%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ITP018+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 07:41:31 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))),
file('theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))),
file('theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0] : 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)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__plus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))),
file('theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
fof(arityeq1_2Ec_2Erealax_2Ereal__neg_2E1,axiom,
! [X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),
file('theBenchmark.p',arityeq1_2Ec_2Erealax_2Ereal__neg_2E1) ).
fof(arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,
! [A_27t,A_27w,X0_2E0] : s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))),
file('theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).
fof(thm_2Ebinary__ieee_2Efloat__to__real__negate,axiom,
! [A_27a,A_27b,V0x_2E0] : 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('theBenchmark.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).
fof(thm_2Ebinary__ieee_2Eulp,axiom,
! [A_27t,A_27w] : 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('theBenchmark.p',thm_2Ebinary__ieee_2Eulp) ).
fof(thm_2Ebinary__ieee_2Eneg__ulp,conjecture,
! [A_27t,A_27w] : 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('theBenchmark.p',thm_2Ebinary__ieee_2Eneg__ulp) ).
fof(thm_2Ebinary__ieee_2Eneg__ulp_neg,negated_conjecture,
~ ! [A_27t,A_27w] : 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))))))),
inference(assume_negation,[status(cth)],[thm_2Ebinary__ieee_2Eneg__ulp]) ).
cnf(c_74,plain,
s(tyop_2Ebinary__ieee_2Efloat(A,B),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),C))) = s(tyop_2Ebinary__ieee_2Efloat(A,B),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Ebinary__ieee_2Efloat(A,B)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),C))),
inference(clausify,[status(thm)],[arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b]) ).
cnf(c_75,plain,
s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),C))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),C))),
inference(clausify,[status(thm)],[arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b]) ).
cnf(c_77,plain,
s(tyop_2Ebinary__ieee_2Efloat(A,B),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),C))) = s(tyop_2Ebinary__ieee_2Efloat(A,B),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),tyop_2Ebinary__ieee_2Efloat(A,B)),c_2Ebinary__ieee_2Efloat__plus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),C))),
inference(clausify,[status(thm)],[arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w]) ).
cnf(c_79,plain,
s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,A))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,A))),
inference(clausify,[status(thm)],[arityeq1_2Ec_2Erealax_2Ereal__neg_2E1]) ).
cnf(c_80,plain,
s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),C))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),C))),
inference(clausify,[status(thm)],[arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w]) ).
cnf(c_81,plain,
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,B),C))))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))),
inference(clausify,[status(thm)],[thm_2Ebinary__ieee_2Efloat__to__real__negate]) ).
cnf(c_88,plain,
s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))),
inference(paramod,[status(thm)],[c_75,c_81]) ).
cnf(c_89,plain,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))),
inference(paramod,[status(thm)],[c_79,c_88]) ).
cnf(c_90,plain,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Ebinary__ieee_2Efloat(A,B)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))),
inference(paramod,[status(thm)],[c_74,c_89]) ).
cnf(c_91,plain,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Ebinary__ieee_2Efloat(A,B)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))),
inference(paramod,[status(thm)],[c_75,c_90]) ).
cnf(c_82,plain,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Ebinary__ieee_2Efloat(A,B)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),C))))),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_83,plain,
s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Eulp_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),c_2Ebool_2Ethe__value_2E0))))),
inference(clausify,[status(thm)],[thm_2Ebinary__ieee_2Eulp]) ).
cnf(c_92,plain,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),c_2Ebool_2Ethe__value_2E0))))),
inference(paramod,[status(thm)],[c_80,c_83]) ).
cnf(c_93,plain,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A,B),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),tyop_2Ebinary__ieee_2Efloat(A,B)),c_2Ebinary__ieee_2Efloat__plus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),c_2Ebool_2Ethe__value_2E0))))),
inference(paramod,[status(thm)],[c_77,c_92]) ).
cnf(c_94,plain,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),c_2Ebool_2Ethe__value_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),tyop_2Ebinary__ieee_2Efloat(A,B)),c_2Ebinary__ieee_2Efloat__plus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),c_2Ebool_2Ethe__value_2E0))))),
inference(paramod,[status(thm)],[c_75,c_93]) ).
cnf(c_84,plain,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A,B),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A,B),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),tyop_2Ebinary__ieee_2Efloat(A,B)),c_2Ebinary__ieee_2Efloat__plus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),c_2Ebool_2Ethe__value_2E0))))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A,B)),c_2Ebool_2Ethe__value_2E0))),
inference(copy,[status(thm)],[c_94]) ).
fof(nnf_31,plain,
? [A_27t,A_27w] : 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))))))),
inference(fof_nnf,[status(thm)],[thm_2Ebinary__ieee_2Eneg__ulp_neg]) ).
fof(sk_thm_2Ebinary__ieee_2Eneg__ulp_neg,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(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))) != s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A_27t,sK0),skolemize(A_27w,sK1)],[nnf_31]) ).
cnf(c_86,negated_conjecture,
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(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))) != s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))))),
inference(split_conjunct,[status(thm)],[sk_thm_2Ebinary__ieee_2Eneg__ulp_neg]) ).
cnf(c_95,negated_conjecture,
s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E1(s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))) != s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))))),
inference(paramod,[status(thm)],[c_80,c_86]) ).
cnf(c_96,negated_conjecture,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))) != s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__plus__min_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))))),
inference(paramod,[status(thm)],[c_79,c_95]) ).
cnf(c_97,negated_conjecture,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))) != s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),c_2Ebinary__ieee_2Efloat__negate_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Ebinary__ieee_2Efloat(sK0,sK1)),c_2Ebinary__ieee_2Efloat__plus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))))),
inference(paramod,[status(thm)],[c_77,c_96]) ).
cnf(c_98,negated_conjecture,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))) != s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Ebinary__ieee_2Efloat(sK0,sK1)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Ebinary__ieee_2Efloat(sK0,sK1)),c_2Ebinary__ieee_2Efloat__plus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))))),
inference(paramod,[status(thm)],[c_74,c_97]) ).
cnf(c_99,negated_conjecture,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))) != s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Ebinary__ieee_2Efloat(sK0,sK1)),c_2Ebinary__ieee_2Efloat__negate_2E0),s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Ebinary__ieee_2Efloat(sK0,sK1)),c_2Ebinary__ieee_2Efloat__plus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))))),
inference(paramod,[status(thm)],[c_75,c_98]) ).
cnf(c_100,negated_conjecture,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))) != s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(sK0,sK1),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Ebinary__ieee_2Efloat(sK0,sK1)),c_2Ebinary__ieee_2Efloat__plus__min_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))))),
inference(paramod,[status(thm)],[c_82,c_99]) ).
cnf(c_101,negated_conjecture,
s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))) != s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__neg_2E0),s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Eulp_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(sK0,sK1)),c_2Ebool_2Ethe__value_2E0))))),
inference(paramod,[status(thm)],[c_84,c_100]) ).
cnf(c_87,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP018+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n018.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Fri Sep 25 17:28:35 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2490864 was started by sandbox on n018,
% 0.13/0.36 % Fri Sep 25 17:28:35 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 19.
% 0.13/0.38 % Level of proof is 3.
% 0.13/0.38 % Maximum clause weight is 53.000.
% 0.13/0.38 % Given clauses 0.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------