TSTP Solution File: ALG236-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG236-1 : 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 18:03:09 EDT 2022
% Result : Unsatisfiable 1.53s 1.72s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 0 equ; 2 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 : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,mult(v,mult(u,v))),mult(u,v)),
file('ALG236-1.p',unknown),
[] ).
cnf(2,axiom,
equal(mult(u,mult(v,mult(w,x))),mult(w,mult(v,mult(u,x)))),
file('ALG236-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(mult(u,mult(v,mult(w,v))),x),mult(u,mult(x,mult(mult(w,v),x)))),
file('ALG236-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(mult(mult(a,b),mult(c,mult(d,e))),mult(a,mult(c,mult(mult(d,b),e)))),
file('ALG236-1.p',unknown),
[] ).
cnf(5,plain,
~ equal(mult(d,mult(c,mult(mult(a,b),e))),mult(a,mult(c,mult(mult(d,b),e)))),
inference(rew,[status(thm),theory(equality)],[2,4]),
[iquote('0:Rew:2.0,4.0')] ).
cnf(11,plain,
equal(mult(u,mult(v,mult(w,mult(x,y)))),mult(w,mult(x,mult(u,mult(v,y))))),
inference(spr,[status(thm),theory(equality)],[2]),
[iquote('0:SpR:2.0,2.0')] ).
cnf(26,plain,
equal(mult(u,mult(v,mult(w,mult(x,mult(u,x))))),mult(w,mult(v,mult(u,x)))),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(27,plain,
equal(mult(u,mult(v,mult(w,mult(v,u)))),mult(w,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[1,2]),
[iquote('0:SpR:1.0,2.0')] ).
cnf(62,plain,
equal(mult(u,mult(v,mult(w,mult(x,mult(u,v))))),mult(w,mult(x,mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[27,2]),
[iquote('0:SpR:27.0,2.0')] ).
cnf(75,plain,
equal(mult(mult(u,v),mult(v,mult(u,v))),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[1,27]),
[iquote('0:SpR:1.0,27.0')] ).
cnf(83,plain,
equal(mult(u,mult(v,mult(mult(u,v),v))),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[2,75]),
[iquote('0:Rew:2.0,75.0')] ).
cnf(124,plain,
equal(mult(mult(u,v),mult(w,mult(x,w))),mult(mult(x,mult(v,mult(u,v))),w)),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(142,plain,
equal(mult(u,mult(v,mult(mult(u,w),v))),mult(mult(u,w),v)),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(143,plain,
equal(mult(mult(u,mult(v,mult(w,v))),x),mult(w,mult(x,mult(mult(u,v),x)))),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(155,plain,
equal(mult(mult(u,v),v),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[142,83]),
[iquote('0:Rew:142.0,83.0')] ).
cnf(213,plain,
equal(mult(mult(u,v),mult(w,mult(x,v))),mult(x,mult(w,mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[155,2]),
[iquote('0:SpR:155.0,2.0')] ).
cnf(264,plain,
equal(mult(u,mult(v,mult(mult(mult(u,w),x),v))),mult(mult(mult(u,w),x),v)),
inference(spr,[status(thm),theory(equality)],[142]),
[iquote('0:SpR:142.0,142.0')] ).
cnf(633,plain,
equal(mult(u,mult(v,mult(w,mult(x,mult(y,z))))),mult(w,mult(x,mult(y,mult(v,mult(u,z)))))),
inference(spr,[status(thm),theory(equality)],[2,11]),
[iquote('0:SpR:2.0,11.0')] ).
cnf(788,plain,
equal(mult(u,mult(v,mult(u,mult(w,mult(x,w))))),mult(x,mult(v,mult(u,w)))),
inference(spr,[status(thm),theory(equality)],[2,26]),
[iquote('0:SpR:2.0,26.0')] ).
cnf(1366,plain,
equal(mult(mult(u,v),mult(w,mult(x,w))),mult(u,mult(w,mult(mult(x,v),w)))),
inference(spr,[status(thm),theory(equality)],[143,124]),
[iquote('0:SpR:143.0,124.0')] ).
cnf(1403,plain,
equal(mult(u,mult(v,mult(mult(w,mult(x,mult(y,x))),z))),mult(y,mult(v,mult(u,mult(z,mult(mult(w,x),z)))))),
inference(spr,[status(thm),theory(equality)],[143,2]),
[iquote('0:SpR:143.0,2.0')] ).
cnf(1461,plain,
equal(mult(mult(u,v),mult(w,mult(mult(u,x),w))),mult(mult(mult(u,v),x),w)),
inference(spr,[status(thm),theory(equality)],[142,143]),
[iquote('0:SpR:142.0,143.0')] ).
cnf(1552,plain,
equal(mult(mult(mult(u,v),w),x),mult(mult(mult(u,w),v),x)),
inference(rew,[status(thm),theory(equality)],[264,1461,1366]),
[iquote('0:Rew:264.0,1461.0,1366.0,1461.0')] ).
cnf(1834,plain,
equal(mult(mult(mult(u,v),w),v),mult(mult(u,w),v)),
inference(spr,[status(thm),theory(equality)],[1552,155]),
[iquote('0:SpR:1552.0,155.0')] ).
cnf(1903,plain,
equal(mult(mult(mult(u,v),w),mult(x,mult(y,v))),mult(y,mult(x,mult(mult(u,w),v)))),
inference(spr,[status(thm),theory(equality)],[1552,213]),
[iquote('0:SpR:1552.0,213.0')] ).
cnf(1904,plain,
equal(mult(mult(mult(u,v),mult(w,mult(x,w))),y),mult(x,mult(y,mult(mult(mult(u,w),v),y)))),
inference(spr,[status(thm),theory(equality)],[1552,143]),
[iquote('0:SpR:1552.0,143.0')] ).
cnf(2004,plain,
equal(mult(mult(u,mult(v,mult(mult(w,x),v))),y),mult(w,mult(y,mult(mult(mult(u,v),x),y)))),
inference(rew,[status(thm),theory(equality)],[1366,1904]),
[iquote('0:Rew:1366.0,1904.0')] ).
cnf(2106,plain,
equal(mult(mult(mult(u,v),w),mult(v,mult(x,mult(y,mult(mult(u,w),v))))),mult(x,mult(y,mult(mult(u,w),v)))),
inference(spr,[status(thm),theory(equality)],[1834,62]),
[iquote('0:SpR:1834.0,62.0')] ).
cnf(2186,plain,
equal(mult(mult(mult(mult(u,v),w),x),v),mult(mult(mult(u,w),x),v)),
inference(spr,[status(thm),theory(equality)],[1552,1834]),
[iquote('0:SpR:1552.0,1834.0')] ).
cnf(2261,plain,
equal(mult(mult(mult(u,v),v),mult(w,mult(x,y))),mult(u,mult(w,mult(mult(x,v),y)))),
inference(rew,[status(thm),theory(equality)],[788,2106,2186,1366,2004,1403,633]),
[iquote('0:Rew:788.0,2106.0,2186.0,2106.0,1366.0,2106.0,2004.0,2106.0,1366.0,2106.0,1403.0,2106.0,1366.0,2106.0,1366.0,2106.0,633.0,2106.0')] ).
cnf(2262,plain,
equal(mult(mult(u,v),mult(w,mult(x,y))),mult(u,mult(w,mult(mult(x,v),y)))),
inference(rew,[status(thm),theory(equality)],[155,2261]),
[iquote('0:Rew:155.0,2261.0')] ).
cnf(2336,plain,
equal(mult(mult(u,v),mult(w,mult(mult(x,y),v))),mult(x,mult(w,mult(mult(u,y),v)))),
inference(rew,[status(thm),theory(equality)],[2262,1903]),
[iquote('0:Rew:2262.0,1903.0')] ).
cnf(2351,plain,
equal(mult(u,mult(v,mult(mult(mult(w,x),y),y))),mult(w,mult(v,mult(mult(u,x),y)))),
inference(rew,[status(thm),theory(equality)],[2262,2336]),
[iquote('0:Rew:2262.0,2336.0')] ).
cnf(2352,plain,
equal(mult(u,mult(v,mult(mult(w,x),y))),mult(w,mult(v,mult(mult(u,x),y)))),
inference(rew,[status(thm),theory(equality)],[155,2351]),
[iquote('0:Rew:155.0,2351.0')] ).
cnf(2353,plain,
$false,
inference(unc,[status(thm)],[2352,5]),
[iquote('0:UnC:2352.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ALG236-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n021.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 : Wed Jun 8 15:06:52 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.53/1.72
% 1.53/1.72 SPASS V 3.9
% 1.53/1.72 SPASS beiseite: Proof found.
% 1.53/1.72 % SZS status Theorem
% 1.53/1.72 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.53/1.72 SPASS derived 1377 clauses, backtracked 0 clauses, performed 0 splits and kept 409 clauses.
% 1.53/1.72 SPASS allocated 67558 KBytes.
% 1.53/1.72 SPASS spent 0:00:01.35 on the problem.
% 1.53/1.72 0:00:00.04 for the input.
% 1.53/1.72 0:00:00.00 for the FLOTTER CNF translation.
% 1.53/1.72 0:00:00.02 for inferences.
% 1.53/1.72 0:00:00.00 for the backtracking.
% 1.53/1.72 0:00:01.27 for the reduction.
% 1.53/1.72
% 1.53/1.72
% 1.53/1.72 Here is a proof with depth 4, length 35 :
% 1.53/1.72 % SZS output start Refutation
% See solution above
% 1.53/1.72 Formulae used in the proof : c01 c02 c03 goals
% 1.53/1.72
%------------------------------------------------------------------------------