%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ITP018+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 : Thu Sep 24 08:45:34 AM UTC 2026
% Result : Theorem 181.80s 192.18s
% Output : Proof 185.37s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(bool_ne,axiom,
ne(bool),
file('ITP001+2.ax',bool_ne) ).
fof(ind_ne,axiom,
ne(ind),
file('ITP001+2.ax',ind_ne) ).
fof(arr_ne,axiom,
! [A] :
( ne(A)
=> ! [B] :
( ne(B)
=> ne(arr(A,B)) ) ),
file('ITP001+2.ax',arr_ne) ).
fof(ap_tp,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
file('ITP001+2.ax',ap_tp) ).
fof(boolext,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> Q = R ) ) ),
file('ITP001+2.ax',boolext) ).
fof(funcext,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [G] :
( mem(G,arr(A,B))
=> ( ! [X] :
( mem(X,A)
=> ap(F,X) = ap(G,X) )
=> F = G ) ) ),
file('ITP001+2.ax',funcext) ).
fof(kbeta,axiom,
! [A,Y,X] :
( mem(X,A)
=> ap(k(A,Y),X) = Y ),
file('ITP001+2.ax',kbeta) ).
fof(ibeta,axiom,
! [A,X] :
( mem(X,A)
=> ap(i(A),X) = X ),
file('ITP001+2.ax',ibeta) ).
fof(ne_ty_2Erealax_2Ereal,axiom,
ne(ty_2Erealax_2Ereal),
file('theBenchmark.p',ne_ty_2Erealax_2Ereal) ).
fof(mem_c_2Erealax_2Ereal__neg,axiom,
mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
file('theBenchmark.p',mem_c_2Erealax_2Ereal__neg) ).
fof(ne_ty_2Ebinary__ieee_2Efloat,axiom,
! [A0] :
( ne(A0)
=> ! [A1] :
( ne(A1)
=> ne(ty_2Ebinary__ieee_2Efloat(A0,A1)) ) ),
file('theBenchmark.p',ne_ty_2Ebinary__ieee_2Efloat) ).
fof(mem_c_2Ebinary__ieee_2Efloat__negate,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> mem(c_2Ebinary__ieee_2Efloat__negate(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))) ) ),
file('theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__negate) ).
fof(ne_ty_2Epair_2Eprod,axiom,
! [A0] :
( ne(A0)
=> ! [A1] :
( ne(A1)
=> ne(ty_2Epair_2Eprod(A0,A1)) ) ),
file('theBenchmark.p',ne_ty_2Epair_2Eprod) ).
fof(ne_ty_2Ebool_2Eitself,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Ebool_2Eitself(A0)) ),
file('theBenchmark.p',ne_ty_2Ebool_2Eitself) ).
fof(mem_c_2Ebinary__ieee_2Efloat__plus__min,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))) ) ),
file('theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__plus__min) ).
fof(mem_c_2Ebinary__ieee_2Efloat__to__real,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Erealax_2Ereal)) ) ),
file('theBenchmark.p',mem_c_2Ebinary__ieee_2Efloat__to__real) ).
fof(mem_c_2Ebool_2Ethe__value,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a)) ),
file('theBenchmark.p',mem_c_2Ebool_2Ethe__value) ).
fof(mem_c_2Ebinary__ieee_2Eulp,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> mem(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),ty_2Erealax_2Ereal)) ) ),
file('theBenchmark.p',mem_c_2Ebinary__ieee_2Eulp) ).
fof(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool),
file('theBenchmark.p',mem_c_2Ebool_2ET) ).
fof(ax_true_p,axiom,
p(c_2Ebool_2ET),
file('theBenchmark.p',ax_true_p) ).
fof(mem_c_2Emin_2E_3D,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ),
file('theBenchmark.p',mem_c_2Emin_2E_3D) ).
fof(ax_eq_p,axiom,
! [A] :
( ne(A)
=> ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ),
file('theBenchmark.p',ax_eq_p) ).
fof(mem_c_2Ebool_2E_21,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ),
file('theBenchmark.p',mem_c_2Ebool_2E_21) ).
fof(ax_all_p,axiom,
! [A] :
( ne(A)
=> ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ),
file('theBenchmark.p',ax_all_p) ).
fof(conj_thm_2Ebinary__ieee_2Efloat__to__real__negate,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b))
=> ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__negate(A_27a,A_27b),V0x)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0x)) ) ) ),
file('theBenchmark.p',conj_thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
fof(conj_thm_2Ebinary__ieee_2Eulp,axiom,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) ) ),
file('theBenchmark.p',conj_thm_2Ebinary__ieee_2Eulp) ).
fof(conj_thm_2Ebool_2ETRUTH,axiom,
$true,
file('theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
fof(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ( V0x = V0x
<=> $true ) ) ),
file('theBenchmark.p',conj_thm_2Ebool_2EREFL__CLAUSE) ).
fof(conj_thm_2Ebinary__ieee_2Eneg__ulp,conjecture,
! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__negate(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) ) ),
file('theBenchmark.p',conj_thm_2Ebinary__ieee_2Eneg__ulp) ).
fof(f_1_1,plain,
ne(bool),
inference(fof_nnf,[status(thm)],[bool_ne]) ).
fof(f_1_2,plain,
ne(bool),
inference(definitional_conversion,[status(esa)],[f_1_1]) ).
cnf(f_1_3,plain,
ne(bool),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
ne(ind),
inference(fof_nnf,[status(thm)],[ind_ne]) ).
fof(f_2_2,plain,
ne(ind),
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
ne(ind),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ! [B] :
( ne(arr(A,B))
| ~ ne(B) )
| ~ ne(A) ),
inference(fof_nnf,[status(thm)],[arr_ne]) ).
fof(f_3_2,plain,
! [U_1] :
( ! [U_0] :
( ne(arr(U_1,U_0))
| ~ ne(U_0) )
| ~ ne(U_1) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_0,U_1] :
( ne(arr(U_1,U_0))
| ~ ne(U_0)
| ~ ne(U_1) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( ne(arr(U_1,U_0))
| ~ ne(U_0)
| ~ ne(U_1) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B,F] :
( ! [X] :
( mem(ap(F,X),B)
| ~ mem(X,A) )
| ~ mem(F,arr(A,B)) ),
inference(fof_nnf,[status(thm)],[ap_tp]) ).
fof(f_4_2,plain,
! [U_5,U_4,U_3] :
( ! [U_2] :
( mem(ap(U_3,U_2),U_4)
| ~ mem(U_2,U_5) )
| ~ mem(U_3,arr(U_5,U_4)) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_2,U_3,U_4,U_5] :
( mem(ap(U_3,U_2),U_4)
| ~ mem(U_2,U_5)
| ~ mem(U_3,arr(U_5,U_4)) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( mem(ap(U_3,U_2),U_4)
| ~ mem(U_2,U_5)
| ~ mem(U_3,arr(U_5,U_4)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [Q] :
( ! [R] :
( Q = R
| ( ~ p(Q)
& p(R) )
| ( ~ p(R)
& p(Q) )
| ~ mem(R,bool) )
| ~ mem(Q,bool) ),
inference(fof_nnf,[status(thm)],[boolext]) ).
fof(f_5_2,plain,
! [U_7] :
( ! [U_6] :
( U_7 = U_6
| ( ~ p(U_7)
& p(U_6) )
| ( ~ p(U_6)
& p(U_7) )
| ~ mem(U_6,bool) )
| ~ mem(U_7,bool) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_7,U_6] :
( ~ p(U_7)
| ~ sP1(U_7,U_6) )
& ! [U_7,U_6] :
( p(U_6)
| ~ sP1(U_7,U_6) )
& ! [U_7,U_6] :
( ~ p(U_6)
| ~ sP0(U_7,U_6) )
& ! [U_7,U_6] :
( p(U_7)
| ~ sP0(U_7,U_6) )
& ! [U_7,U_6] :
( U_7 = U_6
| sP1(U_7,U_6)
| sP0(U_7,U_6)
| ~ mem(U_6,bool)
| ~ mem(U_7,bool) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_5_2]) ).
cnf(f_5_4,plain,
( U_7 = U_6
| sP1(U_7,U_6)
| sP0(U_7,U_6)
| ~ mem(U_6,bool)
| ~ mem(U_7,bool) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( p(U_7)
| ~ sP0(U_7,U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( ~ p(U_6)
| ~ sP0(U_7,U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_7,plain,
( p(U_6)
| ~ sP1(U_7,U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_8,plain,
( ~ p(U_7)
| ~ sP1(U_7,U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B,F] :
( ! [G] :
( F = G
| ? [X] :
( ap(F,X) != ap(G,X)
& mem(X,A) )
| ~ mem(G,arr(A,B)) )
| ~ mem(F,arr(A,B)) ),
inference(fof_nnf,[status(thm)],[funcext]) ).
fof(f_6_2,plain,
! [U_12,U_11,U_10] :
( ! [U_9] :
( U_10 = U_9
| ? [U_8] :
( ap(U_10,U_8) != ap(U_9,U_8)
& mem(U_8,U_12) )
| ~ mem(U_9,arr(U_12,U_11)) )
| ~ mem(U_10,arr(U_12,U_11)) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_12,U_11,U_10] :
( ! [U_9] :
( U_10 = U_9
| ( ap(U_10,sK1(U_12,U_11,U_10,U_9)) != ap(U_9,sK1(U_12,U_11,U_10,U_9))
& mem(sK1(U_12,U_11,U_10,U_9),U_12) )
| ~ mem(U_9,arr(U_12,U_11)) )
| ~ mem(U_10,arr(U_12,U_11)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1(U_12,U_11,U_10,U_9))],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_11,U_10,U_12,U_9] :
( ap(U_10,sK1(U_12,U_11,U_10,U_9)) != ap(U_9,sK1(U_12,U_11,U_10,U_9))
| ~ sP2(U_11,U_10,U_12,U_9) )
& ! [U_11,U_10,U_12,U_9] :
( mem(sK1(U_12,U_11,U_10,U_9),U_12)
| ~ sP2(U_11,U_10,U_12,U_9) )
& ! [U_11,U_10,U_12,U_9] :
( U_10 = U_9
| sP2(U_11,U_10,U_12,U_9)
| ~ mem(U_9,arr(U_12,U_11))
| ~ mem(U_10,arr(U_12,U_11)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_6_3]) ).
cnf(f_6_5,plain,
( U_10 = U_9
| sP2(U_11,U_10,U_12,U_9)
| ~ mem(U_9,arr(U_12,U_11))
| ~ mem(U_10,arr(U_12,U_11)) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( mem(sK1(U_12,U_11,U_10,U_9),U_12)
| ~ sP2(U_11,U_10,U_12,U_9) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( ap(U_10,sK1(U_12,U_11,U_10,U_9)) != ap(U_9,sK1(U_12,U_11,U_10,U_9))
| ~ sP2(U_11,U_10,U_12,U_9) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [A,Y,X] :
( ap(k(A,Y),X) = Y
| ~ mem(X,A) ),
inference(fof_nnf,[status(thm)],[kbeta]) ).
fof(f_7_2,plain,
! [U_15,U_14,U_13] :
( ap(k(U_15,U_14),U_13) = U_14
| ~ mem(U_13,U_15) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_15,U_13,U_14] :
( ap(k(U_15,U_14),U_13) = U_14
| ~ mem(U_13,U_15) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( ap(k(U_15,U_14),U_13) = U_14
| ~ mem(U_13,U_15) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,X] :
( ap(i(A),X) = X
| ~ mem(X,A) ),
inference(fof_nnf,[status(thm)],[ibeta]) ).
fof(f_8_2,plain,
! [U_17,U_16] :
( ap(i(U_17),U_16) = U_16
| ~ mem(U_16,U_17) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_16,U_17] :
( ap(i(U_17),U_16) = U_16
| ~ mem(U_16,U_17) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( ap(i(U_17),U_16) = U_16
| ~ mem(U_16,U_17) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
ne(ty_2Erealax_2Ereal),
inference(fof_nnf,[status(thm)],[ne_ty_2Erealax_2Ereal]) ).
fof(f_9_2,plain,
ne(ty_2Erealax_2Ereal),
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
ne(ty_2Erealax_2Ereal),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(fof_nnf,[status(thm)],[mem_c_2Erealax_2Ereal__neg]) ).
fof(f_10_2,plain,
mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A0] :
( ! [A1] :
( ne(ty_2Ebinary__ieee_2Efloat(A0,A1))
| ~ ne(A1) )
| ~ ne(A0) ),
inference(fof_nnf,[status(thm)],[ne_ty_2Ebinary__ieee_2Efloat]) ).
fof(f_11_2,plain,
! [U_19] :
( ! [U_18] :
( ne(ty_2Ebinary__ieee_2Efloat(U_19,U_18))
| ~ ne(U_18) )
| ~ ne(U_19) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_18,U_19] :
( ne(ty_2Ebinary__ieee_2Efloat(U_19,U_18))
| ~ ne(U_18)
| ~ ne(U_19) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( ne(ty_2Ebinary__ieee_2Efloat(U_19,U_18))
| ~ ne(U_18)
| ~ ne(U_19) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A_27t] :
( ! [A_27w] :
( mem(c_2Ebinary__ieee_2Efloat__negate(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))
| ~ ne(A_27w) )
| ~ ne(A_27t) ),
inference(fof_nnf,[status(thm)],[mem_c_2Ebinary__ieee_2Efloat__negate]) ).
fof(f_12_2,plain,
! [U_21] :
( ! [U_20] :
( mem(c_2Ebinary__ieee_2Efloat__negate(U_21,U_20),arr(ty_2Ebinary__ieee_2Efloat(U_21,U_20),ty_2Ebinary__ieee_2Efloat(U_21,U_20)))
| ~ ne(U_20) )
| ~ ne(U_21) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_21,U_20] :
( mem(c_2Ebinary__ieee_2Efloat__negate(U_21,U_20),arr(ty_2Ebinary__ieee_2Efloat(U_21,U_20),ty_2Ebinary__ieee_2Efloat(U_21,U_20)))
| ~ ne(U_20)
| ~ ne(U_21) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( mem(c_2Ebinary__ieee_2Efloat__negate(U_21,U_20),arr(ty_2Ebinary__ieee_2Efloat(U_21,U_20),ty_2Ebinary__ieee_2Efloat(U_21,U_20)))
| ~ ne(U_20)
| ~ ne(U_21) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A0] :
( ! [A1] :
( ne(ty_2Epair_2Eprod(A0,A1))
| ~ ne(A1) )
| ~ ne(A0) ),
inference(fof_nnf,[status(thm)],[ne_ty_2Epair_2Eprod]) ).
fof(f_13_2,plain,
! [U_23] :
( ! [U_22] :
( ne(ty_2Epair_2Eprod(U_23,U_22))
| ~ ne(U_22) )
| ~ ne(U_23) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_23,U_22] :
( ne(ty_2Epair_2Eprod(U_23,U_22))
| ~ ne(U_22)
| ~ ne(U_23) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( ne(ty_2Epair_2Eprod(U_23,U_22))
| ~ ne(U_22)
| ~ ne(U_23) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A0] :
( ne(ty_2Ebool_2Eitself(A0))
| ~ ne(A0) ),
inference(fof_nnf,[status(thm)],[ne_ty_2Ebool_2Eitself]) ).
fof(f_14_2,plain,
! [U_24] :
( ne(ty_2Ebool_2Eitself(U_24))
| ~ ne(U_24) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_24] :
( ne(ty_2Ebool_2Eitself(U_24))
| ~ ne(U_24) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( ne(ty_2Ebool_2Eitself(U_24))
| ~ ne(U_24) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A_27t] :
( ! [A_27w] :
( mem(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))
| ~ ne(A_27w) )
| ~ ne(A_27t) ),
inference(fof_nnf,[status(thm)],[mem_c_2Ebinary__ieee_2Efloat__plus__min]) ).
fof(f_15_2,plain,
! [U_26] :
( ! [U_25] :
( mem(c_2Ebinary__ieee_2Efloat__plus__min(U_26,U_25),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(U_26,U_25)),ty_2Ebinary__ieee_2Efloat(U_26,U_25)))
| ~ ne(U_25) )
| ~ ne(U_26) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_25,U_26] :
( mem(c_2Ebinary__ieee_2Efloat__plus__min(U_26,U_25),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(U_26,U_25)),ty_2Ebinary__ieee_2Efloat(U_26,U_25)))
| ~ ne(U_25)
| ~ ne(U_26) ),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
( mem(c_2Ebinary__ieee_2Efloat__plus__min(U_26,U_25),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(U_26,U_25)),ty_2Ebinary__ieee_2Efloat(U_26,U_25)))
| ~ ne(U_25)
| ~ ne(U_26) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A_27t] :
( ! [A_27w] :
( mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Erealax_2Ereal))
| ~ ne(A_27w) )
| ~ ne(A_27t) ),
inference(fof_nnf,[status(thm)],[mem_c_2Ebinary__ieee_2Efloat__to__real]) ).
fof(f_16_2,plain,
! [U_28] :
( ! [U_27] :
( mem(c_2Ebinary__ieee_2Efloat__to__real(U_28,U_27),arr(ty_2Ebinary__ieee_2Efloat(U_28,U_27),ty_2Erealax_2Ereal))
| ~ ne(U_27) )
| ~ ne(U_28) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_27,U_28] :
( mem(c_2Ebinary__ieee_2Efloat__to__real(U_28,U_27),arr(ty_2Ebinary__ieee_2Efloat(U_28,U_27),ty_2Erealax_2Ereal))
| ~ ne(U_27)
| ~ ne(U_28) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( mem(c_2Ebinary__ieee_2Efloat__to__real(U_28,U_27),arr(ty_2Ebinary__ieee_2Efloat(U_28,U_27),ty_2Erealax_2Ereal))
| ~ ne(U_27)
| ~ ne(U_28) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A_27a] :
( mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a))
| ~ ne(A_27a) ),
inference(fof_nnf,[status(thm)],[mem_c_2Ebool_2Ethe__value]) ).
fof(f_17_2,plain,
! [U_29] :
( mem(c_2Ebool_2Ethe__value(U_29),ty_2Ebool_2Eitself(U_29))
| ~ ne(U_29) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_29] :
( mem(c_2Ebool_2Ethe__value(U_29),ty_2Ebool_2Eitself(U_29))
| ~ ne(U_29) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( mem(c_2Ebool_2Ethe__value(U_29),ty_2Ebool_2Eitself(U_29))
| ~ ne(U_29) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A_27t] :
( ! [A_27w] :
( mem(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),ty_2Erealax_2Ereal))
| ~ ne(A_27w) )
| ~ ne(A_27t) ),
inference(fof_nnf,[status(thm)],[mem_c_2Ebinary__ieee_2Eulp]) ).
fof(f_18_2,plain,
! [U_31] :
( ! [U_30] :
( mem(c_2Ebinary__ieee_2Eulp(U_31,U_30),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(U_31,U_30)),ty_2Erealax_2Ereal))
| ~ ne(U_30) )
| ~ ne(U_31) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_30,U_31] :
( mem(c_2Ebinary__ieee_2Eulp(U_31,U_30),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(U_31,U_30)),ty_2Erealax_2Ereal))
| ~ ne(U_30)
| ~ ne(U_31) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( mem(c_2Ebinary__ieee_2Eulp(U_31,U_30),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(U_31,U_30)),ty_2Erealax_2Ereal))
| ~ ne(U_30)
| ~ ne(U_31) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
mem(c_2Ebool_2ET,bool),
inference(fof_nnf,[status(thm)],[mem_c_2Ebool_2ET]) ).
fof(f_19_2,plain,
mem(c_2Ebool_2ET,bool),
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,plain,
mem(c_2Ebool_2ET,bool),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
p(c_2Ebool_2ET),
inference(fof_nnf,[status(thm)],[ax_true_p]) ).
fof(f_20_2,plain,
p(c_2Ebool_2ET),
inference(definitional_conversion,[status(esa)],[f_20_1]) ).
cnf(f_20_3,plain,
p(c_2Ebool_2ET),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A_27a] :
( mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool)))
| ~ ne(A_27a) ),
inference(fof_nnf,[status(thm)],[mem_c_2Emin_2E_3D]) ).
fof(f_21_2,plain,
! [U_32] :
( mem(c_2Emin_2E_3D(U_32),arr(U_32,arr(U_32,bool)))
| ~ ne(U_32) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_32] :
( mem(c_2Emin_2E_3D(U_32),arr(U_32,arr(U_32,bool)))
| ~ ne(U_32) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( mem(c_2Emin_2E_3D(U_32),arr(U_32,arr(U_32,bool)))
| ~ ne(U_32) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A] :
( ! [X] :
( ! [Y] :
( ( ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
| X != Y )
& ( X = Y
| ~ p(ap(ap(c_2Emin_2E_3D(A),X),Y)) ) )
| ~ mem(Y,A) )
| ~ mem(X,A) )
| ~ ne(A) ),
inference(fof_nnf,[status(thm)],[ax_eq_p]) ).
fof(f_22_2,plain,
! [U_35] :
( ! [U_34] :
( ! [U_33] :
( ( ( p(ap(ap(c_2Emin_2E_3D(U_35),U_34),U_33))
| U_34 != U_33 )
& ( U_34 = U_33
| ~ p(ap(ap(c_2Emin_2E_3D(U_35),U_34),U_33)) ) )
| ~ mem(U_33,U_35) )
| ~ mem(U_34,U_35) )
| ~ ne(U_35) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_33,U_34,U_35] :
( p(ap(ap(c_2Emin_2E_3D(U_35),U_34),U_33))
| U_34 != U_33
| ~ sP3(U_33,U_34,U_35) )
& ! [U_33,U_34,U_35] :
( U_34 = U_33
| ~ p(ap(ap(c_2Emin_2E_3D(U_35),U_34),U_33))
| ~ sP3(U_33,U_34,U_35) )
& ! [U_33,U_34,U_35] :
( sP3(U_33,U_34,U_35)
| ~ mem(U_33,U_35)
| ~ mem(U_34,U_35)
| ~ ne(U_35) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_22_2]) ).
cnf(f_22_4,plain,
( sP3(U_33,U_34,U_35)
| ~ mem(U_33,U_35)
| ~ mem(U_34,U_35)
| ~ ne(U_35) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( U_34 = U_33
| ~ p(ap(ap(c_2Emin_2E_3D(U_35),U_34),U_33))
| ~ sP3(U_33,U_34,U_35) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
( p(ap(ap(c_2Emin_2E_3D(U_35),U_34),U_33))
| U_34 != U_33
| ~ sP3(U_33,U_34,U_35) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A_27a] :
( mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool))
| ~ ne(A_27a) ),
inference(fof_nnf,[status(thm)],[mem_c_2Ebool_2E_21]) ).
fof(f_23_2,plain,
! [U_36] :
( mem(c_2Ebool_2E_21(U_36),arr(arr(U_36,bool),bool))
| ~ ne(U_36) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_36] :
( mem(c_2Ebool_2E_21(U_36),arr(arr(U_36,bool),bool))
| ~ ne(U_36) ),
inference(definitional_conversion,[status(esa)],[f_23_2]) ).
cnf(f_23_4,plain,
( mem(c_2Ebool_2E_21(U_36),arr(arr(U_36,bool),bool))
| ~ ne(U_36) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
( ! [Q] :
( ( ( p(ap(c_2Ebool_2E_21(A),Q))
| ? [X] :
( ~ p(ap(Q,X))
& mem(X,A) ) )
& ( ! [X] :
( p(ap(Q,X))
| ~ mem(X,A) )
| ~ p(ap(c_2Ebool_2E_21(A),Q)) ) )
| ~ mem(Q,arr(A,bool)) )
| ~ ne(A) ),
inference(fof_nnf,[status(thm)],[ax_all_p]) ).
fof(f_24_2,plain,
! [U_40] :
( ! [U_39] :
( ( ( p(ap(c_2Ebool_2E_21(U_40),U_39))
| ? [U_38] :
( ~ p(ap(U_39,U_38))
& mem(U_38,U_40) ) )
& ( ! [U_37] :
( p(ap(U_39,U_37))
| ~ mem(U_37,U_40) )
| ~ p(ap(c_2Ebool_2E_21(U_40),U_39)) ) )
| ~ mem(U_39,arr(U_40,bool)) )
| ~ ne(U_40) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_40] :
( ! [U_39] :
( ( ( p(ap(c_2Ebool_2E_21(U_40),U_39))
| ( ~ p(ap(U_39,sK2(U_40,U_39)))
& mem(sK2(U_40,U_39),U_40) ) )
& ( ! [U_37] :
( p(ap(U_39,U_37))
| ~ mem(U_37,U_40) )
| ~ p(ap(c_2Ebool_2E_21(U_40),U_39)) ) )
| ~ mem(U_39,arr(U_40,bool)) )
| ~ ne(U_40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_38,sK2(U_40,U_39))],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_40,U_39] :
( ~ p(ap(U_39,sK2(U_40,U_39)))
| ~ sP4(U_40,U_39) )
& ! [U_40,U_39] :
( mem(sK2(U_40,U_39),U_40)
| ~ sP4(U_40,U_39) )
& ! [U_40,U_37,U_39] :
( p(ap(c_2Ebool_2E_21(U_40),U_39))
| sP4(U_40,U_39)
| ~ sP5(U_40,U_37,U_39) )
& ! [U_40,U_37,U_39] :
( p(ap(U_39,U_37))
| ~ mem(U_37,U_40)
| ~ p(ap(c_2Ebool_2E_21(U_40),U_39))
| ~ sP5(U_40,U_37,U_39) )
& ! [U_40,U_37,U_39] :
( sP5(U_40,U_37,U_39)
| ~ mem(U_39,arr(U_40,bool))
| ~ ne(U_40) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5])],[f_24_3]) ).
cnf(f_24_5,plain,
( sP5(U_40,U_37,U_39)
| ~ mem(U_39,arr(U_40,bool))
| ~ ne(U_40) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
( p(ap(U_39,U_37))
| ~ mem(U_37,U_40)
| ~ p(ap(c_2Ebool_2E_21(U_40),U_39))
| ~ sP5(U_40,U_37,U_39) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_7,plain,
( p(ap(c_2Ebool_2E_21(U_40),U_39))
| sP4(U_40,U_39)
| ~ sP5(U_40,U_37,U_39) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_8,plain,
( mem(sK2(U_40,U_39),U_40)
| ~ sP4(U_40,U_39) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_9,plain,
( ~ p(ap(U_39,sK2(U_40,U_39)))
| ~ sP4(U_40,U_39) ),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
! [A_27a] :
( ! [A_27b] :
( ! [V0x] :
( ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),ap(c_2Ebinary__ieee_2Efloat__negate(A_27a,A_27b),V0x)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0x))
| ~ mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) )
| ~ ne(A_27b) )
| ~ ne(A_27a) ),
inference(fof_nnf,[status(thm)],[conj_thm_2Ebinary__ieee_2Efloat__to__real__negate]) ).
fof(f_25_2,plain,
! [U_43] :
( ! [U_42] :
( ! [U_41] :
( ap(c_2Ebinary__ieee_2Efloat__to__real(U_43,U_42),ap(c_2Ebinary__ieee_2Efloat__negate(U_43,U_42),U_41)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(U_43,U_42),U_41))
| ~ mem(U_41,ty_2Ebinary__ieee_2Efloat(U_43,U_42)) )
| ~ ne(U_42) )
| ~ ne(U_43) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_42,U_43,U_41] :
( ap(c_2Ebinary__ieee_2Efloat__to__real(U_43,U_42),ap(c_2Ebinary__ieee_2Efloat__negate(U_43,U_42),U_41)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(U_43,U_42),U_41))
| ~ mem(U_41,ty_2Ebinary__ieee_2Efloat(U_43,U_42))
| ~ ne(U_42)
| ~ ne(U_43) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( ap(c_2Ebinary__ieee_2Efloat__to__real(U_43,U_42),ap(c_2Ebinary__ieee_2Efloat__negate(U_43,U_42),U_41)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(U_43,U_42),U_41))
| ~ mem(U_41,ty_2Ebinary__ieee_2Efloat(U_43,U_42))
| ~ ne(U_42)
| ~ ne(U_43) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A_27t] :
( ! [A_27w] :
( ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))
| ~ ne(A_27w) )
| ~ ne(A_27t) ),
inference(fof_nnf,[status(thm)],[conj_thm_2Ebinary__ieee_2Eulp]) ).
fof(f_26_2,plain,
! [U_45] :
( ! [U_44] :
( ap(c_2Ebinary__ieee_2Eulp(U_45,U_44),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(U_45,U_44))) = ap(c_2Ebinary__ieee_2Efloat__to__real(U_45,U_44),ap(c_2Ebinary__ieee_2Efloat__plus__min(U_45,U_44),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(U_45,U_44))))
| ~ ne(U_44) )
| ~ ne(U_45) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_44,U_45] :
( ap(c_2Ebinary__ieee_2Eulp(U_45,U_44),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(U_45,U_44))) = ap(c_2Ebinary__ieee_2Efloat__to__real(U_45,U_44),ap(c_2Ebinary__ieee_2Efloat__plus__min(U_45,U_44),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(U_45,U_44))))
| ~ ne(U_44)
| ~ ne(U_45) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( ap(c_2Ebinary__ieee_2Eulp(U_45,U_44),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(U_45,U_44))) = ap(c_2Ebinary__ieee_2Efloat__to__real(U_45,U_44),ap(c_2Ebinary__ieee_2Efloat__plus__min(U_45,U_44),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(U_45,U_44))))
| ~ ne(U_44)
| ~ ne(U_45) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
$true,
inference(fof_nnf,[status(thm)],[conj_thm_2Ebool_2ETRUTH]) ).
fof(f_27_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_27_1]) ).
cnf(f_27_3,plain,
$true,
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A_27a] :
( ! [V0x] :
( ( ( V0x = V0x
| ~ $true )
& ( $true
| V0x != V0x ) )
| ~ mem(V0x,A_27a) )
| ~ ne(A_27a) ),
inference(fof_nnf,[status(thm)],[conj_thm_2Ebool_2EREFL__CLAUSE]) ).
fof(f_28_2,plain,
! [U_47] :
( ! [U_46] :
( ( ( U_46 = U_46
| ~ $true )
& ( $true
| U_46 != U_46 ) )
| ~ mem(U_46,U_47) )
| ~ ne(U_47) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_46] :
( U_46 = U_46
| ~ $true
| ~ sP6(U_46) )
& ! [U_46] :
( $true
| U_46 != U_46
| ~ sP6(U_46) )
& ! [U_46,U_47] :
( sP6(U_46)
| ~ mem(U_46,U_47)
| ~ ne(U_47) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_28_2]) ).
cnf(f_28_4,plain,
( sP6(U_46)
| ~ mem(U_46,U_47)
| ~ ne(U_47) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( $true
| U_46 != U_46
| ~ sP6(U_46) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_6,plain,
( U_46 = U_46
| ~ $true
| ~ sP6(U_46) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,negated_conjecture,
~ ! [A_27t] :
( ne(A_27t)
=> ! [A_27w] :
( ne(A_27w)
=> ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) = ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__negate(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) ) ),
inference(negate,[status(cth)],[conj_thm_2Ebinary__ieee_2Eneg__ulp]) ).
fof(f_29_2,negated_conjecture,
? [A_27t] :
( ? [A_27w] :
( ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))) != ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__negate(A_27t,A_27w),ap(c_2Ebinary__ieee_2Efloat__plus__min(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w)))))
& ne(A_27w) )
& ne(A_27t) ),
inference(fof_nnf,[status(thm)],[f_29_1]) ).
fof(f_29_3,negated_conjecture,
? [U_49] :
( ? [U_48] :
( ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(U_49,U_48),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(U_49,U_48)))) != ap(c_2Ebinary__ieee_2Efloat__to__real(U_49,U_48),ap(c_2Ebinary__ieee_2Efloat__negate(U_49,U_48),ap(c_2Ebinary__ieee_2Efloat__plus__min(U_49,U_48),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(U_49,U_48)))))
& ne(U_48) )
& ne(U_49) ),
inference(variable_rename,[status(thm)],[f_29_2]) ).
fof(f_29_4,negated_conjecture,
( ? [U_48] :
( ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(sK3,U_48),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK3,U_48)))) != ap(c_2Ebinary__ieee_2Efloat__to__real(sK3,U_48),ap(c_2Ebinary__ieee_2Efloat__negate(sK3,U_48),ap(c_2Ebinary__ieee_2Efloat__plus__min(sK3,U_48),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK3,U_48)))))
& ne(U_48) )
& ne(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_49,sK3)],[f_29_3]) ).
fof(f_29_5,negated_conjecture,
( ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(sK3,sK4),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK3,sK4)))) != ap(c_2Ebinary__ieee_2Efloat__to__real(sK3,sK4),ap(c_2Ebinary__ieee_2Efloat__negate(sK3,sK4),ap(c_2Ebinary__ieee_2Efloat__plus__min(sK3,sK4),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK3,sK4)))))
& ne(sK4)
& ne(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_48,sK4)],[f_29_4]) ).
fof(f_29_6,negated_conjecture,
( ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(sK3,sK4),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK3,sK4)))) != ap(c_2Ebinary__ieee_2Efloat__to__real(sK3,sK4),ap(c_2Ebinary__ieee_2Efloat__negate(sK3,sK4),ap(c_2Ebinary__ieee_2Efloat__plus__min(sK3,sK4),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK3,sK4)))))
& ne(sK4)
& ne(sK3) ),
inference(definitional_conversion,[status(esa)],[f_29_5]) ).
cnf(f_29_7,negated_conjecture,
ne(sK3),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_8,negated_conjecture,
ne(sK4),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_9,negated_conjecture,
ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(sK3,sK4),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK3,sK4)))) != ap(c_2Ebinary__ieee_2Efloat__to__real(sK3,sK4),ap(c_2Ebinary__ieee_2Efloat__negate(sK3,sK4),ap(c_2Ebinary__ieee_2Efloat__plus__min(sK3,sK4),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(sK3,sK4))))),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_27_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_27_3]) ).
cnf(f_28_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_5]) ).
cnf(f_28_6_simplified,plain,
( U_46 = U_46
| ~ sP6(U_46) ),
inference(simplify_clause,[status(thm)],[f_28_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( arr(Eq_x_0,Eq_x_1) = arr(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( ap(Eq_x_0,Eq_x_1) = ap(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( k(Eq_x_0,Eq_x_1) = k(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( i(Eq_x_0) = i(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ty_2Ebinary__ieee_2Efloat(Eq_x_0,Eq_x_1) = ty_2Ebinary__ieee_2Efloat(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_2Ebinary__ieee_2Efloat__negate(Eq_x_0,Eq_x_1) = c_2Ebinary__ieee_2Efloat__negate(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( ty_2Epair_2Eprod(Eq_x_0,Eq_x_1) = ty_2Epair_2Eprod(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( ty_2Ebool_2Eitself(Eq_x_0) = ty_2Ebool_2Eitself(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( c_2Ebinary__ieee_2Efloat__plus__min(Eq_x_0,Eq_x_1) = c_2Ebinary__ieee_2Efloat__plus__min(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_2Ebinary__ieee_2Efloat__to__real(Eq_x_0,Eq_x_1) = c_2Ebinary__ieee_2Efloat__to__real(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( c_2Ebool_2Ethe__value(Eq_x_0) = c_2Ebool_2Ethe__value(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( c_2Ebinary__ieee_2Eulp(Eq_x_0,Eq_x_1) = c_2Ebinary__ieee_2Eulp(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( c_2Emin_2E_3D(Eq_x_0) = c_2Emin_2E_3D(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( c_2Ebool_2E_21(Eq_x_0) = c_2Ebool_2E_21(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( ne(Eq_y_0)
| ~ ne(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( mem(Eq_y_0,Eq_y_1)
| ~ mem(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( p(Eq_y_0)
| ~ p(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( sP4(Eq_y_0,Eq_y_1)
| ~ sP4(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP018+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.38 % Computer : n004.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Sat Sep 19 11:26:30 UTC 2026
% 0.11/10.38 % CPUTime :
% 181.80/192.18 % SZS status Theorem for theBenchmark
% 181.80/192.18 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------