TSTP Solution File: KLE114+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE114+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 02:28:35 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 23 RR)
% Number of literals : 23 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE114+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE114+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,zero),zero),
file('KLE114+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(forward_box(skc1,one),one),
file('KLE114+1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE114+1.p',unknown),
[] ).
cnf(9,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE114+1.p',unknown),
[] ).
cnf(12,axiom,
equal(c(u),antidomain(domain__dfg(u))),
file('KLE114+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE114+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE114+1.p',unknown),
[] ).
cnf(19,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE114+1.p',unknown),
[] ).
cnf(21,axiom,
equal(c(forward_diamond(u,c(v))),forward_box(u,v)),
file('KLE114+1.p',unknown),
[] ).
cnf(29,plain,
equal(c(u),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[9,12]),
[iquote('0:Rew:9.0,12.0')] ).
cnf(31,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[13,14]),
[iquote('0:Rew:13.0,14.0')] ).
cnf(33,plain,
equal(antidomain(antidomain(antidomain(forward_diamond(u,antidomain(antidomain(antidomain(v))))))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[29,21]),
[iquote('0:Rew:29.0,21.0,29.0,21.0')] ).
cnf(36,plain,
equal(forward_diamond(u,v),antidomain(antidomain(multiplication(u,antidomain(antidomain(v)))))),
inference(rew,[status(thm),theory(equality)],[9,19]),
[iquote('0:Rew:9.0,19.0,9.0,19.0')] ).
cnf(37,plain,
equal(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v))))))))))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[36,33]),
[iquote('0:Rew:36.0,33.0')] ).
cnf(52,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[8,3]),
[iquote('0:SpR:8.0,3.0')] ).
cnf(63,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[13,1]),
[iquote('0:SpR:13.0,1.0')] ).
cnf(86,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[52,31]),
[iquote('0:SpR:52.0,31.0')] ).
cnf(88,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[63,86]),
[iquote('0:Rew:63.0,86.0')] ).
cnf(613,plain,
equal(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(zero)))))))))),forward_box(u,one)),
inference(spr,[status(thm),theory(equality)],[52,37]),
[iquote('0:SpR:52.0,37.0')] ).
cnf(624,plain,
equal(forward_box(u,one),one),
inference(rew,[status(thm),theory(equality)],[88,613,52,5]),
[iquote('0:Rew:88.0,613.0,52.0,613.0,88.0,613.0,52.0,613.0,88.0,613.0,5.0,613.0,52.0,613.0,88.0,613.0,52.0,613.0,88.0,613.0')] ).
cnf(625,plain,
$false,
inference(unc,[status(thm)],[624,7]),
[iquote('0:UnC:624.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE114+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 12:08:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 475 clauses, backtracked 0 clauses, performed 0 splits and kept 165 clauses.
% 0.19/0.48 SPASS allocated 85736 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.48 0:00:00.03 for the input.
% 0.19/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.01 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.04 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 2, length 23 :
% 0.19/0.48 % SZS output start Refutation
% See solution above
% 0.19/0.48 Formulae used in the proof : additive_identity multiplicative_right_identity right_annihilation goals domain1 domain4 complement additive_commutativity domain3 forward_diamond forward_box
% 0.19/0.48
%------------------------------------------------------------------------------