TSTP Solution File: ALG245-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG245-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 : Thu Jul 14 18:03:11 EDT 2022
% Result : Unsatisfiable 0.75s 0.94s
% Output : Refutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 31 RR)
% Number of literals : 31 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(mult(u,v),mult(u,w)),mult(u,mult(v,w))),
file('ALG245-1.p',unknown),
[] ).
cnf(2,axiom,
equal(mult(mult(u,v),mult(w,v)),mult(mult(u,w),v)),
file('ALG245-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x)))),mult(mult(u,w),mult(v,x))),
file('ALG245-1.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x))),
file('ALG245-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,u),u),
file('ALG245-1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))),mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d)))),
file('ALG245-1.p',unknown),
[] ).
cnf(9,plain,
equal(mult(mult(u,mult(v,w)),mult(mult(x,v),w)),mult(mult(u,mult(x,w)),mult(v,w))),
inference(spr,[status(thm),theory(equality)],[2]),
[iquote('0:SpR:2.0,2.0')] ).
cnf(13,plain,
equal(mult(mult(u,v),u),mult(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(15,plain,
equal(mult(mult(u,v),mult(v,mult(w,v))),mult(mult(u,mult(v,w)),v)),
inference(spr,[status(thm),theory(equality)],[13,2]),
[iquote('0:SpR:13.0,2.0')] ).
cnf(16,plain,
equal(mult(mult(u,mult(v,u)),mult(w,u)),mult(mult(mult(u,v),w),u)),
inference(spr,[status(thm),theory(equality)],[13,2]),
[iquote('0:SpR:13.0,2.0')] ).
cnf(49,plain,
equal(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),y),mult(mult(u,v),mult(w,x))),mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(y,mult(mult(u,w),mult(v,x))))),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(51,plain,
equal(mult(mult(u,mult(mult(mult(v,w),mult(x,y)),mult(mult(v,x),mult(w,y)))),mult(mult(v,x),mult(w,y))),mult(mult(u,mult(mult(v,x),mult(w,y))),mult(mult(v,w),mult(x,y)))),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(52,plain,
equal(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),y),mult(mult(u,w),mult(v,x))),mult(mult(mult(u,v),mult(w,x)),mult(y,mult(mult(u,w),mult(v,x))))),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(53,plain,
equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(mult(mult(u,w),mult(v,x)),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))))),mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))))),
inference(spr,[status(thm),theory(equality)],[4,13]),
[iquote('0:SpR:4.0,13.0')] ).
cnf(121,plain,
equal(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),y),mult(mult(u,v),mult(w,x))),mult(mult(mult(mult(u,v),mult(w,x)),y),mult(mult(u,w),mult(v,x)))),
inference(rew,[status(thm),theory(equality)],[2,49]),
[iquote('0:Rew:2.0,49.0')] ).
cnf(122,plain,
equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,v),mult(w,x)))),mult(mult(u,w),mult(v,x))),mult(mult(u,w),mult(v,x))),
inference(rew,[status(thm),theory(equality)],[15,53,3]),
[iquote('0:Rew:15.0,53.0,3.0,53.0')] ).
cnf(418,plain,
equal(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(y,mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))))),mult(mult(u,w),mult(v,x))),mult(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),y),mult(mult(u,v),mult(w,x))),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))))),
inference(spr,[status(thm),theory(equality)],[3,16]),
[iquote('0:SpR:3.0,16.0')] ).
cnf(558,plain,
equal(mult(mult(mult(mult(mult(u,v),mult(w,x)),y),mult(mult(u,w),mult(v,x))),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x)))),mult(mult(mult(u,v),mult(w,x)),mult(mult(y,mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x))))),
inference(rew,[status(thm),theory(equality)],[51,418,52,121]),
[iquote('0:Rew:51.0,418.0,52.0,418.0,121.0,418.0')] ).
cnf(559,plain,
equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(y,mult(mult(u,v),mult(w,x)))),mult(mult(u,w),mult(v,x))),mult(mult(mult(u,v),mult(w,x)),mult(mult(y,mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x))))),
inference(rew,[status(thm),theory(equality)],[13,558,2]),
[iquote('0:Rew:13.0,558.0,2.0,558.0')] ).
cnf(560,plain,
equal(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(mult(u,w),mult(v,x)),mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x)))),mult(mult(u,w),mult(v,x))),
inference(rew,[status(thm),theory(equality)],[559,122]),
[iquote('0:Rew:559.0,122.0')] ).
cnf(561,plain,
equal(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,v),mult(w,x)))),mult(mult(u,w),mult(v,x))),
inference(rew,[status(thm),theory(equality)],[5,560,1]),
[iquote('0:Rew:5.0,560.0,1.0,560.0,1.0,560.0')] ).
cnf(591,plain,
equal(mult(mult(mult(u,v),mult(u,w)),mult(v,w)),mult(mult(u,v),mult(mult(v,w),w))),
inference(spr,[status(thm),theory(equality)],[9,1]),
[iquote('0:SpR:9.0,1.0')] ).
cnf(653,plain,
equal(mult(mult(u,mult(v,w)),mult(v,w)),mult(mult(u,v),mult(mult(v,w),w))),
inference(rew,[status(thm),theory(equality)],[1,591]),
[iquote('0:Rew:1.0,591.0')] ).
cnf(654,plain,
equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(u,w)),mult(mult(mult(u,w),mult(v,x)),mult(v,x))),mult(mult(u,v),mult(w,x))),
inference(rew,[status(thm),theory(equality)],[653,4]),
[iquote('0:Rew:653.0,4.0')] ).
cnf(712,plain,
equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(u,w)),mult(mult(mult(u,w),v),mult(mult(v,x),x))),mult(mult(u,v),mult(w,x))),
inference(rew,[status(thm),theory(equality)],[653,654]),
[iquote('0:Rew:653.0,654.0')] ).
cnf(818,plain,
equal(mult(mult(u,v),mult(mult(v,u),u)),mult(mult(mult(u,v),v),u)),
inference(spr,[status(thm),theory(equality)],[653,16]),
[iquote('0:SpR:653.0,16.0')] ).
cnf(979,plain,
equal(mult(mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x))),mult(mult(u,v),mult(w,x))),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x)))),mult(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(mult(u,v),mult(w,x))),mult(mult(mult(u,w),mult(v,x)),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x)))))),
inference(spr,[status(thm),theory(equality)],[3,818]),
[iquote('0:SpR:3.0,818.0')] ).
cnf(1049,plain,
equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,v),mult(w,x)))),mult(mult(mult(u,w),mult(v,x)),mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))))),mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(mult(mult(u,w),mult(v,x)),mult(u,v)),mult(mult(mult(u,v),w),mult(mult(w,x),x))),mult(mult(u,w),mult(v,x))))),
inference(rew,[status(thm),theory(equality)],[1,979,653,13]),
[iquote('0:Rew:1.0,979.0,653.0,979.0,653.0,979.0,13.0,979.0,13.0,979.0')] ).
cnf(1050,plain,
equal(mult(mult(mult(u,v),mult(w,x)),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,w),mult(v,x)))),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,v),mult(w,x)))),
inference(rew,[status(thm),theory(equality)],[561,1049,712]),
[iquote('0:Rew:561.0,1049.0,561.0,1049.0,712.0,1049.0')] ).
cnf(1051,plain,
equal(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,w),mult(v,x))),mult(mult(mult(u,w),mult(v,x)),mult(mult(u,v),mult(w,x)))),
inference(rew,[status(thm),theory(equality)],[5,1050,1]),
[iquote('0:Rew:5.0,1050.0,1.0,1050.0,1.0,1050.0')] ).
cnf(1052,plain,
$false,
inference(unc,[status(thm)],[1051,6]),
[iquote('0:UnC:1051.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ALG245-1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 8 09:02:56 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.75/0.94
% 0.75/0.94 SPASS V 3.9
% 0.75/0.94 SPASS beiseite: Proof found.
% 0.75/0.94 % SZS status Theorem
% 0.75/0.94 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.75/0.94 SPASS derived 628 clauses, backtracked 0 clauses, performed 0 splits and kept 375 clauses.
% 0.75/0.94 SPASS allocated 66797 KBytes.
% 0.75/0.94 SPASS spent 0:00:00.59 on the problem.
% 0.75/0.94 0:00:00.04 for the input.
% 0.75/0.94 0:00:00.00 for the FLOTTER CNF translation.
% 0.75/0.94 0:00:00.01 for inferences.
% 0.75/0.94 0:00:00.00 for the backtracking.
% 0.75/0.94 0:00:00.52 for the reduction.
% 0.75/0.94
% 0.75/0.94
% 0.75/0.94 Here is a proof with depth 4, length 31 :
% 0.75/0.94 % SZS output start Refutation
% See solution above
% 0.75/0.94 Formulae used in the proof : c01 c02 c03 c04 c05 goals
% 0.75/0.94
%------------------------------------------------------------------------------