%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW294+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 : n017.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 03:10:14 PM UTC 2026
% Result : Theorem 44.75s 8.77s
% Output : CNFRefutation 44.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 35 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 15 ~; 3 |; 3 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-4 aty)
% Number of variables : 32 ( 5 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Zero__neq__Suc,axiom,
! [X90] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X90),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(conj_0,conjecture,
! [X231,X232] :
( v_P(X231,X232)
=> ! [X233] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),X232,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X233)
=> v_Q(X231,X233) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(fact_evaln__elim__cases_I6_J,axiom,
! [X51,X33,X9,X79] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X79),X9,X33,X51)
=> ~ ! [X70] :
( X33 = hAPP(c_Nat_OSuc,X70)
=> ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X79)),X9,X70,X51) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I6_J) ).
fof(c_0_5,plain,
! [X90] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X90),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_6,negated_conjecture,
~ ! [X231,X232] :
( v_P(X231,X232)
=> ! [X233] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),X232,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X233)
=> v_Q(X231,X233) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_7,plain,
! [X1245] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1245),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
cnf(c_0_8,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_9,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_10,plain,
! [X51,X33,X9,X79] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X79),X9,X33,X51)
=> ~ ! [X70] :
( X33 = hAPP(c_Nat_OSuc,X70)
=> ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X79)),X9,X70,X51) ) ),
inference(fof_simplification,[status(thm)],[fact_evaln__elim__cases_I6_J]) ).
fof(c_0_11,negated_conjecture,
( ~ v_Q(esk493_0,esk495_0)
& c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),esk494_0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),esk495_0)
& v_P(esk493_0,esk494_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_12,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_14,plain,
! [X1211,X1212,X1213,X1214] :
( ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1214),X1213,X1212,X1211)
| c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,X1214)),X1213,esk21_4(X1211,X1212,X1213,X1214),X1211) )
& ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1214),X1213,X1212,X1211)
| X1212 = hAPP(c_Nat_OSuc,esk21_4(X1211,X1212,X1213,X1214)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
cnf(c_0_15,negated_conjecture,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),esk494_0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),esk495_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X4),X3,X1,X2)
| X1 = hAPP(c_Nat_OSuc,esk21_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),esk494_0,hAPP(c_Int_Onat,c_Int_OPls),esk495_0),
inference(rw,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_19,plain,
~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,X1),X2,hAPP(c_Int_Onat,c_Int_OPls),X3),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_18,c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW294+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.09 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n017.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Mon Sep 21 09:41:12 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.54 Running first-order theorem proving
% 0.25/0.54 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
% 44.75/8.77 % Version: 3.5.1
% 44.75/8.77 % Preprocessing class: FMLMSMSMSSSNFFN.
% 44.75/8.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 44.75/8.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 44.75/8.77 % Starting new_bool_3 with 300s (1) cores
% 44.75/8.77 % Starting new_bool_1 with 300s (1) cores
% 44.75/8.77 % Starting sh5l with 300s (1) cores
% 44.75/8.77 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2017760 completed with status 0
% 44.75/8.77 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 44.75/8.77 % Preprocessing class: FMLMSMSMSSSNFFN.
% 44.75/8.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 44.75/8.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 44.75/8.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 44.75/8.77 % No SInE strategy applied
% 44.75/8.77 % Search class: FGHSM-SMLM33-DFFFFFNN
% 44.75/8.77 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 44.75/8.77 % Starting SubtermCWHack with 135s (1) cores
% 44.75/8.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 44.75/8.77 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 44.75/8.77 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 44.75/8.77 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 44.75/8.77 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2017768 completed with status 0
% 44.75/8.77 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 44.75/8.77 % Preprocessing class: FMLMSMSMSSSNFFN.
% 44.75/8.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 44.75/8.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 44.75/8.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 44.75/8.77 % No SInE strategy applied
% 44.75/8.77 % Search class: FGHSM-SMLM33-DFFFFFNN
% 44.75/8.77 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 44.75/8.77 % Starting SubtermCWHack with 135s (1) cores
% 44.75/8.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 44.75/8.77 % Preprocessing time : 0.313 s
% 44.75/8.77 % Presaturation interreduction done
% 44.75/8.77
% 44.75/8.77 % Proof found!
% 44.75/8.77 % SZS status Theorem
% 44.75/8.77 % SZS output start CNFRefutation
% See solution above
% 44.75/8.77 % Parsed axioms : 5207
% 44.75/8.77 % Removed by relevancy pruning/SinE : 0
% 44.75/8.77 % Initial clauses : 7488
% 44.75/8.77 % Removed in clause preprocessing : 254
% 44.75/8.77 % Initial clauses in saturation : 7234
% 44.75/8.77 % Processed clauses : 9264
% 44.75/8.77 % ...of these trivial : 232
% 44.75/8.77 % ...subsumed : 1225
% 44.75/8.77 % ...remaining for further processing : 7807
% 44.75/8.77 % Other redundant clauses eliminated : 598
% 44.75/8.77 % Clauses deleted for lack of memory : 0
% 44.75/8.77 % Backward-subsumed : 20
% 44.75/8.77 % Backward-rewritten : 186
% 44.75/8.77 % Generated clauses : 5982
% 44.75/8.77 % ...of the previous two non-redundant : 4992
% 44.75/8.77 % ...aggressively subsumed : 0
% 44.75/8.77 % Contextual simplify-reflections : 23
% 44.75/8.77 % Paramodulations : 5388
% 44.75/8.77 % Factorizations : 0
% 44.75/8.77 % NegExts : 0
% 44.75/8.77 % Equation resolutions : 656
% 44.75/8.77 % Disequality decompositions : 0
% 44.75/8.77 % Total rewrite steps : 7905
% 44.75/8.77 % ...of those cached : 6058
% 44.75/8.77 % Propositional unsat checks : 2
% 44.75/8.77 % Propositional check models : 2
% 44.75/8.77 % Propositional check unsatisfiable : 0
% 44.75/8.77 % Propositional clauses : 0
% 44.75/8.77 % Propositional clauses after purity: 0
% 44.75/8.77 % Propositional unsat core size : 0
% 44.75/8.77 % Propositional preprocessing time : 0.000
% 44.75/8.77 % Propositional encoding time : 0.125
% 44.75/8.77 % Propositional solver time : 0.043
% 44.75/8.77 % Success case prop preproc time : 0.000
% 44.75/8.77 % Success case prop encoding time : 0.000
% 44.75/8.77 % Success case prop solver time : 0.000
% 44.75/8.77 % Current number of processed clauses : 1325
% 44.75/8.77 % Positive orientable unit clauses : 580
% 44.75/8.77 % Positive unorientable unit clauses: 2
% 44.75/8.77 % Negative unit clauses : 101
% 44.75/8.77 % Non-unit-clauses : 642
% 44.75/8.77 % Current number of unprocessed clauses: 7902
% 44.75/8.77 % ...number of literals in the above : 19049
% 44.75/8.77 % Current number of archived formulas : 0
% 44.75/8.77 % Current number of archived clauses : 6031
% 44.75/8.77 % Clause-clause subsumption calls (NU) : 3743473
% 44.75/8.77 % Rec. Clause-clause subsumption calls : 1496596
% 44.75/8.77 % Non-unit clause-clause subsumptions : 1025
% 44.75/8.77 % Unit Clause-clause subsumption calls : 36789
% 44.75/8.77 % Rewrite failures with RHS unbound : 0
% 44.75/8.77 % BW rewrite match attempts : 32760
% 44.75/8.77 % BW rewrite match successes : 454
% 44.75/8.77 % Condensation attempts : 0
% 44.75/8.77 % Condensation successes : 0
% 44.75/8.77 % Termbank termtop insertions : 1397640
% 44.75/8.77 % Search garbage collected termcells : 99107
% 44.75/8.77
% 44.75/8.77 % -------------------------------------------------
% 44.75/8.77 % User time : 7.373 s
% 44.75/8.77 % System time : 0.260 s
% 44.75/8.77 % Total time : 7.633 s
% 44.75/8.77 % Maximum resident set size: 42416 pages
% 44.75/8.77
% 44.75/8.77 % -------------------------------------------------
% 44.75/8.77 % User time : 28.021 s
% 44.75/8.77 % System time : 1.013 s
% 44.75/8.77 % Total time : 29.034 s
% 44.75/8.77 % Maximum resident set size: 12288 pages
% 44.75/8.77 % E exiting
%------------------------------------------------------------------------------