TSTP Solution File: ITP018_3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP018_3 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 06:59:05 EDT 2024
% Result : Theorem 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 120
% Syntax : Number of formulae : 291 ( 89 unt; 43 typ; 0 def)
% Number of atoms : 559 ( 107 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 492 ( 181 ~; 187 |; 39 &)
% ( 72 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 30 ( 21 >; 9 *; 0 +; 0 <<)
% Number of predicates : 47 ( 45 usr; 45 prp; 0-2 aty)
% Number of functors : 38 ( 38 usr; 7 con; 0-4 aty)
% Number of variables : 459 ( 410 !; 14 ?; 459 :)
% ( 35 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Ebinary__ieee_2Efloat: ( $tType * $tType ) > $tType ).
tff(type_def_6,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
tff(type_def_7,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_8,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(type_def_9,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(type_def_10,type,
tyop_2Erealax_2Ereal: $tType ).
tff(type_def_11,type,
sK0: $tType ).
tff(type_def_12,type,
sK1: $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_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_9,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_10,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_11,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_12,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_13,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_14,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_15,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_16,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_17,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_18,type,
c_2Ebinary__ieee_2Efloat__negate_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Ebinary__ieee_2Efloat(X0,X1)) ).
tff(func_def_19,type,
c_2Ebinary__ieee_2Efloat__negate_2E1:
!>[X0: $tType,X1: $tType] : ( tyop_2Ebinary__ieee_2Efloat(X0,X1) > tyop_2Ebinary__ieee_2Efloat(X0,X1) ) ).
tff(func_def_20,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)),tyop_2Ebinary__ieee_2Efloat(X0,X1)) ).
tff(func_def_21,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E1:
!>[X0: $tType,X1: $tType] : ( tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)) > tyop_2Ebinary__ieee_2Efloat(X0,X1) ) ).
tff(func_def_22,type,
c_2Ebinary__ieee_2Efloat__to__real_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal) ).
tff(func_def_23,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1:
!>[X0: $tType,X1: $tType] : ( tyop_2Ebinary__ieee_2Efloat(X0,X1) > tyop_2Erealax_2Ereal ) ).
tff(func_def_24,type,
c_2Erealax_2Ereal__neg_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(func_def_25,type,
c_2Erealax_2Ereal__neg_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(func_def_26,type,
c_2Ebool_2Ethe__value_2E0:
!>[X0: $tType] : tyop_2Ebool_2Eitself(X0) ).
tff(func_def_27,type,
c_2Ebinary__ieee_2Eulp_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)),tyop_2Erealax_2Ereal) ).
tff(func_def_28,type,
c_2Ebinary__ieee_2Eulp_2E1:
!>[X0: $tType,X1: $tType] : ( tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)) > tyop_2Erealax_2Ereal ) ).
tff(func_def_29,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_30,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_31,type,
sK2:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_32,type,
sK3:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).
tff(func_def_33,type,
sK4:
!>[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(f517,plain,
$false,
inference(avatar_sat_refutation,[],[f172,f177,f181,f185,f189,f194,f198,f202,f206,f210,f214,f218,f233,f238,f242,f264,f268,f272,f276,f280,f289,f293,f327,f331,f335,f341,f345,f349,f353,f357,f361,f398,f402,f406,f419,f435,f439,f443,f447,f474,f479,f500,f512,f516]) ).
tff(f516,plain,
( spl5_23
| ~ spl5_44 ),
inference(avatar_contradiction_clause,[],[f515]) ).
tff(f515,plain,
( $false
| spl5_23
| ~ spl5_44 ),
inference(trivial_inequality_removal,[],[f514]) ).
tff(f514,plain,
( ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(sK0,sK1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) != app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(sK0,sK1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) )
| spl5_23
| ~ spl5_44 ),
inference(forward_demodulation,[],[f513,f157]) ).
tff(f157,plain,
! [X1: $tType,X0: $tType] : ( app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(X0,X1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))) = app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(X0,X1),app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)),tyop_2Ebinary__ieee_2Efloat(X0,X1),c_2Ebinary__ieee_2Efloat__plus__min_2E0(X0,X1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) ),
inference(definition_unfolding,[],[f115,f145,f143,f148]) ).
tff(f148,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1))] : ( c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,X2) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)),tyop_2Ebinary__ieee_2Efloat(X0,X1),c_2Ebinary__ieee_2Efloat__plus__min_2E0(X0,X1),X2) ),
inference(cnf_transformation,[],[f61]) ).
tff(f61,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1))] : ( c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,X2) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)),tyop_2Ebinary__ieee_2Efloat(X0,X1),c_2Ebinary__ieee_2Efloat__plus__min_2E0(X0,X1),X2) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X3: $tType,X4: $tType,X14: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X3,X4))] : ( c_2Ebinary__ieee_2Efloat__plus__min_2E1(X3,X4,X14) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X3,X4)),tyop_2Ebinary__ieee_2Efloat(X3,X4),c_2Ebinary__ieee_2Efloat__plus__min_2E0(X3,X4),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
tff(f143,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,X2) = app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(X0,X1),X2) ),
inference(cnf_transformation,[],[f56]) ).
tff(f56,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,X2) = app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(X0,X1),X2) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType,X1: $tType,X14: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,X14) = app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(X0,X1),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).
tff(f145,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1))] : ( c_2Ebinary__ieee_2Eulp_2E1(X0,X1,X2) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(X0,X1),X2) ),
inference(cnf_transformation,[],[f58]) ).
tff(f58,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1))] : ( c_2Ebinary__ieee_2Eulp_2E1(X0,X1,X2) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X0,X1)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(X0,X1),X2) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X3: $tType,X4: $tType,X14: tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X3,X4))] : ( c_2Ebinary__ieee_2Eulp_2E1(X3,X4,X14) = app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(X3,X4)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(X3,X4),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
tff(f115,plain,
! [X1: $tType,X0: $tType] : ( c_2Ebinary__ieee_2Eulp_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))) = c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0: $tType,X1: $tType] : ( c_2Ebinary__ieee_2Eulp_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))) = c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X3: $tType,X4: $tType] : ( c_2Ebinary__ieee_2Eulp_2E1(X3,X4,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X3,X4))) = c_2Ebinary__ieee_2Efloat__to__real_2E1(X3,X4,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X3,X4,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X3,X4)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eulp) ).
tff(f513,plain,
( ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(sK0,sK1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) != app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,app_2E2(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(sK0,sK1),app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__plus__min_2E0(sK0,sK1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1))))) )
| spl5_23
| ~ spl5_44 ),
inference(superposition,[],[f326,f511]) ).
tff(f511,plain,
( ! [X1: $tType,X0: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(X0,X1),app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Ebinary__ieee_2Efloat(X0,X1),c_2Ebinary__ieee_2Efloat__negate_2E0(X0,X1),X2)) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(X0,X1),X2)) )
| ~ spl5_44 ),
inference(avatar_component_clause,[],[f510]) ).
tff(f510,plain,
( spl5_44
<=> ! [X1: $tType,X0: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(X0,X1),app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Ebinary__ieee_2Efloat(X0,X1),c_2Ebinary__ieee_2Efloat__negate_2E0(X0,X1),X2)) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_44])]) ).
tff(f326,plain,
( ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(sK0,sK1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) != app_2E2(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(sK0,sK1),app_2E2(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__negate_2E0(sK0,sK1),app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__plus__min_2E0(sK0,sK1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1))))) )
| spl5_23 ),
inference(avatar_component_clause,[],[f324]) ).
tff(f324,plain,
( spl5_23
<=> ( app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(sK0,sK1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) = app_2E2(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(sK0,sK1),app_2E2(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__negate_2E0(sK0,sK1),app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__plus__min_2E0(sK0,sK1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).
tff(f512,plain,
spl5_44,
inference(avatar_split_clause,[],[f162,f510]) ).
tff(f162,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(X0,X1),app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Ebinary__ieee_2Efloat(X0,X1),c_2Ebinary__ieee_2Efloat__negate_2E0(X0,X1),X2)) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(X0,X1),X2)) ),
inference(definition_unfolding,[],[f142,f143,f146,f106,f143]) ).
tff(f106,plain,
! [X0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__neg_2E1(X0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,X0) ),
inference(cnf_transformation,[],[f37]) ).
tff(f37,plain,
! [X0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__neg_2E1(X0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,X0) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X14: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__neg_2E1(X14) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Erealax_2Ereal__neg_2E1) ).
tff(f146,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,X2) = app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Ebinary__ieee_2Efloat(X0,X1),c_2Ebinary__ieee_2Efloat__negate_2E0(X0,X1),X2) ),
inference(cnf_transformation,[],[f59]) ).
tff(f59,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,X2) = app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Ebinary__ieee_2Efloat(X0,X1),c_2Ebinary__ieee_2Efloat__negate_2E0(X0,X1),X2) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X0: $tType,X1: $tType,X14: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,X14) = app_2E2(tyop_2Ebinary__ieee_2Efloat(X0,X1),tyop_2Ebinary__ieee_2Efloat(X0,X1),c_2Ebinary__ieee_2Efloat__negate_2E0(X0,X1),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).
tff(f142,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,X2)) = c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,X2)) ),
inference(cnf_transformation,[],[f55]) ).
tff(f55,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,X2)) = c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,X2)) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType,X1: $tType,X11: tyop_2Ebinary__ieee_2Efloat(X0,X1)] : ( c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,X11)) = c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
tff(f500,plain,
spl5_43,
inference(avatar_split_clause,[],[f154,f498]) ).
tff(f498,plain,
( spl5_43
<=> ! [X1: $tType,X0: $tType,X3: tyop_2Emin_2Efun(X0,X1),X2: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ( app_2E2(X0,X1,X2,sK4(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK4(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_43])]) ).
tff(f154,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ( app_2E2(X0,X1,X2,sK4(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK4(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f101]) ).
tff(f101,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ( app_2E2(X0,X1,X2,sK4(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK4(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f71,f100]) ).
tff(f100,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ? [X4: X0] : ( app_2E2(X0,X1,X2,X4) != app_2E2(X0,X1,X3,X4) )
=> ( app_2E2(X0,X1,X2,sK4(X0,X1,X2,X3)) != app_2E2(X0,X1,X3,sK4(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f71,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ( X2 = X3 )
| ? [X4: X0] : ( app_2E2(X0,X1,X2,X4) != app_2E2(X0,X1,X3,X4) ) ),
inference(ennf_transformation,[],[f65]) ).
tff(f65,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Emin_2Efun(X0,X1)] :
( ! [X4: X0] : ( app_2E2(X0,X1,X2,X4) = app_2E2(X0,X1,X3,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X0: $tType,X1: $tType,X5: tyop_2Emin_2Efun(X0,X1),X6: tyop_2Emin_2Efun(X0,X1)] :
( ! [X7: X0] : ( app_2E2(X0,X1,X5,X7) = app_2E2(X0,X1,X6,X7) )
=> ( X5 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eeq__ext) ).
tff(f479,plain,
spl5_42,
inference(avatar_split_clause,[],[f161,f477]) ).
tff(f477,plain,
( spl5_42
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK3(X0,X1)))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_42])]) ).
tff(f161,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK3(X0,X1)))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1)) ),
inference(definition_unfolding,[],[f131,f114]) ).
tff(f114,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType,X14: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(X0,X14) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
tff(f131,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK3(X0,X1)))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ),
inference(cnf_transformation,[],[f91]) ).
tff(f91,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK3(X0,X1)))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f89,f90]) ).
tff(f90,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
=> p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK3(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f89,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ? [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
inference(rectify,[],[f88]) ).
tff(f88,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ! [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| ~ p(c_2Ebool_2E_3F_2E1(X0,X1)) ) ),
inference(nnf_transformation,[],[f51]) ).
tff(f51,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(X0,X1))
<=> ? [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType,X5: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(X0,X5))
<=> ? [X13: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X5,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_3F) ).
tff(f474,plain,
spl5_41,
inference(avatar_split_clause,[],[f158,f472]) ).
tff(f472,plain,
( spl5_41
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_41])]) ).
tff(f158,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1))) ),
inference(definition_unfolding,[],[f130,f113]) ).
tff(f113,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X1) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType,X14: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(X0,X14) = app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
tff(f130,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(X0,X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1))) ),
inference(cnf_transformation,[],[f87]) ).
tff(f87,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_21_2E1(X0,X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1))) )
& ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f85,f86]) ).
tff(f86,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
=> ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,sK2(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f85,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_21_2E1(X0,X1))
| ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ! [X3: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
inference(rectify,[],[f84]) ).
tff(f84,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2E_21_2E1(X0,X1))
| ? [X2: X0] : ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) )
& ( ! [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ) ),
inference(nnf_transformation,[],[f50]) ).
tff(f50,plain,
! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(X0,X1))
<=> ! [X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType,X5: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(X0,X5))
<=> ! [X13: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,X5,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_21) ).
tff(f447,plain,
spl5_40,
inference(avatar_split_clause,[],[f150,f445]) ).
tff(f445,plain,
( spl5_40
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_40])]) ).
tff(f150,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ),
inference(cnf_transformation,[],[f98]) ).
tff(f98,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( ( X1 = X2 )
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) )
& ( p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2))
| ( X1 != X2 ) ) ),
inference(nnf_transformation,[],[f62]) ).
tff(f62,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
<=> p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2)) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType,X14: X0,X15: X0] :
( ( X14 = X15 )
<=> p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X14),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
tff(f443,plain,
spl5_39,
inference(avatar_split_clause,[],[f141,f441]) ).
tff(f441,plain,
( spl5_39
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_39])]) ).
tff(f141,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f97]) ).
tff(f97,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ( ~ p(X1)
& p(X0) ) ) ),
inference(flattening,[],[f96]) ).
tff(f96,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ( ~ p(X1)
& p(X0) ) ) ),
inference(nnf_transformation,[],[f70]) ).
tff(f70,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| ~ p(X0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
inference(ennf_transformation,[],[f54]) ).
tff(f54,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X0)
=> p(X1) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1)) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X14: tyop_2Emin_2Ebool,X15: tyop_2Emin_2Ebool] :
( ( p(X14)
=> p(X15) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X14),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
tff(f439,plain,
spl5_38,
inference(avatar_split_clause,[],[f138,f437]) ).
tff(f437,plain,
( spl5_38
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_38])]) ).
tff(f138,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f95]) ).
tff(f95,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ( ~ p(X1)
& ~ p(X0) ) ) ),
inference(flattening,[],[f94]) ).
tff(f94,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ( ~ p(X1)
& ~ p(X0) ) ) ),
inference(nnf_transformation,[],[f53]) ).
tff(f53,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
| p(X0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1)) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X14: tyop_2Emin_2Ebool,X15: tyop_2Emin_2Ebool] :
( ( p(X15)
| p(X14) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X14),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
tff(f435,plain,
spl5_37,
inference(avatar_split_clause,[],[f133,f433]) ).
tff(f433,plain,
( spl5_37
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).
tff(f133,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f93]) ).
tff(f93,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( ( p(X1)
& p(X0) )
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ) ),
inference(flattening,[],[f92]) ).
tff(f92,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( ( p(X1)
& p(X0) )
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1))
| ~ p(X1)
| ~ p(X0) ) ),
inference(nnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X1)
& p(X0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X14: tyop_2Emin_2Ebool,X15: tyop_2Emin_2Ebool] :
( ( p(X15)
& p(X14) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X14),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
tff(f419,plain,
( spl5_35
| ~ spl5_36
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f224,f192,f416,f413]) ).
tff(f413,plain,
( spl5_35
<=> ! [X0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EF_2E0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_35])]) ).
tff(f416,plain,
( spl5_36
<=> ( c_2Ebool_2ET_2E0 = c_2Ebool_2EF_2E0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_36])]) ).
tff(f192,plain,
( spl5_6
<=> ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
tff(f224,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0 )
| ( c_2Ebool_2EF_2E0 = X0 ) )
| ~ spl5_6 ),
inference(equality_factoring,[],[f193]) ).
tff(f193,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ( c_2Ebool_2EF_2E0 = X0 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f192]) ).
tff(f406,plain,
spl5_34,
inference(avatar_split_clause,[],[f160,f404]) ).
tff(f404,plain,
( spl5_34
<=> ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).
tff(f160,plain,
! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(X0),X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(definition_unfolding,[],[f132,f114]) ).
tff(f132,plain,
! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(X0,X1))
| ~ p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X2)) ),
inference(cnf_transformation,[],[f91]) ).
tff(f402,plain,
spl5_33,
inference(avatar_split_clause,[],[f159,f400]) ).
tff(f400,plain,
( spl5_33
<=> ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_33])]) ).
tff(f159,plain,
! [X0: $tType,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(X0),X1)) ),
inference(definition_unfolding,[],[f129,f113]) ).
tff(f129,plain,
! [X0: $tType,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,X1,X3))
| ~ p(c_2Ebool_2E_21_2E1(X0,X1)) ),
inference(cnf_transformation,[],[f87]) ).
tff(f398,plain,
spl5_32,
inference(avatar_split_clause,[],[f153,f396]) ).
tff(f396,plain,
( spl5_32
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_32])]) ).
tff(f153,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ),
inference(cnf_transformation,[],[f64]) ).
tff(f64,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X2),X3) = X2 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X1: $tType,X11: X0,X12: X1] : ( app_2E2(X1,X0,app_2E2(X0,tyop_2Emin_2Efun(X1,X0),combin_k_2E0(X0,X1),X11),X12) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ek__thm) ).
tff(f361,plain,
spl5_31,
inference(avatar_split_clause,[],[f140,f359]) ).
tff(f359,plain,
( spl5_31
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).
tff(f140,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f97]) ).
tff(f357,plain,
spl5_30,
inference(avatar_split_clause,[],[f139,f355]) ).
tff(f355,plain,
( spl5_30
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).
tff(f139,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0),X1))
| p(X0) ),
inference(cnf_transformation,[],[f97]) ).
tff(f353,plain,
spl5_29,
inference(avatar_split_clause,[],[f137,f351]) ).
tff(f351,plain,
( spl5_29
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).
tff(f137,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f95]) ).
tff(f349,plain,
spl5_28,
inference(avatar_split_clause,[],[f136,f347]) ).
tff(f347,plain,
( spl5_28
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).
tff(f136,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0),X1))
| ~ p(X0) ),
inference(cnf_transformation,[],[f95]) ).
tff(f345,plain,
spl5_27,
inference(avatar_split_clause,[],[f135,f343]) ).
tff(f343,plain,
( spl5_27
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).
tff(f135,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f93]) ).
tff(f341,plain,
spl5_26,
inference(avatar_split_clause,[],[f134,f339]) ).
tff(f339,plain,
( spl5_26
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).
tff(f134,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0),X1)) ),
inference(cnf_transformation,[],[f93]) ).
tff(f335,plain,
spl5_25,
inference(avatar_split_clause,[],[f165,f333]) ).
tff(f333,plain,
( spl5_25
<=> ! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).
tff(f165,plain,
! [X0: $tType,X2: X0] : p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X2),X2)),
inference(equality_resolution,[],[f149]) ).
tff(f149,plain,
! [X0: $tType,X2: X0,X1: X0] :
( p(app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(X0),X1),X2))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f98]) ).
tff(f331,plain,
( spl5_24
| ~ spl5_2
| ~ spl5_15 ),
inference(avatar_split_clause,[],[f257,f240,f174,f329]) ).
tff(f329,plain,
( spl5_24
<=> ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).
tff(f174,plain,
( spl5_2
<=> p(c_2Ebool_2ET_2E0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
tff(f240,plain,
( spl5_15
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ~ p(X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).
tff(f257,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
| ~ spl5_2
| ~ spl5_15 ),
inference(resolution,[],[f241,f176]) ).
tff(f176,plain,
( p(c_2Ebool_2ET_2E0)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f174]) ).
tff(f241,plain,
( ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ~ p(X1)
| ( X0 = X1 )
| ~ p(X0) )
| ~ spl5_15 ),
inference(avatar_component_clause,[],[f240]) ).
tff(f327,plain,
~ spl5_23,
inference(avatar_split_clause,[],[f156,f324]) ).
tff(f156,plain,
app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E0(sK0,sK1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) != app_2E2(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E0(sK0,sK1),app_2E2(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__negate_2E0(sK0,sK1),app_2E2(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__plus__min_2E0(sK0,sK1),c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1))))),
inference(definition_unfolding,[],[f102,f106,f145,f143,f146,f148]) ).
tff(f102,plain,
c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) != c_2Ebinary__ieee_2Efloat__to__real_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__negate_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1))))),
inference(cnf_transformation,[],[f73]) ).
tff(f73,plain,
c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) != c_2Ebinary__ieee_2Efloat__to__real_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__negate_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1))))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f67,f72]) ).
tff(f72,plain,
( ? [X0: $tType,X1: $tType] : ( c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) != c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))))) )
=> ( c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1)))) != c_2Ebinary__ieee_2Efloat__to__real_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__negate_2E1(sK0,sK1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(sK0,sK1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(sK0,sK1))))) ) ),
introduced(choice_axiom,[]) ).
tff(f67,plain,
? [X0: $tType,X1: $tType] : ( c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) != c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))))) ),
inference(ennf_transformation,[],[f36]) ).
tff(f36,plain,
~ ! [X0: $tType,X1: $tType] : ( c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1)))) = c_2Ebinary__ieee_2Efloat__to__real_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__negate_2E1(X0,X1,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X0,X1,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X0,X1))))) ),
inference(rectify,[],[f35]) ).
tff(f35,negated_conjecture,
~ ! [X3: $tType,X4: $tType] : ( c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(X3,X4,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X3,X4)))) = c_2Ebinary__ieee_2Efloat__to__real_2E1(X3,X4,c_2Ebinary__ieee_2Efloat__negate_2E1(X3,X4,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X3,X4,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X3,X4))))) ),
inference(negated_conjecture,[],[f34]) ).
tff(f34,conjecture,
! [X3: $tType,X4: $tType] : ( c_2Erealax_2Ereal__neg_2E1(c_2Ebinary__ieee_2Eulp_2E1(X3,X4,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X3,X4)))) = c_2Ebinary__ieee_2Efloat__to__real_2E1(X3,X4,c_2Ebinary__ieee_2Efloat__negate_2E1(X3,X4,c_2Ebinary__ieee_2Efloat__plus__min_2E1(X3,X4,c_2Ebool_2Ethe__value_2E0(tyop_2Epair_2Eprod(X3,X4))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eneg__ulp) ).
tff(f293,plain,
spl5_22,
inference(avatar_split_clause,[],[f151,f291]) ).
tff(f291,plain,
( spl5_22
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).
tff(f151,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ),
inference(cnf_transformation,[],[f99]) ).
tff(f99,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ~ p(c_2Emin_2E_3D_2E2(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f63]) ).
tff(f63,plain,
! [X0: $tType,X1: X0,X2: X0] :
( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
<=> ( X1 = X2 ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType,X8: X0,X9: X0] :
( p(c_2Emin_2E_3D_2E2(X0,X8,X9))
<=> ( X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D) ).
tff(f289,plain,
spl5_21,
inference(avatar_split_clause,[],[f126,f287]) ).
tff(f287,plain,
( spl5_21
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).
tff(f126,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f83]) ).
tff(f83,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ( ~ p(X1)
& p(X0) ) )
& ( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
inference(flattening,[],[f82]) ).
tff(f82,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ( ~ p(X1)
& p(X0) ) )
& ( p(X1)
| ~ p(X0)
| ~ p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1)) ) ),
inference(nnf_transformation,[],[f69]) ).
tff(f69,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
<=> ( p(X1)
| ~ p(X0) ) ),
inference(ennf_transformation,[],[f49]) ).
tff(f49,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
<=> ( p(X0)
=> p(X1) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X8: tyop_2Emin_2Ebool,X9: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X8,X9))
<=> ( p(X8)
=> p(X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
tff(f280,plain,
spl5_20,
inference(avatar_split_clause,[],[f123,f278]) ).
tff(f278,plain,
( spl5_20
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).
tff(f123,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f81]) ).
tff(f81,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ( ~ p(X1)
& ~ p(X0) ) )
& ( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
inference(flattening,[],[f80]) ).
tff(f80,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ( ~ p(X1)
& ~ p(X0) ) )
& ( p(X1)
| p(X0)
| ~ p(c_2Ebool_2E_5C_2F_2E2(X0,X1)) ) ),
inference(nnf_transformation,[],[f48]) ).
tff(f48,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
<=> ( p(X1)
| p(X0) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X8: tyop_2Emin_2Ebool,X9: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X8,X9))
<=> ( p(X9)
| p(X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
tff(f276,plain,
spl5_19,
inference(avatar_split_clause,[],[f122,f274]) ).
tff(f274,plain,
( spl5_19
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).
tff(f122,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f79]) ).
tff(f79,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) )
& ( ( p(X1)
& p(X0) )
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
inference(flattening,[],[f78]) ).
tff(f78,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
| ~ p(X1)
| ~ p(X0) )
& ( ( p(X1)
& p(X0) )
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
inference(nnf_transformation,[],[f47]) ).
tff(f47,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X0,X1))
<=> ( p(X1)
& p(X0) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X8: tyop_2Emin_2Ebool,X9: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(X8,X9))
<=> ( p(X9)
& p(X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
tff(f272,plain,
spl5_18,
inference(avatar_split_clause,[],[f112,f270]) ).
tff(f270,plain,
( spl5_18
<=> ! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).
tff(f112,plain,
! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ),
inference(cnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: $tType,X1: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X1) = X1 ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType,X11: X0] : ( app_2E2(X0,X0,combin_i_2E0(X0),X11) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ei__thm) ).
tff(f268,plain,
spl5_17,
inference(avatar_split_clause,[],[f109,f266]) ).
tff(f266,plain,
( spl5_17
<=> ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).
tff(f109,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ),
inference(cnf_transformation,[],[f74]) ).
tff(f74,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ~ p(X0)
| ~ p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) )
& ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) ) ),
inference(nnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0)) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X14: tyop_2Emin_2Ebool] :
( ~ p(X14)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
tff(f264,plain,
spl5_16,
inference(avatar_split_clause,[],[f108,f262]) ).
tff(f262,plain,
( spl5_16
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).
tff(f108,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0))
| p(X0) ),
inference(cnf_transformation,[],[f74]) ).
tff(f242,plain,
spl5_15,
inference(avatar_split_clause,[],[f117,f240]) ).
tff(f117,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f76]) ).
tff(f76,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X1)
| p(X0) ) ) ),
inference(nnf_transformation,[],[f68]) ).
tff(f68,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( p(X0)
<~> p(X1) ) ),
inference(ennf_transformation,[],[f45]) ).
tff(f45,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X0)
<=> p(X1) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X8: tyop_2Emin_2Ebool,X9: tyop_2Emin_2Ebool] :
( ( p(X8)
<=> p(X9) )
=> ( X8 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).
tff(f238,plain,
spl5_14,
inference(avatar_split_clause,[],[f116,f236]) ).
tff(f236,plain,
( spl5_14
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| p(X1)
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
tff(f116,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| p(X1)
| p(X0) ),
inference(cnf_transformation,[],[f76]) ).
tff(f233,plain,
( spl5_13
| ~ spl5_2
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f220,f192,f174,f231]) ).
tff(f231,plain,
( spl5_13
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
tff(f220,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( p(X0)
| ( c_2Ebool_2EF_2E0 = X0 ) )
| ~ spl5_2
| ~ spl5_6 ),
inference(superposition,[],[f176,f193]) ).
tff(f218,plain,
spl5_12,
inference(avatar_split_clause,[],[f128,f216]) ).
tff(f216,plain,
( spl5_12
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
tff(f128,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f83]) ).
tff(f214,plain,
spl5_11,
inference(avatar_split_clause,[],[f127,f212]) ).
tff(f212,plain,
( spl5_11
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
tff(f127,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(X0,X1))
| p(X0) ),
inference(cnf_transformation,[],[f83]) ).
tff(f210,plain,
spl5_10,
inference(avatar_split_clause,[],[f125,f208]) ).
tff(f208,plain,
( spl5_10
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
tff(f125,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X1) ),
inference(cnf_transformation,[],[f81]) ).
tff(f206,plain,
spl5_9,
inference(avatar_split_clause,[],[f124,f204]) ).
tff(f204,plain,
( spl5_9
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
tff(f124,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(X0,X1))
| ~ p(X0) ),
inference(cnf_transformation,[],[f81]) ).
tff(f202,plain,
spl5_8,
inference(avatar_split_clause,[],[f121,f200]) ).
tff(f200,plain,
( spl5_8
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
tff(f121,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f79]) ).
tff(f198,plain,
spl5_7,
inference(avatar_split_clause,[],[f120,f196]) ).
tff(f196,plain,
( spl5_7
<=> ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
tff(f120,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X0)
| ~ p(c_2Ebool_2E_2F_5C_2E2(X0,X1)) ),
inference(cnf_transformation,[],[f79]) ).
tff(f194,plain,
spl5_6,
inference(avatar_split_clause,[],[f107,f192]) ).
tff(f107,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X0 ) ),
inference(cnf_transformation,[],[f38]) ).
tff(f38,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X0 ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X10: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 = X10 )
| ( c_2Ebool_2ET_2E0 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).
tff(f189,plain,
spl5_5,
inference(avatar_split_clause,[],[f166,f187]) ).
tff(f187,plain,
( spl5_5
<=> ! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
tff(f166,plain,
! [X0: $tType,X2: X0] : p(c_2Emin_2E_3D_2E2(X0,X2,X2)),
inference(equality_resolution,[],[f152]) ).
tff(f152,plain,
! [X0: $tType,X2: X0,X1: X0] :
( p(c_2Emin_2E_3D_2E2(X0,X1,X2))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f99]) ).
tff(f185,plain,
spl5_4,
inference(avatar_split_clause,[],[f111,f183]) ).
tff(f183,plain,
( spl5_4
<=> ! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
tff(f111,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) ),
inference(cnf_transformation,[],[f75]) ).
tff(f75,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( p(c_2Ebool_2E_7E_2E1(X0))
| p(X0) )
& ( ~ p(X0)
| ~ p(c_2Ebool_2E_7E_2E1(X0)) ) ),
inference(nnf_transformation,[],[f40]) ).
tff(f40,plain,
! [X0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X0))
<=> ~ p(X0) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X8: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(X8))
<=> ~ p(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_7E) ).
tff(f181,plain,
spl5_3,
inference(avatar_split_clause,[],[f110,f179]) ).
tff(f179,plain,
( spl5_3
<=> ! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(c_2Ebool_2E_7E_2E1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
tff(f110,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ~ p(c_2Ebool_2E_7E_2E1(X0)) ),
inference(cnf_transformation,[],[f75]) ).
tff(f177,plain,
spl5_2,
inference(avatar_split_clause,[],[f104,f174]) ).
tff(f104,plain,
p(c_2Ebool_2ET_2E0),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
p(c_2Ebool_2ET_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).
tff(f172,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f103,f169]) ).
tff(f169,plain,
( spl5_1
<=> p(c_2Ebool_2EF_2E0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
tff(f103,plain,
~ p(c_2Ebool_2EF_2E0),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
~ p(c_2Ebool_2EF_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ITP018_3 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 19:13:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (19736)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (19742)WARNING: value z3 for option sas not known
% 0.15/0.39 % (19743)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (19740)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (19741)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (19744)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39 % (19742)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.39 % (19745)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39 % (19746)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 % (19746)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.40 % (19744)First to succeed.
% 0.22/0.40 % (19755)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.40 % (19744)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19736"
% 0.22/0.40 % (19757)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.40 % (19756)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.41 % (19744)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Theorem for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41 % (19744)------------------------------
% 0.22/0.41 % (19744)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.41 % (19744)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (19744)Memory used [KB]: 1027
% 0.22/0.41 % (19744)Time elapsed: 0.020 s
% 0.22/0.41 % (19744)Instructions burned: 28 (million)
% 0.22/0.41 % (19736)Success in time 0.038 s
%------------------------------------------------------------------------------