TSTP Solution File: GRP406-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP406-1 : TPTP v8.1.0. Released v2.6.0.
% 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 : Sat Jul 16 11:47:13 EDT 2022
% Result : Unsatisfiable 25.29s 25.49s
% Output : Refutation 25.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 22 RR)
% Number of literals : 22 ( 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 : 12 ( 12 usr; 10 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)),multiply(inverse(v),multiply(inverse(v),v))))),w),
file('GRP406-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP406-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(u,inverse(multiply(inverse(v),multiply(inverse(w),multiply(inverse(w),w))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,w)),x)),v)),multiply(inverse(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)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),multiply(inverse(x),multiply(inverse(x),x))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),multiply(inverse(x),multiply(inverse(x),x))))),inverse(multiply(inverse(multiply(inverse(multiply(u,x)),v)),multiply(inverse(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),multiply(inverse(v),multiply(inverse(v),v)))))),w),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(57,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(u,inverse(multiply(inverse(multiply(inverse(multiply(u,v)),w)),multiply(inverse(v),multiply(inverse(v),v)))))),x)),multiply(inverse(w),y))),multiply(inverse(x),multiply(inverse(x),x)))),y),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(104,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(inverse(u),v)),multiply(inverse(u),w))),multiply(inverse(v),multiply(inverse(v),v)))),w),
inference(rew,[status(thm),theory(equality)],[1,57]),
[iquote('0:Rew:1.0,57.0')] ).
cnf(131,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)],[104,21]),
[iquote('0:SpR:104.0,21.0')] ).
cnf(140,plain,
equal(inverse(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,w))),multiply(inverse(v),multiply(inverse(v),v)))),w),
inference(spr,[status(thm),theory(equality)],[104]),
[iquote('0:SpR:104.0,104.0')] ).
cnf(191,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,w)),multiply(inverse(multiply(x,v)),multiply(x,w))),
inference(spr,[status(thm),theory(equality)],[131]),
[iquote('0:SpR:131.0,131.0')] ).
cnf(197,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,inverse(multiply(inverse(multiply(w,x)),multiply(w,multiply(inverse(v),v)))))),multiply(inverse(v),x)),
inference(spr,[status(thm),theory(equality)],[131,21]),
[iquote('0:SpR:131.0,21.0')] ).
cnf(256,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,inverse(multiply(inverse(x),multiply(inverse(multiply(v,w)),multiply(inverse(multiply(y,w)),multiply(y,w))))))),x),
inference(spr,[status(thm),theory(equality)],[191,21]),
[iquote('0:SpR:191.0,21.0')] ).
cnf(276,plain,
equal(multiply(inverse(multiply(u,v)),multiply(u,multiply(w,x))),multiply(inverse(multiply(inverse(multiply(w,y)),v)),multiply(inverse(multiply(z,y)),multiply(z,x)))),
inference(spr,[status(thm),theory(equality)],[191]),
[iquote('0:SpR:191.0,191.0')] ).
cnf(277,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,x)),multiply(inverse(multiply(inverse(multiply(y,z)),multiply(y,w))),multiply(inverse(multiply(v,z)),x))),
inference(spr,[status(thm),theory(equality)],[191]),
[iquote('0:SpR:191.0,191.0')] ).
cnf(326,plain,
equal(multiply(inverse(multiply(u,multiply(inverse(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)],[140,191]),
[iquote('0:SpR:140.0,191.0')] ).
cnf(1813,plain,
equal(multiply(inverse(multiply(u,multiply(v,w))),multiply(u,multiply(v,x))),multiply(inverse(multiply(y,multiply(z,w))),multiply(y,multiply(z,x)))),
inference(spr,[status(thm),theory(equality)],[276,277]),
[iquote('0:SpR:276.0,277.0')] ).
cnf(3043,plain,
equal(multiply(inverse(multiply(u,multiply(v,multiply(w,x)))),multiply(u,inverse(multiply(inverse(multiply(y,z)),multiply(y,multiply(inverse(multiply(x1,multiply(x2,x))),multiply(x1,multiply(x2,x)))))))),multiply(inverse(multiply(v,multiply(w,x))),z)),
inference(spr,[status(thm),theory(equality)],[1813,197]),
[iquote('0:SpR:1813.0,197.0')] ).
cnf(4886,plain,
equal(multiply(inverse(multiply(u,multiply(inverse(multiply(v,w)),multiply(v,inverse(x))))),multiply(u,inverse(multiply(inverse(multiply(y,multiply(inverse(w),multiply(inverse(w),w)))),multiply(y,multiply(inverse(multiply(z,multiply(v,inverse(x)))),multiply(z,multiply(v,inverse(x))))))))),x),
inference(spr,[status(thm),theory(equality)],[326,256]),
[iquote('0:SpR:326.0,256.0')] ).
cnf(5098,plain,
equal(multiply(inverse(multiply(inverse(multiply(u,v)),multiply(u,inverse(w)))),multiply(inverse(v),multiply(inverse(v),v))),w),
inference(rew,[status(thm),theory(equality)],[3043,4886]),
[iquote('0:Rew:3043.0,4886.0')] ).
cnf(5139,plain,
equal(multiply(inverse(multiply(u,multiply(inverse(v),multiply(inverse(v),v)))),multiply(u,multiply(inverse(v),multiply(inverse(v),v)))),multiply(inverse(w),w)),
inference(spr,[status(thm),theory(equality)],[5098,326]),
[iquote('0:SpR:5098.0,326.0')] ).
cnf(5358,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[5139]),
[iquote('0:SpR:5139.0,5139.0')] ).
cnf(5704,plain,
$false,
inference(unc,[status(thm)],[5358,2]),
[iquote('0:UnC:5358.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP406-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 01:50:33 EDT 2022
% 0.14/0.34 % CPUTime :
% 25.29/25.49
% 25.29/25.49 SPASS V 3.9
% 25.29/25.49 SPASS beiseite: Proof found.
% 25.29/25.49 % SZS status Theorem
% 25.29/25.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.29/25.49 SPASS derived 5063 clauses, backtracked 0 clauses, performed 0 splits and kept 2153 clauses.
% 25.29/25.49 SPASS allocated 102650 KBytes.
% 25.29/25.49 SPASS spent 0:0:24.88 on the problem.
% 25.29/25.49 0:00:00.03 for the input.
% 25.29/25.49 0:00:00.00 for the FLOTTER CNF translation.
% 25.29/25.49 0:00:00.12 for inferences.
% 25.29/25.49 0:00:00.00 for the backtracking.
% 25.29/25.49 0:0:24.70 for the reduction.
% 25.29/25.49
% 25.29/25.49
% 25.29/25.49 Here is a proof with depth 8, length 22 :
% 25.29/25.49 % SZS output start Refutation
% See solution above
% 25.29/25.49 Formulae used in the proof : single_axiom prove_these_axioms_1
% 25.29/25.49
%------------------------------------------------------------------------------