%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n012.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 2.76s 1.16s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 41 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 44 ( 19 ~; 10 |; 14 &)
% ( 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 : 47 ( 47 usr; 13 con; 0-4 aty)
% Number of variables : 32 ( 31 !; 1 ?; 32 :)
% 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,
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_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(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(f5,axiom,
! [X0: tyop_2Emin_2Ebool] :
( ( X0 = c_2Ebool_2ET_2E0 )
| ( X0 = c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).
tff(f35,axiom,
p(c_2Ebool_2ET_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
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(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(f47,axiom,
! [X0: tyop_2Enum_2Enum] : ~ p(c_2Eprim__rec_2E_3C_2E2(X0,c_2Enum_2E0_2E0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__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(f52,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(f61,plain,
c_2Ewords_2En2w_2E1(sK0,c_2Enum_2E0_2E0) != c_2Einteger__word_2Ei2w_2E1(sK0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f52]) ).
tff(f63,plain,
! [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)))
| ( ( c_2Enum_2E0_2E0 = X0 )
& ( c_2Enum_2E0_2E0 = X1 ) ) )
& ( ( X0 != c_2Enum_2E0_2E0 )
| ( X1 != c_2Enum_2E0_2E0 )
| ~ 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))) )
& ( 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 ) ),
inference(nnf_transformation,[],[f44]) ).
tff(f64,plain,
! [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)))
| ( ( c_2Enum_2E0_2E0 = X0 )
& ( c_2Enum_2E0_2E0 = X1 ) ) )
& ( ( X0 != c_2Enum_2E0_2E0 )
| ( X1 != c_2Enum_2E0_2E0 )
| ~ 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))) )
& ( 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 ) ),
inference(flattening,[],[f63]) ).
tff(f69,plain,
c_2Ewords_2En2w_2E1(sK0,c_2Enum_2E0_2E0) != c_2Einteger__word_2Ei2w_2E1(sK0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),
inference(cnf_transformation,[],[f61]) ).
tff(f72,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(f73,plain,
! [X0: $tType,X3: X0,X4: X0] : ( c_2Ebool_2ECOND_2E3(X0,c_2Ebool_2EF_2E0,X3,X4) = X4 ),
inference(cnf_transformation,[],[f42]) ).
tff(f79,plain,
! [X0: tyop_2Enum_2Enum] : ( c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__of__num_2E1(X0)) = X0 ),
inference(cnf_transformation,[],[f45]) ).
tff(f85,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,[],[f64]) ).
tff(f89,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(cnf_transformation,[],[f5]) ).
tff(f93,plain,
p(c_2Ebool_2ET_2E0),
inference(cnf_transformation,[],[f35]) ).
tff(f107,plain,
! [X0: tyop_2Enum_2Enum] : ~ p(c_2Eprim__rec_2E_3C_2E2(X0,c_2Enum_2E0_2E0)),
inference(cnf_transformation,[],[f47]) ).
tff(f108,plain,
c_2Ewords_2En2w_2E1(sK0,c_2Enum_2E0_2E0) != c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Ewords_2Eword__2comp_2E1(sK0,c_2Ewords_2En2w_2E1(sK0,c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))))),c_2Ewords_2En2w_2E1(sK0,c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)))),
inference(definition_unfolding,[],[f69,f72]) ).
tff(f110,plain,
! [X0: tyop_2Enum_2Enum] : ~ p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))),
inference(definition_unfolding,[],[f107,f85]) ).
tff(f124,plain,
c_2Ewords_2En2w_2E1(sK0,c_2Enum_2E0_2E0) != c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Ewords_2Eword__2comp_2E1(sK0,c_2Ewords_2En2w_2E1(sK0,c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))))),c_2Ewords_2En2w_2E1(sK0,c_2Enum_2E0_2E0)),
inference(superposition,[],[f108,f79]) ).
tff(f141,plain,
! [X0: tyop_2Enum_2Enum] :
( ~ p(c_2Ebool_2ET_2E0)
| ( c_2Ebool_2EF_2E0 = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ),
inference(superposition,[],[f110,f89]) ).
tff(f142,plain,
! [X0: tyop_2Enum_2Enum] : ( c_2Ebool_2EF_2E0 = c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(X0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ),
inference(forward_subsumption_resolution,[],[f141,f93]) ).
tff(f160,plain,
c_2Ewords_2En2w_2E1(sK0,c_2Enum_2E0_2E0) != c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,sK0),c_2Ebool_2EF_2E0,c_2Ewords_2Eword__2comp_2E1(sK0,c_2Ewords_2En2w_2E1(sK0,c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))))),c_2Ewords_2En2w_2E1(sK0,c_2Enum_2E0_2E0)),
inference(superposition,[],[f124,f142]) ).
tff(f164,plain,
$false,
inference(forward_subsumption_resolution,[],[f160,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP015_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.33 % Computer : n012.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Sun Sep 27 12:01:50 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 Running first-order theorem proving
% 0.10/0.36 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
% 2.76/1.16 % (2254763)Detected formulas, will run a generic FOF schedule.
% 2.76/1.16 % (2254770)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=3238368966:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.16 % (2254770)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.76/1.16 % (2254769)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=3787831070:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.16 % (2254771)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=213666092:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.16 % (2254768)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=1017325322:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.16 % (2254771)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.76/1.16 % (2254771)Refutation not found, incomplete strategy
% 2.76/1.16 % (2254771)------------------------------
% 2.76/1.16 % (2254771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.16 % (2254771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.16 % (2254771)CaDiCaL version: 2.1.3
% 2.76/1.16 % (2254771)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.16 % (2254771)Time elapsed: 0.001 s
% 2.76/1.16 % (2254771)Peak memory usage: 88 MB
% 2.76/1.16 % (2254772)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3497020532:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.16 % (2254774)dis-21_1_sil=8000:lcm=predicate:random_seed=3828929211: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)
% 2.76/1.16 % (2254773)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2201193917:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.16 % (2254772)First to succeed.
% 2.76/1.16 % (2254772)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2254763"
% 2.76/1.16 % (2254773)Also succeeded, but the first one will report.
% 2.76/1.16 % (2254774)Instruction limit reached!
% 2.76/1.16 % (2254774)------------------------------
% 2.76/1.16 % (2254774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.16 % (2254774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.16 % (2254774)CaDiCaL version: 2.1.3
% 2.76/1.16 % (2254774)Termination reason: Instruction limit
% 2.76/1.16 % (2254774)Termination phase: Saturation
% 2.76/1.16 % (2254774)Time elapsed: 0.055 s
% 2.76/1.16 % (2254774)Peak memory usage: 89 MB
% 2.76/1.16 % (2254774)Instructions burned: 131 (million)
% 2.76/1.16 % Exception at run slice level
% 2.76/1.16 User error: GNN currently only supports monomorphic FOL.
% 2.76/1.16 % (2254771)------------------------------
% 2.76/1.16 % (2254771)------------------------------
% 2.76/1.16 % (2254772)Refutation found. Thanks to Tanya!
% 2.76/1.16 % SZS status Theorem for theBenchmark
% 2.76/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.36 % (2254772)------------------------------
% 3.64/1.36 % (2254772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.36 % (2254772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.36 % (2254772)CaDiCaL version: 2.1.3
% 3.64/1.36 % (2254772)Termination reason: Refutation
% 3.64/1.36 % (2254772)Time elapsed: 0.004 s
% 3.64/1.36 % (2254772)Peak memory usage: 88 MB
% 3.64/1.36 % (2254772)Instructions burned: 6 (million)
% 3.64/1.36 % (2254772)------------------------------
% 3.64/1.36 % (2254772)------------------------------
% 3.64/1.36 % (2254763)Success in time 0.446 s
% 3.64/1.36 % Vampire exiting
%------------------------------------------------------------------------------