TSTP Solution File: GRP669-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP669-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:48:53 EDT 2022
% Result : Unsatisfiable 0.91s 1.11s
% Output : Refutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 37 RR)
% Number of literals : 37 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP669-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP669-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP669-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP669-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,unit),u),
file('GRP669-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP669-1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(mult(u,v),u),w),mult(u,mult(v,mult(u,w)))),
file('GRP669-1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(mult(mult(u,v),w),v),mult(u,mult(v,mult(w,v)))),
file('GRP669-1.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(mult(u,mult(v,w)),u),mult(mult(u,v),mult(w,u))),
file('GRP669-1.p',unknown),
[] ).
cnf(10,axiom,
equal(mult(mult(u,v),mult(w,u)),mult(u,mult(mult(v,w),u))),
file('GRP669-1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(mult(mult(mult(a,mult(b,c)),a),b),mult(mult(a,b),mult(c,mult(a,b)))),
file('GRP669-1.p',unknown),
[] ).
cnf(12,plain,
equal(mult(mult(u,mult(v,w)),u),mult(u,mult(mult(v,w),u))),
inference(rew,[status(thm),theory(equality)],[10,9]),
[iquote('0:Rew:10.0,9.0')] ).
cnf(13,plain,
~ equal(mult(mult(a,mult(mult(b,c),a)),b),mult(mult(a,b),mult(c,mult(a,b)))),
inference(rew,[status(thm),theory(equality)],[12,11]),
[iquote('0:Rew:12.0,11.0')] ).
cnf(32,plain,
equal(ld(u,u),unit),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(58,plain,
equal(rd(mult(u,mult(v,mult(w,v))),v),mult(mult(u,v),w)),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(63,plain,
equal(mult(unit,mult(u,mult(v,u))),mult(mult(u,v),u)),
inference(spr,[status(thm),theory(equality)],[6,8]),
[iquote('0:SpR:6.0,8.0')] ).
cnf(70,plain,
equal(mult(mult(u,v),u),mult(u,mult(v,u))),
inference(rew,[status(thm),theory(equality)],[6,63]),
[iquote('0:Rew:6.0,63.0')] ).
cnf(71,plain,
equal(mult(mult(u,mult(v,u)),w),mult(u,mult(v,mult(u,w)))),
inference(rew,[status(thm),theory(equality)],[70,7]),
[iquote('0:Rew:70.0,7.0')] ).
cnf(74,plain,
~ equal(mult(mult(a,b),mult(c,mult(a,b))),mult(a,mult(mult(b,c),mult(a,b)))),
inference(rew,[status(thm),theory(equality)],[71,13]),
[iquote('0:Rew:71.0,13.0')] ).
cnf(75,plain,
~ equal(mult(mult(a,b),mult(c,mult(a,b))),mult(a,mult(b,mult(mult(c,a),b)))),
inference(rew,[status(thm),theory(equality)],[10,74]),
[iquote('0:Rew:10.0,74.0')] ).
cnf(77,plain,
equal(rd(mult(u,mult(v,u)),u),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[70,4]),
[iquote('0:SpR:70.0,4.0')] ).
cnf(85,plain,
equal(mult(u,mult(ld(u,v),u)),mult(v,u)),
inference(spr,[status(thm),theory(equality)],[1,70]),
[iquote('0:SpR:1.0,70.0')] ).
cnf(105,plain,
equal(mult(mult(u,v),mult(w,mult(u,mult(x,u)))),mult(u,mult(mult(v,mult(mult(w,u),x)),u))),
inference(spr,[status(thm),theory(equality)],[8,10]),
[iquote('0:SpR:8.0,10.0')] ).
cnf(109,plain,
equal(mult(u,mult(mult(ld(u,v),w),u)),mult(v,mult(w,u))),
inference(spr,[status(thm),theory(equality)],[1,10]),
[iquote('0:SpR:1.0,10.0')] ).
cnf(160,plain,
equal(rd(mult(u,v),u),mult(u,rd(v,u))),
inference(spr,[status(thm),theory(equality)],[3,77]),
[iquote('0:SpR:3.0,77.0')] ).
cnf(211,plain,
equal(mult(ld(u,v),u),ld(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[85,2]),
[iquote('0:SpR:85.0,2.0')] ).
cnf(247,plain,
equal(rd(mult(u,mult(v,mult(u,w))),w),mult(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[71,4]),
[iquote('0:SpR:71.0,4.0')] ).
cnf(736,plain,
equal(rd(mult(u,mult(v,ld(v,mult(w,v)))),v),mult(mult(u,v),ld(v,w))),
inference(spr,[status(thm),theory(equality)],[211,58]),
[iquote('0:SpR:211.0,58.0')] ).
cnf(771,plain,
equal(rd(mult(u,mult(v,w)),w),mult(mult(u,w),ld(w,v))),
inference(rew,[status(thm),theory(equality)],[1,736]),
[iquote('0:Rew:1.0,736.0')] ).
cnf(2607,plain,
equal(mult(u,rd(mult(mult(ld(u,v),w),u),u)),rd(mult(v,mult(w,u)),u)),
inference(spr,[status(thm),theory(equality)],[109,160]),
[iquote('0:SpR:109.0,160.0')] ).
cnf(2661,plain,
equal(rd(mult(u,mult(v,w)),w),mult(w,mult(ld(w,u),v))),
inference(rew,[status(thm),theory(equality)],[4,2607]),
[iquote('0:Rew:4.0,2607.0')] ).
cnf(2662,plain,
equal(mult(mult(u,v),ld(v,w)),mult(v,mult(ld(v,u),w))),
inference(rew,[status(thm),theory(equality)],[771,2661]),
[iquote('0:Rew:771.0,2661.0')] ).
cnf(2668,plain,
equal(rd(mult(u,mult(v,w)),w),mult(w,mult(ld(w,u),v))),
inference(rew,[status(thm),theory(equality)],[2662,771]),
[iquote('0:Rew:2662.0,771.0')] ).
cnf(3085,plain,
equal(rd(mult(mult(u,v),mult(w,mult(u,mult(v,u)))),u),mult(mult(u,v),mult(w,mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[70,247]),
[iquote('0:SpR:70.0,247.0')] ).
cnf(3142,plain,
equal(mult(u,mult(ld(u,u),mult(v,mult(mult(w,u),v)))),mult(mult(u,v),mult(w,mult(u,v)))),
inference(rew,[status(thm),theory(equality)],[2668,3085,105]),
[iquote('0:Rew:2668.0,3085.0,105.0,3085.0')] ).
cnf(3143,plain,
equal(mult(mult(u,v),mult(w,mult(u,v))),mult(u,mult(v,mult(mult(w,u),v)))),
inference(rew,[status(thm),theory(equality)],[6,3142,32]),
[iquote('0:Rew:6.0,3142.0,32.0,3142.0')] ).
cnf(3144,plain,
$false,
inference(unc,[status(thm)],[3143,75]),
[iquote('0:UnC:3143.0,75.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP669-1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 09:53:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.91/1.11
% 0.91/1.11 SPASS V 3.9
% 0.91/1.11 SPASS beiseite: Proof found.
% 0.91/1.11 % SZS status Theorem
% 0.91/1.11 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.91/1.11 SPASS derived 1768 clauses, backtracked 0 clauses, performed 0 splits and kept 720 clauses.
% 0.91/1.11 SPASS allocated 68017 KBytes.
% 0.91/1.11 SPASS spent 0:00:00.75 on the problem.
% 0.91/1.11 0:00:00.04 for the input.
% 0.91/1.11 0:00:00.00 for the FLOTTER CNF translation.
% 0.91/1.11 0:00:00.02 for inferences.
% 0.91/1.11 0:00:00.00 for the backtracking.
% 0.91/1.11 0:00:00.66 for the reduction.
% 0.91/1.11
% 0.91/1.11
% 0.91/1.11 Here is a proof with depth 4, length 37 :
% 0.91/1.11 % SZS output start Refutation
% See solution above
% 0.91/1.11 Formulae used in the proof : c01 c02 c03 c04 c05 c06 c07 c08 c09 c10 goals
% 0.91/1.11
%------------------------------------------------------------------------------