TSTP Solution File: GRP748-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP748-3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:49:15 EDT 2022
% Result : Unsatisfiable 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 31 ( 23 unt; 8 nHn; 31 RR)
% Number of literals : 39 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP748-3.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP748-3.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP748-3.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP748-3.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP748-3.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(mult(u,v),w),v),mult(u,mult(mult(v,w),v))),
file('GRP748-3.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(mult(u,v),i(v)),u),
file('GRP748-3.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(u,i(u)),unit),
file('GRP748-3.p',unknown),
[] ).
cnf(10,axiom,
equal(mult(i(u),u),unit),
file('GRP748-3.p',unknown),
[] ).
cnf(11,axiom,
( equal(mult(u,v),mult(v,u))
| equal(mult(i(u),mult(u,v)),v) ),
file('GRP748-3.p',unknown),
[] ).
cnf(12,axiom,
~ equal(mult(mult(mult(a,b),c),b),mult(a,mult(b,mult(c,b)))),
file('GRP748-3.p',unknown),
[] ).
cnf(13,plain,
~ equal(mult(a,mult(mult(b,c),b)),mult(a,mult(b,mult(c,b)))),
inference(rew,[status(thm),theory(equality)],[7,12]),
[iquote('0:Rew:7.0,12.0')] ).
cnf(26,plain,
equal(rd(unit,u),i(u)),
inference(spr,[status(thm),theory(equality)],[10,4]),
[iquote('0:SpR:10.0,4.0')] ).
cnf(28,plain,
equal(rd(unit,i(u)),u),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(29,plain,
equal(i(i(u)),u),
inference(rew,[status(thm),theory(equality)],[26,28]),
[iquote('0:Rew:26.0,28.0')] ).
cnf(102,plain,
equal(mult(u,i(v)),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.0')] ).
cnf(112,plain,
( equal(mult(u,v),mult(v,u))
| equal(ld(i(u),v),mult(u,v)) ),
inference(spr,[status(thm),theory(equality)],[11,2]),
[iquote('0:SpR:11.1,2.0')] ).
cnf(118,plain,
( equal(mult(ld(u,v),u),mult(u,ld(u,v)))
| equal(mult(i(u),v),ld(u,v)) ),
inference(spr,[status(thm),theory(equality)],[1,11]),
[iquote('0:SpR:1.0,11.1')] ).
cnf(126,plain,
( equal(mult(ld(u,v),u),v)
| equal(mult(i(u),v),ld(u,v)) ),
inference(rew,[status(thm),theory(equality)],[1,118]),
[iquote('0:Rew:1.0,118.0')] ).
cnf(196,plain,
equal(mult(i(u),mult(mult(u,v),u)),mult(mult(unit,v),u)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(208,plain,
equal(mult(i(u),mult(mult(u,v),u)),mult(v,u)),
inference(rew,[status(thm),theory(equality)],[6,196]),
[iquote('0:Rew:6.0,196.0')] ).
cnf(399,plain,
equal(ld(i(u),mult(v,u)),mult(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[208,2]),
[iquote('0:SpR:208.0,2.0')] ).
cnf(793,plain,
( equal(mult(i(u),v),mult(v,i(u)))
| equal(mult(i(u),v),ld(u,v)) ),
inference(spr,[status(thm),theory(equality)],[29,112]),
[iquote('0:SpR:29.0,112.1')] ).
cnf(801,plain,
( equal(mult(i(u),v),rd(v,u))
| equal(mult(i(u),v),ld(u,v)) ),
inference(rew,[status(thm),theory(equality)],[102,793]),
[iquote('0:Rew:102.0,793.0')] ).
cnf(1005,plain,
( equal(mult(i(u),v),ld(u,v))
| equal(rd(v,u),ld(u,v)) ),
inference(spr,[status(thm),theory(equality)],[126,4]),
[iquote('0:SpR:126.0,4.0')] ).
cnf(1033,plain,
( equal(mult(i(u),v),ld(u,v))
| equal(mult(i(u),v),ld(u,v)) ),
inference(rew,[status(thm),theory(equality)],[1005,801]),
[iquote('0:Rew:1005.1,801.0')] ).
cnf(1034,plain,
equal(mult(i(u),v),ld(u,v)),
inference(obv,[status(thm),theory(equality)],[1033]),
[iquote('0:Obv:1033.0')] ).
cnf(1087,plain,
equal(ld(i(u),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[29,1034]),
[iquote('0:SpR:29.0,1034.0')] ).
cnf(1094,plain,
equal(mult(mult(u,v),u),mult(u,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[1087,399]),
[iquote('0:Rew:1087.0,399.0')] ).
cnf(1113,plain,
~ equal(mult(a,mult(b,mult(c,b))),mult(a,mult(b,mult(c,b)))),
inference(rew,[status(thm),theory(equality)],[1094,13]),
[iquote('0:Rew:1094.0,13.0')] ).
cnf(1160,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1113]),
[iquote('0:Obv:1113.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP748-3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 06:04:06 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.51
% 0.21/0.51 SPASS V 3.9
% 0.21/0.51 SPASS beiseite: Proof found.
% 0.21/0.51 % SZS status Theorem
% 0.21/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51 SPASS derived 737 clauses, backtracked 0 clauses, performed 0 splits and kept 217 clauses.
% 0.21/0.51 SPASS allocated 64306 KBytes.
% 0.21/0.51 SPASS spent 0:00:00.14 on the problem.
% 0.21/0.51 0:00:00.03 for the input.
% 0.21/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.51 0:00:00.01 for inferences.
% 0.21/0.51 0:00:00.00 for the backtracking.
% 0.21/0.51 0:00:00.08 for the reduction.
% 0.21/0.51
% 0.21/0.51
% 0.21/0.51 Here is a proof with depth 3, length 31 :
% 0.21/0.51 % SZS output start Refutation
% See solution above
% 0.21/0.51 Formulae used in the proof : f01 f02 f03 f04 f06 f07 f08 f09 f10 f11 goals
% 0.21/0.51
%------------------------------------------------------------------------------