TSTP Solution File: ALG240-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG240-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 18:03:10 EDT 2022
% Result : Unsatisfiable 1.08s 1.29s
% Output : Refutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 34 RR)
% Number of literals : 34 ( 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 : 9 ( 9 usr; 8 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('ALG240-1.p',unknown),
[] ).
cnf(2,axiom,
equal(mult(mult(u,v),mult(w,v)),mult(mult(u,w),v)),
file('ALG240-1.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('ALG240-1.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('ALG240-1.p',unknown),
[] ).
cnf(5,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('ALG240-1.p',unknown),
[] ).
cnf(6,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(u,mult(v,v)),mult(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(23,plain,
equal(mult(mult(mult(u,u),v),mult(u,mult(w,w))),mult(mult(u,u),mult(v,w))),
inference(spr,[status(thm),theory(equality)],[13,1]),
[iquote('0:SpR:13.0,1.0')] ).
cnf(29,plain,
equal(mult(u,mult(mult(v,v),w)),mult(mult(u,u),mult(v,w))),
inference(spr,[status(thm),theory(equality)],[2,13]),
[iquote('0:SpR:2.0,13.0')] ).
cnf(38,plain,
equal(mult(u,mult(mult(mult(v,v),w),mult(mult(v,v),w))),mult(mult(mult(u,u),mult(u,u)),mult(v,w))),
inference(spr,[status(thm),theory(equality)],[29,13]),
[iquote('0:SpR:29.0,13.0')] ).
cnf(55,plain,
equal(mult(u,mult(mult(v,v),u)),mult(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[29,2]),
[iquote('0:SpR:29.0,2.0')] ).
cnf(72,plain,
equal(mult(mult(u,v),mult(mult(w,w),x)),mult(mult(mult(u,u),v),mult(w,x))),
inference(spr,[status(thm),theory(equality)],[2,29]),
[iquote('0:SpR:2.0,29.0')] ).
cnf(81,plain,
equal(mult(mult(u,v),mult(mult(u,u),mult(w,w))),mult(mult(u,u),mult(v,w))),
inference(rew,[status(thm),theory(equality)],[72,23]),
[iquote('0:Rew:72.0,23.0')] ).
cnf(93,plain,
equal(mult(u,mult(mult(v,v),mult(w,w))),mult(mult(u,mult(u,mult(u,u))),mult(v,w))),
inference(rew,[status(thm),theory(equality)],[1,38,13,29]),
[iquote('0:Rew:1.0,38.0,13.0,38.0,29.0,38.0')] ).
cnf(162,plain,
equal(mult(mult(mult(u,mult(v,w)),mult(mult(u,u),mult(v,w))),mult(mult(u,u),mult(v,w))),mult(u,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(169,plain,
equal(mult(mult(u,mult(u,mult(u,u))),mult(v,w)),mult(u,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[13,162,1,2]),
[iquote('0:Rew:13.0,162.0,1.0,162.0,2.0,162.0,2.0,162.0')] ).
cnf(173,plain,
equal(mult(u,mult(mult(v,v),mult(w,w))),mult(u,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[169,93]),
[iquote('0:Rew:169.0,93.0')] ).
cnf(176,plain,
equal(mult(mult(u,v),mult(u,w)),mult(mult(u,u),mult(v,w))),
inference(rew,[status(thm),theory(equality)],[173,81]),
[iquote('0:Rew:173.0,81.0')] ).
cnf(177,plain,
equal(mult(mult(u,u),mult(v,w)),mult(u,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[1,176]),
[iquote('0:Rew:1.0,176.0')] ).
cnf(178,plain,
equal(mult(u,mult(mult(v,v),w)),mult(u,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[177,29]),
[iquote('0:Rew:177.0,29.0')] ).
cnf(185,plain,
equal(mult(u,mult(v,mult(w,w))),mult(u,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[177,173]),
[iquote('0:Rew:177.0,173.0')] ).
cnf(195,plain,
equal(mult(mult(u,v),u),mult(u,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[178,55]),
[iquote('0:Rew:178.0,55.0')] ).
cnf(322,plain,
equal(mult(mult(u,mult(v,u)),mult(w,u)),mult(mult(mult(u,v),w),u)),
inference(spr,[status(thm),theory(equality)],[195,2]),
[iquote('0:SpR:195.0,2.0')] ).
cnf(1698,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)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(1790,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)],[1,1698]),
[iquote('0:Rew:1.0,1698.0')] ).
cnf(1791,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)],[1790,4]),
[iquote('0:Rew:1790.0,4.0')] ).
cnf(1882,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)],[1790,1791]),
[iquote('0:Rew:1790.0,1791.0')] ).
cnf(2391,plain,
equal(mult(mult(u,v),mult(mult(v,u),u)),mult(mult(mult(u,v),v),u)),
inference(spr,[status(thm),theory(equality)],[1790,322]),
[iquote('0:SpR:1790.0,322.0')] ).
cnf(2452,plain,
equal(mult(mult(mult(mult(u,v),mult(w,x)),mult(mult(u,v),mult(w,x))),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(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)],[3,1790]),
[iquote('0:SpR:3.0,1790.0')] ).
cnf(2575,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)],[185,2452,1,1882,1790]),
[iquote('0:Rew:185.0,2452.0,1.0,2452.0,1.0,2452.0,185.0,2452.0,1.0,2452.0,1.0,2452.0,1882.0,2452.0,1790.0,2452.0,1790.0,2452.0')] ).
cnf(2648,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)],[3,2391]),
[iquote('0:SpR:3.0,2391.0')] ).
cnf(2776,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(u,w),mult(v,x)))),
inference(rew,[status(thm),theory(equality)],[185,2648,1,1882,1790,195]),
[iquote('0:Rew:185.0,2648.0,1.0,2648.0,1.0,2648.0,1.0,2648.0,1882.0,2648.0,1790.0,2648.0,1790.0,2648.0,195.0,2648.0,195.0,2648.0')] ).
cnf(2777,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)],[2575,2776]),
[iquote('0:Rew:2575.0,2776.0,2575.0,2776.0')] ).
cnf(2778,plain,
$false,
inference(unc,[status(thm)],[2777,5]),
[iquote('0:UnC:2777.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG240-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.11/0.31 % Computer : n021.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 9 04:18:38 EDT 2022
% 0.11/0.32 % CPUTime :
% 1.08/1.29
% 1.08/1.29 SPASS V 3.9
% 1.08/1.29 SPASS beiseite: Proof found.
% 1.08/1.29 % SZS status Theorem
% 1.08/1.29 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.08/1.29 SPASS derived 1535 clauses, backtracked 0 clauses, performed 0 splits and kept 507 clauses.
% 1.08/1.29 SPASS allocated 69556 KBytes.
% 1.08/1.29 SPASS spent 0:00:00.94 on the problem.
% 1.08/1.29 0:00:00.04 for the input.
% 1.08/1.29 0:00:00.00 for the FLOTTER CNF translation.
% 1.08/1.29 0:00:00.02 for inferences.
% 1.08/1.29 0:00:00.00 for the backtracking.
% 1.08/1.29 0:00:00.86 for the reduction.
% 1.08/1.29
% 1.08/1.29
% 1.08/1.29 Here is a proof with depth 6, length 34 :
% 1.08/1.29 % SZS output start Refutation
% See solution above
% 1.08/1.29 Formulae used in the proof : c01 c02 c03 c04 goals
% 1.08/1.29
%------------------------------------------------------------------------------