TSTP Solution File: SWW245+1 by Vampire-SAT---4.9
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : SWW245+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:49:10 EDT 2024
% Result : Theorem 89.97s 13.36s
% Output : Refutation 89.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 47
% Syntax : Number of formulae : 193 ( 41 unt; 0 def)
% Number of atoms : 560 ( 318 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 605 ( 238 ~; 228 |; 72 &)
% ( 30 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 28 ( 26 usr; 23 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-4 aty)
% Number of variables : 227 ( 182 !; 45 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f190565,plain,
$false,
inference(avatar_sat_refutation,[],[f5261,f5266,f5274,f5279,f5289,f5293,f5298,f5303,f5308,f48424,f56347,f117408,f124269,f124270,f135719,f135727,f147437,f147641,f176283,f178284,f178659,f188787,f188788,f190439]) ).
fof(f190439,plain,
( ~ spl34_39
| ~ spl34_15
| ~ spl34_17
| ~ spl34_790 ),
inference(avatar_split_clause,[],[f190307,f17885,f5310,f5300,f5731]) ).
fof(f5731,plain,
( spl34_39
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_39])]) ).
fof(f5300,plain,
( spl34_15
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK8),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_15])]) ).
fof(f5310,plain,
( spl34_17
<=> v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_17])]) ).
fof(f17885,plain,
( spl34_790
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_790])]) ).
fof(f190307,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_15
| ~ spl34_17
| ~ spl34_790 ),
inference(superposition,[],[f17886,f190202]) ).
fof(f190202,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK6,c_If(tc_Nat_Onat,c_fequal(sK8,v_cs____),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK8)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_15
| ~ spl34_17 ),
inference(forward_demodulation,[],[f188942,f5312]) ).
fof(f5312,plain,
( v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl34_17 ),
inference(avatar_component_clause,[],[f5310]) ).
fof(f188942,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK6,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK8)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_15 ),
inference(forward_demodulation,[],[f188941,f3904]) ).
fof(f3904,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(cnf_transformation,[],[f1340]) ).
fof(f1340,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(rectify,[],[f70]) ).
fof(f70,axiom,
! [X18,X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f188941,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK6,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK8),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_15 ),
inference(forward_demodulation,[],[f5302,f3904]) ).
fof(f5302,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK8),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK6),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_15 ),
inference(avatar_component_clause,[],[f5300]) ).
fof(f17886,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1)
| ~ spl34_790 ),
inference(avatar_component_clause,[],[f17885]) ).
fof(f188788,plain,
( spl34_6523
| ~ spl34_14 ),
inference(avatar_split_clause,[],[f188078,f5295,f134965]) ).
fof(f134965,plain,
( spl34_6523
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK6,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK8))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_6523])]) ).
fof(f5295,plain,
( spl34_14
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK8),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_14])]) ).
fof(f188078,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK6,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK8))))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| ~ spl34_14 ),
inference(superposition,[],[f9385,f124291]) ).
fof(f124291,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK6,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK8)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| ~ spl34_14 ),
inference(forward_demodulation,[],[f124290,f3904]) ).
fof(f124290,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK6,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK8)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_14 ),
inference(forward_demodulation,[],[f124289,f3904]) ).
fof(f124289,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK6,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK8),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_14 ),
inference(forward_demodulation,[],[f5297,f3904]) ).
fof(f5297,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK8),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK6),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_14 ),
inference(avatar_component_clause,[],[f5295]) ).
fof(f9385,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(forward_demodulation,[],[f9338,f3905]) ).
fof(f3905,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
inference(cnf_transformation,[],[f1341]) ).
fof(f1341,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
inference(rectify,[],[f401]) ).
fof(f401,axiom,
! [X18,X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X18),X18) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f9338,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0)),
inference(resolution,[],[f4113,f3899]) ).
fof(f3899,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
inference(cnf_transformation,[],[f1335]) ).
fof(f1335,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
inference(rectify,[],[f522]) ).
fof(f522,axiom,
! [X50,X48] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X48,X50),X50),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4113,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
inference(cnf_transformation,[],[f2667]) ).
fof(f2667,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1543]) ).
fof(f1543,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) = X1 ),
inference(rectify,[],[f616]) ).
fof(f616,axiom,
! [X18,X21] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X18)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X18)) = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f188787,plain,
( spl34_6561
| ~ spl34_10 ),
inference(avatar_split_clause,[],[f188077,f5276,f135724]) ).
fof(f135724,plain,
( spl34_6561
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK3,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK5))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_6561])]) ).
fof(f5276,plain,
( spl34_10
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK3),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_10])]) ).
fof(f188077,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK3,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK5)))))
| ~ spl34_10 ),
inference(superposition,[],[f9385,f126718]) ).
fof(f126718,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK3,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK5)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_10 ),
inference(forward_demodulation,[],[f126717,f3904]) ).
fof(f126717,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK3,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK5)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_10 ),
inference(forward_demodulation,[],[f126716,f3904]) ).
fof(f126716,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK3,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK5),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_10 ),
inference(forward_demodulation,[],[f5278,f3904]) ).
fof(f5278,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK3),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_10 ),
inference(avatar_component_clause,[],[f5276]) ).
fof(f178659,plain,
( spl34_916
| ~ spl34_101 ),
inference(avatar_split_clause,[],[f178598,f7136,f19480]) ).
fof(f19480,plain,
( spl34_916
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_916])]) ).
fof(f7136,plain,
( spl34_101
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_101])]) ).
fof(f178598,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(superposition,[],[f4249,f7696]) ).
fof(f7696,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[],[f4949,f3758]) ).
fof(f3758,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f1196]) ).
fof(f1196,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f98]) ).
fof(f98,axiom,
! [X18] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4949,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(definition_unfolding,[],[f3765,f3762]) ).
fof(f3762,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1200]) ).
fof(f1200,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rectify,[],[f189]) ).
fof(f189,axiom,
! [X18] : c_Nat_OSuc(X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3765,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1203]) ).
fof(f1203,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f431]) ).
fof(f431,axiom,
! [X18] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X18),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4249,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3443]) ).
fof(f3443,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)) ) ),
inference(nnf_transformation,[],[f1629]) ).
fof(f1629,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(rectify,[],[f612]) ).
fof(f612,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f178284,plain,
( spl34_101
| spl34_39 ),
inference(avatar_split_clause,[],[f178171,f5731,f7136]) ).
fof(f178171,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(superposition,[],[f5091,f7661]) ).
fof(f7661,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[],[f3757,f4947]) ).
fof(f4947,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(definition_unfolding,[],[f3763,f3762]) ).
fof(f3763,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1201]) ).
fof(f1201,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(rectify,[],[f188]) ).
fof(f188,axiom,
! [X18] : c_Nat_OSuc(X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f3757,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1195]) ).
fof(f1195,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f99]) ).
fof(f99,axiom,
! [X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5091,plain,
! [X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1) ),
inference(equality_resolution,[],[f4981]) ).
fof(f4981,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X0 != X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4117,f3762]) ).
fof(f4117,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| X0 != X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3392]) ).
fof(f3392,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| X0 != X1 )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(nnf_transformation,[],[f2671]) ).
fof(f2671,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> X0 = X1 )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1546]) ).
fof(f1546,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> X0 = X1 ) ),
inference(rectify,[],[f513]) ).
fof(f513,axiom,
! [X20,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
<=> X19 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f176283,plain,
( ~ spl34_916
| ~ spl34_2895 ),
inference(avatar_split_clause,[],[f176270,f89162,f19480]) ).
fof(f89162,plain,
( spl34_2895
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl34_2895])]) ).
fof(f176270,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl34_2895 ),
inference(superposition,[],[f6714,f89163]) ).
fof(f89163,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| ~ spl34_2895 ),
inference(avatar_component_clause,[],[f89162]) ).
fof(f6714,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[],[f3899,f4947]) ).
fof(f147641,plain,
( spl34_2895
| ~ spl34_6579 ),
inference(avatar_split_clause,[],[f147634,f147348,f89162]) ).
fof(f147348,plain,
( spl34_6579
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_6579])]) ).
fof(f147634,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| ~ spl34_6579 ),
inference(resolution,[],[f147349,f4060]) ).
fof(f4060,plain,
! [X0,X1] :
( ~ class_Groups_Ocomm__monoid__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(cnf_transformation,[],[f2619]) ).
fof(f2619,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(ennf_transformation,[],[f1499]) ).
fof(f1499,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f138]) ).
fof(f138,axiom,
! [X7,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> c_Groups_Oplus__class_Oplus(X9,X7,c_Groups_Ozero__class_Ozero(X9)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f147349,plain,
( class_Groups_Ocomm__monoid__add(tc_Nat_Onat)
| ~ spl34_6579 ),
inference(avatar_component_clause,[],[f147348]) ).
fof(f147437,plain,
spl34_6579,
inference(avatar_split_clause,[],[f3700,f147348]) ).
fof(f3700,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1092]) ).
fof(f1092,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f135727,plain,
( spl34_12
| ~ spl34_6561
| ~ spl34_6
| ~ spl34_9 ),
inference(avatar_split_clause,[],[f135722,f5272,f5259,f135724,f5286]) ).
fof(f5286,plain,
( spl34_12
<=> c_Groups_Ozero__class_Ozero(t_a) = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl34_12])]) ).
fof(f5259,plain,
( spl34_6
<=> ! [X2,X0,X1] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2)))
| c_Groups_Ozero__class_Ozero(t_a) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_6])]) ).
fof(f5272,plain,
( spl34_9
<=> ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,sK5)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_9])]) ).
fof(f135722,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK3,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK5)))))
| c_Groups_Ozero__class_Ozero(t_a) = sK4
| ~ spl34_6
| ~ spl34_9 ),
inference(forward_demodulation,[],[f135716,f3904]) ).
fof(f135716,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK5))),sK3))
| c_Groups_Ozero__class_Ozero(t_a) = sK4
| ~ spl34_6
| ~ spl34_9 ),
inference(trivial_inequality_removal,[],[f135715]) ).
fof(f135715,plain,
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(sK3,sK4,sK5)) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(sK3,sK4,sK5))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK5))),sK3))
| c_Groups_Ozero__class_Ozero(t_a) = sK4
| ~ spl34_6
| ~ spl34_9 ),
inference(superposition,[],[f135004,f5273]) ).
fof(f5273,plain,
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,sK5)),X3))
| ~ spl34_9 ),
inference(avatar_component_clause,[],[f5272]) ).
fof(f135004,plain,
( ! [X2,X0,X1] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0))
| c_Groups_Ozero__class_Ozero(t_a) = X1 )
| ~ spl34_6 ),
inference(forward_demodulation,[],[f135003,f3904]) ).
fof(f135003,plain,
( ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2)))
| c_Groups_Ozero__class_Ozero(t_a) = X1 )
| ~ spl34_6 ),
inference(forward_demodulation,[],[f135002,f3904]) ).
fof(f135002,plain,
( ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0))
| hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2)))
| c_Groups_Ozero__class_Ozero(t_a) = X1 )
| ~ spl34_6 ),
inference(forward_demodulation,[],[f5260,f3904]) ).
fof(f5260,plain,
( ! [X2,X0,X1] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2)))
| c_Groups_Ozero__class_Ozero(t_a) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
| ~ spl34_6 ),
inference(avatar_component_clause,[],[f5259]) ).
fof(f135719,plain,
( spl34_16
| ~ spl34_6523
| ~ spl34_6
| ~ spl34_13 ),
inference(avatar_split_clause,[],[f135718,f5291,f5259,f134965,f5305]) ).
fof(f5305,plain,
( spl34_16
<=> c_Groups_Ozero__class_Ozero(t_a) = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl34_16])]) ).
fof(f5291,plain,
( spl34_13
<=> ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,sK8)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_13])]) ).
fof(f135718,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK6,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK8))))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
| c_Groups_Ozero__class_Ozero(t_a) = sK7
| ~ spl34_6
| ~ spl34_13 ),
inference(forward_demodulation,[],[f135717,f3904]) ).
fof(f135717,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK8))),sK6))
| c_Groups_Ozero__class_Ozero(t_a) = sK7
| ~ spl34_6
| ~ spl34_13 ),
inference(trivial_inequality_removal,[],[f135713]) ).
fof(f135713,plain,
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(sK6,sK7,sK8)) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(sK6,sK7,sK8))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK8))),sK6))
| c_Groups_Ozero__class_Ozero(t_a) = sK7
| ~ spl34_6
| ~ spl34_13 ),
inference(superposition,[],[f135004,f5292]) ).
fof(f5292,plain,
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,sK8)),X3))
| ~ spl34_13 ),
inference(avatar_component_clause,[],[f5291]) ).
fof(f124270,plain,
( ~ spl34_4764
| spl34_17
| ~ spl34_5 ),
inference(avatar_split_clause,[],[f124256,f5255,f5310,f113161]) ).
fof(f113161,plain,
( spl34_4764
<=> class_Groups_Ozero(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_4764])]) ).
fof(f5255,plain,
( spl34_5
<=> c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_5])]) ).
fof(f124256,plain,
( v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a)
| ~ spl34_5 ),
inference(trivial_inequality_removal,[],[f124250]) ).
fof(f124250,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a)
| ~ spl34_5 ),
inference(superposition,[],[f4518,f5257]) ).
fof(f5257,plain,
( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ spl34_5 ),
inference(avatar_component_clause,[],[f5255]) ).
fof(f4518,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f3513]) ).
fof(f3513,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0) ) )
| ~ class_Groups_Ozero(X2) ),
inference(flattening,[],[f3512]) ).
fof(f3512,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
| c_Groups_Ozero__class_Ozero(X2) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0) ) )
| ~ class_Groups_Ozero(X2) ),
inference(nnf_transformation,[],[f2964]) ).
fof(f2964,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Groups_Ozero(X2) ),
inference(ennf_transformation,[],[f1884]) ).
fof(f1884,plain,
! [X0,X1,X2] :
( class_Groups_Ozero(X2)
=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
& c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X11,X12,X13] :
( class_Groups_Ozero(X13)
=> ( c_Polynomial_OpCons(X13,X12,X11) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X13))
<=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) = X11
& c_Groups_Ozero__class_Ozero(X13) = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f124269,plain,
( ~ spl34_4764
| spl34_8
| ~ spl34_5 ),
inference(avatar_split_clause,[],[f124257,f5255,f5268,f113161]) ).
fof(f5268,plain,
( spl34_8
<=> c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
introduced(avatar_definition,[new_symbols(naming,[spl34_8])]) ).
fof(f124257,plain,
( c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Groups_Ozero(t_a)
| ~ spl34_5 ),
inference(trivial_inequality_removal,[],[f124249]) ).
fof(f124249,plain,
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Groups_Ozero(t_a)
| ~ spl34_5 ),
inference(superposition,[],[f4517,f5257]) ).
fof(f4517,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
| c_Groups_Ozero__class_Ozero(X2) = X1
| ~ class_Groups_Ozero(X2) ),
inference(cnf_transformation,[],[f3513]) ).
fof(f117408,plain,
( ~ spl34_2
| spl34_4764 ),
inference(avatar_split_clause,[],[f117407,f113161,f5243]) ).
fof(f5243,plain,
( spl34_2
<=> class_Rings_Oidom(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_2])]) ).
fof(f117407,plain,
( ~ class_Rings_Oidom(t_a)
| spl34_4764 ),
inference(resolution,[],[f113163,f3841]) ).
fof(f3841,plain,
! [X0] :
( class_Groups_Ozero(X0)
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2486]) ).
fof(f2486,plain,
! [X0] :
( class_Groups_Ozero(X0)
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1285]) ).
fof(f1285,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Groups_Ozero(X0) ),
inference(rectify,[],[f1021]) ).
fof(f1021,axiom,
! [X87] :
( class_Rings_Oidom(X87)
=> class_Groups_Ozero(X87) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f113163,plain,
( ~ class_Groups_Ozero(t_a)
| spl34_4764 ),
inference(avatar_component_clause,[],[f113161]) ).
fof(f56347,plain,
( spl34_790
| ~ spl34_125 ),
inference(avatar_split_clause,[],[f56304,f7835,f17885]) ).
fof(f7835,plain,
( spl34_125
<=> ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl34_125])]) ).
fof(f56304,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0)
| ~ spl34_125 ),
inference(superposition,[],[f7836,f3904]) ).
fof(f7836,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0)
| ~ spl34_125 ),
inference(avatar_component_clause,[],[f7835]) ).
fof(f48424,plain,
( spl34_125
| spl34_101 ),
inference(avatar_split_clause,[],[f48414,f7136,f7835]) ).
fof(f48414,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) ),
inference(superposition,[],[f4250,f3908]) ).
fof(f3908,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f1344]) ).
fof(f1344,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(rectify,[],[f427]) ).
fof(f427,axiom,
! [X21,X18] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4250,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f3443]) ).
fof(f5308,plain,
( ~ spl34_2
| ~ spl34_8
| ~ spl34_16 ),
inference(avatar_split_clause,[],[f3719,f5305,f5268,f5243]) ).
fof(f3719,plain,
( c_Groups_Ozero__class_Ozero(t_a) != sK7
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f3343]) ).
fof(f3343,plain,
( ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,sK8)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& c_Groups_Ozero__class_Ozero(t_a) != sK7 )
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f2421,f3342,f3341]) ).
fof(f3341,plain,
( ? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X1 )
=> ( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,X2)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),sK6))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),sK6))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != sK7 ) ),
introduced(choice_axiom,[]) ).
fof(f3342,plain,
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,X2)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),sK6))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),sK6))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
=> ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,sK8)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f2421,plain,
( ? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X1 )
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(flattening,[],[f2420]) ).
fof(f2420,plain,
( ? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X1 )
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(ennf_transformation,[],[f1165]) ).
fof(f1165,plain,
( class_Rings_Oidom(t_a)
=> ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
=> ? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X1 ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
( class_Rings_Oidom(t_a)
=> ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
=> ? [X4,X5] :
( ? [X6] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3))
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5303,plain,
( ~ spl34_2
| ~ spl34_8
| ~ spl34_5
| spl34_15 ),
inference(avatar_split_clause,[],[f4933,f5300,f5255,f5268,f5243]) ).
fof(f4933,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK8),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK6),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(definition_unfolding,[],[f3720,f3762,f3762]) ).
fof(f3720,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f3343]) ).
fof(f5298,plain,
( ~ spl34_2
| ~ spl34_8
| spl34_5
| spl34_14 ),
inference(avatar_split_clause,[],[f4932,f5295,f5255,f5268,f5243]) ).
fof(f4932,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK8),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK6),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(definition_unfolding,[],[f3721,f3762,f3762,f3762]) ).
fof(f3721,plain,
( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f3343]) ).
fof(f5293,plain,
( ~ spl34_2
| ~ spl34_8
| spl34_13 ),
inference(avatar_split_clause,[],[f3722,f5291,f5268,f5243]) ).
fof(f3722,plain,
! [X3] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,sK8)),X3))
| c_Groups_Ozero__class_Ozero(t_a) != v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f3343]) ).
fof(f5289,plain,
( ~ spl34_2
| spl34_8
| ~ spl34_12 ),
inference(avatar_split_clause,[],[f3715,f5286,f5268,f5243]) ).
fof(f3715,plain,
( c_Groups_Ozero__class_Ozero(t_a) != sK4
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f3340]) ).
fof(f3340,plain,
( ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,sK5)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& c_Groups_Ozero__class_Ozero(t_a) != sK4 )
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f2419,f3339,f3338]) ).
fof(f3338,plain,
( ? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X1 )
=> ( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,X2)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),sK3))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),sK3))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != sK4 ) ),
introduced(choice_axiom,[]) ).
fof(f3339,plain,
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,X2)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),sK3))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),sK3))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
=> ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,sK5)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f2419,plain,
( ? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X1 )
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(flattening,[],[f2418]) ).
fof(f2418,plain,
( ? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
& ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X1 )
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(ennf_transformation,[],[f1164]) ).
fof(f1164,plain,
( class_Rings_Oidom(t_a)
=> ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
=> ? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X1 ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
( class_Rings_Oidom(t_a)
=> ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
=> ? [X4,X5] :
( ? [X6] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3))
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5279,plain,
( ~ spl34_2
| spl34_8
| spl34_5
| spl34_10 ),
inference(avatar_split_clause,[],[f4930,f5276,f5255,f5268,f5243]) ).
fof(f4930,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,sK5),c_Groups_Oone__class_Oone(tc_Nat_Onat))),sK3),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(definition_unfolding,[],[f3717,f3762,f3762,f3762]) ).
fof(f3717,plain,
( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f3340]) ).
fof(f5274,plain,
( ~ spl34_2
| spl34_8
| spl34_9 ),
inference(avatar_split_clause,[],[f3718,f5272,f5268,f5243]) ).
fof(f3718,plain,
! [X3] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,sK5)),X3))
| c_Groups_Ozero__class_Ozero(t_a) = v_c____
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f3340]) ).
fof(f5266,plain,
spl34_2,
inference(avatar_split_clause,[],[f3624,f5243]) ).
fof(f3624,plain,
class_Rings_Oidom(t_a),
inference(cnf_transformation,[],[f1162]) ).
fof(f1162,axiom,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f5261,plain,
( spl34_5
| spl34_6 ),
inference(avatar_split_clause,[],[f4927,f5259,f5255]) ).
fof(f4927,plain,
! [X2,X0,X1] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) = X1 ),
inference(definition_unfolding,[],[f3622,f3762,f3762,f3762]) ).
fof(f3622,plain,
! [X2,X0,X1] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2)))
| c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
| c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Groups_Ozero__class_Ozero(t_a) = X1 ),
inference(cnf_transformation,[],[f3337]) ).
fof(f3337,plain,
! [X0,X1] :
( ! [X2] :
( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2)))
| ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
& c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
& c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
| c_Groups_Ozero__class_Ozero(t_a) = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f2417,f3336]) ).
fof(f3336,plain,
! [X0,X1,X2] :
( ? [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
=> hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK2(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK2(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK2(X0,X1,X2))) ),
introduced(choice_axiom,[]) ).
fof(f2417,plain,
! [X0,X1] :
( ! [X2] :
( ? [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
| ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
& c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))
& c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
| c_Groups_Ozero__class_Ozero(t_a) = X1 ),
inference(ennf_transformation,[],[f1163]) ).
fof(f1163,plain,
~ ? [X0,X1] :
( ? [X2] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X1 ),
inference(rectify,[],[f1161]) ).
fof(f1161,negated_conjecture,
~ ? [X4,X5] :
( ? [X6] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3))
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X5 ),
inference(negated_conjecture,[],[f1160]) ).
fof(f1160,conjecture,
? [X4,X5] :
( ? [X6] :
( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3))
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
& ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) ) )
& c_Groups_Ozero__class_Ozero(t_a) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW245+1 : TPTP v8.2.0. Released v5.2.0.
% 0.10/0.12 % Command : run_vampire %s %d SAT
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jun 19 09:25:54 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.36 Running first-order model finding
% 0.13/0.36 Running /export/starexec/sandbox/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.51 % (32563)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (32569)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (2999ds/146Mi)
% 0.22/0.51 % (32563)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (32567)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (2999ds/152523Mi)
% 0.22/0.51 % (32563)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (32564)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (2999ds/98885Mi)
% 0.22/0.51 % (32563)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (32568)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (2999ds/104Mi)
% 0.22/0.51 % (32563)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (32565)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency:i=99418_0 on theBenchmark for (2999ds/99418Mi)
% 0.22/0.51 % (32563)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (32570)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (2999ds/115Mi)
% 0.22/0.51 % (32563)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.51 % (32566)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (2999ds/214858Mi)
% 0.22/0.56 % (32568)Instruction limit reached!
% 0.22/0.56 % (32568)------------------------------
% 0.22/0.56 % (32568)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.56 % (32568)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.57 % (32568)Termination reason: Time limit
% 0.22/0.57 % (32568)Termination phase: Saturation
% 0.22/0.57
% 0.22/0.57 % (32568)Memory used [KB]: 3750
% 0.22/0.57 % (32568)Time elapsed: 0.057 s
% 0.22/0.57 % (32568)Instructions burned: 105 (million)
% 0.22/0.57 % (32570)Instruction limit reached!
% 0.22/0.57 % (32570)------------------------------
% 0.22/0.57 % (32570)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.57 % (32570)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.57 % (32570)Termination reason: Time limit
% 0.22/0.57 % (32570)Termination phase: Saturation
% 0.22/0.57
% 0.22/0.57 % (32570)Memory used [KB]: 3903
% 0.22/0.57 % (32570)Time elapsed: 0.059 s
% 0.22/0.57 % (32570)Instructions burned: 115 (million)
% 1.16/0.59 % (32569)Instruction limit reached!
% 1.16/0.59 % (32569)------------------------------
% 1.16/0.59 % (32569)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.16/0.59 % (32569)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.16/0.59 % (32569)Termination reason: Time limit
% 1.16/0.59 % (32569)Termination phase: Saturation
% 1.16/0.59
% 1.16/0.59 % (32569)Memory used [KB]: 4024
% 1.16/0.59 % (32569)Time elapsed: 0.079 s
% 1.16/0.59 % (32569)Instructions burned: 147 (million)
% 1.28/0.63 % (32563)Running in auto input_syntax mode. Trying TPTP
% 1.28/0.63 % (32572)ott-21_1:1_sil=4000:sp=const_frequency:i=175:fsr=off:fs=off:av=off_0 on theBenchmark for (2998ds/175Mi)
% 1.28/0.63 % (32563)Running in auto input_syntax mode. Trying TPTP
% 1.28/0.63 % (32571)dis+11_1:3_bsr=unit_only:sil=2000:rp=on:newcnf=on:i=404:kws=precedence:lsd=100_0 on theBenchmark for (2998ds/404Mi)
% 1.43/0.65 % (32563)Running in auto input_syntax mode. Trying TPTP
% 1.43/0.65 % (32573)ott+33_1:1_to=lpo:sil=8000:sp=weighted_frequency:rp=on:i=270:nm=3:fsr=off:sac=on_0 on theBenchmark for (2998ds/270Mi)
% 1.43/0.72 % (32572)Instruction limit reached!
% 1.43/0.72 % (32572)------------------------------
% 1.43/0.72 % (32572)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.43/0.72 % (32572)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.43/0.72 % (32572)Termination reason: Time limit
% 1.43/0.72 % (32572)Termination phase: Saturation
% 1.43/0.72
% 1.43/0.72 % (32572)Memory used [KB]: 4289
% 1.43/0.72 % (32572)Time elapsed: 0.094 s
% 1.43/0.72 % (32572)Instructions burned: 175 (million)
% 2.02/0.77 Cannot represent all propositional literals internally
% 2.02/0.77 % (32567)Refutation not found, incomplete strategy% (32567)------------------------------
% 2.02/0.77 % (32567)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.02/0.77 % (32567)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.02/0.77 % (32567)Termination reason: Refutation not found, incomplete strategy
% 2.02/0.77
% 2.02/0.77 % (32567)Memory used [KB]: 11586
% 2.02/0.77 % (32567)Time elapsed: 0.264 s
% 2.02/0.77 % (32567)Instructions burned: 537 (million)
% 2.02/0.77 % (32567)------------------------------
% 2.02/0.77 % (32567)------------------------------
% 2.02/0.78 % (32563)Running in auto input_syntax mode. Trying TPTP
% 2.02/0.78 % (32574)ott+4_1:1_sil=2000:i=900:bd=off:fsr=off_0 on theBenchmark for (2997ds/900Mi)
% 2.33/0.80 TRYING [1]
% 2.33/0.81 % (32573)Instruction limit reached!
% 2.33/0.81 % (32573)------------------------------
% 2.33/0.81 % (32573)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.33/0.81 % (32573)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.33/0.81 % (32573)Termination reason: Time limit
% 2.33/0.81 % (32573)Termination phase: Saturation
% 2.33/0.81
% 2.33/0.81 % (32573)Memory used [KB]: 6228
% 2.33/0.81 % (32573)Time elapsed: 0.160 s
% 2.33/0.81 % (32573)Instructions burned: 271 (million)
% 2.33/0.84 % (32563)Running in auto input_syntax mode. Trying TPTP
% 2.33/0.84 % (32575)fmb+10_1:1_sil=8000:fde=unused:fmbes=contour:i=7859:nm=2:fmbswr=0_0 on theBenchmark for (2996ds/7859Mi)
% 2.33/0.84 TRYING [2]
% 2.83/0.87 % (32563)Running in auto input_syntax mode. Trying TPTP
% 2.83/0.87 % (32576)ott+11_1:2_anc=none:sil=2000:sp=const_max:spb=units:s2a=on:i=2145:s2at=5.0:awrs=converge:awrsf=170:rawr=on:gs=on:fsr=off_0 on theBenchmark for (2996ds/2145Mi)
% 2.88/0.87 % (32571)Instruction limit reached!
% 2.88/0.87 % (32571)------------------------------
% 2.88/0.87 % (32571)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.88/0.87 % (32571)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.88/0.87 % (32571)Termination reason: Time limit
% 2.88/0.87 % (32571)Termination phase: Saturation
% 2.88/0.87
% 2.88/0.87 % (32571)Memory used [KB]: 6162
% 2.88/0.87 % (32571)Time elapsed: 0.246 s
% 2.88/0.87 % (32571)Instructions burned: 405 (million)
% 2.99/0.93 % (32563)Running in auto input_syntax mode. Trying TPTP
% 2.99/0.93 % (32577)ott-30_1:1024_sil=4000:alpa=true:newcnf=on:i=1187:bs=unit_only:ins=1:amm=off_0 on theBenchmark for (2995ds/1187Mi)
% 3.37/1.06 TRYING [1]
% 3.56/1.09 TRYING [2]
% 5.71/1.27 % (32574)Instruction limit reached!
% 5.71/1.27 % (32574)------------------------------
% 5.71/1.27 % (32574)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 5.71/1.27 % (32574)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 5.71/1.27 % (32574)Termination reason: Time limit
% 5.71/1.28 % (32574)Termination phase: Saturation
% 5.71/1.28
% 5.71/1.28 % (32574)Memory used [KB]: 10777
% 5.71/1.28 % (32574)Time elapsed: 0.493 s
% 5.71/1.28 % (32574)Instructions burned: 901 (million)
% 6.23/1.34 % (32563)Running in auto input_syntax mode. Trying TPTP
% 6.23/1.34 % (32578)fmb+10_1:1_sil=32000:i=23580:newcnf=on_0 on theBenchmark for (2991ds/23580Mi)
% 7.44/1.52 TRYING [3]
% 7.55/1.56 % (32577)Instruction limit reached!
% 7.55/1.56 % (32577)------------------------------
% 7.55/1.56 % (32577)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 7.55/1.56 % (32577)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 7.55/1.56 % (32577)Termination reason: Time limit
% 7.55/1.56 % (32577)Termination phase: Saturation
% 7.55/1.56
% 7.55/1.56 % (32577)Memory used [KB]: 9063
% 7.55/1.56 % (32577)Time elapsed: 0.645 s
% 7.55/1.56 % (32577)Instructions burned: 1187 (million)
% 7.55/1.59 TRYING [1]
% 7.99/1.62 % (32563)Running in auto input_syntax mode. Trying TPTP
% 7.99/1.62 % (32579)fmb+10_1:1_sil=32000:fmbss=17:fmbsr=2.0:i=2892_0 on theBenchmark for (2988ds/2892Mi)
% 7.99/1.63 TRYING [2]
% 7.99/1.67 TRYING [3]
% 11.57/2.08 % (32576)Instruction limit reached!
% 11.57/2.08 % (32576)------------------------------
% 11.57/2.08 % (32576)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 11.57/2.08 % (32576)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 11.57/2.08 % (32576)Termination reason: Time limit
% 11.57/2.08 % (32576)Termination phase: Saturation
% 11.57/2.08
% 11.57/2.08 % (32576)Memory used [KB]: 14348
% 11.57/2.08 % (32576)Time elapsed: 1.216 s
% 11.57/2.08 % (32576)Instructions burned: 2146 (million)
% 11.84/2.14 % (32563)Running in auto input_syntax mode. Trying TPTP
% 11.84/2.14 % (32580)ott-10_1:1_sil=4000:i=1693_0 on theBenchmark for (2983ds/1693Mi)
% 13.85/2.41 TRYING [3]
% 16.07/2.82 % (32579)Instruction limit reached!
% 16.07/2.82 % (32579)------------------------------
% 16.07/2.82 % (32579)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 16.07/2.82 % (32579)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 16.07/2.82 % (32579)Termination reason: Time limit
% 16.07/2.82 % (32579)Termination phase: Finite model building constraint generation
% 16.07/2.82
% 16.07/2.82 % (32579)Memory used [KB]: 12067
% 16.07/2.82 % (32579)Time elapsed: 1.197 s
% 16.07/2.82 % (32579)Instructions burned: 2893 (million)
% 16.79/2.90 % (32563)Running in auto input_syntax mode. Trying TPTP
% 16.79/2.90 % (32581)dis+21_1:1_sil=4000:gs=on:sac=on:newcnf=on:gsem=off:i=1735:gsaa=full_model:abs=on:anc=none_0 on theBenchmark for (2975ds/1735Mi)
% 18.46/3.11 % (32580)Instruction limit reached!
% 18.46/3.11 % (32580)------------------------------
% 18.46/3.11 % (32580)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 18.46/3.11 % (32580)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 18.46/3.11 % (32580)Termination reason: Time limit
% 18.46/3.11 % (32580)Termination phase: Saturation
% 18.46/3.11
% 18.46/3.11 % (32580)Memory used [KB]: 14676
% 18.46/3.11 % (32580)Time elapsed: 0.972 s
% 18.46/3.11 % (32580)Instructions burned: 1694 (million)
% 18.63/3.17 % (32563)Running in auto input_syntax mode. Trying TPTP
% 18.63/3.17 % (32582)fmb+10_1:1_fmbas=expand:sil=128000:i=131798:nm=2:fmbksg=on:fmbss=4:fmbsr=1.77:rp=on_0 on theBenchmark for (2973ds/131798Mi)
% 22.51/3.66 TRYING [4]
% 24.08/3.89 % (32575)Instruction limit reached!
% 24.08/3.89 % (32575)------------------------------
% 24.08/3.89 % (32575)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 24.08/3.89 % (32575)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 24.08/3.89 % (32575)Termination reason: Time limit
% 24.08/3.89 % (32575)Termination phase: Finite model building SAT solving
% 24.08/3.89
% 24.08/3.89 % (32575)Memory used [KB]: 53108
% 24.08/3.89 % (32575)Time elapsed: 3.050 s
% 24.08/3.89 % (32575)Instructions burned: 7862 (million)
% 24.08/3.91 % (32581)Instruction limit reached!
% 24.08/3.91 % (32581)------------------------------
% 24.08/3.91 % (32581)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 24.08/3.91 % (32581)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 24.08/3.91 % (32581)Termination reason: Time limit
% 24.08/3.91 % (32581)Termination phase: Saturation
% 24.08/3.91
% 24.08/3.91 % (32581)Memory used [KB]: 25503
% 24.08/3.91 % (32581)Time elapsed: 1.012 s
% 24.08/3.91 % (32581)Instructions burned: 1736 (million)
% 24.08/3.96 % (32563)Running in auto input_syntax mode. Trying TPTP
% 24.08/3.96 % (32583)fmb+10_1:1_sil=16000:fmbss=16:i=3451:newcnf=on_0 on theBenchmark for (2965ds/3451Mi)
% 24.69/3.97 % (32563)Running in auto input_syntax mode. Trying TPTP
% 24.69/3.97 % (32584)ott+11_1:64_sil=4000:rp=on:i=3978:bd=off:fsr=off_0 on theBenchmark for (2965ds/3978Mi)
% 28.27/4.54 TRYING [4]
% 34.18/5.38 % (32583)Instruction limit reached!
% 34.18/5.38 % (32583)------------------------------
% 34.18/5.38 % (32583)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 34.18/5.38 % (32583)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 34.18/5.38 % (32583)Termination reason: Time limit
% 34.18/5.38 % (32583)Termination phase: Finite model building constraint generation
% 34.18/5.38
% 34.18/5.38 % (32583)Memory used [KB]: 12006
% 34.18/5.38 % (32583)Time elapsed: 1.421 s
% 34.18/5.38 % (32583)Instructions burned: 3451 (million)
% 34.68/5.39 TRYING [4]
% 34.68/5.47 % (32563)Running in auto input_syntax mode. Trying TPTP
% 34.68/5.47 % (32585)dis+35_1:64_to=lpo:sil=32000:sp=occurrence:urr=on:sac=on:i=33091:fsr=off_0 on theBenchmark for (2950ds/33091Mi)
% 39.06/6.02 % (32584)Instruction limit reached!
% 39.06/6.02 % (32584)------------------------------
% 39.06/6.02 % (32584)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 39.06/6.02 % (32584)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 39.06/6.02 % (32584)Termination reason: Time limit
% 39.06/6.02 % (32584)Termination phase: Saturation
% 39.06/6.02
% 39.06/6.02 % (32584)Memory used [KB]: 18489
% 39.06/6.02 % (32584)Time elapsed: 2.047 s
% 39.06/6.02 % (32584)Instructions burned: 3979 (million)
% 39.06/6.08 % (32563)Running in auto input_syntax mode. Trying TPTP
% 39.06/6.08 % (32586)dis-4_1:1_sil=16000:sp=const_frequency:sac=on:newcnf=on:i=9564_0 on theBenchmark for (2944ds/9564Mi)
% 67.63/10.11 % (32578)Instruction limit reached!
% 67.63/10.11 % (32578)------------------------------
% 67.63/10.11 % (32578)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 67.63/10.11 % (32578)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 67.63/10.11 % (32578)Termination reason: Time limit
% 67.63/10.11 % (32578)Termination phase: Finite model building SAT solving
% 67.63/10.11
% 67.63/10.11 % (32578)Memory used [KB]: 206086
% 67.63/10.11 % (32578)Time elapsed: 8.789 s
% 67.63/10.11 % (32578)Instructions burned: 23582 (million)
% 68.04/10.20 % (32563)Running in auto input_syntax mode. Trying TPTP
% 68.04/10.20 % (32587)fmb+10_1:1_sil=64000:i=50409:nm=2:gsp=on_0 on theBenchmark for (2903ds/50409Mi)
% 69.47/10.44 TRYING [1]
% 69.83/10.48 TRYING [2]
% 73.53/10.97 % (32586)Instruction limit reached!
% 73.53/10.97 % (32586)------------------------------
% 73.53/10.97 % (32586)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 73.53/10.97 % (32586)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 73.53/10.97 % (32586)Termination reason: Time limit
% 73.53/10.97 % (32586)Termination phase: Saturation
% 73.53/10.97
% 73.53/10.97 % (32586)Memory used [KB]: 44547
% 73.53/10.97 % (32586)Time elapsed: 4.894 s
% 73.53/10.97 % (32586)Instructions burned: 9564 (million)
% 73.53/11.04 % (32563)Running in auto input_syntax mode. Trying TPTP
% 73.53/11.04 % (32588)dis+2_3:1_bsr=on:sil=64000:abs=on:i=10852:gsp=on:fs=off:fsr=off_0 on theBenchmark for (2894ds/10852Mi)
% 75.08/11.17 TRYING [3]
% 89.97/13.31 % (32588)First to succeed.
% 89.97/13.35 % (32588)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-32563"
% 89.97/13.36 % (32563)Running in auto input_syntax mode. Trying TPTP
% 89.97/13.36 % (32588)Refutation found. Thanks to Tanya!
% 89.97/13.36 % SZS status Theorem for theBenchmark
% 89.97/13.36 % SZS output start Proof for theBenchmark
% See solution above
% 89.97/13.36 % (32588)------------------------------
% 89.97/13.36 % (32588)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 89.97/13.36 % (32588)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 89.97/13.36 % (32588)Termination reason: Refutation
% 89.97/13.36
% 89.97/13.36 % (32588)Memory used [KB]: 56633
% 89.97/13.36 % (32588)Time elapsed: 2.314 s
% 89.97/13.36 % (32588)Instructions burned: 6407 (million)
% 89.97/13.36 % (32588)------------------------------
% 89.97/13.36 % (32588)------------------------------
% 89.97/13.36 % (32563)Success in time 12.898 s
%------------------------------------------------------------------------------