TSTP Solution File: GRP708-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP708-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:49:06 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 26 RR)
% Number of literals : 26 ( 0 equ; 2 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; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP708-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP708-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP708-1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(u,mult(v,u)),w),mult(u,mult(v,mult(u,w)))),
file('GRP708-1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(op_c,u),mult(u,op_c)),
file('GRP708-1.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(mult(mult(op_c,op_c),u),v),mult(mult(op_c,op_c),mult(u,v))),
file('GRP708-1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(mult(mult(a,b),op_c),mult(a,mult(b,op_c))),
file('GRP708-1.p',unknown),
[] ).
cnf(11,plain,
~ equal(mult(a,mult(op_c,b)),mult(op_c,mult(a,b))),
inference(rew,[status(thm),theory(equality)],[8,10]),
[iquote('0:Rew:8.0,10.0,8.0,10.0')] ).
cnf(26,plain,
equal(mult(op_c,rd(u,op_c)),u),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(63,plain,
equal(rd(u,op_c),ld(op_c,u)),
inference(spr,[status(thm),theory(equality)],[26,2]),
[iquote('0:SpR:26.0,2.0')] ).
cnf(127,plain,
equal(mult(mult(op_c,op_c),mult(u,op_c)),mult(op_c,mult(mult(op_c,op_c),u))),
inference(spr,[status(thm),theory(equality)],[9,8]),
[iquote('0:SpR:9.0,8.0')] ).
cnf(137,plain,
equal(mult(mult(op_c,mult(op_c,op_c)),u),mult(mult(op_c,op_c),mult(op_c,u))),
inference(spr,[status(thm),theory(equality)],[8,9]),
[iquote('0:SpR:8.0,9.0')] ).
cnf(143,plain,
equal(mult(mult(op_c,op_c),mult(op_c,u)),mult(op_c,mult(op_c,mult(op_c,u)))),
inference(rew,[status(thm),theory(equality)],[7,137]),
[iquote('0:Rew:7.0,137.0')] ).
cnf(150,plain,
equal(mult(mult(op_c,op_c),mult(op_c,u)),mult(op_c,mult(mult(op_c,op_c),u))),
inference(spr,[status(thm),theory(equality)],[8,127]),
[iquote('0:SpR:8.0,127.0')] ).
cnf(151,plain,
equal(mult(op_c,mult(mult(op_c,op_c),rd(u,op_c))),mult(mult(op_c,op_c),u)),
inference(spr,[status(thm),theory(equality)],[3,127]),
[iquote('0:SpR:3.0,127.0')] ).
cnf(156,plain,
equal(mult(op_c,mult(mult(op_c,op_c),u)),mult(op_c,mult(op_c,mult(op_c,u)))),
inference(rew,[status(thm),theory(equality)],[143,150]),
[iquote('0:Rew:143.0,150.0')] ).
cnf(160,plain,
equal(mult(op_c,mult(mult(op_c,op_c),ld(op_c,u))),mult(mult(op_c,op_c),u)),
inference(rew,[status(thm),theory(equality)],[63,151]),
[iquote('0:Rew:63.0,151.0')] ).
cnf(161,plain,
equal(mult(op_c,mult(op_c,mult(op_c,ld(op_c,u)))),mult(mult(op_c,op_c),u)),
inference(rew,[status(thm),theory(equality)],[156,160]),
[iquote('0:Rew:156.0,160.0')] ).
cnf(162,plain,
equal(mult(mult(op_c,op_c),u),mult(op_c,mult(op_c,u))),
inference(rew,[status(thm),theory(equality)],[1,161]),
[iquote('0:Rew:1.0,161.0')] ).
cnf(163,plain,
equal(mult(mult(mult(op_c,op_c),u),v),mult(op_c,mult(op_c,mult(u,v)))),
inference(rew,[status(thm),theory(equality)],[162,9]),
[iquote('0:Rew:162.0,9.0')] ).
cnf(172,plain,
equal(mult(mult(op_c,mult(op_c,u)),v),mult(op_c,mult(op_c,mult(u,v)))),
inference(rew,[status(thm),theory(equality)],[162,163]),
[iquote('0:Rew:162.0,163.0')] ).
cnf(198,plain,
equal(mult(mult(op_c,mult(u,op_c)),v),mult(op_c,mult(op_c,mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[8,172]),
[iquote('0:SpR:8.0,172.0')] ).
cnf(205,plain,
equal(mult(op_c,mult(u,mult(op_c,v))),mult(op_c,mult(op_c,mult(u,v)))),
inference(rew,[status(thm),theory(equality)],[7,198]),
[iquote('0:Rew:7.0,198.0')] ).
cnf(942,plain,
equal(ld(op_c,mult(op_c,mult(op_c,mult(u,v)))),mult(u,mult(op_c,v))),
inference(spr,[status(thm),theory(equality)],[205,2]),
[iquote('0:SpR:205.0,2.0')] ).
cnf(995,plain,
equal(mult(op_c,mult(u,v)),mult(u,mult(op_c,v))),
inference(rew,[status(thm),theory(equality)],[2,942]),
[iquote('0:Rew:2.0,942.0')] ).
cnf(996,plain,
$false,
inference(unc,[status(thm)],[995,11]),
[iquote('0:UnC:995.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP708-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 12:21:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 714 clauses, backtracked 0 clauses, performed 0 splits and kept 207 clauses.
% 0.19/0.52 SPASS allocated 64150 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.52 0:00:00.04 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.10 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 2, length 26 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.52 Formulae used in the proof : c01 c02 c03 c07 c08 c09 goals
% 0.19/0.52
%------------------------------------------------------------------------------