%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP018+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Wed Oct 7 10:23:26 AM UTC 2026
% Result : Theorem 0.22s 0.33s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 36 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 471 ( 2 ~; 0 |; 0 &; 469 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 24 con; 0-2 aty)
% Number of variables : 35 ( 0 ^; 35 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_app_2E2,type,
app_2E2: $i > $i > $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__negate_2E0,type,
c_2Ebinary__ieee_2Efloat__negate_2E0: $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__negate_2E1,type,
c_2Ebinary__ieee_2Efloat__negate_2E1: $i > $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__min_2E0,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E0: $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__plus__min_2E1,type,
c_2Ebinary__ieee_2Efloat__plus__min_2E1: $i > $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__to__real_2E0,type,
c_2Ebinary__ieee_2Efloat__to__real_2E0: $i ).
thf(tp_c_2Ebinary__ieee_2Efloat__to__real_2E1,type,
c_2Ebinary__ieee_2Efloat__to__real_2E1: $i > $i ).
thf(tp_c_2Ebinary__ieee_2Eulp_2E0,type,
c_2Ebinary__ieee_2Eulp_2E0: $i ).
thf(tp_c_2Ebinary__ieee_2Eulp_2E1,type,
c_2Ebinary__ieee_2Eulp_2E1: $i > $i ).
thf(tp_c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: $i ).
thf(tp_c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: $i ).
thf(tp_c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: $i ).
thf(tp_c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: $i > $i ).
thf(tp_c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: $i ).
thf(tp_c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: $i > $i > $i ).
thf(tp_c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: $i ).
thf(tp_c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: $i > $i ).
thf(tp_c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: $i ).
thf(tp_c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: $i > $i > $i ).
thf(tp_c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: $i ).
thf(tp_c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: $i > $i ).
thf(tp_c_2Ebool_2Ethe__value_2E0,type,
c_2Ebool_2Ethe__value_2E0: $i ).
thf(tp_c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: $i ).
thf(tp_c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: $i > $i > $i ).
thf(tp_c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: $i ).
thf(tp_c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: $i > $i > $i ).
thf(tp_c_2Erealax_2Ereal__neg_2E0,type,
c_2Erealax_2Ereal__neg_2E0: $i ).
thf(tp_c_2Erealax_2Ereal__neg_2E1,type,
c_2Erealax_2Ereal__neg_2E1: $i > $i ).
thf(tp_combin_i_2E0,type,
combin_i_2E0: $i ).
thf(tp_combin_k_2E0,type,
combin_k_2E0: $i ).
thf(tp_combin_s_2E0,type,
combin_s_2E0: $i ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_s,type,
s: $i > $i > $i ).
thf(tp_sK1_A_27t,type,
sK1_A_27t: $i ).
thf(tp_sK2_SY7,type,
sK2_SY7: $i ).
thf(tp_tyop_2Ebinary__ieee_2Efloat,type,
tyop_2Ebinary__ieee_2Efloat: $i > $i > $i ).
thf(tp_tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $i > $i ).
thf(tp_tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $i ).
thf(tp_tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $i > $i > $i ).
thf(tp_tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $i > $i > $i ).
thf(tp_tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: $i ).
thf(3,axiom,
! [A_27t: $i,A_27w: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eulp) ).
thf(4,axiom,
! [A_27a: $i,A_27b: $i,V0x_2E0: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
thf(34,conjecture,
! [A_27t: $i,A_27w: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eneg__ulp) ).
thf(35,negated_conjecture,
( ( ! [A_27t: $i,A_27w: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[34]) ).
thf(36,plain,
( ( ! [A_27t: $i,A_27w: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [A_27t: $i,A_27w: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [A_27a: $i,A_27b: $i,V0x_2E0: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(39,plain,
( ( ! [SY7: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1_A_27t @ SY7 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1_A_27t @ SY7 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1_A_27t @ SY7 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1_A_27t @ SY7 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(40,plain,
( ( ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1_A_27t @ sK2_SY7 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1_A_27t @ sK2_SY7 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1_A_27t @ sK2_SY7 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1_A_27t @ sK2_SY7 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(41,plain,
( ( ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1_A_27t @ sK2_SY7 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
!= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1_A_27t @ sK2_SY7 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1_A_27t @ sK2_SY7 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1_A_27t @ sK2_SY7 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[40]) ).
thf(42,plain,
( ( ! [A_27a: $i,A_27b: $i,V0x_2E0: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(43,plain,
( ( ! [A_27t: $i,A_27w: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A_27t @ A_27w ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A_27t @ A_27w ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(44,plain,
( ( ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1_A_27t @ sK2_SY7 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
!= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1_A_27t @ sK2_SY7 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1_A_27t @ sK2_SY7 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1_A_27t @ sK2_SY7 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(45,plain,
! [SV1: $i] :
( ( ! [SY8: $i,SY9: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV1 @ SY8 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV1 @ SY8 ) @ SY9 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV1 @ SY8 ) @ SY9 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV2: $i] :
( ( ! [SY10: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ SV2 @ SY10 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV2 @ SY10 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ SV2 @ SY10 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
( ( ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1_A_27t @ sK2_SY7 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1_A_27t @ sK2_SY7 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sK1_A_27t @ sK2_SY7 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sK1_A_27t @ sK2_SY7 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV3: $i,SV1: $i] :
( ( ! [SY11: $i] :
( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV1 @ SV3 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV1 @ SV3 ) @ SY11 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV1 @ SV3 ) @ SY11 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV4: $i,SV2: $i] :
( ( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ SV2 @ SV4 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV2 @ SV4 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ SV2 @ SV4 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(50,plain,
! [SV5: $i,SV3: $i,SV1: $i] :
( ( ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV1 @ SV3 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV1 @ SV3 ) @ SV5 ) ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( c_2Erealax_2Ereal__neg_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ SV1 @ SV3 ) @ SV5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,50,49]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP018+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.22 % Computer : n017.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Oct 6 11:05:30 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.33
% 0.22/0.33 No.of.Axioms: 2
% 0.22/0.33
% 0.22/0.33 Length.of.Defs: 0
% 0.22/0.33
% 0.22/0.33 Contains.Choice.Funs: false
% 0.22/0.33 .
% 0.22/0.33
% 0.22/0.33 ********************************
% 0.22/0.33 * All subproblems solved! *
% 0.22/0.33 ********************************
% 0.22/0.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:51,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.22/0.33
% 0.22/0.33 %**** Beginning of derivation protocol ****
% 0.22/0.33 % SZS output start CNFRefutation
% See solution above
% 0.22/0.33
% 0.22/0.33 %**** End of derivation protocol ****
% 0.22/0.33 %**** no. of clauses in derivation: 21 ****
% 0.22/0.33 %**** clause counter: 51 ****
% 0.22/0.33
% 0.22/0.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:51,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------