TSTP Solution File: GRP683-11 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP683-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 11:48:57 EDT 2022
% Result : Unsatisfiable 0.81s 1.00s
% Output : Refutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 54 RR)
% Number of literals : 54 ( 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ld(u,mult(u,u)),u),
file('GRP683-11.p',unknown),
[] ).
cnf(2,axiom,
equal(rd(mult(u,u),u),u),
file('GRP683-11.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
file('GRP683-11.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(rd(u,v),v),rd(mult(u,v),v)),
file('GRP683-11.p',unknown),
[] ).
cnf(5,axiom,
equal(ld(ld(u,v),mult(ld(u,v),mult(w,x))),mult(ld(u,mult(u,w)),x)),
file('GRP683-11.p',unknown),
[] ).
cnf(6,axiom,
equal(rd(mult(mult(u,v),rd(w,x)),rd(w,x)),mult(u,rd(mult(v,x),x))),
file('GRP683-11.p',unknown),
[] ).
cnf(7,axiom,
equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
file('GRP683-11.p',unknown),
[] ).
cnf(8,axiom,
~ equal(mult(rd(mult(x3__dfg,x4__dfg),x4__dfg),x5__dfg),mult(x3__dfg,x5__dfg)),
file('GRP683-11.p',unknown),
[] ).
cnf(21,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(rd(u,u),v),v),v)),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(23,plain,
equal(rd(rd(mult(u,u),u),u),ld(u,mult(u,ld(u,u)))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(24,plain,
equal(rd(u,u),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[2,23,1,3]),
[iquote('0:Rew:2.0,23.0,1.0,23.0,3.0,23.0')] ).
cnf(25,plain,
equal(rd(mult(ld(u,u),v),v),ld(u,mult(u,ld(v,v)))),
inference(rew,[status(thm),theory(equality)],[24,7]),
[iquote('0:Rew:24.0,7.0')] ).
cnf(27,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),rd(mult(mult(ld(u,u),v),v),v)),
inference(rew,[status(thm),theory(equality)],[24,21]),
[iquote('0:Rew:24.0,21.0')] ).
cnf(29,plain,
equal(mult(ld(u,u),u),rd(mult(u,u),u)),
inference(spr,[status(thm),theory(equality)],[24,4]),
[iquote('0:SpR:24.0,4.0')] ).
cnf(31,plain,
equal(mult(ld(u,u),u),u),
inference(rew,[status(thm),theory(equality)],[2,29]),
[iquote('0:Rew:2.0,29.0')] ).
cnf(51,plain,
equal(mult(u,rd(mult(v,w),w)),rd(mult(mult(u,v),w),w)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(63,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),mult(ld(u,u),rd(mult(u,w),w))),
inference(spr,[status(thm),theory(equality)],[31,6]),
[iquote('0:SpR:31.0,6.0')] ).
cnf(70,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(mult(ld(u,u),u),w),w)),
inference(rew,[status(thm),theory(equality)],[51,63]),
[iquote('0:Rew:51.0,63.0')] ).
cnf(71,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[31,70]),
[iquote('0:Rew:31.0,70.0')] ).
cnf(102,plain,
equal(rd(mult(mult(u,v),v),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[2,51]),
[iquote('0:SpR:2.0,51.0')] ).
cnf(105,plain,
equal(mult(u,ld(v,mult(v,ld(w,w)))),rd(mult(mult(u,ld(v,v)),w),w)),
inference(spr,[status(thm),theory(equality)],[25,51]),
[iquote('0:SpR:25.0,51.0')] ).
cnf(106,plain,
equal(mult(ld(u,mult(u,ld(v,v))),v),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[102,27]),
[iquote('0:Rew:102.0,27.0')] ).
cnf(130,plain,
equal(rd(mult(rd(u,v),v),v),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[71,2]),
[iquote('0:SpR:71.0,2.0')] ).
cnf(135,plain,
equal(rd(mult(mult(u,rd(v,w)),rd(v,w)),rd(v,w)),mult(rd(mult(u,w),w),rd(v,w))),
inference(spr,[status(thm),theory(equality)],[71,4]),
[iquote('0:SpR:71.0,4.0')] ).
cnf(139,plain,
equal(rd(mult(u,mult(v,w)),mult(v,w)),rd(mult(u,w),w)),
inference(spr,[status(thm),theory(equality)],[102,71]),
[iquote('0:SpR:102.0,71.0')] ).
cnf(145,plain,
equal(rd(rd(mult(mult(u,v),w),w),rd(mult(v,w),w)),rd(mult(u,w),w)),
inference(spr,[status(thm),theory(equality)],[51,71]),
[iquote('0:SpR:51.0,71.0')] ).
cnf(148,plain,
equal(rd(rd(mult(u,v),v),v),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[4,130]),
[iquote('0:Rew:4.0,130.0')] ).
cnf(165,plain,
equal(mult(rd(mult(u,v),v),rd(w,v)),mult(u,rd(w,v))),
inference(rew,[status(thm),theory(equality)],[102,135]),
[iquote('0:Rew:102.0,135.0')] ).
cnf(178,plain,
equal(mult(ld(u,mult(u,v)),w),ld(u,mult(u,mult(v,w)))),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(191,plain,
equal(ld(u,mult(u,mult(ld(v,v),v))),mult(ld(u,u),v)),
inference(rew,[status(thm),theory(equality)],[178,106]),
[iquote('0:Rew:178.0,106.0')] ).
cnf(192,plain,
equal(mult(ld(u,u),v),ld(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[31,191]),
[iquote('0:Rew:31.0,191.0')] ).
cnf(227,plain,
equal(rd(rd(mult(u,v),v),rd(w,v)),rd(u,rd(w,v))),
inference(spr,[status(thm),theory(equality)],[71,148]),
[iquote('0:SpR:71.0,148.0')] ).
cnf(232,plain,
equal(rd(mult(u,v),rd(mult(v,w),w)),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[227,145]),
[iquote('0:Rew:227.0,145.0')] ).
cnf(398,plain,
equal(rd(mult(u,ld(v,mult(v,w))),ld(v,mult(v,w))),rd(mult(u,w),w)),
inference(spr,[status(thm),theory(equality)],[192,139]),
[iquote('0:SpR:192.0,139.0')] ).
cnf(399,plain,
equal(rd(mult(u,ld(v,mult(v,w))),ld(v,mult(v,w))),rd(mult(u,ld(v,w)),ld(v,w))),
inference(spr,[status(thm),theory(equality)],[3,139]),
[iquote('0:SpR:3.0,139.0')] ).
cnf(412,plain,
equal(rd(mult(u,ld(v,w)),ld(v,w)),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[398,399]),
[iquote('0:Rew:398.0,399.0')] ).
cnf(470,plain,
equal(ld(u,mult(u,mult(u,v))),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[1,178]),
[iquote('0:SpR:1.0,178.0')] ).
cnf(1049,plain,
equal(rd(mult(u,rd(v,w)),rd(mult(rd(v,w),x),x)),rd(mult(rd(mult(u,w),w),x),x)),
inference(spr,[status(thm),theory(equality)],[165,232]),
[iquote('0:SpR:165.0,232.0')] ).
cnf(1066,plain,
equal(rd(mult(rd(mult(u,v),v),w),w),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[232,1049]),
[iquote('0:Rew:232.0,1049.0')] ).
cnf(1243,plain,
equal(rd(rd(mult(u,v),v),ld(w,v)),rd(u,ld(w,v))),
inference(spr,[status(thm),theory(equality)],[412,148]),
[iquote('0:SpR:412.0,148.0')] ).
cnf(1454,plain,
equal(rd(mult(mult(u,ld(u,u)),v),v),ld(u,mult(u,mult(u,ld(v,v))))),
inference(spr,[status(thm),theory(equality)],[105,3]),
[iquote('0:SpR:105.0,3.0')] ).
cnf(1486,plain,
equal(mult(u,ld(v,v)),rd(mult(u,v),v)),
inference(rew,[status(thm),theory(equality)],[1,1454,3,470]),
[iquote('0:Rew:1.0,1454.0,3.0,1454.0,470.0,1454.0')] ).
cnf(1616,plain,
equal(rd(rd(mult(u,v),v),ld(v,v)),rd(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[1486,412]),
[iquote('0:SpR:1486.0,412.0')] ).
cnf(1644,plain,
equal(rd(mult(u,v),v),rd(u,ld(v,v))),
inference(rew,[status(thm),theory(equality)],[1243,1616]),
[iquote('0:Rew:1243.0,1616.0')] ).
cnf(1653,plain,
equal(rd(mult(u,v),ld(v,v)),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[1644,102]),
[iquote('0:Rew:1644.0,102.0')] ).
cnf(1654,plain,
~ equal(mult(rd(x3__dfg,ld(x4__dfg,x4__dfg)),x5__dfg),mult(x3__dfg,x5__dfg)),
inference(rew,[status(thm),theory(equality)],[1644,8]),
[iquote('0:Rew:1644.0,8.0')] ).
cnf(1658,plain,
equal(mult(rd(u,v),v),rd(u,ld(v,v))),
inference(rew,[status(thm),theory(equality)],[1644,4]),
[iquote('0:Rew:1644.0,4.0')] ).
cnf(1673,plain,
equal(rd(rd(mult(u,v),v),ld(w,w)),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[1644,1066]),
[iquote('0:Rew:1644.0,1066.0')] ).
cnf(1783,plain,
equal(rd(rd(u,ld(v,v)),ld(w,w)),rd(u,ld(w,w))),
inference(rew,[status(thm),theory(equality)],[1644,1673]),
[iquote('0:Rew:1644.0,1673.0,1644.0,1673.0')] ).
cnf(1894,plain,
equal(mult(rd(u,ld(v,v)),v),rd(mult(u,v),ld(v,v))),
inference(spr,[status(thm),theory(equality)],[1644,1658]),
[iquote('0:SpR:1644.0,1658.0')] ).
cnf(1900,plain,
equal(mult(rd(u,ld(v,v)),v),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[1653,1894]),
[iquote('0:Rew:1653.0,1894.0')] ).
cnf(3449,plain,
equal(mult(rd(u,ld(v,v)),v),mult(rd(u,ld(w,w)),v)),
inference(spr,[status(thm),theory(equality)],[1783,1900]),
[iquote('0:SpR:1783.0,1900.0')] ).
cnf(3495,plain,
equal(mult(rd(u,ld(v,v)),w),mult(u,w)),
inference(rew,[status(thm),theory(equality)],[1900,3449]),
[iquote('0:Rew:1900.0,3449.0')] ).
cnf(3496,plain,
$false,
inference(unc,[status(thm)],[3495,1654]),
[iquote('0:UnC:3495.0,1654.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP683-11 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n023.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 00:49:51 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.81/1.00
% 0.81/1.00 SPASS V 3.9
% 0.81/1.00 SPASS beiseite: Proof found.
% 0.81/1.00 % SZS status Theorem
% 0.81/1.00 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.81/1.00 SPASS derived 2055 clauses, backtracked 0 clauses, performed 0 splits and kept 584 clauses.
% 0.81/1.00 SPASS allocated 68315 KBytes.
% 0.81/1.00 SPASS spent 0:00:00.61 on the problem.
% 0.81/1.00 0:00:00.04 for the input.
% 0.81/1.00 0:00:00.00 for the FLOTTER CNF translation.
% 0.81/1.00 0:00:00.03 for inferences.
% 0.81/1.00 0:00:00.00 for the backtracking.
% 0.81/1.00 0:00:00.52 for the reduction.
% 0.81/1.00
% 0.81/1.00
% 0.81/1.00 Here is a proof with depth 8, length 54 :
% 0.81/1.00 % SZS output start Refutation
% See solution above
% 0.81/1.00 Formulae used in the proof : f01 f02 f03 f04 f05 f06 f07 goal
% 0.81/1.00
%------------------------------------------------------------------------------