%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP013_3 : 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 : n003.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 11:28:10 AM UTC 2026
% Result : Theorem 3.54s 1.53s
% Output : Refutation 5.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 59 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 70 ( 26 ~; 17 |; 21 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 41 ( 41 usr; 11 con; 0-4 aty)
% Number of variables : 89 ( 86 !; 3 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Efcp_2Ecart: ( $tType * $tType ) > $tType ).
tff(type_def_6,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_7,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(type_def_8,type,
tyop_2Enum_2Enum: $tType ).
tff(type_def_9,type,
sK0: $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_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(func_def_7,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(func_def_8,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(func_def_9,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(func_def_10,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_11,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_12,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(func_def_13,type,
c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(func_def_14,type,
c_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_15,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_16,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_17,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_18,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_19,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_20,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_21,type,
c_2Ebool_2ECOND_2E3:
!>[X0: $tType] : ( ( tyop_2Emin_2Ebool * X0 * X0 ) > X0 ) ).
tff(func_def_22,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_23,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_24,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_25,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_26,type,
c_2Ewords_2En2w_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)) ).
tff(func_def_27,type,
c_2Ewords_2En2w_2E1:
!>[X0: $tType] : ( tyop_2Enum_2Enum > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) ).
tff(func_def_28,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_29,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_30,type,
c_2Ewords_2Eword__add_2E0:
!>[X0: $tType] : 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))) ).
tff(func_def_31,type,
c_2Ewords_2Eword__add_2E2:
!>[X0: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) ).
tff(func_def_32,type,
c_2Ewords_2Eword__sub_2E0:
!>[X0: $tType] : 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))) ).
tff(func_def_33,type,
c_2Ewords_2Eword__sub_2E2:
!>[X0: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0) ) ).
tff(func_def_34,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_35,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_36,type,
sK1: tyop_2Enum_2Enum ).
tff(func_def_37,type,
sK2: tyop_2Enum_2Enum ).
tff(func_def_38,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(f18,axiom,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_2D_2E2) ).
tff(f20,axiom,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_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_2Earithmetic_2E_3C_3D_2E0,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) ).
tff(f24,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(f28,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_27b) ).
tff(f30,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_27b) ).
tff(f32,axiom,
! [X0: $tType,X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__add_2E2(X0,X1,X2) = 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)),c_2Ewords_2Eword__add_2E0(X0),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27b) ).
tff(f33,axiom,
! [X0: $tType,X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__sub_2E2(X0,X1,X2) = 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)),c_2Ewords_2Eword__sub_2E0(X0),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a) ).
tff(f39,axiom,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = X0 )
<=> p(X0) )
& ( ( X0 = c_2Ebool_2ET_2E0 )
<=> p(X0) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
<=> ~ p(X0) )
& ( ( X0 = c_2Ebool_2EF_2E0 )
<=> ~ p(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
tff(f43,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(f44,axiom,
! [X0: $tType,X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X2: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__sub_2E2(X0,X1,X2) = c_2Ewords_2Eword__add_2E2(X0,X1,c_2Ewords_2Eword__2comp_2E1(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).
tff(f45,axiom,
! [X0: $tType,X1: $tType] :
( ! [X2: tyop_2Enum_2Enum,X3: tyop_2Enum_2Enum] : ( c_2Ewords_2Eword__add_2E2(X0,c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,X2)),c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,X3))) = c_2Ewords_2Eword__2comp_2E1(X0,c_2Ewords_2En2w_2E1(X0,c_2Earithmetic_2E_2B_2E2(X2,X3))) )
& ! [X4: tyop_2Enum_2Enum,X5: tyop_2Enum_2Enum] : ( c_2Ewords_2Eword__add_2E2(X1,c_2Ewords_2En2w_2E1(X1,X4),c_2Ewords_2Eword__2comp_2E1(X1,c_2Ewords_2En2w_2E1(X1,X5))) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Earithmetic_2E_3C_3D_2E2(X5,X4),c_2Ewords_2En2w_2E1(X1,c_2Earithmetic_2E_2D_2E2(X4,X5)),c_2Ewords_2Eword__2comp_2E1(X1,c_2Ewords_2En2w_2E1(X1,c_2Earithmetic_2E_2D_2E2(X5,X4)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD) ).
tff(f46,conjecture,
! [X0: $tType,X1: tyop_2Enum_2Enum,X2: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(X2,X1))
=> ( c_2Ewords_2En2w_2E1(X0,c_2Earithmetic_2E_2D_2E2(X1,X2)) = c_2Ewords_2Eword__sub_2E2(X0,c_2Ewords_2En2w_2E1(X0,X1),c_2Ewords_2En2w_2E1(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).
tff(f47,negated_conjecture,
~ ! [X0: $tType,X1: tyop_2Enum_2Enum,X2: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(X2,X1))
=> ( c_2Ewords_2En2w_2E1(X0,c_2Earithmetic_2E_2D_2E2(X1,X2)) = c_2Ewords_2Eword__sub_2E2(X0,c_2Ewords_2En2w_2E1(X0,X1),c_2Ewords_2En2w_2E1(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
tff(f49,plain,
? [X0: $tType,X1: tyop_2Enum_2Enum,X2: tyop_2Enum_2Enum] :
( ( c_2Ewords_2En2w_2E1(X0,c_2Earithmetic_2E_2D_2E2(X1,X2)) != c_2Ewords_2Eword__sub_2E2(X0,c_2Ewords_2En2w_2E1(X0,X1),c_2Ewords_2En2w_2E1(X0,X2)) )
& p(c_2Earithmetic_2E_3C_3D_2E2(X2,X1)) ),
inference(ennf_transformation,[],[f47]) ).
tff(f59,plain,
( ( c_2Ewords_2En2w_2E1(sK0,c_2Earithmetic_2E_2D_2E2(sK1,sK2)) != c_2Ewords_2Eword__sub_2E2(sK0,c_2Ewords_2En2w_2E1(sK0,sK1),c_2Ewords_2En2w_2E1(sK0,sK2)) )
& p(c_2Earithmetic_2E_3C_3D_2E2(sK2,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f49]) ).
tff(f67,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2ET_2E0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2EF_2E0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) ) ),
inference(nnf_transformation,[],[f39]) ).
tff(f68,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2ET_2E0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2EF_2E0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) ) ),
inference(flattening,[],[f67]) ).
tff(f72,plain,
p(c_2Earithmetic_2E_3C_3D_2E2(sK2,sK1)),
inference(cnf_transformation,[],[f59]) ).
tff(f73,plain,
c_2Ewords_2En2w_2E1(sK0,c_2Earithmetic_2E_2D_2E2(sK1,sK2)) != c_2Ewords_2Eword__sub_2E2(sK0,c_2Ewords_2En2w_2E1(sK0,sK1),c_2Ewords_2En2w_2E1(sK0,sK2)),
inference(cnf_transformation,[],[f59]) ).
tff(f92,plain,
! [X1: $tType,X4: tyop_2Enum_2Enum,X5: tyop_2Enum_2Enum] : ( c_2Ewords_2Eword__add_2E2(X1,c_2Ewords_2En2w_2E1(X1,X4),c_2Ewords_2Eword__2comp_2E1(X1,c_2Ewords_2En2w_2E1(X1,X5))) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Earithmetic_2E_3C_3D_2E2(X5,X4),c_2Ewords_2En2w_2E1(X1,c_2Earithmetic_2E_2D_2E2(X4,X5)),c_2Ewords_2Eword__2comp_2E1(X1,c_2Ewords_2En2w_2E1(X1,c_2Earithmetic_2E_2D_2E2(X5,X4)))) ),
inference(cnf_transformation,[],[f45]) ).
tff(f94,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0,X1) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0),X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f95,plain,
! [X0: tyop_2Enum_2Enum,X1: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_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_2Earithmetic_2E_3C_3D_2E0,X0),X1) ),
inference(cnf_transformation,[],[f20]) ).
tff(f96,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,[],[f28]) ).
tff(f98,plain,
! [X0: $tType,X2: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__sub_2E2(X0,X1,X2) = c_2Ewords_2Eword__add_2E2(X0,X1,c_2Ewords_2Eword__2comp_2E1(X0,X2)) ),
inference(cnf_transformation,[],[f44]) ).
tff(f99,plain,
! [X0: $tType,X2: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__sub_2E2(X0,X1,X2) = 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)),c_2Ewords_2Eword__sub_2E0(X0),X1),X2) ),
inference(cnf_transformation,[],[f33]) ).
tff(f102,plain,
! [X0: $tType,X2: X0,X1: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2ET_2E0,X1,X2) = X1 ),
inference(cnf_transformation,[],[f43]) ).
tff(f108,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,[],[f24]) ).
tff(f109,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,[],[f30]) ).
tff(f111,plain,
! [X0: $tType,X2: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__add_2E2(X0,X1,X2) = 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)),c_2Ewords_2Eword__add_2E0(X0),X1),X2) ),
inference(cnf_transformation,[],[f32]) ).
tff(f119,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2ET_2E0 = X0 ) ),
inference(cnf_transformation,[],[f68]) ).
tff(f143,plain,
! [X0: $tType,X2: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( c_2Ewords_2Eword__sub_2E2(X0,X1,X2) = 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)),c_2Ewords_2Eword__add_2E0(X0),X1),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),X2)) ),
inference(definition_unfolding,[],[f98,f111,f109]) ).
tff(f144,plain,
app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,sK1),sK2)) != app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0)),c_2Ewords_2Eword__add_2E0(sK0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),sK1)),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2Eword__2comp_2E0(sK0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),sK2))),
inference(definition_unfolding,[],[f73,f96,f94,f143,f96,f96]) ).
tff(f145,plain,
p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,sK2),sK1)),
inference(definition_unfolding,[],[f72,f95]) ).
tff(f147,plain,
! [X1: $tType,X4: tyop_2Enum_2Enum,X5: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),c_2Ewords_2Eword__add_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),X4)),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),X5))) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X5),X4)),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X4),X5))),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X5),X4)))) ),
inference(definition_unfolding,[],[f92,f111,f96,f109,f96,f108,f95,f96,f94,f109,f96,f94]) ).
tff(f149,plain,
! [X0: $tType,X2: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),X1: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0)] : ( 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)),c_2Ewords_2Eword__sub_2E0(X0),X1),X2) = 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)),c_2Ewords_2Eword__add_2E0(X0),X1),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2Eword__2comp_2E0(X0),X2)) ),
inference(definition_unfolding,[],[f99,f143]) ).
tff(f150,plain,
! [X0: $tType,X2: X0,X1: 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_2ET_2E0),X1),X2) = X1 ),
inference(definition_unfolding,[],[f102,f108]) ).
tff(f188,plain,
! [X1: $tType,X4: tyop_2Enum_2Enum,X5: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X5),X4)),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X4),X5))),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2Eword__2comp_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X5),X4)))) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1)),c_2Ewords_2Eword__sub_2E0(X1),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),X4)),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X1),c_2Ewords_2En2w_2E0(X1),X5)) ),
inference(forward_demodulation,[],[f147,f149]) ).
tff(f190,plain,
app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,sK1),sK2)) != app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0)),c_2Ewords_2Eword__sub_2E0(sK0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),sK1)),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),sK2)),
inference(forward_demodulation,[],[f144,f149]) ).
tff(f192,plain,
c_2Ebool_2ET_2E0 = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,sK2),sK1),
inference(resolution,[],[f119,f145]) ).
tff(f435,plain,
! [X0: $tType] : ( 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)),c_2Ewords_2Eword__sub_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),sK1)),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),sK2)) = 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_2ET_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,sK1),sK2))),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_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,sK2),sK1)))) ),
inference(superposition,[],[f188,f192]) ).
tff(f450,plain,
! [X0: $tType] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,sK1),sK2)) = 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)),c_2Ewords_2Eword__sub_2E0(X0),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),sK1)),app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,X0),c_2Ewords_2En2w_2E0(X0),sK2)) ),
inference(forward_demodulation,[],[f435,f150]) ).
tff(f451,plain,
app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,sK1),sK2)) != app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ewords_2En2w_2E0(sK0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,sK1),sK2)),
inference(superposition,[],[f190,f450]) ).
tff(f452,plain,
$false,
inference(trivial_inequality_removal,[],[f451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP013_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 12:01:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.54/1.53 % (400600)Detected formulas, will run a generic FOF schedule.
% 3.54/1.53 % (400605)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=2533149778:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.54/1.53 % (400610)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3872777131:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.54/1.53 % (400609)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1902272045:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.54/1.53 % (400608)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2962508818:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.54/1.53 % (400611)dis-21_1_sil=8000:lcm=predicate:random_seed=2037568226: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)
% 3.54/1.53 % (400607)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=2608925194:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.54/1.53 % (400606)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=3018342998:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.54/1.53 % (400608)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.54/1.53 % (400609)Refutation not found, incomplete strategy
% 3.54/1.53 % (400609)------------------------------
% 3.54/1.53 % (400609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.53 % (400609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.53 % (400609)CaDiCaL version: 2.1.3
% 3.54/1.53 % (400609)Termination reason: Refutation not found, incomplete strategy
% 3.54/1.53 % (400609)Time elapsed: 0.001 s
% 3.54/1.53 % (400609)Peak memory usage: 88 MB
% 3.54/1.53 % (400609)Instructions burned: 1 (million)
% 3.54/1.53 % (400608)Refutation not found, incomplete strategy
% 3.54/1.53 % (400608)------------------------------
% 3.54/1.53 % (400608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.53 % (400608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.53 % (400608)CaDiCaL version: 2.1.3
% 3.54/1.53 % (400608)Termination reason: Refutation not found, incomplete strategy
% 3.54/1.53 % (400608)Time elapsed: 0.002 s
% 3.54/1.53 % (400608)Peak memory usage: 88 MB
% 3.54/1.53 % (400608)Instructions burned: 1 (million)
% 3.54/1.53 % (400607)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.54/1.53 % (400611)Instruction limit reached!
% 3.54/1.53 % (400611)------------------------------
% 3.54/1.53 % (400611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.53 % (400611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.53 % (400611)CaDiCaL version: 2.1.3
% 3.54/1.53 % (400611)Termination reason: Instruction limit
% 3.54/1.53 % (400611)Termination phase: Saturation
% 3.54/1.53 % (400611)Time elapsed: 0.064 s
% 3.54/1.53 % (400611)Peak memory usage: 89 MB
% 3.54/1.53 % (400611)Instructions burned: 131 (million)
% 3.54/1.53 % (400610)Instruction limit reached!
% 3.54/1.53 % (400610)------------------------------
% 3.54/1.53 % (400610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.53 % (400610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.53 % (400610)CaDiCaL version: 2.1.3
% 3.54/1.53 % (400610)Termination reason: Instruction limit
% 3.54/1.53 % (400610)Termination phase: Saturation
% 3.54/1.53 % (400610)Time elapsed: 0.084 s
% 3.54/1.53 % (400610)Peak memory usage: 89 MB
% 3.54/1.53 % (400610)Instructions burned: 139 (million)
% 3.54/1.53 % Exception at run slice level
% 3.54/1.53 User error: GNN currently only supports monomorphic FOL.
% 3.54/1.53 % (400658)lrs+10_1_sil=8000:sp=occurrence:random_seed=2935338272:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.54/1.53 % (400661)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4254140644:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.54/1.53 % (400658)First to succeed.
% 3.54/1.53 % (400658)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-400600"
% 3.54/1.53 % (400661)Refutation not found, incomplete strategy
% 3.54/1.53 % (400661)------------------------------
% 3.54/1.53 % (400661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.53 % (400661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.53 % (400661)CaDiCaL version: 2.1.3
% 3.54/1.53 % (400661)Termination reason: Refutation not found, incomplete strategy
% 3.54/1.53 % (400661)Time elapsed: 0.003 s
% 3.54/1.53 % (400661)Peak memory usage: 88 MB
% 3.54/1.53 % (400661)Instructions burned: 3 (million)
% 3.54/1.53 % (400608)------------------------------
% 3.54/1.53 % (400608)------------------------------
% 3.54/1.53 % (400609)------------------------------
% 3.54/1.53 % (400609)------------------------------
% 3.54/1.53 % (400682)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1575856436:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.54/1.53 % (400682)Also succeeded, but the first one will report.
% 3.54/1.53 % Exception at run slice level
% 3.54/1.53 User error: GNN currently only supports monomorphic FOL.
% 3.54/1.53 % Exception at run slice level
% 3.54/1.53 User error: GNN currently only supports monomorphic FOL.
% 3.54/1.53 % (400691)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1730617462:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 3.54/1.53 % (400690)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=3761624800:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.54/1.53 % (400691)Refutation not found, incomplete strategy
% 3.54/1.53 % (400691)------------------------------
% 3.54/1.53 % (400691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.53 % (400691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.53 % (400691)CaDiCaL version: 2.1.3
% 3.54/1.53 % (400691)Termination reason: Refutation not found, incomplete strategy
% 3.54/1.53 % (400691)Time elapsed: 0.004 s
% 3.54/1.53 % (400691)Peak memory usage: 88 MB
% 3.54/1.53 % (400691)Instructions burned: 5 (million)
% 3.54/1.53 % (400661)------------------------------
% 3.54/1.53 % (400661)------------------------------
% 3.54/1.53 % (400658)Refutation found. Thanks to Tanya!
% 3.54/1.53 % SZS status Theorem for theBenchmark
% 3.54/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.31/1.72 % (400658)------------------------------
% 5.31/1.72 % (400658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.72 % (400658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.72 % (400658)CaDiCaL version: 2.1.3
% 5.31/1.72 % (400658)Termination reason: Refutation
% 5.31/1.72 % (400658)Time elapsed: 0.017 s
% 5.31/1.72 % (400658)Peak memory usage: 89 MB
% 5.31/1.72 % (400658)Instructions burned: 26 (million)
% 5.31/1.72 % (400658)------------------------------
% 5.31/1.72 % (400658)------------------------------
% 5.31/1.72 % (400600)Success in time 0.666 s
% 5.31/1.72 % Vampire exiting
%------------------------------------------------------------------------------