%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP015_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:28:15 AM UTC 2026
% Result : Theorem 26.43s 4.88s
% Output : Refutation 27.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 26
% Syntax : Number of formulae : 117 ( 79 unt; 0 typ; 1 def)
% Number of atoms : 918 ( 97 equ)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 205 ( 84 ~; 72 |; 26 &)
% ( 12 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 680 ( 680 fml; 0 var)
% Number of types : 6 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 39 ( 39 usr; 8 con; 0-3 aty)
% Number of variables : 133 ( 0 sgn 132 !; 1 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
del: $tType ).
tff(type_def_6,type,
tp__o: $tType ).
tff(type_def_7,type,
tp__ty_2Einteger_2Eint: $tType ).
tff(type_def_8,type,
tp__ty_2Enum_2Enum: $tType ).
tff(func_def_0,type,
bool: del ).
tff(func_def_1,type,
ind: del ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
tff(func_def_4,type,
k: ( del * $i ) > $i ).
tff(func_def_5,type,
i: del > $i ).
tff(func_def_6,type,
inj__o: tp__o > $i ).
tff(func_def_7,type,
surj__o: $i > tp__o ).
tff(func_def_9,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(func_def_11,type,
fo__c_2Ebool_2ET: tp__o ).
tff(func_def_13,type,
fo__c_2Ebool_2EF: tp__o ).
tff(func_def_15,type,
fo__c_2Ebool_2E_5C_2F: ( tp__o * tp__o ) > tp__o ).
tff(func_def_17,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(func_def_18,type,
ty_2Einteger_2Eint: del ).
tff(func_def_19,type,
inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i ).
tff(func_def_20,type,
surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint ).
tff(func_def_22,type,
fo__c_2Einteger_2Eint__neg: tp__ty_2Einteger_2Eint > tp__ty_2Einteger_2Eint ).
tff(func_def_23,type,
ty_2Enum_2Enum: del ).
tff(func_def_24,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
tff(func_def_25,type,
surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
tff(func_def_27,type,
fo__c_2Einteger_2ENum: tp__ty_2Einteger_2Eint > tp__ty_2Enum_2Enum ).
tff(func_def_29,type,
fo__c_2Einteger_2Eint__of__num: tp__ty_2Enum_2Enum > tp__ty_2Einteger_2Eint ).
tff(func_def_31,type,
fo__c_2Einteger_2Eint__lt: ( tp__ty_2Einteger_2Eint * tp__ty_2Einteger_2Eint ) > tp__o ).
tff(func_def_32,type,
c_2Ebool_2ECOND: del > $i ).
tff(func_def_33,type,
ty_2Efcp_2Ecart: ( del * del ) > del ).
tff(func_def_34,type,
c_2Einteger__word_2Ei2w: del > $i ).
tff(func_def_36,type,
fo__c_2Eprim__rec_2E_3C: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__o ).
tff(func_def_38,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(func_def_39,type,
ty_2Ebool_2Eitself: del > del ).
tff(func_def_40,type,
c_2Ebool_2Ethe__value: del > $i ).
tff(func_def_41,type,
c_2Ewords_2Edimword: del > $i ).
tff(func_def_43,type,
fo__c_2Earithmetic_2EMOD: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__ty_2Enum_2Enum ).
tff(func_def_44,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_46,type,
fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
tff(func_def_47,type,
c_2Ewords_2En2w: del > $i ).
tff(func_def_48,type,
c_2Ewords_2Eword__2comp: del > $i ).
tff(func_def_49,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_50,type,
sK0: del ).
tff(func_def_51,type,
sK1: ( del * $i ) > $i ).
tff(func_def_52,type,
sK2: ( del * $i * $i ) > $i ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(f1,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,X1))
=> ! [X3: $i] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
tff(f2,axiom,
! [X0: $i] :
( mem(X0,bool)
=> ! [X1: $i] :
( mem(X1,bool)
=> ( ( p(X0)
<=> p(X1) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolext) ).
tff(f6,axiom,
! [X0: tp__o] : ( surj__o(inj__o(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_o) ).
tff(f7,axiom,
! [X0: tp__o] : mem(inj__o(X0),bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o) ).
tff(f15,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
tff(f16,axiom,
inj__o(fo__c_2Ebool_2EF) = c_2Ebool_2EF,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2EF) ).
tff(f17,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
tff(f24,axiom,
! [X0: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Einteger_2Eint) ).
tff(f28,axiom,
! [X0: tp__ty_2Einteger_2Eint] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X0)) = ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__neg) ).
tff(f29,axiom,
! [X0: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Enum_2Enum) ).
tff(f33,axiom,
! [X0: tp__ty_2Einteger_2Eint] : ( inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X0)) = ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2ENum) ).
tff(f35,axiom,
! [X0: tp__ty_2Enum_2Enum] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(X0)) = ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__of__num) ).
tff(f37,axiom,
! [X0: tp__ty_2Einteger_2Eint,X1: tp__ty_2Einteger_2Eint] : ( inj__o(fo__c_2Einteger_2Eint__lt(X0,X1)) = ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X0)),inj__ty_2Einteger_2Eint(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Einteger_2Eint__lt) ).
tff(f41,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : ( inj__o(fo__c_2Eprim__rec_2E_3C(X0,X1)) = ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Eprim__rec_2E_3C) ).
tff(f51,axiom,
mem(c_2Enum_2E0,ty_2Enum_2Enum),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Enum_2E0) ).
tff(f52,axiom,
inj__ty_2Enum_2Enum(fo__c_2Enum_2E0) = c_2Enum_2E0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Enum_2E0) ).
tff(f53,axiom,
! [X0: del] : mem(c_2Ewords_2En2w(X0),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ewords_2En2w) ).
tff(f64,axiom,
! [X0: del] :
( ! [X1: $i] :
( mem(X1,X0)
=> ! [X2: $i] :
( mem(X2,X0)
=> ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2ET)),X1),X2) = X1 ) ) )
& ! [X3: $i] :
( mem(X3,X0)
=> ! [X4: $i] :
( mem(X4,X0)
=> ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2EF)),X3),X4) = X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2Ebool__case__thm) ).
tff(f65,axiom,
surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__NEG__0) ).
tff(f66,axiom,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X1)),inj__ty_2Enum_2Enum(X0))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))
<=> ( ( X0 != fo__c_2Enum_2E0 )
| ( X1 != fo__c_2Enum_2E0 ) ) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))))
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger_2EINT__LT__CALCULATE) ).
tff(f67,axiom,
! [X0: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger_2ENUM__OF__INT) ).
tff(f68,axiom,
! [X0: del,X1: tp__ty_2Einteger_2Eint] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(X1)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X1)),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X1)))))),ap(c_2Ewords_2En2w(X0),ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Einteger__word_2Ei2w__def) ).
tff(f69,axiom,
! [X0: tp__ty_2Enum_2Enum] : ~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eprim__rec_2ENOT__LESS__0) ).
tff(f71,axiom,
! [X0: del] : ( ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ewords_2EWORD__NEG__0) ).
tff(f72,conjecture,
! [X0: del] : ( ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Einteger__word_2Ei2w__0) ).
tff(f73,negated_conjecture,
~ ! [X0: del] : ( ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) = ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) ),
inference(negated_conjecture,[status(cth)],[f72]) ).
tff(f75,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X1)),inj__ty_2Enum_2Enum(X0))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))
<=> ( ( X0 != fo__c_2Enum_2E0 )
| ( X1 != fo__c_2Enum_2E0 ) ) )
& ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))) ),
inference(true_and_false_elimination,[],[f66]) ).
tff(f76,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))))
<=> p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X1)),inj__ty_2Enum_2Enum(X0))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))
<=> ( ( X0 != fo__c_2Enum_2E0 )
| ( X1 != fo__c_2Enum_2E0 ) ) )
& ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))) ),
inference(flattening,[],[f75]) ).
tff(f78,plain,
? [X0: del] : ( ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) != ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ),
inference(ennf_transformation,[],[f73]) ).
tff(f94,plain,
! [X0: $i] :
( ! [X1: $i] :
( ( X0 = X1 )
| ( p(X0)
<~> p(X1) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f2]) ).
tff(f95,plain,
! [X0: $i] :
( ! [X1: $i] :
( ( X0 = X1 )
| ( p(X0)
<~> p(X1) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(flattening,[],[f94]) ).
tff(f97,plain,
! [X0: del] :
( ! [X1: $i] :
( ! [X2: $i] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2ET)),X1),X2) = X1 )
| ~ mem(X2,X0) )
| ~ mem(X1,X0) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2EF)),X3),X4) = X4 )
| ~ mem(X4,X0) )
| ~ mem(X3,X0) ) ),
inference(ennf_transformation,[],[f64]) ).
tff(f101,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f1]) ).
tff(f102,plain,
ap(c_2Ewords_2En2w(sK0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) != ap(c_2Einteger__word_2Ei2w(sK0),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f78]) ).
tff(f105,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1))) )
& ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))
| ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))))
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X1)),inj__ty_2Enum_2Enum(X0))) )
& ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X1)),inj__ty_2Enum_2Enum(X0)))
| ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))
| ( ( fo__c_2Enum_2E0 = X0 )
& ( fo__c_2Enum_2E0 = X1 ) ) )
& ( ( X0 != fo__c_2Enum_2E0 )
| ( X1 != fo__c_2Enum_2E0 )
| ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))) )
& ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))) ),
inference(nnf_transformation,[],[f76]) ).
tff(f106,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1))) )
& ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))
| ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))))
| ~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X1)),inj__ty_2Enum_2Enum(X0))) )
& ( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X1)),inj__ty_2Enum_2Enum(X0)))
| ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))) )
& ( p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))
| ( ( fo__c_2Enum_2E0 = X0 )
& ( fo__c_2Enum_2E0 = X1 ) ) )
& ( ( X0 != fo__c_2Enum_2E0 )
| ( X1 != fo__c_2Enum_2E0 )
| ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))) )
& ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1))))) ),
inference(flattening,[],[f105]) ).
tff(f122,plain,
! [X0: $i] :
( ! [X1: $i] :
( ( X0 = X1 )
| ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X1)
| p(X0) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(nnf_transformation,[],[f95]) ).
tff(f124,plain,
ap(c_2Ewords_2En2w(sK0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) != ap(c_2Einteger__word_2Ei2w(sK0),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),
inference(cnf_transformation,[],[f102]) ).
tff(f128,plain,
! [X0: del] : ( ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) = ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))) ),
inference(cnf_transformation,[],[f71]) ).
tff(f131,plain,
! [X0: tp__ty_2Enum_2Enum] : ~ p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),
inference(cnf_transformation,[],[f69]) ).
tff(f132,plain,
! [X0: del,X1: tp__ty_2Einteger_2Eint] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(X1)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X1)),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X1)))))),ap(c_2Ewords_2En2w(X0),ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(X1)))) ),
inference(cnf_transformation,[],[f68]) ).
tff(f133,plain,
! [X0: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)))) = X0 ),
inference(cnf_transformation,[],[f67]) ).
tff(f140,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)))
| ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))) ),
inference(cnf_transformation,[],[f106]) ).
tff(f142,plain,
surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__neg,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) = surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),
inference(cnf_transformation,[],[f65]) ).
tff(f143,plain,
c_2Enum_2E0 = inj__ty_2Enum_2Enum(fo__c_2Enum_2E0),
inference(cnf_transformation,[],[f52]) ).
tff(f145,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] : ( inj__o(fo__c_2Eprim__rec_2E_3C(X0,X1)) = ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(X0)),inj__ty_2Enum_2Enum(X1)) ),
inference(cnf_transformation,[],[f41]) ).
tff(f146,plain,
! [X0: tp__ty_2Enum_2Enum] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(X0)) = ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0)) ),
inference(cnf_transformation,[],[f35]) ).
tff(f147,plain,
! [X0: tp__ty_2Einteger_2Eint] : ( inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X0)) = ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(X0)) ),
inference(cnf_transformation,[],[f33]) ).
tff(f150,plain,
! [X0: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(X0)) = X0 ),
inference(cnf_transformation,[],[f29]) ).
tff(f153,plain,
! [X0: del] : mem(c_2Ewords_2En2w(X0),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,X0))),
inference(cnf_transformation,[],[f53]) ).
tff(f193,plain,
~ p(c_2Ebool_2EF),
inference(cnf_transformation,[],[f17]) ).
tff(f198,plain,
! [X0: $i,X1: $i] :
( ~ mem(X1,bool)
| p(X1)
| p(X0)
| ( X0 = X1 )
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f122]) ).
tff(f201,plain,
! [X0: tp__ty_2Einteger_2Eint,X1: tp__ty_2Einteger_2Eint] : ( inj__o(fo__c_2Einteger_2Eint__lt(X0,X1)) = ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X0)),inj__ty_2Einteger_2Eint(X1)) ),
inference(cnf_transformation,[],[f37]) ).
tff(f202,plain,
! [X0: tp__ty_2Einteger_2Eint] : ( inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X0)) = ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X0)) ),
inference(cnf_transformation,[],[f28]) ).
tff(f205,plain,
! [X0: tp__ty_2Einteger_2Eint] : ( surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(X0)) = X0 ),
inference(cnf_transformation,[],[f24]) ).
tff(f209,plain,
! [X3: $i,X0: del,X4: $i] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X0),inj__o(fo__c_2Ebool_2EF)),X3),X4) = X4 )
| ~ mem(X4,X0)
| ~ mem(X3,X0) ),
inference(cnf_transformation,[],[f97]) ).
tff(f212,plain,
mem(c_2Enum_2E0,ty_2Enum_2Enum),
inference(cnf_transformation,[],[f51]) ).
tff(f216,plain,
c_2Ebool_2EF = inj__o(fo__c_2Ebool_2EF),
inference(cnf_transformation,[],[f16]) ).
tff(f220,plain,
! [X0: tp__o] : mem(inj__o(X0),bool),
inference(cnf_transformation,[],[f7]) ).
tff(f221,plain,
! [X0: tp__o] : ( surj__o(inj__o(X0)) = X0 ),
inference(cnf_transformation,[],[f6]) ).
tff(f224,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0)
| ~ mem(X2,arr(X0,X1)) ),
inference(cnf_transformation,[],[f101]) ).
tff(f230,plain,
mem(c_2Ebool_2EF,bool),
inference(cnf_transformation,[],[f15]) ).
tff(f265,plain,
! [X3: $i,X0: del,X4: $i] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X0),c_2Ebool_2EF),X3),X4) = X4 )
| ~ mem(X4,X0)
| ~ mem(X3,X0) ),
inference(forward_demodulation,[],[f209,f216]) ).
tff(f267,plain,
surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))) = surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0))),
inference(forward_demodulation,[],[f142,f146]) ).
tff(f274,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( p(inj__o(fo__c_2Eprim__rec_2E_3C(X0,X1)))
| ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X1)))) ),
inference(forward_demodulation,[],[f140,f145]) ).
tff(f276,plain,
! [X0: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(X0)))) = X0 ),
inference(forward_demodulation,[],[f133,f146]) ).
tff(f277,plain,
! [X0: del,X1: tp__ty_2Einteger_2Eint] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(X1)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X1)),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),ap(c_2Einteger_2ENum,ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X1)))))),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X1)))) ),
inference(forward_demodulation,[],[f132,f147]) ).
tff(f278,plain,
! [X0: tp__ty_2Enum_2Enum] : ~ p(inj__o(fo__c_2Eprim__rec_2E_3C(X0,fo__c_2Enum_2E0))),
inference(forward_demodulation,[],[f131,f145]) ).
tff(f279,plain,
! [X0: del] : ( ap(c_2Ewords_2En2w(X0),c_2Enum_2E0) = ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) ),
inference(forward_demodulation,[],[f128,f143]) ).
tff(f280,plain,
ap(c_2Ewords_2En2w(sK0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)) != ap(c_2Einteger__word_2Ei2w(sK0),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0))),
inference(forward_demodulation,[],[f124,f146]) ).
tff(f281,plain,
fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0) = surj__ty_2Einteger_2Eint(ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),
inference(forward_demodulation,[],[f267,f205]) ).
tff(f288,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ~ p(ap(ap(c_2Einteger_2Eint__lt,ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(X0))),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(X1))))
| p(inj__o(fo__c_2Eprim__rec_2E_3C(X0,X1))) ),
inference(forward_demodulation,[],[f274,f146]) ).
tff(f290,plain,
! [X0: tp__ty_2Enum_2Enum] : ( surj__ty_2Enum_2Enum(inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(fo__c_2Einteger_2Eint__of__num(X0)))) = X0 ),
inference(forward_demodulation,[],[f276,f147]) ).
tff(f291,plain,
! [X0: del,X1: tp__ty_2Einteger_2Eint] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(X1)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X1)),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),ap(c_2Einteger_2ENum,inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X1)))))),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X1)))) ),
inference(forward_demodulation,[],[f277,f202]) ).
tff(f292,plain,
ap(c_2Einteger__word_2Ei2w(sK0),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0))) != ap(c_2Ewords_2En2w(sK0),c_2Enum_2E0),
inference(forward_demodulation,[],[f280,f143]) ).
tff(f293,plain,
fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0) = surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),
inference(forward_demodulation,[],[f281,f202]) ).
tff(f300,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ~ p(ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(X0))),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(X1))))
| p(inj__o(fo__c_2Eprim__rec_2E_3C(X0,X1))) ),
inference(forward_demodulation,[],[f288,f146]) ).
tff(f302,plain,
! [X0: tp__ty_2Enum_2Enum] : ( fo__c_2Einteger_2ENum(fo__c_2Einteger_2Eint__of__num(X0)) = X0 ),
inference(forward_demodulation,[],[f290,f150]) ).
tff(f303,plain,
! [X0: del,X1: tp__ty_2Einteger_2Eint] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(X1)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X1)),ap(c_2Einteger_2Eint__of__num,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(fo__c_2Einteger_2Eint__neg(X1)))))),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X1)))) ),
inference(forward_demodulation,[],[f291,f147]) ).
tff(f304,plain,
fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0) = fo__c_2Einteger_2Eint__neg(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)),
inference(forward_demodulation,[],[f293,f205]) ).
tff(f310,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ~ p(inj__o(fo__c_2Einteger_2Eint__lt(fo__c_2Einteger_2Eint__of__num(X0),fo__c_2Einteger_2Eint__of__num(X1))))
| p(inj__o(fo__c_2Eprim__rec_2E_3C(X0,X1))) ),
inference(forward_demodulation,[],[f300,f201]) ).
tff(f312,plain,
! [X0: del,X1: tp__ty_2Einteger_2Eint] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(X1)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),ap(ap(c_2Einteger_2Eint__lt,inj__ty_2Einteger_2Eint(X1)),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(fo__c_2Einteger_2Eint__neg(X1)))))),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X1)))) ),
inference(forward_demodulation,[],[f303,f146]) ).
tff(f315,plain,
! [X0: del,X1: tp__ty_2Einteger_2Eint] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(X1)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),inj__o(fo__c_2Einteger_2Eint__lt(X1,fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(fo__c_2Einteger_2Eint__neg(X1)))))),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(X1)))) ),
inference(forward_demodulation,[],[f312,f201]) ).
tff(f335,plain,
! [X0: $i] :
( p(c_2Ebool_2EF)
| p(X0)
| ( c_2Ebool_2EF = X0 )
| ~ mem(X0,bool) ),
inference(resolution,[],[f230,f198]) ).
tff(f336,plain,
! [X0: $i] :
( ~ mem(X0,bool)
| ( c_2Ebool_2EF = X0 )
| p(X0) ),
inference(forward_subsumption_resolution,[],[f335,f193]) ).
tff(f338,plain,
! [X0: tp__o] :
( ( inj__o(X0) = c_2Ebool_2EF )
| p(inj__o(X0)) ),
inference(resolution,[],[f336,f220]) ).
tff(f347,plain,
! [X0: tp__ty_2Enum_2Enum,X1: del] : ( ap(c_2Einteger__word_2Ei2w(X1),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(X0))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X1)),inj__o(fo__c_2Einteger_2Eint__lt(fo__c_2Einteger_2Eint__of__num(X0),fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X1),ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(fo__c_2Einteger_2Eint__neg(fo__c_2Einteger_2Eint__of__num(X0))))))),ap(c_2Ewords_2En2w(X1),inj__ty_2Enum_2Enum(X0))) ),
inference(superposition,[],[f315,f302]) ).
tff(f592,plain,
fo__c_2Ebool_2EF = surj__o(c_2Ebool_2EF),
inference(superposition,[],[f221,f216]) ).
tff(f593,plain,
! [X0: tp__o] :
( ( surj__o(c_2Ebool_2EF) = X0 )
| p(inj__o(X0)) ),
inference(superposition,[],[f221,f338]) ).
tff(f597,plain,
! [X0: tp__o] :
( p(inj__o(X0))
| ( fo__c_2Ebool_2EF = X0 ) ),
inference(superposition,[],[f592,f593]) ).
tff(f598,plain,
! [X0: tp__ty_2Enum_2Enum,X1: tp__ty_2Enum_2Enum] :
( ( fo__c_2Ebool_2EF = fo__c_2Einteger_2Eint__lt(fo__c_2Einteger_2Eint__of__num(X0),fo__c_2Einteger_2Eint__of__num(X1)) )
| p(inj__o(fo__c_2Eprim__rec_2E_3C(X0,X1))) ),
inference(resolution,[],[f597,f310]) ).
tff(f734,plain,
inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)) = ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0),
inference(superposition,[],[f146,f143]) ).
tff(f741,plain,
! [X0: del] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),inj__o(fo__c_2Einteger_2Eint__lt(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0),fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(fo__c_2Einteger_2Eint__neg(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0))))))),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) ),
inference(superposition,[],[f347,f143]) ).
tff(f752,plain,
! [X0: del] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),inj__o(fo__c_2Einteger_2Eint__lt(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0),fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Einteger_2ENum(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))))),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) ),
inference(forward_demodulation,[],[f741,f304]) ).
tff(f754,plain,
! [X0: del] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),inj__o(fo__c_2Einteger_2Eint__lt(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0),fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) ),
inference(forward_demodulation,[],[f752,f302]) ).
tff(f756,plain,
! [X0: del] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),inj__o(fo__c_2Einteger_2Eint__lt(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0),fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),ap(c_2Ewords_2Eword__2comp(X0),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0))),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) ),
inference(forward_demodulation,[],[f754,f143]) ).
tff(f758,plain,
! [X0: del] : ( ap(c_2Einteger__word_2Ei2w(X0),inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),inj__o(fo__c_2Einteger_2Eint__lt(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0),fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) ),
inference(forward_demodulation,[],[f756,f279]) ).
tff(f760,plain,
! [X0: del] : ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),inj__o(fo__c_2Einteger_2Eint__lt(fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0),fo__c_2Einteger_2Eint__of__num(fo__c_2Enum_2E0)))),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) = ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) ),
inference(forward_demodulation,[],[f758,f734]) ).
tff(f766,definition,
( spl3_4
<=> ! [X0: del] : ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),c_2Ebool_2EF),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) = ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f767,plain,
( ! [X0: del] : ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),c_2Ebool_2EF),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) = ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f766]) ).
tff(f769,plain,
! [X0: del] :
( ( ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),inj__o(fo__c_2Ebool_2EF)),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) )
| p(inj__o(fo__c_2Eprim__rec_2E_3C(fo__c_2Enum_2E0,fo__c_2Enum_2E0))) ),
inference(superposition,[],[f760,f598]) ).
tff(f780,plain,
! [X0: del] : ( ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),inj__o(fo__c_2Ebool_2EF)),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) ),
inference(forward_subsumption_resolution,[],[f769,f278]) ).
tff(f781,plain,
! [X0: del] : ( ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,X0)),c_2Ebool_2EF),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)),ap(c_2Ewords_2En2w(X0),c_2Enum_2E0)) = ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) ),
inference(forward_demodulation,[],[f780,f216]) ).
tff(f782,plain,
spl3_4,
inference(avatar_split_clause,[],[f781,f766]) ).
tff(f784,plain,
( ! [X0: del] :
( ( ap(c_2Ewords_2En2w(X0),c_2Enum_2E0) = ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) )
| ~ mem(ap(c_2Ewords_2En2w(X0),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,X0))
| ~ mem(ap(c_2Ewords_2En2w(X0),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,X0)) )
| ~ spl3_4 ),
inference(superposition,[],[f265,f767]) ).
tff(f786,plain,
( ! [X0: del] :
( ( ap(c_2Ewords_2En2w(X0),c_2Enum_2E0) = ap(c_2Einteger__word_2Ei2w(X0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)) )
| ~ mem(ap(c_2Ewords_2En2w(X0),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,X0)) )
| ~ spl3_4 ),
inference(duplicate_literal_removal,[],[f784]) ).
tff(f859,plain,
ap(c_2Ewords_2En2w(sK0),c_2Enum_2E0) != ap(c_2Einteger__word_2Ei2w(sK0),ap(c_2Einteger_2Eint__of__num,c_2Enum_2E0)),
inference(superposition,[],[f292,f734]) ).
tff(f872,plain,
( ( ap(c_2Ewords_2En2w(sK0),c_2Enum_2E0) != ap(c_2Ewords_2En2w(sK0),c_2Enum_2E0) )
| ~ mem(ap(c_2Ewords_2En2w(sK0),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,sK0))
| ~ spl3_4 ),
inference(superposition,[],[f859,f786]) ).
tff(f873,plain,
( ~ mem(ap(c_2Ewords_2En2w(sK0),c_2Enum_2E0),ty_2Efcp_2Ecart(bool,sK0))
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f872]) ).
tff(f874,plain,
( ! [X0: del] :
( ~ mem(c_2Ewords_2En2w(sK0),arr(X0,ty_2Efcp_2Ecart(bool,sK0)))
| ~ mem(c_2Enum_2E0,X0) )
| ~ spl3_4 ),
inference(resolution,[],[f873,f224]) ).
tff(f875,plain,
( ~ mem(c_2Enum_2E0,ty_2Enum_2Enum)
| ~ spl3_4 ),
inference(resolution,[],[f874,f153]) ).
tff(f876,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f875,f212]) ).
tff(f877,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f876]) ).
cnf(s6,plain,
spl3_4,
inference(sat_conversion,[],[f782]) ).
cnf(s9,plain,
~ spl3_4,
inference(sat_conversion,[],[f877]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s9]) ).
tff(f878,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP015_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n007.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 12:00:10 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.19/3.80 % (1282666)Detected formulas, will run a generic FOF schedule.
% 19.19/3.80 % (1282672)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2138217791:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 19.19/3.80 % (1282671)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2274461895:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 19.19/3.80 % (1282675)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3603065696:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 19.19/3.80 % (1282674)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1287068279:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 19.19/3.80 % (1282677)dis-21_1_sil=8000:lcm=predicate:random_seed=570086962:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 19.19/3.80 % (1282676)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1973023558:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 19.19/3.80 % (1282673)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2528683426:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 19.19/3.80 % (1282674)Refutation not found, incomplete strategy
% 19.19/3.80 % (1282674)------------------------------
% 19.19/3.80 % (1282674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.19/3.80 % (1282674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.19/3.80 % (1282674)CaDiCaL version: 2.1.3
% 19.19/3.80 % (1282674)Termination reason: Refutation not found, incomplete strategy
% 19.19/3.80 % (1282674)Time elapsed: 0.003 s
% 19.19/3.80 % (1282674)Peak memory usage: 88 MB
% 19.19/3.80 % (1282674)Instructions burned: 1 (million)
% 19.19/3.80 % (1282675)Instruction limit reached!
% 19.19/3.80 % (1282675)------------------------------
% 19.19/3.80 % (1282675)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.19/3.80 % (1282675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.19/3.80 % (1282675)CaDiCaL version: 2.1.3
% 19.19/3.80 % (1282675)Termination reason: Instruction limit
% 19.19/3.80 % (1282675)Termination phase: Saturation
% 19.19/3.80 % (1282675)Time elapsed: 0.108 s
% 19.19/3.80 % (1282675)Peak memory usage: 88 MB
% 19.19/3.80 % (1282675)Instructions burned: 119 (million)
% 19.19/3.80 % (1282677)Instruction limit reached!
% 19.19/3.80 % (1282677)------------------------------
% 19.19/3.80 % (1282677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.19/3.80 % (1282677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.19/3.80 % (1282677)CaDiCaL version: 2.1.3
% 19.19/3.80 % (1282677)Termination reason: Instruction limit
% 19.19/3.80 % (1282677)Termination phase: Saturation
% 19.19/3.80 % (1282677)Time elapsed: 0.125 s
% 19.19/3.80 % (1282677)Peak memory usage: 91 MB
% 19.19/3.80 % (1282677)Instructions burned: 130 (million)
% 19.19/3.80 % (1282676)Instruction limit reached!
% 19.19/3.80 % (1282676)------------------------------
% 19.19/3.80 % (1282676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.19/3.80 % (1282676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.19/3.80 % (1282676)CaDiCaL version: 2.1.3
% 19.19/3.80 % (1282676)Termination reason: Instruction limit
% 19.19/3.80 % (1282676)Termination phase: Saturation
% 19.19/3.80 % (1282676)Time elapsed: 0.136 s
% 19.19/3.80 % (1282676)Peak memory usage: 89 MB
% 19.19/3.80 % (1282676)Instructions burned: 140 (million)
% 19.19/3.80 % (1282687)lrs+10_1_sil=8000:sp=occurrence:random_seed=828266291:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 19.19/3.80 % (1282674)------------------------------
% 19.19/3.80 % (1282674)------------------------------
% 19.19/3.80 % (1282688)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3658687857:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 19.19/3.80 % (1282689)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2939786124:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 19.19/3.80 % (1282688)Refutation not found, incomplete strategy
% 19.19/3.80 % (1282688)------------------------------
% 19.19/3.80 % (1282688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.45/4.73 % (1282688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.45/4.73 % (1282688)CaDiCaL version: 2.1.3
% 25.45/4.73 % (1282688)Termination reason: Refutation not found, incomplete strategy
% 25.45/4.73 % (1282688)Time elapsed: 0.011 s
% 25.45/4.73 % (1282688)Peak memory usage: 88 MB
% 25.45/4.73 % (1282688)Instructions burned: 10 (million)
% 25.45/4.73 % (1282687)Instruction limit reached!
% 25.45/4.73 % (1282687)------------------------------
% 25.45/4.73 % (1282687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.45/4.73 % (1282687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.45/4.73 % (1282687)CaDiCaL version: 2.1.3
% 25.45/4.73 % (1282687)Termination reason: Instruction limit
% 25.45/4.73 % (1282687)Termination phase: Saturation
% 25.45/4.73 % (1282687)Time elapsed: 0.183 s
% 25.45/4.73 % (1282687)Peak memory usage: 91 MB
% 25.45/4.73 % (1282687)Instructions burned: 285 (million)
% 25.45/4.73 % (1282691)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1822885794:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 25.45/4.73 % (1282689)Instruction limit reached!
% 25.45/4.73 % (1282689)------------------------------
% 25.45/4.73 % (1282689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.45/4.73 % (1282689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.45/4.73 % (1282689)CaDiCaL version: 2.1.3
% 25.45/4.73 % (1282689)Termination reason: Instruction limit
% 25.45/4.73 % (1282689)Termination phase: Saturation
% 25.45/4.73 % (1282689)Time elapsed: 0.299 s
% 25.45/4.73 % (1282689)Peak memory usage: 90 MB
% 25.45/4.73 % (1282689)Instructions burned: 325 (million)
% 25.45/4.73 % (1282694)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3613122858:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 25.45/4.73 % (1282694)Refutation not found, incomplete strategy
% 25.45/4.73 % (1282694)------------------------------
% 25.45/4.73 % (1282694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.45/4.73 % (1282694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.45/4.73 % (1282694)CaDiCaL version: 2.1.3
% 25.45/4.73 % (1282694)Termination reason: Refutation not found, incomplete strategy
% 25.45/4.73 % (1282694)Time elapsed: 0.008 s
% 25.45/4.73 % (1282694)Peak memory usage: 88 MB
% 25.45/4.73 % (1282694)Instructions burned: 5 (million)
% 25.45/4.73 % (1282688)------------------------------
% 25.45/4.73 % (1282688)------------------------------
% 25.45/4.73 % (1282691)Instruction limit reached!
% 25.45/4.73 % (1282691)------------------------------
% 25.45/4.73 % (1282691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.45/4.73 % (1282691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.45/4.73 % (1282691)CaDiCaL version: 2.1.3
% 25.45/4.73 % (1282691)Termination reason: Instruction limit
% 25.45/4.73 % (1282691)Termination phase: Saturation
% 25.45/4.73 % (1282691)Time elapsed: 0.205 s
% 25.45/4.73 % (1282691)Peak memory usage: 91 MB
% 25.45/4.73 % (1282691)Instructions burned: 249 (million)
% 25.45/4.73 % (1282696)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=652430131:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 25.45/4.73 % (1282673)Refutation not found, incomplete strategy
% 25.45/4.73 % (1282673)------------------------------
% 25.45/4.73 % (1282673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.45/4.73 % (1282673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.45/4.73 % (1282673)CaDiCaL version: 2.1.3
% 25.45/4.73 % (1282673)Termination reason: Refutation not found, incomplete strategy
% 25.45/4.73 % (1282673)Time elapsed: 0.998 s
% 25.45/4.73 % (1282673)Peak memory usage: 129 MB
% 25.45/4.73 % (1282673)Instructions burned: 921 (million)
% 25.45/4.73 % (1282698)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=707159554:cts=off:i=113:fsr=off:ss=included:sgt=4_2988 on theBenchmark for (2988ds/113Mi)
% 25.45/4.73 % (1282698)Refutation not found, incomplete strategy
% 25.45/4.73 % (1282698)------------------------------
% 25.45/4.73 % (1282698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 25.45/4.73 % (1282698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 25.45/4.73 % (1282698)CaDiCaL version: 2.1.3
% 25.45/4.73 % (1282698)Termination reason: Refutation not found, incomplete strategy
% 26.43/4.88 % (1282698)Time elapsed: 0.010 s
% 26.43/4.88 % (1282698)Peak memory usage: 89 MB
% 26.43/4.88 % (1282698)Instructions burned: 7 (million)
% 26.43/4.88 % (1282694)------------------------------
% 26.43/4.88 % (1282694)------------------------------
% 26.43/4.88 % (1282699)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=151408444:i=127:av=off:fsr=off:sup=off_2988 on theBenchmark for (2988ds/127Mi)
% 26.43/4.88 % (1282699)Refutation not found, incomplete strategy
% 26.43/4.88 % (1282699)------------------------------
% 26.43/4.88 % (1282699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282699)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282699)Termination reason: Refutation not found, incomplete strategy
% 26.43/4.88 % (1282699)Time elapsed: 0.007 s
% 26.43/4.88 % (1282699)Peak memory usage: 88 MB
% 26.43/4.88 % (1282699)Instructions burned: 6 (million)
% 26.43/4.88 % (1282673)------------------------------
% 26.43/4.88 % (1282673)------------------------------
% 26.43/4.88 % (1282702)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1595834095:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2985 on theBenchmark for (2985ds/114Mi)
% 26.43/4.88 % (1282698)------------------------------
% 26.43/4.88 % (1282698)------------------------------
% 26.43/4.88 % (1282702)Instruction limit reached!
% 26.43/4.88 % (1282702)------------------------------
% 26.43/4.88 % (1282702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282702)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282702)Termination reason: Instruction limit
% 26.43/4.88 % (1282702)Termination phase: Saturation
% 26.43/4.88 % (1282702)Time elapsed: 0.104 s
% 26.43/4.88 % (1282702)Peak memory usage: 89 MB
% 26.43/4.88 % (1282702)Instructions burned: 115 (million)
% 26.43/4.88 % (1282699)------------------------------
% 26.43/4.88 % (1282699)------------------------------
% 26.43/4.88 % (1282704)lrs+10_1_sil=8000:sp=occurrence:random_seed=187136004:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2983 on theBenchmark for (2983ds/907Mi)
% 26.43/4.88 % (1282706)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2527432981:i=437:sd=1:aac=none:ss=included_2981 on theBenchmark for (2981ds/437Mi)
% 26.43/4.88 % (1282706)Refutation not found, incomplete strategy
% 26.43/4.88 % (1282706)------------------------------
% 26.43/4.88 % (1282706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282706)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282706)Termination reason: Refutation not found, incomplete strategy
% 26.43/4.88 % (1282706)Time elapsed: 0.009 s
% 26.43/4.88 % (1282706)Peak memory usage: 88 MB
% 26.43/4.88 % (1282706)Instructions burned: 7 (million)
% 26.43/4.88 % (1282708)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1703461203:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2981 on theBenchmark for (2981ds/134Mi)
% 26.43/4.88 % (1282707)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=53151792:i=5202:ss=axioms:sgt=16_2981 on theBenchmark for (2981ds/5202Mi)
% 26.43/4.88 % (1282708)Instruction limit reached!
% 26.43/4.88 % (1282708)------------------------------
% 26.43/4.88 % (1282708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282708)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282708)Termination reason: Instruction limit
% 26.43/4.88 % (1282708)Termination phase: Saturation
% 26.43/4.88 % (1282708)Time elapsed: 0.121 s
% 26.43/4.88 % (1282708)Peak memory usage: 89 MB
% 26.43/4.88 % (1282708)Instructions burned: 135 (million)
% 26.43/4.88 % (1282706)------------------------------
% 26.43/4.88 % (1282706)------------------------------
% 26.43/4.88 % (1282713)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3570802902:st=8:i=592:sd=3:ep=RST:ss=axioms_2977 on theBenchmark for (2977ds/592Mi)
% 26.43/4.88 % (1282714)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3437442144:st=3:i=13193:sd=3:ss=axioms_2975 on theBenchmark for (2975ds/13193Mi)
% 26.43/4.88 % (1282704)Instruction limit reached!
% 26.43/4.88 % (1282704)------------------------------
% 26.43/4.88 % (1282704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282704)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282704)Termination reason: Instruction limit
% 26.43/4.88 % (1282704)Termination phase: Saturation
% 26.43/4.88 % (1282704)Time elapsed: 0.810 s
% 26.43/4.88 % (1282704)Peak memory usage: 93 MB
% 26.43/4.88 % (1282704)Instructions burned: 908 (million)
% 26.43/4.88 % (1282713)Instruction limit reached!
% 26.43/4.88 % (1282713)------------------------------
% 26.43/4.88 % (1282713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282713)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282713)Termination reason: Instruction limit
% 26.43/4.88 % (1282713)Termination phase: Saturation
% 26.43/4.88 % (1282713)Time elapsed: 0.454 s
% 26.43/4.88 % (1282713)Peak memory usage: 90 MB
% 26.43/4.88 % (1282713)Instructions burned: 592 (million)
% 26.43/4.88 % (1282717)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=1529533944:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2972 on theBenchmark for (2972ds/125Mi)
% 26.43/4.88 % (1282717)Instruction limit reached!
% 26.43/4.88 % (1282717)------------------------------
% 26.43/4.88 % (1282717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282717)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282717)Termination reason: Instruction limit
% 26.43/4.88 % (1282717)Termination phase: Saturation
% 26.43/4.88 % (1282717)Time elapsed: 0.124 s
% 26.43/4.88 % (1282717)Peak memory usage: 90 MB
% 26.43/4.88 % (1282717)Instructions burned: 125 (million)
% 26.43/4.88 % (1282719)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=3258242536:i=134:gtgl=5:slsql=off:gtg=exists_sym_2969 on theBenchmark for (2969ds/134Mi)
% 26.43/4.88 % (1282720)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=1604530519:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2968 on theBenchmark for (2968ds/141Mi)
% 26.43/4.88 % (1282720)Refutation not found, incomplete strategy
% 26.43/4.88 % (1282720)------------------------------
% 26.43/4.88 % (1282720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282720)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282720)Termination reason: Refutation not found, incomplete strategy
% 26.43/4.88 % (1282720)Time elapsed: 0.003 s
% 26.43/4.88 % (1282720)Peak memory usage: 88 MB
% 26.43/4.88 % (1282720)Instructions burned: 1 (million)
% 26.43/4.88 % (1282707)First to succeed.
% 26.43/4.88 % (1282707)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1282666"
% 26.43/4.88 % (1282696)Instruction limit reached!
% 26.43/4.88 % (1282696)------------------------------
% 26.43/4.88 % (1282696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282696)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282696)Termination reason: Instruction limit
% 26.43/4.88 % (1282696)Termination phase: Saturation
% 26.43/4.88 % (1282696)Time elapsed: 2.164 s
% 26.43/4.88 % (1282696)Peak memory usage: 133 MB
% 26.43/4.88 % (1282696)Instructions burned: 2351 (million)
% 26.43/4.88 % (1282719)Instruction limit reached!
% 26.43/4.88 % (1282719)------------------------------
% 26.43/4.88 % (1282719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282719)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282719)Termination reason: Instruction limit
% 26.43/4.88 % (1282719)Termination phase: Saturation
% 26.43/4.88 % (1282719)Time elapsed: 0.152 s
% 26.43/4.88 % (1282719)Peak memory usage: 91 MB
% 26.43/4.88 % (1282719)Instructions burned: 135 (million)
% 26.43/4.88 % (1282723)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=419935779:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2965 on theBenchmark for (2965ds/431Mi)
% 26.43/4.88 % (1282723)Refutation not found, incomplete strategy
% 26.43/4.88 % (1282723)------------------------------
% 26.43/4.88 % (1282723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 26.43/4.88 % (1282723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.43/4.88 % (1282723)CaDiCaL version: 2.1.3
% 26.43/4.88 % (1282723)Termination reason: Refutation not found, incomplete strategy
% 26.43/4.88 % (1282723)Time elapsed: 0.008 s
% 26.43/4.88 % (1282723)Peak memory usage: 88 MB
% 26.43/4.88 % (1282723)Instructions burned: 6 (million)
% 26.43/4.88 % (1282720)------------------------------
% 26.43/4.88 % (1282720)------------------------------
% 26.43/4.88 % (1282724)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=1552460288:i=6060:aac=none:ins=25_2965 on theBenchmark for (2965ds/6060Mi)
% 26.43/4.88 % (1282707)Refutation found. Thanks to Tanya!
% 26.43/4.88 % SZS status Theorem for theBenchmark
% 26.43/4.88 % SZS output start Proof for theBenchmark
% See solution above
% 27.81/5.20 % (1282707)------------------------------
% 27.81/5.20 % (1282707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 27.81/5.20 % (1282707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.81/5.20 % (1282707)CaDiCaL version: 2.1.3
% 27.81/5.20 % (1282707)Termination reason: Refutation
% 27.81/5.20 % (1282707)Time elapsed: 1.278 s
% 27.81/5.20 % (1282707)Peak memory usage: 132 MB
% 27.81/5.20 % (1282707)Instructions burned: 1169 (million)
% 27.81/5.20 % (1282707)------------------------------
% 27.81/5.20 % (1282707)------------------------------
% 27.81/5.20 % (1282666)Success in time 3.826 s
% 27.81/5.20 % Vampire exiting
%------------------------------------------------------------------------------