TSTP Solution File: GRP659-10 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP659-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 11:48:45 EDT 2022
% Result : Unsatisfiable 5.15s 5.39s
% Output : Refutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of clauses : 83 ( 83 unt; 0 nHn; 83 RR)
% Number of literals : 83 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP659-10.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP659-10.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP659-10.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP659-10.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(mult(u,mult(v,w)),v),mult(mult(u,v),mult(w,v))),
file('GRP659-10.p',unknown),
[] ).
cnf(6,axiom,
~ equal(tuple(mult(u,x1__dfg(u)),mult(x1_2(u),u)),tuple(x1__dfg(u),x1_2(u))),
file('GRP659-10.p',unknown),
[] ).
cnf(12,plain,
equal(ld(rd(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(13,plain,
equal(rd(u,ld(v,u)),v),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(17,plain,
equal(rd(mult(mult(u,v),mult(w,v)),v),mult(u,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(23,plain,
equal(mult(mult(u,v),mult(ld(v,w),v)),mult(mult(u,w),v)),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(24,plain,
equal(mult(mult(rd(u,mult(v,w)),v),mult(w,v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(36,plain,
equal(rd(mult(mult(u,v),w),v),mult(u,mult(v,rd(w,v)))),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(39,plain,
equal(rd(mult(u,mult(v,w)),w),mult(rd(u,w),mult(w,v))),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(72,plain,
equal(ld(mult(u,v),mult(mult(u,w),v)),mult(ld(v,w),v)),
inference(spr,[status(thm),theory(equality)],[23,2]),
[iquote('0:SpR:23.0,2.0')] ).
cnf(93,plain,
equal(rd(mult(u,v),mult(w,v)),mult(rd(u,mult(v,w)),v)),
inference(spr,[status(thm),theory(equality)],[24,4]),
[iquote('0:SpR:24.0,4.0')] ).
cnf(129,plain,
equal(mult(u,mult(v,rd(v,v))),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[36,4]),
[iquote('0:SpR:36.0,4.0')] ).
cnf(147,plain,
equal(ld(u,mult(u,v)),mult(v,rd(v,v))),
inference(spr,[status(thm),theory(equality)],[129,2]),
[iquote('0:SpR:129.0,2.0')] ).
cnf(167,plain,
equal(mult(u,rd(u,u)),u),
inference(rew,[status(thm),theory(equality)],[2,147]),
[iquote('0:Rew:2.0,147.0')] ).
cnf(231,plain,
equal(rd(u,u),ld(u,u)),
inference(spr,[status(thm),theory(equality)],[167,2]),
[iquote('0:SpR:167.0,2.0')] ).
cnf(263,plain,
equal(mult(ld(u,u),u),u),
inference(spr,[status(thm),theory(equality)],[231,3]),
[iquote('0:SpR:231.0,3.0')] ).
cnf(264,plain,
equal(ld(ld(u,u),u),u),
inference(spr,[status(thm),theory(equality)],[231,12]),
[iquote('0:SpR:231.0,12.0')] ).
cnf(669,plain,
equal(mult(rd(ld(mult(u,v),mult(u,v)),v),mult(v,u)),rd(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[263,39]),
[iquote('0:SpR:263.0,39.0')] ).
cnf(680,plain,
equal(mult(rd(ld(mult(u,v),mult(u,v)),v),mult(v,u)),u),
inference(rew,[status(thm),theory(equality)],[4,669]),
[iquote('0:Rew:4.0,669.0')] ).
cnf(964,plain,
equal(ld(mult(rd(u,v),w),mult(u,w)),mult(ld(w,v),w)),
inference(spr,[status(thm),theory(equality)],[3,72]),
[iquote('0:SpR:3.0,72.0')] ).
cnf(966,plain,
equal(mult(ld(u,ld(v,w)),u),ld(mult(v,u),mult(w,u))),
inference(spr,[status(thm),theory(equality)],[1,72]),
[iquote('0:SpR:1.0,72.0')] ).
cnf(1304,plain,
equal(mult(rd(ld(u,u),mult(u,v)),u),rd(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[263,93]),
[iquote('0:SpR:263.0,93.0')] ).
cnf(2807,plain,
equal(rd(ld(mult(u,v),mult(u,v)),v),rd(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[680,4]),
[iquote('0:SpR:680.0,4.0')] ).
cnf(3548,plain,
equal(ld(mult(rd(ld(u,u),v),u),u),mult(ld(u,v),u)),
inference(spr,[status(thm),theory(equality)],[263,964]),
[iquote('0:SpR:263.0,964.0')] ).
cnf(3592,plain,
equal(rd(ld(mult(u,v),mult(w,v)),v),ld(v,ld(u,w))),
inference(spr,[status(thm),theory(equality)],[966,4]),
[iquote('0:SpR:966.0,4.0')] ).
cnf(3672,plain,
equal(rd(u,mult(v,u)),ld(v,ld(u,u))),
inference(rew,[status(thm),theory(equality)],[3592,2807]),
[iquote('0:Rew:3592.0,2807.0')] ).
cnf(3677,plain,
equal(mult(rd(ld(u,u),mult(u,v)),u),ld(v,ld(u,u))),
inference(rew,[status(thm),theory(equality)],[3672,1304]),
[iquote('0:Rew:3672.0,1304.0')] ).
cnf(3750,plain,
equal(ld(ld(u,ld(v,v)),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[3672,12]),
[iquote('0:SpR:3672.0,12.0')] ).
cnf(3764,plain,
equal(ld(rd(u,v),ld(v,v)),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[3,3672]),
[iquote('0:SpR:3.0,3672.0')] ).
cnf(4167,plain,
equal(mult(rd(ld(u,u),v),u),ld(v,u)),
inference(spr,[status(thm),theory(equality)],[12,3750]),
[iquote('0:SpR:12.0,3750.0')] ).
cnf(4174,plain,
equal(mult(ld(u,v),u),ld(ld(v,u),u)),
inference(rew,[status(thm),theory(equality)],[4167,3548]),
[iquote('0:Rew:4167.0,3548.0')] ).
cnf(4175,plain,
equal(ld(mult(u,v),u),ld(v,ld(u,u))),
inference(rew,[status(thm),theory(equality)],[4167,3677]),
[iquote('0:Rew:4167.0,3677.0')] ).
cnf(4527,plain,
equal(mult(rd(u,v),rd(v,u)),ld(v,v)),
inference(spr,[status(thm),theory(equality)],[3764,1]),
[iquote('0:SpR:3764.0,1.0')] ).
cnf(4532,plain,
equal(rd(ld(u,u),rd(u,v)),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[3764,13]),
[iquote('0:SpR:3764.0,13.0')] ).
cnf(4563,plain,
equal(rd(ld(u,v),v),rd(ld(v,v),u)),
inference(spr,[status(thm),theory(equality)],[4167,4]),
[iquote('0:SpR:4167.0,4.0')] ).
cnf(4564,plain,
equal(ld(rd(ld(u,u),v),ld(v,u)),u),
inference(spr,[status(thm),theory(equality)],[4167,2]),
[iquote('0:SpR:4167.0,2.0')] ).
cnf(4671,plain,
equal(rd(ld(ld(u,v),v),v),ld(v,u)),
inference(spr,[status(thm),theory(equality)],[4174,4]),
[iquote('0:SpR:4174.0,4.0')] ).
cnf(4709,plain,
equal(rd(u,ld(ld(v,u),u)),ld(ld(u,v),ld(u,u))),
inference(spr,[status(thm),theory(equality)],[4174,3672]),
[iquote('0:SpR:4174.0,3672.0')] ).
cnf(4730,plain,
equal(rd(ld(u,u),ld(v,u)),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[4563,4671]),
[iquote('0:Rew:4563.0,4671.0')] ).
cnf(4732,plain,
equal(ld(ld(u,v),ld(u,u)),ld(v,u)),
inference(rew,[status(thm),theory(equality)],[13,4709]),
[iquote('0:Rew:13.0,4709.0')] ).
cnf(4951,plain,
equal(ld(u,ld(rd(v,u),rd(v,u))),ld(v,rd(v,u))),
inference(spr,[status(thm),theory(equality)],[3,4175]),
[iquote('0:SpR:3.0,4175.0')] ).
cnf(5091,plain,
equal(ld(rd(u,v),ld(rd(v,u),rd(v,u))),ld(ld(u,u),rd(v,u))),
inference(spr,[status(thm),theory(equality)],[4527,4175]),
[iquote('0:SpR:4527.0,4175.0')] ).
cnf(5114,plain,
equal(ld(rd(u,v),ld(rd(v,u),rd(v,u))),rd(rd(v,u),ld(v,v))),
inference(spr,[status(thm),theory(equality)],[4527,3672]),
[iquote('0:SpR:4527.0,3672.0')] ).
cnf(5120,plain,
equal(mult(rd(ld(u,v),v),u),ld(v,v)),
inference(spr,[status(thm),theory(equality)],[13,4527]),
[iquote('0:SpR:13.0,4527.0')] ).
cnf(5171,plain,
equal(ld(ld(u,u),rd(v,u)),rd(rd(v,u),ld(v,v))),
inference(rew,[status(thm),theory(equality)],[5091,5114]),
[iquote('0:Rew:5091.0,5114.0')] ).
cnf(5201,plain,
equal(rd(ld(ld(u,u),ld(u,u)),rd(v,u)),rd(rd(u,v),ld(u,u))),
inference(spr,[status(thm),theory(equality)],[4532]),
[iquote('0:SpR:4532.0,4532.0')] ).
cnf(5229,plain,
equal(rd(ld(u,u),rd(v,u)),rd(rd(u,v),ld(u,u))),
inference(rew,[status(thm),theory(equality)],[4732,5201]),
[iquote('0:Rew:4732.0,5201.0')] ).
cnf(5269,plain,
equal(mult(rd(ld(u,v),v),rd(u,ld(v,v))),ld(u,u)),
inference(spr,[status(thm),theory(equality)],[4563,4527]),
[iquote('0:SpR:4563.0,4527.0')] ).
cnf(5270,plain,
equal(rd(ld(ld(u,u),ld(u,u)),rd(ld(v,u),u)),rd(v,ld(u,u))),
inference(spr,[status(thm),theory(equality)],[4563,4532]),
[iquote('0:SpR:4563.0,4532.0')] ).
cnf(5306,plain,
equal(rd(ld(u,u),rd(ld(v,u),u)),rd(v,ld(u,u))),
inference(rew,[status(thm),theory(equality)],[4732,5270]),
[iquote('0:Rew:4732.0,5270.0')] ).
cnf(5446,plain,
equal(ld(rd(ld(ld(u,u),ld(u,u)),rd(v,u)),rd(u,v)),ld(u,u)),
inference(spr,[status(thm),theory(equality)],[3764,4564]),
[iquote('0:SpR:3764.0,4564.0')] ).
cnf(5467,plain,
equal(ld(rd(ld(u,u),rd(v,u)),rd(u,v)),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[4732,5446]),
[iquote('0:Rew:4732.0,5446.0')] ).
cnf(5499,plain,
equal(rd(ld(u,u),v),ld(u,rd(u,v))),
inference(spr,[status(thm),theory(equality)],[12,4730]),
[iquote('0:SpR:12.0,4730.0')] ).
cnf(5512,plain,
equal(rd(ld(ld(u,u),ld(u,u)),rd(u,v)),ld(ld(u,u),rd(v,u))),
inference(spr,[status(thm),theory(equality)],[3764,4730]),
[iquote('0:SpR:3764.0,4730.0')] ).
cnf(5516,plain,
equal(ld(u,rd(u,rd(u,v))),rd(v,u)),
inference(rew,[status(thm),theory(equality)],[5499,4532]),
[iquote('0:Rew:5499.0,4532.0')] ).
cnf(5517,plain,
equal(rd(ld(u,v),v),ld(v,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[5499,4563]),
[iquote('0:Rew:5499.0,4563.0')] ).
cnf(5521,plain,
equal(ld(u,rd(u,rd(ld(v,u),u))),rd(v,ld(u,u))),
inference(rew,[status(thm),theory(equality)],[5499,5306]),
[iquote('0:Rew:5499.0,5306.0')] ).
cnf(5524,plain,
equal(rd(rd(u,v),ld(u,u)),ld(u,rd(u,rd(v,u)))),
inference(rew,[status(thm),theory(equality)],[5499,5229]),
[iquote('0:Rew:5499.0,5229.0')] ).
cnf(5525,plain,
equal(ld(ld(u,rd(u,rd(v,u))),rd(u,v)),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[5499,5467]),
[iquote('0:Rew:5499.0,5467.0')] ).
cnf(5584,plain,
equal(mult(ld(u,rd(u,v)),v),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[5517,5120]),
[iquote('0:Rew:5517.0,5120.0')] ).
cnf(5587,plain,
equal(mult(ld(u,rd(u,v)),rd(v,ld(u,u))),ld(v,v)),
inference(rew,[status(thm),theory(equality)],[5517,5269]),
[iquote('0:Rew:5517.0,5269.0')] ).
cnf(5600,plain,
equal(ld(u,rd(u,ld(u,rd(u,v)))),rd(v,ld(u,u))),
inference(rew,[status(thm),theory(equality)],[5517,5521]),
[iquote('0:Rew:5517.0,5521.0')] ).
cnf(5602,plain,
equal(ld(ld(u,u),rd(v,u)),ld(v,rd(v,rd(u,v)))),
inference(rew,[status(thm),theory(equality)],[5524,5171]),
[iquote('0:Rew:5524.0,5171.0')] ).
cnf(5612,plain,
equal(ld(ld(u,u),rd(v,u)),rd(v,u)),
inference(rew,[status(thm),theory(equality)],[5516,5512,5499,4732]),
[iquote('0:Rew:5516.0,5512.0,5499.0,5512.0,4732.0,5512.0')] ).
cnf(5615,plain,
equal(ld(u,rd(u,rd(v,u))),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[5612,5602]),
[iquote('0:Rew:5612.0,5602.0')] ).
cnf(5620,plain,
equal(ld(rd(u,v),rd(u,v)),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[5615,5525]),
[iquote('0:Rew:5615.0,5525.0')] ).
cnf(5649,plain,
equal(ld(u,ld(v,v)),ld(v,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[5620,4951]),
[iquote('0:Rew:5620.0,4951.0')] ).
cnf(5688,plain,
equal(ld(u,rd(u,ld(u,v))),ld(v,u)),
inference(rew,[status(thm),theory(equality)],[5649,4732]),
[iquote('0:Rew:5649.0,4732.0')] ).
cnf(5689,plain,
equal(rd(u,ld(v,v)),ld(rd(v,u),v)),
inference(rew,[status(thm),theory(equality)],[5688,5600]),
[iquote('0:Rew:5688.0,5600.0')] ).
cnf(5691,plain,
equal(rd(u,ld(v,v)),u),
inference(rew,[status(thm),theory(equality)],[12,5689]),
[iquote('0:Rew:12.0,5689.0')] ).
cnf(5707,plain,
equal(mult(ld(u,rd(u,v)),v),ld(v,v)),
inference(rew,[status(thm),theory(equality)],[5691,5587]),
[iquote('0:Rew:5691.0,5587.0')] ).
cnf(5755,plain,
equal(ld(u,u),ld(v,v)),
inference(rew,[status(thm),theory(equality)],[5584,5707]),
[iquote('0:Rew:5584.0,5707.0')] ).
cnf(5961,plain,
equal(mult(u,ld(v,v)),u),
inference(spr,[status(thm),theory(equality)],[5691,4]),
[iquote('0:SpR:5691.0,4.0')] ).
cnf(6175,plain,
equal(mult(ld(u,u),v),ld(ld(v,v),v)),
inference(spr,[status(thm),theory(equality)],[5755,4174]),
[iquote('0:SpR:5755.0,4174.0')] ).
cnf(6179,plain,
equal(ld(ld(u,u),v),v),
inference(spr,[status(thm),theory(equality)],[5755,264]),
[iquote('0:SpR:5755.0,264.0')] ).
cnf(6217,plain,
equal(mult(ld(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[6179,6175]),
[iquote('0:Rew:6179.0,6175.0')] ).
cnf(7348,plain,
~ equal(tuple(mult(ld(u,u),x1__dfg(ld(u,u))),x1_2(ld(u,u))),tuple(x1__dfg(ld(u,u)),x1_2(ld(u,u)))),
inference(spl,[status(thm),theory(equality)],[5961,6]),
[iquote('0:SpL:5961.0,6.0')] ).
cnf(7397,plain,
~ equal(tuple(x1__dfg(ld(u,u)),x1_2(ld(u,u))),tuple(x1__dfg(ld(u,u)),x1_2(ld(u,u)))),
inference(rew,[status(thm),theory(equality)],[6217,7348]),
[iquote('0:Rew:6217.0,7348.0')] ).
cnf(7398,plain,
$false,
inference(obv,[status(thm),theory(equality)],[7397]),
[iquote('0:Obv:7397.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP659-10 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 22:16:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.15/5.39
% 5.15/5.39 SPASS V 3.9
% 5.15/5.39 SPASS beiseite: Proof found.
% 5.15/5.39 % SZS status Theorem
% 5.15/5.39 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.15/5.39 SPASS derived 4685 clauses, backtracked 0 clauses, performed 0 splits and kept 2458 clauses.
% 5.15/5.39 SPASS allocated 80102 KBytes.
% 5.15/5.39 SPASS spent 0:00:04.97 on the problem.
% 5.15/5.39 0:00:00.04 for the input.
% 5.15/5.39 0:00:00.00 for the FLOTTER CNF translation.
% 5.15/5.39 0:00:00.04 for inferences.
% 5.15/5.39 0:00:00.00 for the backtracking.
% 5.15/5.39 0:00:04.86 for the reduction.
% 5.15/5.39
% 5.15/5.39
% 5.15/5.39 Here is a proof with depth 14, length 83 :
% 5.15/5.39 % SZS output start Refutation
% See solution above
% 5.15/5.39 Formulae used in the proof : f01 f02 f03 f04 f05 goal
% 5.15/5.39
%------------------------------------------------------------------------------