TSTP Solution File: GRP403-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP403-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:47:13 EDT 2022
% Result : Unsatisfiable 84.32s 84.60s
% Output : Refutation 84.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 24 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),inverse(multiply(v,multiply(inverse(v),v)))))),w),
file('GRP403-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP403-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(inverse(v),inverse(multiply(w,multiply(inverse(w),w)))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),v)),inverse(multiply(x,multiply(inverse(x),x)))))),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(4,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(v),w)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),inverse(multiply(x,multiply(inverse(x),x))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),inverse(multiply(x,multiply(inverse(x),x)))))),inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),inverse(multiply(x,multiply(inverse(x),x))))))))))),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(21,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(w),inverse(multiply(v,multiply(inverse(v),v))))))),w),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(56,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),inverse(multiply(v,multiply(inverse(v),v))))))),x)),multiply(inverse(w),y))),inverse(multiply(x,multiply(inverse(x),x))))),y),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(100,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(u),w))),inverse(multiply(v,multiply(inverse(v),v))))),w),
inference(rew,[status(thm),theory(equality)],[1,56]),
[iquote('0:Rew:1.0,56.0')] ).
cnf(127,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(inverse(x),v)),multiply(inverse(x),w))),
inference(spr,[status(thm),theory(equality)],[100,21]),
[iquote('0:SpR:100.0,21.0')] ).
cnf(136,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),inverse(multiply(v,multiply(inverse(v),v))))),w),
inference(spr,[status(thm),theory(equality)],[100]),
[iquote('0:SpR:100.0,100.0')] ).
cnf(188,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[127]),
[iquote('0:SpR:127.0,127.0')] ).
cnf(244,plain,
equal(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,multiply(v,w))),x)),inverse(multiply(multiply(v,w),multiply(inverse(multiply(y,w)),multiply(y,w))))))),x),
inference(spr,[status(thm),theory(equality)],[188,1]),
[iquote('0:SpR:188.0,1.0')] ).
cnf(245,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,inverse(multiply(inverse(x),inverse(multiply(multiply(v,w),multiply(inverse(multiply(y,w)),multiply(y,w)))))))),x),
inference(spr,[status(thm),theory(equality)],[188,21]),
[iquote('0:SpR:188.0,21.0')] ).
cnf(279,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(v,w)),x)),inverse(multiply(w,multiply(inverse(w),w))))))),multiply(u,y)),multiply(inverse(x),multiply(v,y))),
inference(spr,[status(thm),theory(equality)],[1,188]),
[iquote('0:SpR:1.0,188.0')] ).
cnf(313,plain,
equal(multiply(inverse(multiply(u,inverse(multiply(v,multiply(inverse(v),v))))),multiply(u,w)),multiply(x,multiply(inverse(multiply(inverse(multiply(y,v)),multiply(y,x))),w))),
inference(spr,[status(thm),theory(equality)],[136,188]),
[iquote('0:SpR:136.0,188.0')] ).
cnf(320,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,x))),inverse(multiply(multiply(v,w),multiply(inverse(multiply(y,w)),multiply(y,w)))))),x),
inference(spr,[status(thm),theory(equality)],[188,136]),
[iquote('0:SpR:188.0,136.0')] ).
cnf(2638,plain,
equal(multiply(inverse(multiply(u,v)),inverse(multiply(w,inverse(multiply(multiply(u,w),multiply(inverse(multiply(x,w)),multiply(x,w))))))),inverse(multiply(v,multiply(inverse(v),v)))),
inference(spr,[status(thm),theory(equality)],[136,244]),
[iquote('0:SpR:136.0,244.0')] ).
cnf(4225,plain,
equal(multiply(u,multiply(inverse(multiply(inverse(multiply(v,w)),multiply(v,u))),x)),multiply(y,multiply(inverse(multiply(inverse(multiply(z,w)),multiply(z,y))),x))),
inference(spr,[status(thm),theory(equality)],[136,313]),
[iquote('0:SpR:136.0,313.0')] ).
cnf(5081,plain,
equal(multiply(u,multiply(inverse(multiply(inverse(multiply(v,inverse(multiply(inverse(multiply(inverse(multiply(w,x)),y)),inverse(multiply(x,multiply(inverse(x),x))))))),multiply(v,u))),z)),multiply(x1,multiply(inverse(multiply(inverse(y),multiply(w,x1))),z))),
inference(spr,[status(thm),theory(equality)],[1,4225]),
[iquote('0:SpR:1.0,4225.0')] ).
cnf(5138,plain,
equal(multiply(u,multiply(inverse(multiply(inverse(v),multiply(w,u))),x)),multiply(y,multiply(inverse(multiply(inverse(v),multiply(w,y))),x))),
inference(rew,[status(thm),theory(equality)],[279,5081]),
[iquote('0:Rew:279.0,5081.0')] ).
cnf(5464,plain,
equal(multiply(u,multiply(inverse(multiply(v,multiply(w,u))),x)),multiply(y,multiply(inverse(multiply(v,multiply(w,y))),x))),
inference(spr,[status(thm),theory(equality)],[320,5138]),
[iquote('0:SpR:320.0,5138.0')] ).
cnf(8240,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),inverse(multiply(v,multiply(inverse(v),v)))),w),
inference(spr,[status(thm),theory(equality)],[2638,245]),
[iquote('0:SpR:2638.0,245.0')] ).
cnf(9361,plain,
equal(multiply(inverse(u),u),multiply(v,multiply(inverse(multiply(inverse(multiply(w,x)),multiply(w,v))),inverse(multiply(x,multiply(inverse(x),x)))))),
inference(spr,[status(thm),theory(equality)],[8240,5464]),
[iquote('0:SpR:8240.0,5464.0')] ).
cnf(9886,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[9361]),
[iquote('0:SpR:9361.0,9361.0')] ).
cnf(10076,plain,
$false,
inference(unc,[status(thm)],[9886,2]),
[iquote('0:UnC:9886.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP403-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.09/0.28 % Computer : n011.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Tue Jun 14 11:02:19 EDT 2022
% 0.09/0.29 % CPUTime :
% 84.32/84.60
% 84.32/84.60 SPASS V 3.9
% 84.32/84.60 SPASS beiseite: Proof found.
% 84.32/84.60 % SZS status Theorem
% 84.32/84.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 84.32/84.60 SPASS derived 9009 clauses, backtracked 0 clauses, performed 0 splits and kept 3790 clauses.
% 84.32/84.60 SPASS allocated 142657 KBytes.
% 84.32/84.60 SPASS spent 0:1:23.73 on the problem.
% 84.32/84.60 0:00:00.03 for the input.
% 84.32/84.60 0:00:00.00 for the FLOTTER CNF translation.
% 84.32/84.60 0:00:00.31 for inferences.
% 84.32/84.60 0:00:00.00 for the backtracking.
% 84.32/84.60 0:1:23.37 for the reduction.
% 84.32/84.60
% 84.32/84.60
% 84.32/84.60 Here is a proof with depth 10, length 24 :
% 84.32/84.60 % SZS output start Refutation
% See solution above
% 84.32/84.60 Formulae used in the proof : single_axiom prove_these_axioms_1
% 84.32/84.60
%------------------------------------------------------------------------------