%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP658+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 : Theorem 1.26s 1.46s
% Output : Refutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of clauses : 58 ( 56 unt; 0 nHn; 58 RR)
% Number of literals : 60 ( 0 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP658+1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP658+1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP658+1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP658+1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(mult(u,mult(v,v)),w),mult(mult(u,v),mult(v,w))),
file('GRP658+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(mult(u,skf3(u)),skf3(u))
| ~ equal(mult(skf2(u),u),skf2(u)) ),
file('GRP658+1.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(17,plain,
equal(rd(mult(mult(u,v),mult(v,w)),w),mult(u,mult(v,v))),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(23,plain,
equal(mult(mult(rd(u,mult(v,v)),v),mult(v,w)),mult(u,w)),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(38,plain,
equal(rd(mult(mult(u,v),w),ld(v,w)),mult(u,mult(v,v))),
inference(spr,[status(thm),theory(equality)],[1,17]),
[iquote('0:SpR:1.0,17.0')] ).
cnf(40,plain,
equal(rd(mult(u,mult(v,w)),w),mult(rd(u,v),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[3,17]),
[iquote('0:SpR:3.0,17.0')] ).
cnf(98,plain,
equal(rd(mult(u,v),mult(w,v)),mult(rd(u,mult(w,w)),w)),
inference(spr,[status(thm),theory(equality)],[23,4]),
[iquote('0:SpR:23.0,4.0')] ).
cnf(99,plain,
equal(ld(mult(rd(u,mult(v,v)),v),mult(u,w)),mult(v,w)),
inference(spr,[status(thm),theory(equality)],[23,2]),
[iquote('0:SpR:23.0,2.0')] ).
cnf(108,plain,
equal(mult(mult(rd(u,mult(v,v)),v),w),mult(u,ld(v,w))),
inference(spr,[status(thm),theory(equality)],[1,23]),
[iquote('0:SpR:1.0,23.0')] ).
cnf(130,plain,
equal(rd(mult(u,v),ld(w,v)),mult(rd(u,w),mult(w,w))),
inference(spr,[status(thm),theory(equality)],[3,38]),
[iquote('0:SpR:3.0,38.0')] ).
cnf(149,plain,
equal(mult(rd(mult(u,mult(v,w)),w),x),mult(mult(rd(u,v),v),mult(v,x))),
inference(spr,[status(thm),theory(equality)],[40,5]),
[iquote('0:SpR:40.0,5.0')] ).
cnf(162,plain,
equal(mult(rd(mult(u,mult(v,w)),w),x),mult(u,mult(v,x))),
inference(rew,[status(thm),theory(equality)],[3,149]),
[iquote('0:Rew:3.0,149.0')] ).
cnf(273,plain,
equal(ld(rd(u,mult(v,v)),rd(mult(u,w),mult(v,w))),v),
inference(spr,[status(thm),theory(equality)],[98,2]),
[iquote('0:SpR:98.0,2.0')] ).
cnf(278,plain,
equal(rd(mult(u,v),mult(w,v)),rd(mult(u,x),mult(w,x))),
inference(spr,[status(thm),theory(equality)],[98]),
[iquote('0:SpR:98.0,98.0')] ).
cnf(284,plain,
equal(mult(rd(rd(u,v),mult(w,w)),w),rd(u,mult(w,v))),
inference(spr,[status(thm),theory(equality)],[3,98]),
[iquote('0:SpR:3.0,98.0')] ).
cnf(312,plain,
equal(ld(mult(rd(u,mult(v,v)),v),w),mult(v,ld(u,w))),
inference(spr,[status(thm),theory(equality)],[1,99]),
[iquote('0:SpR:1.0,99.0')] ).
cnf(516,plain,
equal(rd(mult(u,mult(v,v)),rd(mult(w,x),ld(v,x))),mult(rd(u,mult(rd(w,v),rd(w,v))),rd(w,v))),
inference(spr,[status(thm),theory(equality)],[130,98]),
[iquote('0:SpR:130.0,98.0')] ).
cnf(902,plain,
equal(mult(rd(mult(u,v),w),x),mult(u,mult(rd(v,w),x))),
inference(spr,[status(thm),theory(equality)],[3,162]),
[iquote('0:SpR:3.0,162.0')] ).
cnf(910,plain,
equal(mult(rd(u,mult(v,w)),mult(v,x)),mult(rd(u,w),x)),
inference(spr,[status(thm),theory(equality)],[3,162]),
[iquote('0:SpR:3.0,162.0')] ).
cnf(1255,plain,
equal(mult(rd(mult(u,v),mult(w,v)),mult(w,x)),mult(u,x)),
inference(spr,[status(thm),theory(equality)],[278,3]),
[iquote('0:SpR:278.0,3.0')] ).
cnf(1283,plain,
equal(rd(mult(u,v),mult(rd(w,x),v)),rd(mult(u,x),w)),
inference(spr,[status(thm),theory(equality)],[3,278]),
[iquote('0:SpR:3.0,278.0')] ).
cnf(1307,plain,
equal(rd(mult(u,v),mult(rd(w,x),v)),rd(mult(u,mult(x,x)),rd(mult(w,y),ld(x,y)))),
inference(spr,[status(thm),theory(equality)],[130,278]),
[iquote('0:SpR:130.0,278.0')] ).
cnf(1319,plain,
equal(mult(u,mult(rd(v,v),w)),mult(u,w)),
inference(rew,[status(thm),theory(equality)],[910,1255,902]),
[iquote('0:Rew:910.0,1255.0,902.0,1255.0')] ).
cnf(1333,plain,
equal(rd(mult(u,mult(v,v)),rd(mult(w,x),ld(v,x))),rd(mult(u,v),w)),
inference(rew,[status(thm),theory(equality)],[1283,1307]),
[iquote('0:Rew:1283.0,1307.0')] ).
cnf(1334,plain,
equal(mult(rd(u,mult(rd(v,w),rd(v,w))),rd(v,w)),rd(mult(u,w),v)),
inference(rew,[status(thm),theory(equality)],[1333,516]),
[iquote('0:Rew:1333.0,516.0')] ).
cnf(1371,plain,
equal(ld(u,mult(u,v)),mult(rd(w,w),v)),
inference(spr,[status(thm),theory(equality)],[1319,2]),
[iquote('0:SpR:1319.0,2.0')] ).
cnf(1435,plain,
equal(mult(rd(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[2,1371]),
[iquote('0:Rew:2.0,1371.0')] ).
cnf(1505,plain,
equal(rd(u,u),rd(v,v)),
inference(spr,[status(thm),theory(equality)],[1435,4]),
[iquote('0:SpR:1435.0,4.0')] ).
cnf(1509,plain,
equal(rd(u,mult(v,u)),mult(rd(rd(w,w),mult(v,v)),v)),
inference(spr,[status(thm),theory(equality)],[1435,98]),
[iquote('0:SpR:1435.0,98.0')] ).
cnf(1567,plain,
equal(rd(u,mult(v,u)),rd(w,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[284,1509]),
[iquote('0:Rew:284.0,1509.0')] ).
cnf(1665,plain,
equal(ld(rd(u,mult(u,u)),rd(v,v)),u),
inference(spr,[status(thm),theory(equality)],[1505,273]),
[iquote('0:SpR:1505.0,273.0')] ).
cnf(1992,plain,
equal(ld(rd(u,mult(v,u)),w),mult(v,w)),
inference(spr,[status(thm),theory(equality)],[1567,12]),
[iquote('0:SpR:1567.0,12.0')] ).
cnf(1995,plain,
equal(rd(mult(u,v),mult(u,v)),mult(rd(w,mult(u,w)),u)),
inference(spr,[status(thm),theory(equality)],[1567,98]),
[iquote('0:SpR:1567.0,98.0')] ).
cnf(1996,plain,
equal(mult(mult(rd(u,mult(v,u)),v),w),mult(v,ld(v,w))),
inference(spr,[status(thm),theory(equality)],[1567,108]),
[iquote('0:SpR:1567.0,108.0')] ).
cnf(2036,plain,
equal(mult(u,rd(v,v)),u),
inference(rew,[status(thm),theory(equality)],[1992,1665]),
[iquote('0:Rew:1992.0,1665.0')] ).
cnf(2040,plain,
equal(mult(mult(rd(u,mult(v,u)),v),w),w),
inference(rew,[status(thm),theory(equality)],[1,1996]),
[iquote('0:Rew:1.0,1996.0')] ).
cnf(2265,plain,
equal(rd(u,rd(v,v)),u),
inference(spr,[status(thm),theory(equality)],[2036,4]),
[iquote('0:SpR:2036.0,4.0')] ).
cnf(2269,plain,
equal(rd(u,mult(v,rd(w,w))),mult(rd(u,mult(v,v)),v)),
inference(spr,[status(thm),theory(equality)],[2036,98]),
[iquote('0:SpR:2036.0,98.0')] ).
cnf(2318,plain,
( ~ equal(mult(rd(u,u),skf3(rd(u,u))),skf3(rd(u,u)))
| ~ equal(skf2(rd(u,u)),skf2(rd(u,u))) ),
inference(spl,[status(thm),theory(equality)],[2036,6]),
[iquote('0:SpL:2036.0,6.1')] ).
cnf(2327,plain,
equal(mult(rd(u,mult(v,v)),v),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[2036,2269]),
[iquote('0:Rew:2036.0,2269.0')] ).
cnf(2328,plain,
equal(rd(mult(u,v),mult(w,v)),rd(u,w)),
inference(rew,[status(thm),theory(equality)],[2327,98]),
[iquote('0:Rew:2327.0,98.0')] ).
cnf(2329,plain,
equal(mult(rd(u,v),w),mult(u,ld(v,w))),
inference(rew,[status(thm),theory(equality)],[2327,108]),
[iquote('0:Rew:2327.0,108.0')] ).
cnf(2340,plain,
equal(rd(mult(u,v),w),rd(u,rd(w,v))),
inference(rew,[status(thm),theory(equality)],[2327,1334]),
[iquote('0:Rew:2327.0,1334.0')] ).
cnf(2357,plain,
equal(mult(u,ld(v,w)),ld(rd(v,u),w)),
inference(rew,[status(thm),theory(equality)],[2327,312]),
[iquote('0:Rew:2327.0,312.0')] ).
cnf(2368,plain,
equal(mult(rd(u,mult(v,u)),v),rd(v,v)),
inference(rew,[status(thm),theory(equality)],[2328,1995]),
[iquote('0:Rew:2328.0,1995.0')] ).
cnf(2416,plain,
equal(mult(mult(u,ld(mult(v,u),v)),w),w),
inference(rew,[status(thm),theory(equality)],[2329,2040]),
[iquote('0:Rew:2329.0,2040.0')] ).
cnf(2629,plain,
equal(mult(rd(u,v),w),ld(rd(v,u),w)),
inference(rew,[status(thm),theory(equality)],[2357,2329]),
[iquote('0:Rew:2357.0,2329.0')] ).
cnf(2634,plain,
equal(mult(ld(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[2265,2416,2340,2357]),
[iquote('0:Rew:2265.0,2416.0,2340.0,2416.0,2357.0,2416.0')] ).
cnf(2638,plain,
equal(ld(rd(mult(u,v),v),u),rd(u,u)),
inference(rew,[status(thm),theory(equality)],[2629,2368]),
[iquote('0:Rew:2629.0,2368.0')] ).
cnf(2639,plain,
equal(rd(u,u),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[2265,2638,2340]),
[iquote('0:Rew:2265.0,2638.0,2340.0,2638.0')] ).
cnf(2944,plain,
~ equal(mult(rd(u,u),skf3(rd(u,u))),skf3(rd(u,u))),
inference(obv,[status(thm),theory(equality)],[2318]),
[iquote('0:Obv:2318.1')] ).
cnf(2945,plain,
~ equal(skf3(ld(u,u)),skf3(ld(u,u))),
inference(rew,[status(thm),theory(equality)],[2634,2944,2639]),
[iquote('0:Rew:2634.0,2944.0,2639.0,2944.0')] ).
cnf(2946,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2945]),
[iquote('0:Obv:2945.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP658+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n017.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 : Tue Jun 14 00:50:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.26/1.46
% 1.26/1.46 SPASS V 3.9
% 1.26/1.46 SPASS beiseite: Proof found.
% 1.26/1.46 % SZS status Theorem
% 1.26/1.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.26/1.46 SPASS derived 1709 clauses, backtracked 0 clauses, performed 0 splits and kept 743 clauses.
% 1.26/1.46 SPASS allocated 93033 KBytes.
% 1.26/1.46 SPASS spent 0:00:01.06 on the problem.
% 1.26/1.46 0:00:00.04 for the input.
% 1.26/1.46 0:00:00.02 for the FLOTTER CNF translation.
% 1.26/1.46 0:00:00.02 for inferences.
% 1.26/1.46 0:00:00.00 for the backtracking.
% 1.26/1.46 0:00:00.97 for the reduction.
% 1.26/1.46
% 1.26/1.46
% 1.26/1.46 Here is a proof with depth 8, length 58 :
% 1.26/1.46 % SZS output start Refutation
% See solution above
% 1.26/1.46 Formulae used in the proof : f01 f02 f03 f04 f05 goals
% 1.26/1.46
%------------------------------------------------------------------------------