%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP018^2 : 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 : n005.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 Sep 30 08:06:23 AM UTC 2026
% Result : Theorem 5.25s 2.60s
% Output : Refutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 28
% Syntax : Number of formulae : 60 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 32 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 501 ( 2 ~; 0 |; 0 &; 466 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 6 con; 0-2 aty)
% Number of variables : 98 ( 0 ^; 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(del_type,type,
del: $tType ).
thf(tp__ty_2Erealax_2Ereal_type,type,
tp__ty_2Erealax_2Ereal: $tType ).
thf(bool_decl,type,
bool: del ).
thf(arr_decl,type,
arr: del > del > del ).
thf(mem_decl,type,
mem: $i > del > $o ).
thf(ap_decl,type,
ap: $i > $i > $i ).
thf(lam_decl,type,
lam: del > ( $i > $i ) > $i ).
thf(p_decl,type,
p: $i > $o ).
thf(inj__o_decl,type,
inj__o: $o > $i ).
thf(ty_2Erealax_2Ereal_decl,type,
ty_2Erealax_2Ereal: del ).
thf(inj__ty_2Erealax_2Ereal_decl,type,
inj__ty_2Erealax_2Ereal: tp__ty_2Erealax_2Ereal > $i ).
thf(surj__ty_2Erealax_2Ereal_decl,type,
surj__ty_2Erealax_2Ereal: $i > tp__ty_2Erealax_2Ereal ).
thf(c_2Erealax_2Ereal__neg_decl,type,
c_2Erealax_2Ereal__neg: $i ).
thf(fo__c_2Erealax_2Ereal__neg_decl,type,
fo__c_2Erealax_2Ereal__neg: tp__ty_2Erealax_2Ereal > tp__ty_2Erealax_2Ereal ).
thf(ty_2Ebinary__ieee_2Efloat_decl,type,
ty_2Ebinary__ieee_2Efloat: del > del > del ).
thf(c_2Ebinary__ieee_2Efloat__negate_decl,type,
c_2Ebinary__ieee_2Efloat__negate: del > del > $i ).
thf(ty_2Epair_2Eprod_decl,type,
ty_2Epair_2Eprod: del > del > del ).
thf(ty_2Ebool_2Eitself_decl,type,
ty_2Ebool_2Eitself: del > del ).
thf(c_2Ebinary__ieee_2Efloat__plus__min_decl,type,
c_2Ebinary__ieee_2Efloat__plus__min: del > del > $i ).
thf(c_2Ebinary__ieee_2Efloat__to__real_decl,type,
c_2Ebinary__ieee_2Efloat__to__real: del > del > $i ).
thf(c_2Ebool_2Ethe__value_decl,type,
c_2Ebool_2Ethe__value: del > $i ).
thf(c_2Ebinary__ieee_2Eulp_decl,type,
c_2Ebinary__ieee_2Eulp: del > del > $i ).
thf(c_2Ebool_2ET_decl,type,
c_2Ebool_2ET: $i ).
thf(c_2Emin_2E_3D_decl,type,
c_2Emin_2E_3D: del > $i ).
thf(c_2Ebool_2E_21_decl,type,
c_2Ebool_2E_21: del > $i ).
thf(13,axiom,
! [A: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ A ) @ ty_2Erealax_2Ereal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_ty_2Erealax_2Ereal) ).
thf(56,plain,
! [A: tp__ty_2Erealax_2Ereal] : ( mem @ ( inj__ty_2Erealax_2Ereal @ A ) @ ty_2Erealax_2Ereal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
! [A: del,B: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eulp) ).
thf(84,plain,
! [A: del,B: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_all_p) ).
thf(89,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(15,axiom,
! [A: tp__ty_2Erealax_2Ereal] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Erealax_2Ereal__neg @ A ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Erealax_2Ereal__neg) ).
thf(60,plain,
! [A: tp__ty_2Erealax_2Ereal] :
( ( inj__ty_2Erealax_2Ereal @ ( fo__c_2Erealax_2Ereal__neg @ A ) )
= ( ap @ c_2Erealax_2Ereal__neg @ ( inj__ty_2Erealax_2Ereal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(33,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_eq_p) ).
thf(77,plain,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
! [A: $o] :
( ( p @ ( inj__o @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_o) ).
thf(41,plain,
! [A: $o] :
( ( p @ ( inj__o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(34,plain,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,axiom,
! [A: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_ty_2Erealax_2Ereal) ).
thf(98,plain,
! [A: tp__ty_2Erealax_2Ereal] :
( ( surj__ty_2Erealax_2Ereal @ ( inj__ty_2Erealax_2Ereal @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(21,axiom,
! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A @ B ) ) @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__plus__min) ).
thf(80,plain,
! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A @ B ) ) @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
thf(50,plain,
p @ c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(42,plain,
( ( p @ ( inj__o @ $true ) )
= $true ),
inference(instance,[status(thm)],[41]) ).
thf(43,plain,
p @ ( inj__o @ $true ),
inference(simp,[status(thm)],[42]) ).
thf(24,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( ap @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
thf(87,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( ap @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ( ( B = B )
= $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EREFL__CLAUSE) ).
thf(40,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [A: del,B: $i > $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( lam @ A @ B ) @ C )
= ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta) ).
thf(68,plain,
! [A: del,B: $i > $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( lam @ A @ B ) @ C )
= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_o) ).
thf(46,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,axiom,
! [A: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A ) @ ( ty_2Ebool_2Eitself @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2Ethe__value) ).
thf(93,plain,
! [A: del] : ( mem @ ( c_2Ebool_2Ethe__value @ A ) @ ( ty_2Ebool_2Eitself @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(26,axiom,
mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Erealax_2Ereal__neg) ).
thf(92,plain,
mem @ c_2Erealax_2Ereal__neg @ ( arr @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(17,axiom,
! [A: $i] :
( ( mem @ A @ ty_2Erealax_2Ereal )
=> ( A
= ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_ty_2Erealax_2Ereal) ).
thf(65,plain,
! [A: $i] :
( ( mem @ A @ ty_2Erealax_2Ereal )
=> ( A
= ( inj__ty_2Erealax_2Ereal @ ( surj__ty_2Erealax_2Ereal @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ( ! [E: $i] :
( ( mem @ E @ A )
=> ( ( ap @ C @ E )
= ( ap @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(71,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ( ! [E: $i] :
( ( mem @ E @ A )
=> ( ( ap @ C @ E )
= ( ap @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
thf(54,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(49,plain,
mem @ c_2Ebool_2ET @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A @ B ) ) @ ty_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Eulp) ).
thf(63,plain,
! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( arr @ ( ty_2Ebool_2Eitself @ ( ty_2Epair_2Eprod @ A @ B ) ) @ ty_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) )
=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ C ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
thf(95,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) )
=> ( ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ C ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(14,axiom,
! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) @ ty_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__to__real) ).
thf(58,plain,
! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) @ ty_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__negate) ).
thf(82,plain,
! [A: del,B: del] : ( mem @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ ( arr @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) @ ( ty_2Ebinary__ieee_2Efloat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
! [A: del,B: del,C: $i > $i] :
( ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( C @ D ) @ B ) )
=> ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam_tp) ).
thf(36,plain,
! [A: del,B: del,C: $i > $i] :
( ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( C @ D ) @ B ) )
=> ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: del,B: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebinary__ieee_2Eneg__ulp) ).
thf(2,negated_conjecture,
~ ! [A: del,B: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(30,plain,
~ ! [A: del,B: del] :
( ( surj__ty_2Erealax_2Ereal @ ( ap @ c_2Erealax_2Ereal__neg @ ( ap @ ( c_2Ebinary__ieee_2Eulp @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) )
= ( surj__ty_2Erealax_2Ereal @ ( ap @ ( c_2Ebinary__ieee_2Efloat__to__real @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__negate @ A @ B ) @ ( ap @ ( c_2Ebinary__ieee_2Efloat__plus__min @ A @ B ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Epair_2Eprod @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o) ).
thf(51,plain,
! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(110,plain,
$false,
inference(e,[status(thm)],[56,84,89,60,33,77,41,34,98,80,50,43,87,40,68,46,93,92,65,71,54,49,63,95,58,82,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP018^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % 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
% 0.10/0.21 % Computer : n005.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:32:51 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.02 % [INFO] Parsing done (227ms).
% 1.57/1.04 % [INFO] Running in sequential loop mode.
% 2.21/1.42 % [INFO] eprover registered as external prover.
% 2.21/1.43 % [INFO] Scanning for conjecture ...
% 2.38/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 27 axioms. Running axiom selection ...
% 2.57/1.62 % [INFO] Axiom selection finished. Selected 27 axioms (removed 0 axioms).
% 2.57/1.67 % [INFO] Problem is higher-order (TPTP THF).
% 2.57/1.68 % [INFO] Type checking passed.
% 2.57/1.69 % [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 ...
% 4.81/2.59 % External prover 'e' found a proof!
% 4.81/2.60 % [INFO] Killing All external provers ...
% 4.81/2.60 % Time passed: 2242ms (effective reasoning time: 1554ms)
% 4.81/2.60 % 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)>
% 5.25/2.60 % Axioms used in derivation (27): stp_inj_surj_o, ax_eq_p, mem_c_2Ebool_2Ethe__value, mem_c_2Ebool_2E_21, conj_thm_2Ebinary__ieee_2Efloat__to__real__negate, ax_true_p, mem_c_2Emin_2E_3D, stp_inj_mem_ty_2Erealax_2Ereal, conj_thm_2Ebool_2ETRUTH, mem_c_2Ebinary__ieee_2Efloat__to__real, stp_iso_mem_ty_2Erealax_2Ereal, ap_tp, lam_tp, conj_thm_2Ebool_2EREFL__CLAUSE, mem_c_2Ebool_2ET, stp_inj_mem_o, conj_thm_2Ebinary__ieee_2Eulp, funcext, mem_c_2Ebinary__ieee_2Eulp, mem_c_2Ebinary__ieee_2Efloat__plus__min, ax_all_p, mem_c_2Erealax_2Ereal__neg, stp_inj_surj_ty_2Erealax_2Ereal, beta, mem_c_2Ebinary__ieee_2Efloat__negate, stp_iso_mem_o, stp_eq_fo_c_2Erealax_2Ereal__neg
% 5.25/2.60 % No. of inferences in proof: 60
% 5.25/2.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2242 ms resp. 1554 ms w/o parsing
% 5.25/2.63 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.25/2.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------