TSTP Solution File: GRP660-14 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP660-14 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:48:46 EDT 2022
% Result : Unsatisfiable 25.11s 25.29s
% Output : Refutation 25.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of clauses : 71 ( 71 unt; 0 nHn; 71 RR)
% Number of literals : 71 ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP660-14.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP660-14.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP660-14.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP660-14.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(mult(mult(u,v),w),u),mult(u,mult(v,mult(w,u)))),
file('GRP660-14.p',unknown),
[] ).
cnf(6,axiom,
~ equal(mult(ld(x1__dfg,x1__dfg),x0__dfg),x0__dfg),
file('GRP660-14.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(25,plain,
equal(rd(mult(u,mult(v,mult(w,u))),u),mult(mult(u,v),w)),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(28,plain,
equal(mult(mult(u,mult(v,mult(w,u))),mult(u,v)),mult(mult(u,v),mult(w,mult(u,mult(u,v))))),
inference(spr,[status(thm),theory(equality)],[5]),
[iquote('0:SpR:5.0,5.0')] ).
cnf(30,plain,
equal(mult(rd(u,v),mult(v,mult(w,rd(u,v)))),mult(mult(u,w),rd(u,v))),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(31,plain,
equal(mult(u,mult(ld(u,v),mult(w,u))),mult(mult(v,w),u)),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(36,plain,
equal(rd(mult(u,mult(v,w)),u),mult(mult(u,v),rd(w,u))),
inference(spr,[status(thm),theory(equality)],[3,25]),
[iquote('0:SpR:3.0,25.0')] ).
cnf(39,plain,
equal(mult(mult(u,rd(v,mult(w,u))),w),rd(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[3,25]),
[iquote('0:SpR:3.0,25.0')] ).
cnf(68,plain,
equal(mult(ld(u,v),mult(w,u)),ld(u,mult(mult(v,w),u))),
inference(spr,[status(thm),theory(equality)],[31,2]),
[iquote('0:SpR:31.0,2.0')] ).
cnf(78,plain,
equal(mult(mult(u,rd(v,w)),w),mult(w,mult(ld(w,u),v))),
inference(spr,[status(thm),theory(equality)],[3,31]),
[iquote('0:SpR:3.0,31.0')] ).
cnf(130,plain,
equal(mult(mult(u,rd(v,w)),rd(w,u)),rd(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[3,36]),
[iquote('0:SpR:3.0,36.0')] ).
cnf(131,plain,
equal(mult(mult(u,v),rd(ld(v,w),u)),rd(mult(u,w),u)),
inference(spr,[status(thm),theory(equality)],[1,36]),
[iquote('0:SpR:1.0,36.0')] ).
cnf(137,plain,
equal(rd(rd(mult(u,v),u),w),mult(u,rd(v,mult(w,u)))),
inference(spr,[status(thm),theory(equality)],[39,4]),
[iquote('0:SpR:39.0,4.0')] ).
cnf(151,plain,
equal(rd(mult(ld(u,v),w),ld(u,v)),mult(mult(ld(u,v),rd(w,v)),u)),
inference(spr,[status(thm),theory(equality)],[1,39]),
[iquote('0:SpR:1.0,39.0')] ).
cnf(221,plain,
equal(rd(ld(u,mult(mult(v,w),u)),mult(w,u)),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[68,4]),
[iquote('0:SpR:68.0,4.0')] ).
cnf(272,plain,
equal(mult(u,mult(ld(u,rd(v,rd(w,u))),w)),mult(v,u)),
inference(spr,[status(thm),theory(equality)],[3,78]),
[iquote('0:SpR:3.0,78.0')] ).
cnf(363,plain,
equal(mult(mult(u,v),mult(rd(w,u),mult(u,mult(u,v)))),mult(mult(u,mult(v,w)),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[3,28]),
[iquote('0:SpR:3.0,28.0')] ).
cnf(502,plain,
equal(ld(mult(u,v),rd(mult(u,w),u)),rd(ld(v,w),u)),
inference(spr,[status(thm),theory(equality)],[131,2]),
[iquote('0:SpR:131.0,2.0')] ).
cnf(579,plain,
equal(mult(u,rd(ld(u,v),mult(w,u))),rd(rd(v,u),w)),
inference(spr,[status(thm),theory(equality)],[1,137]),
[iquote('0:SpR:1.0,137.0')] ).
cnf(589,plain,
equal(mult(u,rd(u,mult(v,u))),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[4,137]),
[iquote('0:SpR:4.0,137.0')] ).
cnf(706,plain,
equal(rd(u,mult(v,u)),ld(u,rd(u,v))),
inference(spr,[status(thm),theory(equality)],[589,2]),
[iquote('0:SpR:589.0,2.0')] ).
cnf(732,plain,
equal(rd(u,rd(v,u)),mult(u,rd(u,v))),
inference(spr,[status(thm),theory(equality)],[3,589]),
[iquote('0:SpR:3.0,589.0')] ).
cnf(805,plain,
equal(ld(ld(u,rd(u,v)),u),mult(v,u)),
inference(spr,[status(thm),theory(equality)],[706,12]),
[iquote('0:SpR:706.0,12.0')] ).
cnf(816,plain,
equal(ld(ld(u,v),rd(ld(u,v),u)),rd(ld(u,v),v)),
inference(spr,[status(thm),theory(equality)],[1,706]),
[iquote('0:SpR:1.0,706.0')] ).
cnf(842,plain,
equal(ld(mult(u,rd(u,v)),u),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[732,12]),
[iquote('0:SpR:732.0,12.0')] ).
cnf(872,plain,
equal(ld(ld(mult(u,v),u),mult(u,v)),mult(v,mult(u,v))),
inference(spr,[status(thm),theory(equality)],[4,805]),
[iquote('0:SpR:4.0,805.0')] ).
cnf(873,plain,
equal(mult(ld(u,v),v),ld(ld(v,u),v)),
inference(spr,[status(thm),theory(equality)],[13,805]),
[iquote('0:SpR:13.0,805.0')] ).
cnf(927,plain,
equal(rd(ld(u,v),v),ld(mult(v,u),v)),
inference(spr,[status(thm),theory(equality)],[13,842]),
[iquote('0:SpR:13.0,842.0')] ).
cnf(935,plain,
equal(ld(ld(u,v),rd(ld(u,v),u)),ld(mult(v,u),v)),
inference(rew,[status(thm),theory(equality)],[927,816]),
[iquote('0:Rew:927.0,816.0')] ).
cnf(986,plain,
equal(ld(ld(mult(u,v),u),ld(v,u)),u),
inference(spr,[status(thm),theory(equality)],[927,12]),
[iquote('0:SpR:927.0,12.0')] ).
cnf(1255,plain,
equal(rd(ld(u,mult(v,u)),mult(w,u)),ld(u,rd(v,w))),
inference(spr,[status(thm),theory(equality)],[3,221]),
[iquote('0:SpR:3.0,221.0')] ).
cnf(1494,plain,
equal(mult(ld(u,rd(v,rd(w,u))),w),ld(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[272,2]),
[iquote('0:SpR:272.0,2.0')] ).
cnf(1533,plain,
equal(ld(mult(ld(u,rd(v,rd(w,u))),w),rd(mult(ld(u,rd(v,rd(w,u))),w),u)),rd(mult(ld(u,rd(v,rd(w,u))),w),mult(v,u))),
inference(spr,[status(thm),theory(equality)],[272,706]),
[iquote('0:SpR:272.0,706.0')] ).
cnf(1585,plain,
equal(ld(mult(mult(u,v),v),mult(u,v)),ld(v,rd(u,u))),
inference(rew,[status(thm),theory(equality)],[935,1533,1255,1494]),
[iquote('0:Rew:935.0,1533.0,1255.0,1533.0,1494.0,1533.0')] ).
cnf(1706,plain,
equal(rd(ld(ld(u,v),w),u),ld(v,rd(mult(u,w),u))),
inference(spr,[status(thm),theory(equality)],[1,502]),
[iquote('0:SpR:1.0,502.0')] ).
cnf(1986,plain,
equal(rd(rd(u,v),rd(w,v)),mult(v,rd(ld(v,u),w))),
inference(spr,[status(thm),theory(equality)],[3,579]),
[iquote('0:SpR:3.0,579.0')] ).
cnf(2483,plain,
equal(mult(rd(u,v),mult(u,rd(u,v))),ld(rd(v,u),mult(u,rd(u,v)))),
inference(spr,[status(thm),theory(equality)],[842,872]),
[iquote('0:SpR:842.0,872.0')] ).
cnf(3513,plain,
equal(ld(rd(mult(u,u),u),mult(u,rd(u,u))),ld(rd(u,u),rd(u,u))),
inference(spr,[status(thm),theory(equality)],[130,1585]),
[iquote('0:SpR:130.0,1585.0')] ).
cnf(3522,plain,
equal(ld(rd(u,u),rd(u,u)),rd(u,u)),
inference(rew,[status(thm),theory(equality)],[2,3513,4]),
[iquote('0:Rew:2.0,3513.0,4.0,3513.0')] ).
cnf(3563,plain,
equal(mult(rd(u,u),rd(u,u)),rd(u,u)),
inference(spr,[status(thm),theory(equality)],[3522,1]),
[iquote('0:SpR:3522.0,1.0')] ).
cnf(3574,plain,
equal(rd(rd(u,u),rd(u,u)),rd(u,u)),
inference(spr,[status(thm),theory(equality)],[3522,13]),
[iquote('0:SpR:3522.0,13.0')] ).
cnf(3583,plain,
equal(mult(u,rd(ld(u,u),u)),rd(u,u)),
inference(rew,[status(thm),theory(equality)],[1986,3574]),
[iquote('0:Rew:1986.0,3574.0')] ).
cnf(3584,plain,
equal(mult(u,ld(mult(u,u),u)),rd(u,u)),
inference(rew,[status(thm),theory(equality)],[927,3583]),
[iquote('0:Rew:927.0,3583.0')] ).
cnf(3623,plain,
equal(rd(mult(rd(u,u),u),rd(u,u)),mult(rd(u,u),rd(u,rd(u,u)))),
inference(spr,[status(thm),theory(equality)],[3563,130]),
[iquote('0:SpR:3563.0,130.0')] ).
cnf(3636,plain,
equal(mult(mult(u,rd(u,u)),rd(u,u)),mult(rd(u,u),mult(u,rd(u,u)))),
inference(spr,[status(thm),theory(equality)],[3563,30]),
[iquote('0:SpR:3563.0,30.0')] ).
cnf(3654,plain,
equal(mult(rd(u,u),mult(u,rd(u,u))),mult(u,rd(u,u))),
inference(rew,[status(thm),theory(equality)],[732,3623,3]),
[iquote('0:Rew:732.0,3623.0,3.0,3623.0,732.0,3623.0')] ).
cnf(3655,plain,
equal(ld(rd(u,u),mult(u,rd(u,u))),mult(u,rd(u,u))),
inference(rew,[status(thm),theory(equality)],[2483,3654]),
[iquote('0:Rew:2483.0,3654.0')] ).
cnf(3656,plain,
equal(mult(rd(u,u),mult(u,rd(u,u))),u),
inference(rew,[status(thm),theory(equality)],[4,3636,130]),
[iquote('0:Rew:4.0,3636.0,130.0,3636.0')] ).
cnf(3657,plain,
equal(mult(u,rd(u,u)),u),
inference(rew,[status(thm),theory(equality)],[3655,3656,2483]),
[iquote('0:Rew:3655.0,3656.0,2483.0,3656.0')] ).
cnf(3878,plain,
equal(rd(u,u),ld(u,u)),
inference(spr,[status(thm),theory(equality)],[3657,2]),
[iquote('0:SpR:3657.0,2.0')] ).
cnf(3886,plain,
equal(ld(ld(u,u),ld(rd(u,u),u)),u),
inference(spr,[status(thm),theory(equality)],[3657,986]),
[iquote('0:SpR:3657.0,986.0')] ).
cnf(3981,plain,
equal(mult(u,ld(mult(u,u),u)),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[3878,3584]),
[iquote('0:Rew:3878.0,3584.0')] ).
cnf(4001,plain,
equal(ld(ld(u,u),u),u),
inference(rew,[status(thm),theory(equality)],[12,3886]),
[iquote('0:Rew:12.0,3886.0')] ).
cnf(4386,plain,
equal(ld(mult(u,u),u),ld(u,ld(u,u))),
inference(spr,[status(thm),theory(equality)],[3981,2]),
[iquote('0:SpR:3981.0,2.0')] ).
cnf(4564,plain,
equal(mult(ld(u,ld(u,u)),u),ld(ld(u,mult(u,u)),u)),
inference(spr,[status(thm),theory(equality)],[4386,873]),
[iquote('0:SpR:4386.0,873.0')] ).
cnf(4585,plain,
equal(mult(ld(u,ld(u,u)),u),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[2,4564]),
[iquote('0:Rew:2.0,4564.0')] ).
cnf(5073,plain,
equal(mult(ld(u,u),mult(rd(v,ld(u,ld(u,u))),mult(ld(u,ld(u,u)),ld(u,u)))),mult(mult(ld(u,ld(u,u)),mult(u,v)),ld(u,u))),
inference(spr,[status(thm),theory(equality)],[4585,363]),
[iquote('0:SpR:4585.0,363.0')] ).
cnf(5163,plain,
equal(mult(mult(ld(u,ld(u,u)),mult(u,v)),ld(u,u)),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[3,5073,4001,873]),
[iquote('0:Rew:3.0,5073.0,4001.0,5073.0,873.0,5073.0')] ).
cnf(5791,plain,
equal(ld(u,rd(mult(ld(u,u),v),ld(u,u))),rd(ld(u,v),ld(u,u))),
inference(spr,[status(thm),theory(equality)],[4001,1706]),
[iquote('0:SpR:4001.0,1706.0')] ).
cnf(5828,plain,
equal(ld(u,mult(mult(ld(u,u),rd(v,u)),u)),rd(ld(u,v),ld(u,u))),
inference(rew,[status(thm),theory(equality)],[151,5791]),
[iquote('0:Rew:151.0,5791.0')] ).
cnf(5829,plain,
equal(rd(ld(u,v),ld(u,u)),mult(ld(u,ld(u,u)),v)),
inference(rew,[status(thm),theory(equality)],[2,5828,78]),
[iquote('0:Rew:2.0,5828.0,78.0,5828.0')] ).
cnf(13593,plain,
equal(mult(mult(ld(u,ld(u,u)),v),ld(u,u)),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[5829,3]),
[iquote('0:SpR:5829.0,3.0')] ).
cnf(13692,plain,
equal(mult(ld(u,u),v),ld(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[13593,5163]),
[iquote('0:Rew:13593.0,5163.0')] ).
cnf(13695,plain,
equal(mult(ld(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[2,13692]),
[iquote('0:Rew:2.0,13692.0')] ).
cnf(13696,plain,
$false,
inference(unc,[status(thm)],[13695,6]),
[iquote('0:UnC:13695.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP660-14 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n028.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 : Mon Jun 13 23:12:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 25.11/25.29
% 25.11/25.29 SPASS V 3.9
% 25.11/25.29 SPASS beiseite: Proof found.
% 25.11/25.29 % SZS status Theorem
% 25.11/25.29 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.11/25.29 SPASS derived 8512 clauses, backtracked 0 clauses, performed 0 splits and kept 4168 clauses.
% 25.11/25.29 SPASS allocated 110295 KBytes.
% 25.11/25.29 SPASS spent 0:0:24.66 on the problem.
% 25.11/25.29 0:00:00.04 for the input.
% 25.11/25.29 0:00:00.00 for the FLOTTER CNF translation.
% 25.11/25.29 0:00:00.10 for inferences.
% 25.11/25.29 0:00:00.00 for the backtracking.
% 25.11/25.29 0:0:24.50 for the reduction.
% 25.11/25.29
% 25.11/25.29
% 25.11/25.29 Here is a proof with depth 12, length 71 :
% 25.11/25.29 % SZS output start Refutation
% See solution above
% 25.11/25.29 Formulae used in the proof : f01 f02 f03 f04 f05 goal
% 25.11/25.29
%------------------------------------------------------------------------------