%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP018_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 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 : Sun Sep 27 07:35:42 AM UTC 2026
% Result : Theorem 8.83s 3.15s
% Output : Refutation 8.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 240 ( 57 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 1210 ( 23 ~; 6 |; 0 &;1181 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 4 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 95 ( 0 ^; 95 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Erealax_2Ereal_type,type,
tyop_2Erealax_2Ereal: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(app_2E2_decl,type,
app_2E2:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Emin_2Efun ) ) > TB > TA ) ).
thf(c_2Ebinary__ieee_2Efloat__negate_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__negate_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__plus__min_2E0_decl,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E0:
!>[TA: $tType,TB: $tType] : ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) @ ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebinary__ieee_2Efloat__plus__min_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) ) ).
thf(c_2Ebinary__ieee_2Efloat__to__real_2E0_decl,type,
c_2Ebinary__ieee_2Efloat__to__real_2E0:
!>[TA: $tType,TB: $tType] : ( tyop_2Erealax_2Ereal @ ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebinary__ieee_2Efloat__to__real_2E1_decl,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) ) > tyop_2Erealax_2Ereal ) ).
thf(c_2Erealax_2Ereal__neg_2E0_decl,type,
c_2Erealax_2Ereal__neg_2E0: tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Emin_2Efun ) ).
thf(c_2Erealax_2Ereal__neg_2E1_decl,type,
c_2Erealax_2Ereal__neg_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
thf(c_2Ebool_2Ethe__value_2E0_decl,type,
c_2Ebool_2Ethe__value_2E0:
!>[TA: $tType] : ( TA @ tyop_2Ebool_2Eitself ) ).
thf(c_2Ebinary__ieee_2Eulp_2E0_decl,type,
c_2Ebinary__ieee_2Eulp_2E0:
!>[TA: $tType,TB: $tType] : ( tyop_2Erealax_2Ereal @ ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) ) ).
thf(c_2Ebinary__ieee_2Eulp_2E1_decl,type,
c_2Ebinary__ieee_2Eulp_2E1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself ) > tyop_2Erealax_2Ereal ) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) @ ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
thf(106,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) @ ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(107,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself] :
( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
= ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[106]) ).
thf(108,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself] :
( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
= ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eulp) ).
thf(109,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(110,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(111,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) )
= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
thf(103,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) )
= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(104,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) )
= ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(105,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) )
= ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(136,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(rewrite,[status(thm)],[111,105]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
thf(115,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(116,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself] :
( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[115]) ).
thf(117,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself] :
( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E1 ) ) )
= ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(163,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) )
= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(rewrite,[status(thm)],[136,117]) ).
thf(170,plain,
! [TC: $tType,TD: $tType,A: TD @ ( TC @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself] :
( ( ( A @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) ) )
| ( ( A @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TD @ ( TC @ tyop_2Ebinary__ieee_2Efloat ) @ ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TD @ ( TC @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[108,163]) ).
thf(171,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TD @ ( TC @ tyop_2Ebinary__ieee_2Efloat ) @ ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TD @ ( TC @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 ))]]) ).
thf(177,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) )
= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
thf(100,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) )
= ( A @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(101,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) )
= ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 ) ),
inference(cnf,[status(esa)],[100]) ).
thf(102,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
= ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(25,axiom,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Erealax_2Ereal__neg_2E1 )
= ( A @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Erealax_2Ereal__neg_2E1) ).
thf(124,plain,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Erealax_2Ereal__neg_2E1 )
= ( A @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(125,plain,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Erealax_2Ereal__neg_2E1 )
= ( A @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) ) ),
inference(cnf,[status(esa)],[124]) ).
thf(126,plain,
! [A: tyop_2Erealax_2Ereal] :
( ( A @ c_2Erealax_2Ereal__neg_2E1 )
= ( A @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) ) ),
inference(lifteq,[status(thm)],[125]) ).
thf(340,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat )] :
( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) )
= ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(rewrite,[status(thm)],[102,105,126]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eneg__ulp) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(26,plain,
~ ! [TA: $tType,TB: $tType] :
( ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Eulp_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
= ( TA @ ( TB @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TA @ ( TB @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(27,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(127,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) @ c_2Erealax_2Ereal__neg_2E1 )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) ) ),
inference(rewrite,[status(thm)],[28,111]) ).
thf(135,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) @ c_2Erealax_2Ereal__neg_2E1 )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(rewrite,[status(thm)],[127,105]) ).
thf(173,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) )
| ( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ c_2Erealax_2Ereal__neg_2E1 )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[163,135]) ).
thf(174,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ c_2Erealax_2Ereal__neg_2E1 )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[173:[bind_type(TA,$thf( skt1 )),bind_type(TB,$thf( skt2 ))]]) ).
thf(258,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(rewrite,[status(thm)],[174,126]) ).
thf(369,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat )] :
( ( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__negate_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) )
| ( ( A @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[340,258]) ).
thf(370,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E1 ) ) @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[369:[bind(A,$thf( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) )),bind_type(TA,$thf( skt1 )),bind_type(TB,$thf( skt2 ))]]) ).
thf(381,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( c_2Erealax_2Ereal__neg_2E0 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ app_2E2 ) ) ) ) ),
inference(rewrite,[status(thm)],[370,105]) ).
thf(382,plain,
( ( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) )
| ( c_2Erealax_2Ereal__neg_2E0 != c_2Erealax_2Ereal__neg_2E0 ) ),
inference(simp,[status(thm)],[381]) ).
thf(442,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(simp,[status(thm)],[382]) ).
thf(208,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) )
!= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) )
| ( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TD @ ( TC @ tyop_2Ebinary__ieee_2Efloat ) @ ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TD @ ( TC @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[163,177]) ).
thf(209,plain,
! [TC: $tType,TD: $tType] :
( ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TD @ ( TC @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
= ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TD @ ( TC @ tyop_2Ebinary__ieee_2Efloat ) @ ( TD @ ( TC @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( TD @ ( TC @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TD @ ( TC @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[208:[bind_type(TA,$thf( TC )),bind_type(TB,$thf( TD ))]]) ).
thf(214,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E1 ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
= ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(444,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(rewrite,[status(thm)],[442,214]) ).
thf(452,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( TB @ ( TA @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Ebinary__ieee_2Efloat ) @ app_2E2 ) ) ) ) )
| ( ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( TB @ ( TA @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( TB @ ( TA @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[177,444]) ).
thf(453,plain,
( ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) )
!= ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ c_2Ebool_2Ethe__value_2E0 @ ( skt2 @ ( skt1 @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( tyop_2Erealax_2Ereal @ ( skt2 @ ( skt1 @ tyop_2Epair_2Eprod ) @ tyop_2Ebool_2Eitself @ app_2E2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[452:[bind_type(TA,$thf( skt1 )),bind_type(TB,$thf( skt2 ))]]) ).
thf(462,plain,
$false,
inference(simp,[status(thm)],[453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP018_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.07/0.32 % Computer : n012.cluster.edu
% 0.07/0.32 % Model : x86_64 x86_64
% 0.07/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.32 % Memory : 8046.5625MB
% 0.07/0.32 % OS : Linux 6.8.0-71-generic
% 0.07/0.32 % CPULimit : 300
% 0.07/0.32 % WCLimit : 300
% 0.07/0.32 % DateTime : Fri Sep 25 17:27:05 UTC 2026
% 0.07/0.32 % CPUTime :
% 0.07/0.32 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.40/0.61 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.73 % [INFO] Parsing done (120ms).
% 0.66/0.74 % [INFO] Running in sequential loop mode.
% 1.16/0.94 % [INFO] eprover registered as external prover.
% 1.16/0.94 % [INFO] Scanning for conjecture ...
% 1.41/1.01 % [INFO] Found a conjecture (or negated_conjecture) and 33 axioms. Running axiom selection ...
% 1.41/1.06 % [INFO] Axiom selection finished. Selected 23 axioms (removed 10 axioms).
% 1.41/1.10 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.41/1.11 % [INFO] Type checking passed.
% 1.41/1.11 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.83/3.14 % [INFO] Killing All external provers ...
% 8.83/3.14 % Time passed: 2743ms (effective reasoning time: 2394ms)
% 8.83/3.14 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.83/3.14 % Axioms used in derivation (6): arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq1_2Ec_2Erealax_2Ereal__neg_2E1, thm_2Ebinary__ieee_2Efloat__to__real__negate, thm_2Ebinary__ieee_2Eulp
% 8.83/3.14 % No. of inferences in proof: 52
% 8.83/3.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2743 ms resp. 2394 ms w/o parsing
% 8.83/3.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.83/3.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------