%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ITP018+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 00:37:47 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 7 unt; 0 nHn; 20 RR)
% Number of literals : 45 ( 0 equ; 33 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ne(skc3),
file('ITP018+2.p',unknown),
[] ).
cnf(2,axiom,
ne(skc2),
file('ITP018+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ ne(u)
| mem(c_2Ebool_2Ethe__value(u),ty_2Ebool_2Eitself(u)) ),
file('ITP018+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ ne(u)
| ~ ne(v)
| ne(ty_2Epair_2Eprod(v,u)) ),
file('ITP018+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ mem(u,v)
| ~ mem(w,arr(v,x))
| mem(ap(w,u),x) ),
file('ITP018+2.p',unknown),
[] ).
cnf(25,axiom,
( ~ ne(u)
| ~ ne(v)
| mem(c_2Ebinary__ieee_2Efloat__plus__min(v,u),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(v,u)),ty_2Ebinary__ieee_2Efloat(v,u))) ),
file('ITP018+2.p',unknown),
[] ).
cnf(32,axiom,
( ~ ne(u)
| ~ ne(v)
| equal(ap(c_2Ebinary__ieee_2Efloat__to__real(v,u),ap(c_2Ebinary__ieee_2Efloat__plus__min(v,u),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(v,u)))),ap(c_2Ebinary__ieee_2Eulp(v,u),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(v,u)))) ),
file('ITP018+2.p',unknown),
[] ).
cnf(33,axiom,
~ equal(ap(c_2Ebinary__ieee_2Efloat__to__real(skc2,skc3),ap(c_2Ebinary__ieee_2Efloat__negate(skc2,skc3),ap(c_2Ebinary__ieee_2Efloat__plus__min(skc2,skc3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3))))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(skc2,skc3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3))))),
file('ITP018+2.p',unknown),
[] ).
cnf(35,axiom,
( ~ ne(u)
| ~ ne(v)
| ~ mem(w,ty_2Ebinary__ieee_2Efloat(v,u))
| equal(ap(c_2Ebinary__ieee_2Efloat__to__real(v,u),ap(c_2Ebinary__ieee_2Efloat__negate(v,u),w)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(v,u),w))) ),
file('ITP018+2.p',unknown),
[] ).
cnf(43,plain,
( ~ ne(u)
| mem(c_2Ebinary__ieee_2Efloat__plus__min(skc2,u),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(skc2,u)),ty_2Ebinary__ieee_2Efloat(skc2,u))) ),
inference(res,[status(thm),theory(equality)],[2,25]),
[iquote('0:Res:2.0,25.0')] ).
cnf(50,plain,
( ~ ne(u)
| ne(ty_2Epair_2Eprod(skc2,u)) ),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(128,plain,
( ~ ne(u)
| ~ mem(v,ty_2Ebool_2Eitself(ty_2Epair_2Eprod(skc2,u)))
| mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(skc2,u),v),ty_2Ebinary__ieee_2Efloat(skc2,u)) ),
inference(res,[status(thm),theory(equality)],[43,20]),
[iquote('0:Res:43.1,20.1')] ).
cnf(278,plain,
( ~ ne(skc3)
| ~ ne(skc2)
| ~ mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(skc2,skc3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3))),ty_2Ebinary__ieee_2Efloat(skc2,skc3))
| ~ equal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Efloat__to__real(skc2,skc3),ap(c_2Ebinary__ieee_2Efloat__plus__min(skc2,skc3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3))))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(skc2,skc3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3))))) ),
inference(spl,[status(thm),theory(equality)],[35,33]),
[iquote('0:SpL:35.3,33.0')] ).
cnf(293,plain,
( ~ ne(skc3)
| ~ ne(skc2)
| ~ mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(skc2,skc3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3))),ty_2Ebinary__ieee_2Efloat(skc2,skc3))
| ~ equal(ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(skc2,skc3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3)))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ebinary__ieee_2Eulp(skc2,skc3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3))))) ),
inference(rew,[status(thm),theory(equality)],[32,278]),
[iquote('0:Rew:32.2,278.3')] ).
cnf(294,plain,
( ~ ne(skc3)
| ~ ne(skc2)
| ~ mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(skc2,skc3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3))),ty_2Ebinary__ieee_2Efloat(skc2,skc3)) ),
inference(obv,[status(thm),theory(equality)],[293]),
[iquote('0:Obv:293.3')] ).
cnf(295,plain,
~ mem(ap(c_2Ebinary__ieee_2Efloat__plus__min(skc2,skc3),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3))),ty_2Ebinary__ieee_2Efloat(skc2,skc3)),
inference(ssi,[status(thm)],[294,2,1]),
[iquote('0:SSi:294.1,294.0,2.0,1.0')] ).
cnf(296,plain,
( ~ ne(skc3)
| ~ mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3)),ty_2Ebool_2Eitself(ty_2Epair_2Eprod(skc2,skc3))) ),
inference(res,[status(thm),theory(equality)],[128,295]),
[iquote('0:Res:128.2,295.0')] ).
cnf(298,plain,
~ mem(c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(skc2,skc3)),ty_2Ebool_2Eitself(ty_2Epair_2Eprod(skc2,skc3))),
inference(ssi,[status(thm)],[296,1]),
[iquote('0:SSi:296.0,1.0')] ).
cnf(299,plain,
~ ne(ty_2Epair_2Eprod(skc2,skc3)),
inference(res,[status(thm),theory(equality)],[10,298]),
[iquote('0:Res:10.1,298.0')] ).
cnf(300,plain,
$false,
inference(ssi,[status(thm)],[299,50,1]),
[iquote('0:SSi:299.0,50.0,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP018+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 2 12:58:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.50
% 0.19/0.50 SPASS V 3.9
% 0.19/0.50 SPASS beiseite: Proof found.
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50 SPASS derived 212 clauses, backtracked 0 clauses, performed 2 splits and kept 214 clauses.
% 0.19/0.50 SPASS allocated 98114 KBytes.
% 0.19/0.50 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.50 0:00:00.03 for the input.
% 0.19/0.50 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.50 0:00:00.01 for inferences.
% 0.19/0.50 0:00:00.00 for the backtracking.
% 0.19/0.50 0:00:00.04 for the reduction.
% 0.19/0.50
% 0.19/0.50
% 0.19/0.50 Here is a proof with depth 4, length 20 :
% 0.19/0.50 % SZS output start Refutation
% See solution above
% 0.19/0.50 Formulae used in the proof : conj_thm_2Ebinary__ieee_2Eneg__ulp mem_c_2Ebool_2Ethe__value ne_ty_2Epair_2Eprod ap_tp mem_c_2Ebinary__ieee_2Efloat__plus__min conj_thm_2Ebinary__ieee_2Eulp conj_thm_2Ebinary__ieee_2Efloat__to__real__negate
% 0.19/0.50
%------------------------------------------------------------------------------