%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP015_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:35:02 AM UTC 2026
% Result : Theorem 4.23s 1.11s
% Output : Refutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 55 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 59 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 1 |; 4 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 50 ( 50 usr; 13 con; 0-4 aty)
% Number of variables : 82 ( 81 !; 1 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
tff(type_def_6,type,
tyop_2Efcp_2Ecart: ( $tType * $tType ) > $tType ).
tff(type_def_7,type,
tyop_2Einteger_2Eint: $tType ).
tff(type_def_8,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_9,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(type_def_10,type,
tyop_2Enum_2Enum: $tType ).
tff(type_def_11,type,
sK3: $tType ).
tff(func_def_0,type,
app_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_1,type,
combin_i_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,X0) ).
tff(func_def_2,type,
combin_k_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X0)) ).
tff(func_def_3,type,
combin_s_2E0:
!>[X0: $tType,X1: $tType,X2: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2))) ).
tff(func_def_4,type,
c_2Ebool_2E_21_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_5,type,
c_2Ebool_2E_21_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_6,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_7,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_8,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(func_def_9,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(func_def_10,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(func_def_11,type,
c_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_12,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_13,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_14,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_15,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_16,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_17,type,
c_2Ebool_2ECOND_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0))) ).
tff(func_def_18,type,
c_2Ebool_2ECOND_2E3:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * X0 * X0 ) > X0 ) ).
tff(func_def_19,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_20,type,
c_2Earithmetic_2EMOD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(func_def_21,type,
c_2Earithmetic_2EMOD_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(func_def_22,type,
c_2Einteger_2ENum_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Enum_2Enum) ).
tff(func_def_23,type,
c_2Einteger_2ENum_2E1: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).
tff(func_def_24,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_25,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_26,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_27,type,
c_2Ewords_2Edimword_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(X0),tyop_2Enum_2Enum) ).
tff(func_def_28,type,
c_2Ewords_2Edimword_2E1:
!>[X0: $tType] : ( tyop_2Ebool_2Eitself(X0) > tyop_2Enum_2Enum ) ).
tff(func_def_29,type,
c_2Einteger__word_2Ei2w_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)) ).
tff(func_def_30,type,
c_2Einteger__word_2Ei2w_2E1:
!>[X0: $tType] : ( tyop_2Einteger_2Eint > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) ).
tff(func_def_31,type,
c_2Einteger_2Eint__lt_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(func_def_32,type,
c_2Einteger_2Eint__lt_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(func_def_33,type,
c_2Einteger_2Eint__neg_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint) ).
tff(func_def_34,type,
c_2Einteger_2Eint__neg_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
tff(func_def_35,type,
c_2Einteger_2Eint__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint) ).
tff(func_def_36,type,
c_2Einteger_2Eint__of__num_2E1: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
tff(func_def_37,type,
c_2Ewords_2En2w_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)) ).
tff(func_def_38,type,
c_2Ewords_2En2w_2E1:
!>[X0: $tType] : ( tyop_2Enum_2Enum > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) ).
tff(func_def_39,type,
c_2Ebool_2Ethe__value_2E0:
!>[X0: $tType] : tyop_2Ebool_2Eitself(X0) ).
tff(func_def_40,type,
c_2Ewords_2Eword__2comp_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)) ).
tff(func_def_41,type,
c_2Ewords_2Eword__2comp_2E1:
!>[X0: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) ).
tff(func_def_42,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_43,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_44,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_45,type,
sK1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_46,type,
sK2:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(f18,axiom,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) ).
tff(f22,axiom,
! [X0: $tType,X1: tyop_2Emin_2Ebool,X2: X0,X3: X0] : ( c_2Ebool_2ECOND_2E3(X0,X1,X2,X3) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).
tff(f25,axiom,
! [X0: tyop_2Einteger_2Eint] : ( c_2Einteger_2ENum_2E1(X0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2ENum_2E1) ).
tff(f28,axiom,
! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( c_2Einteger__word_2Ei2w_2E1(X0,X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a) ).
tff(f29,axiom,
! [X0: tyop_2Einteger_2Eint,X1: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__lt_2E2(X0,X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Einteger_2Eint__lt_2E2) ).
tff(f30,axiom,
! [X0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__neg_2E1(X0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__neg_2E1) ).
tff(f31,axiom,
! [X0: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__of__num_2E1(X0) = app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__of__num_2E1) ).
tff(f32,axiom,
! [X0: $tType,X1: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a) ).
tff(f33,axiom,
! [X0: $tType,X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__2comp_2E1(X0,X1) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a) ).
tff(f42,axiom,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2ET_2E0,X1,X2) = X1 )
& ! [X3: X0,X4: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2EF_2E0,X3,X4) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
tff(f43,axiom,
c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).
tff(f44,axiom,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] :
( ( c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__of__num_2E1(X1)) = c_2Eprim__rec_2E_3C_2E2(X0,X1) )
& ( c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) = c_2Eprim__rec_2E_3C_2E2(X1,X0) )
& ( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__of__num_2E1(X1)))
<=> ( ( X0 != c_2Enum_2E0_2E0 )
| ( X1 != c_2Enum_2E0_2E0 ) ) )
& ( c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) = c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
tff(f45,axiom,
! [X0: tyop_2Enum_2Enum] : ( c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__of__num_2E1(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).
tff(f46,axiom,
! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( c_2Einteger__word_2Ei2w_2E1(X0,X1) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger_2Eint__lt_2E2(X1,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__neg_2E1(X1)))),c_2Ewords_2En2w_2E1(X0,c_2Einteger_2ENum_2E1(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).
tff(f49,axiom,
! [X0: $tType] : ( c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0)) = c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0) ).
tff(f50,conjecture,
! [X0: $tType] : ( c_2Einteger__word_2Ei2w_2E1(X0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).
tff(f51,negated_conjecture,
~ ! [X0: $tType] : ( c_2Einteger__word_2Ei2w_2E1(X0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
tff(f64,plain,
? [X0: $tType] : ( c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) != c_2Einteger__word_2Ei2w_2E1(X0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ),
inference(ennf_transformation,[],[f51]) ).
tff(f95,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f102,plain,
! [X0: $tType,X2: X0,X3: X0,X1: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(X0,X1,X2,X3) = app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),X1),X2),X3) ),
inference(cnf_transformation,[],[f22]) ).
tff(f105,plain,
! [X0: tyop_2Einteger_2Eint] : ( c_2Einteger_2ENum_2E1(X0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X0) ),
inference(cnf_transformation,[],[f25]) ).
tff(f110,plain,
! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( c_2Einteger__word_2Ei2w_2E1(X0,X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),X1) ),
inference(cnf_transformation,[],[f28]) ).
tff(f111,plain,
! [X0: tyop_2Einteger_2Eint,X1: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__lt_2E2(X0,X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X0),X1) ),
inference(cnf_transformation,[],[f29]) ).
tff(f112,plain,
! [X0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__neg_2E1(X0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X0) ),
inference(cnf_transformation,[],[f30]) ).
tff(f113,plain,
! [X0: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__of__num_2E1(X0) = app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0) ),
inference(cnf_transformation,[],[f31]) ).
tff(f114,plain,
! [X0: $tType,X1: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),X1) ),
inference(cnf_transformation,[],[f32]) ).
tff(f115,plain,
! [X0: $tType,X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__2comp_2E1(X0,X1) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),X1) ),
inference(cnf_transformation,[],[f33]) ).
tff(f127,plain,
! [X0: $tType,X3: X0,X4: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2EF_2E0,X3,X4) = X4 ),
inference(cnf_transformation,[],[f42]) ).
tff(f129,plain,
c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) = c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),
inference(cnf_transformation,[],[f43]) ).
tff(f133,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) ),
inference(cnf_transformation,[],[f44]) ).
tff(f134,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X0)),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(X1))) = c_2Eprim__rec_2E_3C_2E2(X1,X0) ),
inference(cnf_transformation,[],[f44]) ).
tff(f135,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0,X1) = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__of__num_2E1(X1)) ),
inference(cnf_transformation,[],[f44]) ).
tff(f136,plain,
! [X0: tyop_2Enum_2Enum] : ( c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__of__num_2E1(X0)) = X0 ),
inference(cnf_transformation,[],[f45]) ).
tff(f137,plain,
! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( c_2Einteger__word_2Ei2w_2E1(X0,X1) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger_2Eint__lt_2E2(X1,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__neg_2E1(X1)))),c_2Ewords_2En2w_2E1(X0,c_2Einteger_2ENum_2E1(X1))) ),
inference(cnf_transformation,[],[f46]) ).
tff(f141,plain,
! [X0: $tType] : ( c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0) = c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,c_2Enum_2E0_2E0)) ),
inference(cnf_transformation,[],[f49]) ).
tff(f142,plain,
c_2Ewords_2En2w_2E1(sK3,c_2Enum_2E0_2E0) != c_2Einteger__word_2Ei2w_2E1(sK3,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),
inference(cnf_transformation,[],[f64]) ).
tff(f152,plain,
! [X0: $tType,X3: X0,X4: X0] : ( app_2E2(X0,X0,app_2E2(X0,tyop_2Emin_2Efun(X0,X0),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,X0)),c_2Ebool_2ECOND_2E0(X0),c_2Ebool_2EF_2E0),X3),X4) = X4 ),
inference(definition_unfolding,[],[f127,f102]) ).
tff(f153,plain,
app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),
inference(definition_unfolding,[],[f129,f113,f112,f113]) ).
tff(f154,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),X1) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1)) ),
inference(definition_unfolding,[],[f135,f95,f111,f113,f113]) ).
tff(f155,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X1),X0) ),
inference(definition_unfolding,[],[f134,f111,f112,f113,f112,f113,f95]) ).
tff(f156,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X1))) ),
inference(definition_unfolding,[],[f133,f111,f113,f112,f113]) ).
tff(f160,plain,
! [X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0)) = X0 ),
inference(definition_unfolding,[],[f136,f105,f113]) ).
tff(f161,plain,
! [X0: $tType,X1: tyop_2Einteger_2Eint] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),X1) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X1),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X1))))),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X1))) ),
inference(definition_unfolding,[],[f137,f110,f102,f111,f113,f115,f114,f105,f112,f114,f105]) ).
tff(f165,plain,
! [X0: $tType] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0)) ),
inference(definition_unfolding,[],[f141,f114,f115,f114]) ).
tff(f166,plain,
app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Ewords_2En2w_2E0(sK3),c_2Enum_2E0_2E0) != app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Einteger__word_2Ei2w_2E0(sK3),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),
inference(definition_unfolding,[],[f142,f114,f110,f113]) ).
tff(f736,plain,
! [X0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),c_2Enum_2E0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0))) ),
inference(superposition,[],[f155,f153]) ).
tff(f740,plain,
! [X0: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0),c_2Enum_2E0_2E0) ),
inference(forward_demodulation,[],[f736,f156]) ).
tff(f960,plain,
! [X0: $tType] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))))),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)))) ),
inference(superposition,[],[f161,f153]) ).
tff(f964,plain,
! [X0: $tType] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0))),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0)) ),
inference(forward_demodulation,[],[f960,f160]) ).
tff(f966,plain,
! [X0: $tType] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0))),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0)) ),
inference(forward_demodulation,[],[f964,f165]) ).
tff(f967,plain,
! [X0: $tType] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,c_2Enum_2E0_2E0),c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0)) ),
inference(forward_demodulation,[],[f966,f154]) ).
tff(f17089,plain,
! [X0: $tType] : ( app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)),c_2Ebool_2EF_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0)) ),
inference(forward_demodulation,[],[f967,f740]) ).
tff(f17090,plain,
! [X0: $tType] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),c_2Enum_2E0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Einteger__word_2Ei2w_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,c_2Enum_2E0_2E0)) ),
inference(forward_demodulation,[],[f17089,f152]) ).
tff(f17523,plain,
app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Ewords_2En2w_2E0(sK3),c_2Enum_2E0_2E0) != app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK3),c_2Ewords_2En2w_2E0(sK3),c_2Enum_2E0_2E0),
inference(superposition,[],[f166,f17090]) ).
tff(f17525,plain,
$false,
inference(trivial_inequality_removal,[],[f17523]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP015_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n014.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 12:02:02 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.23/1.11 % (684147)Will run a generic schedule for satisfiability detection.
% 4.23/1.11 % (684158)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1299157830:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.23/1.11 % (684153)% WARNING: option uhcvi not known.
% 4.23/1.11 % (684152)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2146035870_2999 on theBenchmark for (2999ds/0Mi)
% 4.23/1.11 % (684157)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1140686036:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.23/1.11 % (684153)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3775995257:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.23/1.11 % (684154)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3172510865:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.23/1.11 % (684155)dis+10_1_sil=32000:sp=arity:random_seed=3177933926:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.23/1.11 % (684156)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1380340218:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.23/1.11 % Exception at run slice level
% 4.23/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/1.11 % (684166)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=519464793:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.23/1.11 % Exception at run slice level
% 4.23/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/1.11 % (684168)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3223911137:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.23/1.11 % (684158)Instruction limit reached!
% 4.23/1.11 % (684158)------------------------------
% 4.23/1.11 % (684158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/1.11 % (684158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.11 % (684158)CaDiCaL version: 2.1.3
% 4.23/1.11 % (684158)Termination reason: Instruction limit
% 4.23/1.11 % (684158)Termination phase: Saturation
% 4.23/1.11 % (684158)Time elapsed: 0.052 s
% 4.23/1.11 % (684158)Peak memory usage: 13 MB
% 4.23/1.11 % (684158)Instructions burned: 161 (million)
% 4.23/1.11 % (684170)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3099324792:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.23/1.11 % (684155)Instruction limit reached!
% 4.23/1.11 % (684155)------------------------------
% 4.23/1.11 % (684155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/1.11 % (684155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.11 % (684155)CaDiCaL version: 2.1.3
% 4.23/1.11 % (684155)Termination reason: Instruction limit
% 4.23/1.11 % (684155)Termination phase: Saturation
% 4.23/1.11 % (684155)Time elapsed: 0.058 s
% 4.23/1.11 % (684155)Peak memory usage: 12 MB
% 4.23/1.11 % (684155)Instructions burned: 104 (million)
% 4.23/1.11 % (684156)Instruction limit reached!
% 4.23/1.11 % (684156)------------------------------
% 4.23/1.11 % (684156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/1.11 % (684156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.11 % (684156)CaDiCaL version: 2.1.3
% 4.23/1.11 % (684156)Termination reason: Instruction limit
% 4.23/1.11 % (684156)Termination phase: Saturation
% 4.23/1.11 % (684156)Time elapsed: 0.068 s
% 4.23/1.11 % (684156)Peak memory usage: 13 MB
% 4.23/1.11 % (684156)Instructions burned: 116 (million)
% 4.23/1.11 % (684157)Instruction limit reached!
% 4.23/1.11 % (684157)------------------------------
% 4.23/1.11 % (684157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/1.11 % (684157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.11 % (684157)CaDiCaL version: 2.1.3
% 4.23/1.11 % (684157)Termination reason: Instruction limit
% 4.23/1.11 % (684157)Termination phase: Saturation
% 4.23/1.11 % (684157)Time elapsed: 0.077 s
% 4.23/1.11 % (684157)Peak memory usage: 13 MB
% 4.23/1.11 % (684157)Instructions burned: 132 (million)
% 4.23/1.11 % (684172)ott-21_1_sil=16000:fs=off:random_seed=751787221:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.23/1.11 % (684173)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2701097643:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 4.23/1.11 % (684175)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1956635901:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 4.23/1.11 % Exception at run slice level
% 4.23/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/1.11 % (684168)Instruction limit reached!
% 4.23/1.11 % (684168)------------------------------
% 4.23/1.11 % (684168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/1.11 % (684168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.11 % (684168)CaDiCaL version: 2.1.3
% 4.23/1.11 % (684168)Termination reason: Instruction limit
% 4.23/1.11 % (684168)Termination phase: Saturation
% 4.23/1.11 % (684168)Time elapsed: 0.072 s
% 4.23/1.11 % (684168)Peak memory usage: 12 MB
% 4.23/1.11 % (684168)Instructions burned: 132 (million)
% 4.23/1.11 % (684178)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1618449926:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 4.23/1.11 % (684180)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=832783577:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 4.23/1.11 % Exception at run slice level
% 4.23/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/1.11 % (684182)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=388232479:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 4.23/1.11 % (684172)Instruction limit reached!
% 4.23/1.11 % (684172)------------------------------
% 4.23/1.11 % (684172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/1.11 % (684172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.11 % (684172)CaDiCaL version: 2.1.3
% 4.23/1.11 % (684172)Termination reason: Instruction limit
% 4.23/1.11 % (684172)Termination phase: Saturation
% 4.23/1.11 % (684172)Time elapsed: 0.088 s
% 4.23/1.11 % (684172)Peak memory usage: 13 MB
% 4.23/1.11 % (684172)Instructions burned: 181 (million)
% 4.23/1.11 % (684184)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1027274827:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 4.23/1.11 % (684170)Instruction limit reached!
% 4.23/1.11 % (684170)------------------------------
% 4.23/1.11 % (684170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/1.11 % (684170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.11 % (684170)CaDiCaL version: 2.1.3
% 4.23/1.11 % (684170)Termination reason: Instruction limit
% 4.23/1.11 % (684170)Termination phase: Saturation
% 4.23/1.11 % (684170)Time elapsed: 0.180 s
% 4.23/1.11 % (684170)Peak memory usage: 15 MB
% 4.23/1.11 % (684170)Instructions burned: 687 (million)
% 4.23/1.11 % (684186)fmb+10_1_sil=64000:random_seed=394012140:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 4.23/1.11 % (684186)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.23/1.11 % Exception at run slice level
% 4.23/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/1.11 % (684188)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=644273429:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 4.23/1.11 % Exception at run slice level
% 4.23/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/1.11 % (684190)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1573008283:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 4.23/1.11 % Exception at run slice level
% 4.23/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/1.11 % (684192)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=849377677:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 4.23/1.11 % (684173)Instruction limit reached!
% 4.23/1.11 % (684173)------------------------------
% 4.23/1.11 % (684173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/1.11 % (684173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.11 % (684173)CaDiCaL version: 2.1.3
% 4.23/1.11 % (684173)Termination reason: Instruction limit
% 4.23/1.11 % (684173)Termination phase: Saturation
% 4.23/1.11 % (684173)Time elapsed: 0.272 s
% 4.23/1.11 % (684173)Peak memory usage: 13 MB
% 4.23/1.11 % (684173)Instructions burned: 479 (million)
% 4.23/1.11 % (684194)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1178883359:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 4.23/1.11 % (684194)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.23/1.11 % (684182)Instruction limit reached!
% 4.23/1.11 % (684182)------------------------------
% 4.23/1.11 % (684182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/1.11 % (684182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.11 % (684182)CaDiCaL version: 2.1.3
% 4.23/1.11 % (684182)Termination reason: Instruction limit
% 4.23/1.11 % (684182)Termination phase: Saturation
% 4.23/1.11 % (684182)Time elapsed: 0.358 s
% 4.23/1.11 % (684182)Peak memory usage: 16 MB
% 4.23/1.11 % (684182)Instructions burned: 692 (million)
% 4.23/1.11 % (684196)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3705736476:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 4.23/1.11 % Exception at run slice level
% 4.23/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/1.11 % (684198)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3064196230:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 4.23/1.11 % Exception at run slice level
% 4.23/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.23/1.11 % (684200)ott-2_1_sil=16000:newcnf=on:random_seed=562491467:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 4.23/1.11 % (684192) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-684147-684192"...
% 4.23/1.11 % (684192)...printing done.
% 4.23/1.11 % (684192)Refutation found. Thanks to Tanya!
% 4.23/1.11 % SZS status Theorem for theBenchmark
% 4.23/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 4.23/1.11 % (684192)------------------------------
% 4.23/1.11 % (684192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.23/1.11 % (684192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.11 % (684192)CaDiCaL version: 2.1.3
% 4.23/1.11 % (684192)Termination reason: Refutation
% 4.23/1.11 % (684192)Time elapsed: 0.359 s
% 4.23/1.11 % (684192)Peak memory usage: 18 MB
% 4.23/1.11 % (684192)Instructions burned: 1341 (million)
% 4.23/1.11 % (684147)Success in time 0.686 s
% 4.23/1.11 % Vampire exiting
%------------------------------------------------------------------------------