TSTP Solution File: GRP683-10 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP683-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:48:57 EDT 2022
% Result : Unsatisfiable 1.08s 1.32s
% Output : Refutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 48 RR)
% Number of literals : 48 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ld(u,mult(u,u)),u),
file('GRP683-10.p',unknown),
[] ).
cnf(2,axiom,
equal(rd(mult(u,u),u),u),
file('GRP683-10.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
file('GRP683-10.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(rd(u,v),v),rd(mult(u,v),v)),
file('GRP683-10.p',unknown),
[] ).
cnf(5,axiom,
equal(ld(ld(u,v),mult(ld(u,v),mult(w,x))),mult(ld(u,mult(u,w)),x)),
file('GRP683-10.p',unknown),
[] ).
cnf(6,axiom,
equal(rd(mult(mult(u,v),rd(w,x)),rd(w,x)),mult(u,rd(mult(v,x),x))),
file('GRP683-10.p',unknown),
[] ).
cnf(7,axiom,
equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
file('GRP683-10.p',unknown),
[] ).
cnf(8,axiom,
~ equal(mult(x3__dfg,ld(x4__dfg,mult(x4__dfg,x5__dfg))),mult(x3__dfg,x5__dfg)),
file('GRP683-10.p',unknown),
[] ).
cnf(19,plain,
equal(ld(u,mult(u,ld(rd(u,u),rd(u,u)))),rd(u,u)),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(21,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(rd(u,u),v),v),v)),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(23,plain,
equal(rd(rd(mult(u,u),u),u),ld(u,mult(u,ld(u,u)))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(24,plain,
equal(rd(u,u),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[2,23,1,3]),
[iquote('0:Rew:2.0,23.0,1.0,23.0,3.0,23.0')] ).
cnf(26,plain,
equal(ld(u,mult(u,ld(ld(u,u),ld(u,u)))),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[24,19]),
[iquote('0:Rew:24.0,19.0')] ).
cnf(27,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(ld(u,u),v),v),v)),
inference(rew,[status(thm),theory(equality)],[24,21]),
[iquote('0:Rew:24.0,21.0')] ).
cnf(29,plain,
equal(mult(ld(u,u),u),rd(mult(u,u),u)),
inference(spr,[status(thm),theory(equality)],[24,4]),
[iquote('0:SpR:24.0,4.0')] ).
cnf(31,plain,
equal(mult(ld(u,u),u),u),
inference(rew,[status(thm),theory(equality)],[2,29]),
[iquote('0:Rew:2.0,29.0')] ).
cnf(44,plain,
equal(ld(u,mult(u,mult(u,ld(ld(u,u),ld(u,u))))),mult(u,ld(u,u))),
inference(spr,[status(thm),theory(equality)],[26,3]),
[iquote('0:SpR:26.0,3.0')] ).
cnf(45,plain,
equal(ld(u,mult(u,mult(u,ld(ld(u,u),ld(u,u))))),u),
inference(rew,[status(thm),theory(equality)],[1,44,3]),
[iquote('0:Rew:1.0,44.0,3.0,44.0')] ).
cnf(51,plain,
equal(mult(u,rd(mult(v,w),w)),rd(mult(mult(u,v),w),w)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(102,plain,
equal(rd(mult(mult(u,v),v),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[2,51]),
[iquote('0:SpR:2.0,51.0')] ).
cnf(106,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[102,27]),
[iquote('0:Rew:102.0,27.0')] ).
cnf(170,plain,
equal(mult(ld(u,mult(u,ld(u,v))),ld(ld(ld(u,v),ld(u,v)),ld(ld(u,v),ld(u,v)))),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[5,45]),
[iquote('0:SpR:5.0,45.0')] ).
cnf(177,plain,
equal(ld(ld(u,v),mult(ld(u,v),w)),mult(ld(u,mult(u,ld(w,w))),w)),
inference(spr,[status(thm),theory(equality)],[31,5]),
[iquote('0:SpR:31.0,5.0')] ).
cnf(178,plain,
equal(mult(ld(u,mult(u,v)),w),ld(u,mult(u,mult(v,w)))),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(191,plain,
equal(ld(u,mult(u,mult(ld(v,v),v))),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[178,106]),
[iquote('0:Rew:178.0,106.0')] ).
cnf(192,plain,
equal(mult(ld(u,u),v),ld(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[31,191]),
[iquote('0:Rew:31.0,191.0')] ).
cnf(198,plain,
equal(ld(ld(u,v),mult(ld(u,v),w)),ld(u,mult(u,ld(w,mult(w,w))))),
inference(rew,[status(thm),theory(equality)],[192,177,178]),
[iquote('0:Rew:192.0,177.0,178.0,177.0')] ).
cnf(199,plain,
equal(ld(ld(u,v),mult(ld(u,v),w)),ld(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[1,198]),
[iquote('0:Rew:1.0,198.0')] ).
cnf(217,plain,
equal(mult(ld(u,ld(u,mult(u,v))),ld(ld(ld(u,v),ld(u,v)),ld(ld(u,v),ld(u,v)))),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[3,170]),
[iquote('0:Rew:3.0,170.0')] ).
cnf(234,plain,
equal(rd(ld(u,mult(u,ld(u,u))),ld(u,u)),ld(u,u)),
inference(spr,[status(thm),theory(equality)],[192,2]),
[iquote('0:SpR:192.0,2.0')] ).
cnf(251,plain,
equal(ld(ld(u,u),ld(u,u)),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[24,234,1,3]),
[iquote('0:Rew:24.0,234.0,1.0,234.0,3.0,234.0')] ).
cnf(254,plain,
equal(mult(ld(u,ld(u,mult(u,v))),ld(ld(u,v),ld(u,v))),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[251,217]),
[iquote('0:Rew:251.0,217.0')] ).
cnf(466,plain,
equal(mult(ld(u,ld(u,mult(u,v))),w),ld(u,mult(u,mult(ld(u,v),w)))),
inference(spr,[status(thm),theory(equality)],[3,178]),
[iquote('0:SpR:3.0,178.0')] ).
cnf(470,plain,
equal(ld(u,mult(u,mult(u,v))),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[1,178]),
[iquote('0:SpR:1.0,178.0')] ).
cnf(477,plain,
equal(ld(u,mult(u,mult(ld(u,v),ld(ld(u,v),ld(u,v))))),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[466,254]),
[iquote('0:Rew:466.0,254.0')] ).
cnf(480,plain,
equal(ld(u,ld(u,mult(u,v))),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[3,477,1]),
[iquote('0:Rew:3.0,477.0,1.0,477.0,3.0,477.0')] ).
cnf(482,plain,
equal(ld(u,mult(u,mult(ld(u,v),w))),mult(ld(u,v),w)),
inference(rew,[status(thm),theory(equality)],[480,466]),
[iquote('0:Rew:480.0,466.0')] ).
cnf(788,plain,
equal(ld(ld(u,v),ld(u,mult(u,w))),ld(ld(u,v),w)),
inference(spr,[status(thm),theory(equality)],[199,480]),
[iquote('0:SpR:199.0,480.0')] ).
cnf(789,plain,
equal(ld(ld(u,v),mult(ld(u,v),mult(ld(u,v),w))),mult(ld(u,v),ld(u,mult(u,w)))),
inference(spr,[status(thm),theory(equality)],[199,3]),
[iquote('0:SpR:199.0,3.0')] ).
cnf(801,plain,
equal(ld(ld(u,mult(u,v)),ld(u,mult(u,mult(v,w)))),ld(u,mult(u,w))),
inference(spr,[status(thm),theory(equality)],[178,199]),
[iquote('0:SpR:178.0,199.0')] ).
cnf(817,plain,
equal(ld(ld(u,mult(u,v)),mult(v,w)),ld(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[788,801]),
[iquote('0:Rew:788.0,801.0')] ).
cnf(827,plain,
equal(mult(ld(u,v),ld(u,mult(u,w))),ld(u,mult(u,mult(ld(u,v),w)))),
inference(rew,[status(thm),theory(equality)],[199,789]),
[iquote('0:Rew:199.0,789.0')] ).
cnf(828,plain,
equal(mult(ld(u,v),ld(u,mult(u,w))),mult(ld(u,v),w)),
inference(rew,[status(thm),theory(equality)],[482,827]),
[iquote('0:Rew:482.0,827.0')] ).
cnf(2316,plain,
equal(ld(ld(u,mult(u,ld(v,w))),mult(ld(v,w),x)),ld(u,mult(u,ld(v,mult(v,x))))),
inference(spr,[status(thm),theory(equality)],[828,817]),
[iquote('0:SpR:828.0,817.0')] ).
cnf(2362,plain,
equal(ld(u,mult(u,ld(v,mult(v,w)))),ld(u,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[817,2316]),
[iquote('0:Rew:817.0,2316.0')] ).
cnf(5752,plain,
equal(ld(u,mult(u,mult(u,ld(v,mult(v,w))))),mult(u,ld(u,mult(u,w)))),
inference(spr,[status(thm),theory(equality)],[2362,3]),
[iquote('0:SpR:2362.0,3.0')] ).
cnf(5835,plain,
equal(mult(u,ld(v,mult(v,w))),mult(u,w)),
inference(rew,[status(thm),theory(equality)],[470,5752,3]),
[iquote('0:Rew:470.0,5752.0,470.0,5752.0,3.0,5752.0')] ).
cnf(5836,plain,
$false,
inference(unc,[status(thm)],[5835,8]),
[iquote('0:UnC:5835.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP683-10 : TPTP v8.1.0. Released v8.1.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 15:06:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.08/1.32
% 1.08/1.32 SPASS V 3.9
% 1.08/1.32 SPASS beiseite: Proof found.
% 1.08/1.32 % SZS status Theorem
% 1.08/1.32 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.08/1.32 SPASS derived 3232 clauses, backtracked 0 clauses, performed 0 splits and kept 757 clauses.
% 1.08/1.32 SPASS allocated 70882 KBytes.
% 1.08/1.32 SPASS spent 0:00:00.93 on the problem.
% 1.08/1.32 0:00:00.03 for the input.
% 1.08/1.32 0:00:00.00 for the FLOTTER CNF translation.
% 1.08/1.32 0:00:00.03 for inferences.
% 1.08/1.32 0:00:00.00 for the backtracking.
% 1.08/1.32 0:00:00.84 for the reduction.
% 1.08/1.32
% 1.08/1.32
% 1.08/1.32 Here is a proof with depth 6, length 48 :
% 1.08/1.32 % SZS output start Refutation
% See solution above
% 1.08/1.32 Formulae used in the proof : f01 f02 f03 f04 f05 f06 f07 goal
% 1.08/1.32
%------------------------------------------------------------------------------