TSTP Solution File: GRP680-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP680-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 11:48:56 EDT 2022
% Result : Unsatisfiable 0.77s 1.00s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 52 RR)
% Number of literals : 52 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP680-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP680-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP680-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP680-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,unit),u),
file('GRP680-1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(u,mult(v,u)),w),mult(u,mult(v,mult(u,w)))),
file('GRP680-1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(i(u),mult(u,v)),v),
file('GRP680-1.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(op_c,u),mult(u,op_c)),
file('GRP680-1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(mult(i(op_c),a),mult(a,i(op_c))),
file('GRP680-1.p',unknown),
[] ).
cnf(52,plain,
equal(ld(op_c,mult(u,op_c)),u),
inference(spr,[status(thm),theory(equality)],[9,2]),
[iquote('0:SpR:9.0,2.0')] ).
cnf(53,plain,
equal(ld(u,u),unit),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(54,plain,
equal(ld(u,mult(op_c,u)),op_c),
inference(spr,[status(thm),theory(equality)],[9,2]),
[iquote('0:SpR:9.0,2.0')] ).
cnf(78,plain,
equal(rd(u,ld(v,u)),v),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(114,plain,
equal(rd(u,mult(v,u)),i(v)),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(115,plain,
equal(ld(i(u),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[8,2]),
[iquote('0:SpR:8.0,2.0')] ).
cnf(122,plain,
equal(mult(i(u),v),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(129,plain,
~ equal(mult(a,i(op_c)),ld(op_c,a)),
inference(rew,[status(thm),theory(equality)],[122,10]),
[iquote('0:Rew:122.0,10.0')] ).
cnf(148,plain,
equal(rd(unit,u),i(u)),
inference(spr,[status(thm),theory(equality)],[5,114]),
[iquote('0:SpR:5.0,114.0')] ).
cnf(149,plain,
equal(rd(op_c,mult(op_c,u)),i(u)),
inference(spr,[status(thm),theory(equality)],[9,114]),
[iquote('0:SpR:9.0,114.0')] ).
cnf(151,plain,
equal(i(rd(u,v)),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[3,114]),
[iquote('0:SpR:3.0,114.0')] ).
cnf(160,plain,
equal(i(ld(u,unit)),u),
inference(spr,[status(thm),theory(equality)],[148,78]),
[iquote('0:SpR:148.0,78.0')] ).
cnf(200,plain,
equal(mult(mult(op_c,mult(op_c,u)),v),mult(op_c,mult(u,mult(op_c,v)))),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(202,plain,
equal(mult(u,mult(rd(v,u),mult(u,w))),mult(mult(u,v),w)),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(251,plain,
equal(mult(u,i(u)),unit),
inference(spr,[status(thm),theory(equality)],[115,53]),
[iquote('0:SpR:115.0,53.0')] ).
cnf(267,plain,
equal(ld(u,unit),i(u)),
inference(spr,[status(thm),theory(equality)],[122,5]),
[iquote('0:SpR:122.0,5.0')] ).
cnf(268,plain,
equal(mult(op_c,i(u)),ld(u,op_c)),
inference(spr,[status(thm),theory(equality)],[122,9]),
[iquote('0:SpR:122.0,9.0')] ).
cnf(281,plain,
equal(i(i(u)),u),
inference(rew,[status(thm),theory(equality)],[267,160]),
[iquote('0:Rew:267.0,160.0')] ).
cnf(430,plain,
equal(mult(rd(u,v),w),ld(rd(v,u),w)),
inference(spr,[status(thm),theory(equality)],[151,115]),
[iquote('0:SpR:151.0,115.0')] ).
cnf(457,plain,
equal(mult(u,ld(rd(u,v),mult(u,w))),mult(mult(u,v),w)),
inference(rew,[status(thm),theory(equality)],[430,202]),
[iquote('0:Rew:430.0,202.0')] ).
cnf(464,plain,
equal(mult(op_c,mult(u,mult(op_c,unit))),mult(op_c,mult(op_c,u))),
inference(spr,[status(thm),theory(equality)],[200,5]),
[iquote('0:SpR:200.0,5.0')] ).
cnf(467,plain,
equal(ld(op_c,mult(op_c,mult(u,mult(op_c,op_c)))),mult(op_c,mult(op_c,u))),
inference(spr,[status(thm),theory(equality)],[200,52]),
[iquote('0:SpR:200.0,52.0')] ).
cnf(483,plain,
equal(mult(op_c,mult(u,op_c)),mult(op_c,mult(op_c,u))),
inference(rew,[status(thm),theory(equality)],[5,464]),
[iquote('0:Rew:5.0,464.0')] ).
cnf(487,plain,
equal(mult(u,mult(op_c,op_c)),mult(op_c,mult(op_c,u))),
inference(rew,[status(thm),theory(equality)],[2,467]),
[iquote('0:Rew:2.0,467.0')] ).
cnf(986,plain,
equal(rd(op_c,mult(op_c,mult(op_c,u))),i(mult(u,op_c))),
inference(spr,[status(thm),theory(equality)],[483,149]),
[iquote('0:SpR:483.0,149.0')] ).
cnf(1030,plain,
equal(i(mult(op_c,u)),i(mult(u,op_c))),
inference(rew,[status(thm),theory(equality)],[149,986]),
[iquote('0:Rew:149.0,986.0')] ).
cnf(1039,plain,
equal(mult(mult(op_c,u),i(mult(u,op_c))),unit),
inference(spr,[status(thm),theory(equality)],[1030,251]),
[iquote('0:SpR:1030.0,251.0')] ).
cnf(1096,plain,
equal(mult(op_c,mult(u,mult(op_c,i(mult(mult(u,op_c),op_c))))),unit),
inference(spr,[status(thm),theory(equality)],[1039,7]),
[iquote('0:SpR:1039.0,7.0')] ).
cnf(1133,plain,
equal(mult(op_c,mult(u,ld(mult(op_c,mult(u,op_c)),op_c))),unit),
inference(rew,[status(thm),theory(equality)],[268,1096,9]),
[iquote('0:Rew:268.0,1096.0,9.0,1096.0')] ).
cnf(1367,plain,
equal(ld(op_c,mult(u,mult(op_c,op_c))),mult(op_c,u)),
inference(spr,[status(thm),theory(equality)],[487,2]),
[iquote('0:SpR:487.0,2.0')] ).
cnf(1929,plain,
equal(mult(mult(op_c,u),rd(op_c,u)),mult(op_c,op_c)),
inference(spr,[status(thm),theory(equality)],[54,457]),
[iquote('0:SpR:54.0,457.0')] ).
cnf(2061,plain,
equal(ld(op_c,ld(u,mult(op_c,op_c))),mult(op_c,i(u))),
inference(spr,[status(thm),theory(equality)],[122,1367]),
[iquote('0:SpR:122.0,1367.0')] ).
cnf(2071,plain,
equal(ld(op_c,ld(u,mult(op_c,op_c))),ld(u,op_c)),
inference(rew,[status(thm),theory(equality)],[268,2061]),
[iquote('0:Rew:268.0,2061.0')] ).
cnf(2783,plain,
equal(ld(mult(op_c,u),mult(op_c,op_c)),rd(op_c,u)),
inference(spr,[status(thm),theory(equality)],[1929,2]),
[iquote('0:SpR:1929.0,2.0')] ).
cnf(3274,plain,
equal(ld(mult(op_c,u),op_c),ld(op_c,rd(op_c,u))),
inference(spr,[status(thm),theory(equality)],[2783,2071]),
[iquote('0:SpR:2783.0,2071.0')] ).
cnf(3303,plain,
equal(mult(op_c,mult(u,ld(op_c,rd(op_c,mult(u,op_c))))),unit),
inference(rew,[status(thm),theory(equality)],[3274,1133]),
[iquote('0:Rew:3274.0,1133.0')] ).
cnf(3316,plain,
equal(mult(op_c,mult(u,ld(op_c,i(u)))),unit),
inference(rew,[status(thm),theory(equality)],[114,3303]),
[iquote('0:Rew:114.0,3303.0')] ).
cnf(3351,plain,
equal(mult(u,ld(op_c,i(u))),ld(op_c,unit)),
inference(spr,[status(thm),theory(equality)],[3316,2]),
[iquote('0:SpR:3316.0,2.0')] ).
cnf(3380,plain,
equal(mult(u,ld(op_c,i(u))),i(op_c)),
inference(rew,[status(thm),theory(equality)],[267,3351]),
[iquote('0:Rew:267.0,3351.0')] ).
cnf(3482,plain,
equal(mult(i(u),ld(op_c,u)),i(op_c)),
inference(spr,[status(thm),theory(equality)],[281,3380]),
[iquote('0:SpR:281.0,3380.0')] ).
cnf(3490,plain,
equal(ld(u,ld(op_c,u)),i(op_c)),
inference(rew,[status(thm),theory(equality)],[122,3482]),
[iquote('0:Rew:122.0,3482.0')] ).
cnf(3541,plain,
equal(mult(u,i(op_c)),ld(op_c,u)),
inference(spr,[status(thm),theory(equality)],[3490,1]),
[iquote('0:SpR:3490.0,1.0')] ).
cnf(3560,plain,
$false,
inference(unc,[status(thm)],[3541,129]),
[iquote('0:UnC:3541.0,129.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP680-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 07:23:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.77/1.00
% 0.77/1.00 SPASS V 3.9
% 0.77/1.00 SPASS beiseite: Proof found.
% 0.77/1.00 % SZS status Theorem
% 0.77/1.00 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/1.00 SPASS derived 2294 clauses, backtracked 0 clauses, performed 0 splits and kept 605 clauses.
% 0.77/1.00 SPASS allocated 67926 KBytes.
% 0.77/1.00 SPASS spent 0:00:00.62 on the problem.
% 0.77/1.00 0:00:00.04 for the input.
% 0.77/1.00 0:00:00.00 for the FLOTTER CNF translation.
% 0.77/1.00 0:00:00.02 for inferences.
% 0.77/1.00 0:00:00.00 for the backtracking.
% 0.77/1.00 0:00:00.53 for the reduction.
% 0.77/1.00
% 0.77/1.00
% 0.77/1.00 Here is a proof with depth 8, length 52 :
% 0.77/1.00 % SZS output start Refutation
% See solution above
% 0.77/1.00 Formulae used in the proof : c01 c02 c03 c04 c05 c07 c08 c09 goals
% 0.77/1.00
%------------------------------------------------------------------------------