 ( 2 sgn 5 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_1,conjecture,
v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(conj_0,hypothesis,
( ? [X1] : v_na____ = 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)
=> v_thesis____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
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/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(fact_even__nat__equiv__def2,axiom,
! [X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
<=> ? [X31] : X15 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__nat__equiv__def2) ).
fof(fact_e,axiom,
c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_e) ).
fof(c_0_5,negated_conjecture,
~ v_thesis____,
inference(assume_negation,[status(cth)],[conj_1]) ).
fof(c_0_6,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,hypothesis,
! [X81] :
( v_thesis____
| v_na____ != 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))),X81) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])])]) ).
fof(c_0_8,negated_conjecture,
~ v_thesis____,
inference(fof_nnf,[status(thm)],[c_0_6]) ).
cnf(c_0_9,hypothesis,
( v_na____ != 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)
| v_thesis____ ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
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,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X1085,X1087,X1088] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1087)
| X1087 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1088) )
& ( X1085 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk12_1(X1085))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1085) ) ),
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)],[fact_even__nat__equiv__def2])])])])])]) ).
cnf(c_0_13,hypothesis,
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(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_14,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| X1 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk12_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(split_conjunct,[status(thm)],[fact_e]) ).
cnf(c_0_16,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14])]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW196+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.43 % Computer : n026.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Mon Sep 21 09:43:30 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.48 Running first-order theorem proving
% 0.16/5.48 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
% 0.20/5.67 % Version: 3.5.1
% 0.20/5.67 % Preprocessing class: FMLSSMSMSSSNFFN.
% 0.20/5.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/5.67 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 0.20/5.67 % Starting new_bool_3 with 600s (2) cores
% 0.20/5.67 % Starting new_bool_1 with 600s (2) cores
% 0.20/5.67 % Starting sh5l with 300s (1) cores
% 0.20/5.67 % new_bool_3 with pid 1958022 completed with status 0
% 0.20/5.67 % Result found by new_bool_3
% 0.20/5.67 % Preprocessing class: FMLSSMSMSSSNFFN.
% 0.20/5.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/5.67 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 0.20/5.67 % Starting new_bool_3 with 600s (2) cores
% 0.20/5.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/5.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/5.67 % Search class: FGHSM-FSLM31-DFFFFFNN
% 0.20/5.67 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.20/5.67 % Starting SubtermCWHack with 55s (1) cores
% 0.20/5.67 % Starting new_bool_3 with 61s (1) cores
% 0.20/5.67 % SubtermCWHack with pid 1958031 completed with status 0
% 0.20/5.67 % Result found by SubtermCWHack
% 0.20/5.67 % Preprocessing class: FMLSSMSMSSSNFFN.
% 0.20/5.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/5.67 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 0.20/5.67 % Starting new_bool_3 with 600s (2) cores
% 0.20/5.67 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/5.67 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/5.67 % Search class: FGHSM-FSLM31-DFFFFFNN
% 0.20/5.67 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.20/5.67 % Starting SubtermCWHack with 55s (1) cores
% 0.20/5.67 % Preprocessing time : 0.014 s
% 0.20/5.67
% 0.20/5.67 % Proof found!
% 0.20/5.67 % SZS status Theorem
% 0.20/5.67 % SZS output start CNFRefutation
% See solution above
% 0.20/5.67 % Parsed axioms : 1172
% 0.20/5.67 % Removed by relevancy pruning/SinE : 474
% 0.20/5.67 % Initial clauses : 1040
% 0.20/5.67 % Removed in clause preprocessing : 52
% 0.20/5.67 % Initial clauses in saturation : 988
% 0.20/5.67 % Processed clauses : 1749
% 0.20/5.67 % ...of these trivial : 164
% 0.20/5.67 % ...subsumed : 970
% 0.20/5.67 % ...remaining for further processing : 615
% 0.20/5.67 % Other redundant clauses eliminated : 95
% 0.20/5.67 % Clauses deleted for lack of memory : 0
% 0.20/5.67 % Backward-subsumed : 8
% 0.20/5.67 % Backward-rewritten : 40
% 0.20/5.67 % Generated clauses : 4045
% 0.20/5.67 % ...of the previous two non-redundant : 2775
% 0.20/5.67 % ...aggressively subsumed : 0
% 0.20/5.67 % Contextual simplify-reflections : 3
% 0.20/5.67 % Paramodulations : 3940
% 0.20/5.67 % Factorizations : 14
% 0.20/5.67 % NegExts : 0
% 0.20/5.67 % Equation resolutions : 102
% 0.20/5.67 % Disequality decompositions : 0
% 0.20/5.67 % Total rewrite steps : 2184
% 0.20/5.67 % ...of those cached : 1897
% 0.20/5.67 % Propositional unsat checks : 0
% 0.20/5.67 % Propositional check models : 0
% 0.20/5.67 % Propositional check unsatisfiable : 0
% 0.20/5.67 % Propositional clauses : 0
% 0.20/5.67 % Propositional clauses after purity: 0
% 0.20/5.67 % Propositional unsat core size : 0
% 0.20/5.67 % Propositional preprocessing time : 0.000
% 0.20/5.67 % Propositional encoding time : 0.000
% 0.20/5.67 % Propositional solver time : 0.000
% 0.20/5.67 % Success case prop preproc time : 0.000
% 0.20/5.67 % Success case prop encoding time : 0.000
% 0.20/5.67 % Success case prop solver time : 0.000
% 0.20/5.67 % Current number of processed clauses : 509
% 0.20/5.67 % Positive orientable unit clauses : 174
% 0.20/5.67 % Positive unorientable unit clauses: 9
% 0.20/5.67 % Negative unit clauses : 98
% 0.20/5.67 % Non-unit-clauses : 228
% 0.20/5.67 % Current number of unprocessed clauses: 1954
% 0.20/5.67 % ...number of literals in the above : 4196
% 0.20/5.67 % Current number of archived formulas : 0
% 0.20/5.67 % Current number of archived clauses : 48
% 0.20/5.67 % Clause-clause subsumption calls (NU) : 7834
% 0.20/5.67 % Rec. Clause-clause subsumption calls : 6164
% 0.20/5.67 % Non-unit clause-clause subsumptions : 284
% 0.20/5.67 % Unit Clause-clause subsumption calls : 3025
% 0.20/5.67 % Rewrite failures with RHS unbound : 0
% 0.20/5.67 % BW rewrite match attempts : 1686
% 0.20/5.67 % BW rewrite match successes : 65
% 0.20/5.67 % Condensation attempts : 0
% 0.20/5.67 % Condensation successes : 0
% 0.20/5.67 % Termbank termtop insertions : 124392
% 0.20/5.67 % Search garbage collected termcells : 13779
% 0.20/5.67
% 0.20/5.67 % -------------------------------------------------
% 0.20/5.67 % User time : 0.115 s
% 0.20/5.67 % System time : 0.021 s
% 0.20/5.67 % Total time : 0.136 s
% 0.20/5.67 % Maximum resident set size: 7448 pages
% 0.20/5.67
% 0.20/5.67 % -------------------------------------------------
% 0.20/5.67 % User time : 0.229 s
% 0.20/5.67 % System time : 0.036 s
% 0.20/5.67 % Total time : 0.265 s
% 0.20/5.67 % Maximum resident set size: 5888 pages
% 0.20/5.67 % E exiting
%------------------------------------------------------------------------------