TSTP Solution File: GRP658-10 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP658-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 11:48:44 EDT 2022
% Result : Unsatisfiable 0.77s 0.97s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 30 RR)
% Number of literals : 30 ( 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP658-10.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP658-10.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP658-10.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(mult(u,mult(v,v)),w),mult(mult(u,v),mult(v,w))),
file('GRP658-10.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('GRP658-10.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(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(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(99,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(150,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(163,plain,
equal(mult(rd(mult(u,mult(v,w)),w),x),mult(u,mult(v,x))),
inference(rew,[status(thm),theory(equality)],[3,150]),
[iquote('0:Rew:3.0,150.0')] ).
cnf(275,plain,
equal(ld(rd(u,mult(v,v)),rd(mult(u,w),mult(v,w))),v),
inference(spr,[status(thm),theory(equality)],[99,2]),
[iquote('0:SpR:99.0,2.0')] ).
cnf(280,plain,
equal(rd(mult(u,v),mult(w,v)),rd(mult(u,x),mult(w,x))),
inference(spr,[status(thm),theory(equality)],[99]),
[iquote('0:SpR:99.0,99.0')] ).
cnf(286,plain,
equal(mult(rd(rd(u,v),mult(w,w)),w),rd(u,mult(w,v))),
inference(spr,[status(thm),theory(equality)],[3,99]),
[iquote('0:SpR:3.0,99.0')] ).
cnf(925,plain,
equal(mult(rd(mult(u,v),w),x),mult(u,mult(rd(v,w),x))),
inference(spr,[status(thm),theory(equality)],[3,163]),
[iquote('0:SpR:3.0,163.0')] ).
cnf(933,plain,
equal(mult(rd(u,mult(v,w)),mult(v,x)),mult(rd(u,w),x)),
inference(spr,[status(thm),theory(equality)],[3,163]),
[iquote('0:SpR:3.0,163.0')] ).
cnf(1228,plain,
equal(mult(rd(mult(u,v),mult(w,v)),mult(w,x)),mult(u,x)),
inference(spr,[status(thm),theory(equality)],[280,3]),
[iquote('0:SpR:280.0,3.0')] ).
cnf(1288,plain,
equal(mult(u,mult(rd(v,v),w)),mult(u,w)),
inference(rew,[status(thm),theory(equality)],[933,1228,925]),
[iquote('0:Rew:933.0,1228.0,925.0,1228.0')] ).
cnf(1335,plain,
equal(ld(u,mult(u,v)),mult(rd(w,w),v)),
inference(spr,[status(thm),theory(equality)],[1288,2]),
[iquote('0:SpR:1288.0,2.0')] ).
cnf(1402,plain,
equal(mult(rd(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[2,1335]),
[iquote('0:Rew:2.0,1335.0')] ).
cnf(1475,plain,
equal(rd(u,u),rd(v,v)),
inference(spr,[status(thm),theory(equality)],[1402,4]),
[iquote('0:SpR:1402.0,4.0')] ).
cnf(1479,plain,
equal(rd(u,mult(v,u)),mult(rd(rd(w,w),mult(v,v)),v)),
inference(spr,[status(thm),theory(equality)],[1402,99]),
[iquote('0:SpR:1402.0,99.0')] ).
cnf(1528,plain,
~ equal(tuple(x1__dfg(rd(u,u)),mult(x1_2(rd(u,u)),rd(u,u))),tuple(x1__dfg(rd(u,u)),x1_2(rd(u,u)))),
inference(spl,[status(thm),theory(equality)],[1402,6]),
[iquote('0:SpL:1402.0,6.0')] ).
cnf(1539,plain,
equal(rd(u,mult(v,u)),rd(w,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[286,1479]),
[iquote('0:Rew:286.0,1479.0')] ).
cnf(1637,plain,
equal(ld(rd(u,mult(u,u)),rd(v,v)),u),
inference(spr,[status(thm),theory(equality)],[1475,275]),
[iquote('0:SpR:1475.0,275.0')] ).
cnf(1955,plain,
equal(ld(rd(u,mult(v,u)),w),mult(v,w)),
inference(spr,[status(thm),theory(equality)],[1539,12]),
[iquote('0:SpR:1539.0,12.0')] ).
cnf(1997,plain,
equal(mult(u,rd(v,v)),u),
inference(rew,[status(thm),theory(equality)],[1955,1637]),
[iquote('0:Rew:1955.0,1637.0')] ).
cnf(1998,plain,
~ equal(tuple(x1__dfg(rd(u,u)),x1_2(rd(u,u))),tuple(x1__dfg(rd(u,u)),x1_2(rd(u,u)))),
inference(rew,[status(thm),theory(equality)],[1997,1528]),
[iquote('0:Rew:1997.0,1528.0')] ).
cnf(2016,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1998]),
[iquote('0:Obv:1998.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP658-10 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.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 : Tue Jun 14 02:00:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.77/0.97
% 0.77/0.97 SPASS V 3.9
% 0.77/0.97 SPASS beiseite: Proof found.
% 0.77/0.97 % SZS status Theorem
% 0.77/0.97 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.77/0.97 SPASS derived 1145 clauses, backtracked 0 clauses, performed 0 splits and kept 452 clauses.
% 0.77/0.97 SPASS allocated 68599 KBytes.
% 0.77/0.97 SPASS spent 0:00:00.59 on the problem.
% 0.77/0.97 0:00:00.04 for the input.
% 0.77/0.97 0:00:00.00 for the FLOTTER CNF translation.
% 0.77/0.97 0:00:00.02 for inferences.
% 0.77/0.97 0:00:00.00 for the backtracking.
% 0.77/0.97 0:00:00.51 for the reduction.
% 0.77/0.97
% 0.77/0.97
% 0.77/0.97 Here is a proof with depth 7, length 30 :
% 0.77/0.97 % SZS output start Refutation
% See solution above
% 0.77/0.97 Formulae used in the proof : f02 f03 f04 f05 goal
% 0.77/0.97
%------------------------------------------------------------------------------