%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP195-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 : Sat Jul 16 11:46:17 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,multiply(v,v)),multiply(v,multiply(v,u))),
file('GRP195-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,multiply(b,multiply(a,b))))))),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b)))))))),
file('GRP195-1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP195-1.p',unknown),
[] ).
cnf(12,plain,
equal(multiply(u,multiply(multiply(v,w),multiply(v,w))),multiply(multiply(v,w),multiply(v,multiply(w,u)))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(15,plain,
equal(multiply(u,multiply(v,multiply(w,w))),multiply(w,multiply(w,multiply(u,v)))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(18,plain,
equal(multiply(multiply(u,multiply(v,v)),w),multiply(v,multiply(multiply(v,u),w))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(21,plain,
equal(multiply(u,multiply(v,multiply(v,w))),multiply(v,multiply(v,multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[3,18]),
[iquote('0:Rew:3.0,18.0,3.0,18.0,3.0,18.0')] ).
cnf(23,plain,
equal(multiply(u,multiply(v,multiply(w,multiply(v,w)))),multiply(v,multiply(w,multiply(v,multiply(w,u))))),
inference(rew,[status(thm),theory(equality)],[3,12]),
[iquote('0:Rew:3.0,12.0,3.0,12.0')] ).
cnf(24,plain,
~ equal(multiply(a,multiply(b,multiply(a,multiply(a,multiply(b,multiply(a,multiply(b,b))))))),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b)))))))),
inference(rew,[status(thm),theory(equality)],[23,2]),
[iquote('0:Rew:23.0,2.0')] ).
cnf(27,plain,
~ equal(multiply(a,multiply(a,multiply(a,multiply(a,multiply(multiply(b,b),multiply(b,b)))))),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b)))))))),
inference(rew,[status(thm),theory(equality)],[15,24,21]),
[iquote('0:Rew:15.0,24.0,21.0,24.0')] ).
cnf(28,plain,
~ equal(multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b))))))),multiply(a,multiply(a,multiply(a,multiply(a,multiply(b,multiply(b,multiply(b,b)))))))),
inference(rew,[status(thm),theory(equality)],[3,27]),
[iquote('0:Rew:3.0,27.0')] ).
cnf(29,plain,
$false,
inference(obv,[status(thm),theory(equality)],[28]),
[iquote('0:Obv:28.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP195-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n011.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jun 13 10:06:18 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.20/0.41 SPASS allocated 63144 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.04 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.00 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 1, length 12 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : condition prove_this associativity_of_multiply
% 0.20/0.41
%------------------------------------------------------------------------------