TSTP Solution File: GRP665+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP665+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 11:48:50 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 17 unt; 0 nHn; 23 RR)
% Number of literals : 32 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP665+1.p',unknown),
[] ).
cnf(4,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP665+1.p',unknown),
[] ).
cnf(6,axiom,
equal(rd(mult(u,v),v),u),
file('GRP665+1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(op_c,u),mult(u,op_c)),
file('GRP665+1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(rd(mult(u,v),u),mult(u,w)),mult(u,mult(v,w))),
file('GRP665+1.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(mult(u,v),ld(v,mult(w,v))),mult(mult(u,w),v)),
file('GRP665+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(mult(mult(op_c,skc6),skc7),mult(op_c,mult(skc6,skc7)))
| ~ equal(mult(mult(skc8,op_c),skc9),mult(skc8,mult(op_c,skc9)))
| ~ equal(mult(mult(skc10,skc11),op_c),mult(skc10,mult(skc11,op_c))) ),
file('GRP665+1.p',unknown),
[] ).
cnf(11,plain,
( ~ equal(mult(skc10,mult(op_c,skc11)),mult(op_c,mult(skc10,skc11)))
| ~ equal(mult(mult(op_c,skc8),skc9),mult(skc8,mult(op_c,skc9)))
| ~ equal(mult(mult(op_c,skc6),skc7),mult(op_c,mult(skc6,skc7))) ),
inference(rew,[status(thm),theory(equality)],[7,10]),
[iquote('0:Rew:7.0,10.2,7.0,10.2,7.0,10.1')] ).
cnf(22,plain,
equal(rd(mult(u,op_c),u),op_c),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(53,plain,
equal(ld(op_c,mult(u,op_c)),u),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(135,plain,
equal(mult(op_c,mult(u,v)),mult(u,mult(op_c,v))),
inference(spr,[status(thm),theory(equality)],[22,8]),
[iquote('0:SpR:22.0,8.0')] ).
cnf(136,plain,
( ~ equal(mult(op_c,mult(skc10,skc11)),mult(op_c,mult(skc10,skc11)))
| ~ equal(mult(mult(op_c,skc8),skc9),mult(skc8,mult(op_c,skc9)))
| ~ equal(mult(mult(op_c,skc6),skc7),mult(op_c,mult(skc6,skc7))) ),
inference(rew,[status(thm),theory(equality)],[135,11]),
[iquote('0:Rew:135.0,11.0')] ).
cnf(156,plain,
( ~ equal(mult(mult(op_c,skc8),skc9),mult(skc8,mult(op_c,skc9)))
| ~ equal(mult(mult(op_c,skc6),skc7),mult(op_c,mult(skc6,skc7))) ),
inference(obv,[status(thm),theory(equality)],[136]),
[iquote('0:Obv:136.0')] ).
cnf(157,plain,
( ~ equal(mult(mult(op_c,skc8),skc9),mult(op_c,mult(skc8,skc9)))
| ~ equal(mult(mult(op_c,skc6),skc7),mult(op_c,mult(skc6,skc7))) ),
inference(rew,[status(thm),theory(equality)],[135,156]),
[iquote('0:Rew:135.0,156.0')] ).
cnf(267,plain,
equal(mult(mult(u,op_c),v),mult(mult(u,v),op_c)),
inference(spr,[status(thm),theory(equality)],[53,9]),
[iquote('0:SpR:53.0,9.0')] ).
cnf(272,plain,
equal(mult(mult(u,op_c),ld(u,mult(v,u))),mult(mult(op_c,v),u)),
inference(spr,[status(thm),theory(equality)],[7,9]),
[iquote('0:SpR:7.0,9.0')] ).
cnf(281,plain,
equal(mult(mult(u,op_c),v),mult(op_c,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[7,267]),
[iquote('0:Rew:7.0,267.0')] ).
cnf(291,plain,
equal(mult(op_c,mult(u,ld(u,mult(v,u)))),mult(mult(op_c,v),u)),
inference(rew,[status(thm),theory(equality)],[281,272]),
[iquote('0:Rew:281.0,272.0')] ).
cnf(292,plain,
equal(mult(mult(op_c,u),v),mult(op_c,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[3,291]),
[iquote('0:Rew:3.0,291.0')] ).
cnf(293,plain,
( ~ equal(mult(mult(op_c,skc8),skc9),mult(op_c,mult(skc8,skc9)))
| ~ equal(mult(op_c,mult(skc6,skc7)),mult(op_c,mult(skc6,skc7))) ),
inference(rew,[status(thm),theory(equality)],[292,157]),
[iquote('0:Rew:292.0,157.1')] ).
cnf(308,plain,
~ equal(mult(mult(op_c,skc8),skc9),mult(op_c,mult(skc8,skc9))),
inference(obv,[status(thm),theory(equality)],[293]),
[iquote('0:Obv:293.1')] ).
cnf(309,plain,
~ equal(mult(op_c,mult(skc8,skc9)),mult(op_c,mult(skc8,skc9))),
inference(rew,[status(thm),theory(equality)],[292,308]),
[iquote('0:Rew:292.0,308.0')] ).
cnf(310,plain,
$false,
inference(obv,[status(thm),theory(equality)],[309]),
[iquote('0:Obv:309.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP665+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 01:09:17 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 233 clauses, backtracked 0 clauses, performed 0 splits and kept 73 clauses.
% 0.19/0.47 SPASS allocated 85422 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.47 0:00:00.04 for the input.
% 0.19/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.02 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 2, length 23 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : f01 f02 f04 f09 f07 f08 goals
% 0.19/0.47
%------------------------------------------------------------------------------