TSTP Solution File: GRP770-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP770-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 11:49:20 EDT 2022
% Result : Unsatisfiable 19.77s 19.96s
% Output : Refutation 19.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of clauses : 89 ( 89 unt; 0 nHn; 89 RR)
% Number of literals : 89 ( 0 equ; 2 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 : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(product(u,one),u),
file('GRP770-1.p',unknown),
[] ).
cnf(2,axiom,
equal(product(one,u),u),
file('GRP770-1.p',unknown),
[] ).
cnf(3,axiom,
equal(product(u,difference(u,v)),v),
file('GRP770-1.p',unknown),
[] ).
cnf(4,axiom,
equal(difference(u,product(u,v)),v),
file('GRP770-1.p',unknown),
[] ).
cnf(5,axiom,
equal(quotient(product(u,v),v),u),
file('GRP770-1.p',unknown),
[] ).
cnf(6,axiom,
equal(product(quotient(u,v),v),u),
file('GRP770-1.p',unknown),
[] ).
cnf(7,axiom,
equal(quotient(product(u,product(v,w)),w),difference(w,product(product(w,u),v))),
file('GRP770-1.p',unknown),
[] ).
cnf(8,axiom,
equal(quotient(quotient(product(u,product(v,w)),w),v),difference(product(v,w),product(v,product(w,u)))),
file('GRP770-1.p',unknown),
[] ).
cnf(9,axiom,
equal(difference(u,one),i(u)),
file('GRP770-1.p',unknown),
[] ).
cnf(10,axiom,
equal(quotient(one,u),j(u)),
file('GRP770-1.p',unknown),
[] ).
cnf(11,axiom,
equal(product(i(u),u),product(u,j(u))),
file('GRP770-1.p',unknown),
[] ).
cnf(12,axiom,
equal(product(i(u),u),eta(u)),
file('GRP770-1.p',unknown),
[] ).
cnf(13,axiom,
equal(product(eta(u),product(u,v)),product(i(i(u)),v)),
file('GRP770-1.p',unknown),
[] ).
cnf(14,axiom,
equal(product(u,product(eta(u),v)),product(j(j(u)),v)),
file('GRP770-1.p',unknown),
[] ).
cnf(16,axiom,
equal(product(product(eta(u),v),w),product(eta(u),product(v,w))),
file('GRP770-1.p',unknown),
[] ).
cnf(19,axiom,
equal(quotient(product(u,v),u),t(u,v)),
file('GRP770-1.p',unknown),
[] ).
cnf(23,axiom,
equal(product(u,i(product(v,u))),i(v)),
file('GRP770-1.p',unknown),
[] ).
cnf(24,axiom,
equal(product(j(product(u,v)),u),j(v)),
file('GRP770-1.p',unknown),
[] ).
cnf(25,axiom,
~ equal(product(quotient(product(x0__dfg,x1__dfg),x0__dfg),product(x0__dfg,x2__dfg)),product(x0__dfg,product(x1__dfg,x2__dfg))),
file('GRP770-1.p',unknown),
[] ).
cnf(26,plain,
equal(product(u,j(u)),eta(u)),
inference(rew,[status(thm),theory(equality)],[12,11]),
[iquote('0:Rew:12.0,11.0')] ).
cnf(27,plain,
~ equal(product(t(x0__dfg,x1__dfg),product(x0__dfg,x2__dfg)),product(x0__dfg,product(x1__dfg,x2__dfg))),
inference(rew,[status(thm),theory(equality)],[19,25]),
[iquote('0:Rew:19.0,25.0')] ).
cnf(28,plain,
equal(quotient(difference(u,product(product(u,v),w)),w),difference(product(w,u),product(w,product(u,v)))),
inference(rew,[status(thm),theory(equality)],[7,8]),
[iquote('0:Rew:7.0,8.0')] ).
cnf(45,plain,
equal(product(j(u),u),one),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.0')] ).
cnf(48,plain,
equal(quotient(u,u),one),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
cnf(86,plain,
equal(difference(j(u),one),u),
inference(spr,[status(thm),theory(equality)],[45,4]),
[iquote('0:SpR:45.0,4.0')] ).
cnf(88,plain,
equal(i(j(u)),u),
inference(rew,[status(thm),theory(equality)],[9,86]),
[iquote('0:Rew:9.0,86.0')] ).
cnf(93,plain,
equal(product(u,i(u)),one),
inference(spr,[status(thm),theory(equality)],[9,3]),
[iquote('0:SpR:9.0,3.0')] ).
cnf(102,plain,
equal(quotient(one,i(u)),u),
inference(spr,[status(thm),theory(equality)],[93,5]),
[iquote('0:SpR:93.0,5.0')] ).
cnf(107,plain,
equal(j(i(u)),u),
inference(rew,[status(thm),theory(equality)],[10,102]),
[iquote('0:Rew:10.0,102.0')] ).
cnf(108,plain,
equal(product(i(u),u),eta(i(u))),
inference(spr,[status(thm),theory(equality)],[107,26]),
[iquote('0:SpR:107.0,26.0')] ).
cnf(114,plain,
equal(eta(i(u)),eta(u)),
inference(rew,[status(thm),theory(equality)],[12,108]),
[iquote('0:Rew:12.0,108.0')] ).
cnf(120,plain,
equal(quotient(j(u),v),j(product(v,u))),
inference(spr,[status(thm),theory(equality)],[24,5]),
[iquote('0:SpR:24.0,5.0')] ).
cnf(121,plain,
equal(difference(j(product(u,v)),j(v)),u),
inference(spr,[status(thm),theory(equality)],[24,4]),
[iquote('0:SpR:24.0,4.0')] ).
cnf(128,plain,
equal(product(j(u),v),j(difference(v,u))),
inference(spr,[status(thm),theory(equality)],[3,24]),
[iquote('0:SpR:3.0,24.0')] ).
cnf(140,plain,
equal(product(u,product(eta(u),v)),j(difference(v,j(u)))),
inference(rew,[status(thm),theory(equality)],[128,14]),
[iquote('0:Rew:128.0,14.0')] ).
cnf(190,plain,
equal(difference(u,i(v)),i(product(v,u))),
inference(spr,[status(thm),theory(equality)],[23,4]),
[iquote('0:SpR:23.0,4.0')] ).
cnf(195,plain,
equal(product(j(u),i(eta(u))),i(u)),
inference(spr,[status(thm),theory(equality)],[26,23]),
[iquote('0:SpR:26.0,23.0')] ).
cnf(198,plain,
equal(product(u,i(v)),i(quotient(v,u))),
inference(spr,[status(thm),theory(equality)],[6,23]),
[iquote('0:SpR:6.0,23.0')] ).
cnf(203,plain,
equal(j(difference(i(eta(u)),u)),i(u)),
inference(rew,[status(thm),theory(equality)],[128,195]),
[iquote('0:Rew:128.0,195.0')] ).
cnf(351,plain,
equal(product(eta(u),u),product(i(i(u)),one)),
inference(spr,[status(thm),theory(equality)],[1,13]),
[iquote('0:SpR:1.0,13.0')] ).
cnf(354,plain,
equal(product(eta(quotient(u,v)),u),product(i(i(quotient(u,v))),v)),
inference(spr,[status(thm),theory(equality)],[6,13]),
[iquote('0:SpR:6.0,13.0')] ).
cnf(360,plain,
equal(product(eta(u),u),i(i(u))),
inference(rew,[status(thm),theory(equality)],[1,351]),
[iquote('0:Rew:1.0,351.0')] ).
cnf(369,plain,
equal(quotient(i(i(u)),u),eta(u)),
inference(spr,[status(thm),theory(equality)],[360,5]),
[iquote('0:SpR:360.0,5.0')] ).
cnf(370,plain,
equal(difference(eta(u),i(i(u))),u),
inference(spr,[status(thm),theory(equality)],[360,4]),
[iquote('0:SpR:360.0,4.0')] ).
cnf(378,plain,
equal(i(product(i(u),eta(u))),u),
inference(rew,[status(thm),theory(equality)],[190,370]),
[iquote('0:Rew:190.0,370.0')] ).
cnf(393,plain,
equal(product(i(u),eta(u)),j(u)),
inference(spr,[status(thm),theory(equality)],[378,107]),
[iquote('0:SpR:378.0,107.0')] ).
cnf(485,plain,
equal(difference(i(u),j(u)),eta(u)),
inference(spr,[status(thm),theory(equality)],[393,4]),
[iquote('0:SpR:393.0,4.0')] ).
cnf(652,plain,
equal(product(eta(u),product(j(eta(u)),v)),product(eta(eta(u)),v)),
inference(spr,[status(thm),theory(equality)],[26,16]),
[iquote('0:SpR:26.0,16.0')] ).
cnf(653,plain,
equal(product(eta(u),product(difference(eta(u),v),w)),product(v,w)),
inference(spr,[status(thm),theory(equality)],[3,16]),
[iquote('0:SpR:3.0,16.0')] ).
cnf(666,plain,
equal(product(eta(u),j(difference(v,eta(u)))),product(eta(eta(u)),v)),
inference(rew,[status(thm),theory(equality)],[128,652]),
[iquote('0:Rew:128.0,652.0')] ).
cnf(737,plain,
equal(difference(i(eta(u)),u),i(i(u))),
inference(spr,[status(thm),theory(equality)],[203,88]),
[iquote('0:SpR:203.0,88.0')] ).
cnf(746,plain,
equal(difference(i(difference(i(eta(u)),u)),i(u)),eta(difference(i(eta(u)),u))),
inference(spr,[status(thm),theory(equality)],[203,485]),
[iquote('0:SpR:203.0,485.0')] ).
cnf(783,plain,
equal(i(i(quotient(i(i(u)),u))),eta(i(i(u)))),
inference(rew,[status(thm),theory(equality)],[198,746,190,737]),
[iquote('0:Rew:198.0,746.0,190.0,746.0,737.0,746.0')] ).
cnf(784,plain,
equal(i(i(eta(u))),eta(u)),
inference(rew,[status(thm),theory(equality)],[369,783,114]),
[iquote('0:Rew:369.0,783.0,114.0,783.0,114.0,783.0')] ).
cnf(794,plain,
equal(j(eta(u)),i(eta(u))),
inference(spr,[status(thm),theory(equality)],[784,107]),
[iquote('0:SpR:784.0,107.0')] ).
cnf(808,plain,
equal(quotient(eta(u),eta(u)),eta(eta(u))),
inference(spr,[status(thm),theory(equality)],[784,369]),
[iquote('0:SpR:784.0,369.0')] ).
cnf(825,plain,
equal(eta(eta(u)),one),
inference(rew,[status(thm),theory(equality)],[48,808]),
[iquote('0:Rew:48.0,808.0')] ).
cnf(826,plain,
equal(product(eta(u),j(difference(v,eta(u)))),product(one,v)),
inference(rew,[status(thm),theory(equality)],[825,666]),
[iquote('0:Rew:825.0,666.0')] ).
cnf(850,plain,
equal(product(eta(u),j(difference(v,eta(u)))),v),
inference(rew,[status(thm),theory(equality)],[2,826]),
[iquote('0:Rew:2.0,826.0')] ).
cnf(887,plain,
equal(difference(u,product(product(u,i(product(v,u))),v)),quotient(eta(product(v,u)),u)),
inference(spr,[status(thm),theory(equality)],[12,7]),
[iquote('0:SpR:12.0,7.0')] ).
cnf(909,plain,
equal(difference(u,product(i(quotient(product(v,u),u)),v)),quotient(eta(product(v,u)),u)),
inference(rew,[status(thm),theory(equality)],[198,887]),
[iquote('0:Rew:198.0,887.0')] ).
cnf(910,plain,
equal(quotient(eta(product(u,v)),v),difference(v,eta(u))),
inference(rew,[status(thm),theory(equality)],[12,909,5]),
[iquote('0:Rew:12.0,909.0,5.0,909.0')] ).
cnf(1176,plain,
equal(quotient(difference(u,product(v,w)),w),difference(product(w,u),product(w,v))),
inference(spr,[status(thm),theory(equality)],[3,28]),
[iquote('0:SpR:3.0,28.0')] ).
cnf(1411,plain,
equal(difference(j(u),j(v)),quotient(u,v)),
inference(spr,[status(thm),theory(equality)],[6,121]),
[iquote('0:SpR:6.0,121.0')] ).
cnf(1523,plain,
equal(j(difference(difference(j(u),v),u)),v),
inference(spr,[status(thm),theory(equality)],[128,3]),
[iquote('0:SpR:128.0,3.0')] ).
cnf(1803,plain,
equal(quotient(u,i(v)),difference(j(u),v)),
inference(spr,[status(thm),theory(equality)],[107,1411]),
[iquote('0:SpR:107.0,1411.0')] ).
cnf(1913,plain,
equal(difference(difference(j(u),v),u),i(v)),
inference(spr,[status(thm),theory(equality)],[1523,88]),
[iquote('0:SpR:1523.0,88.0')] ).
cnf(2217,plain,
equal(j(difference(u,eta(v))),difference(eta(v),u)),
inference(spr,[status(thm),theory(equality)],[850,4]),
[iquote('0:SpR:850.0,4.0')] ).
cnf(2238,plain,
equal(product(eta(u),j(i(v))),difference(j(eta(u)),v)),
inference(spr,[status(thm),theory(equality)],[1913,850]),
[iquote('0:SpR:1913.0,850.0')] ).
cnf(2272,plain,
equal(difference(i(eta(u)),v),product(eta(u),v)),
inference(rew,[status(thm),theory(equality)],[107,2238,794]),
[iquote('0:Rew:107.0,2238.0,794.0,2238.0')] ).
cnf(2444,plain,
equal(difference(j(eta(product(u,i(v)))),v),difference(i(v),eta(u))),
inference(spr,[status(thm),theory(equality)],[910,1803]),
[iquote('0:SpR:910.0,1803.0')] ).
cnf(2480,plain,
equal(difference(i(eta(quotient(u,v))),u),difference(i(u),eta(v))),
inference(rew,[status(thm),theory(equality)],[794,2444,114,198]),
[iquote('0:Rew:794.0,2444.0,114.0,2444.0,198.0,2444.0')] ).
cnf(2481,plain,
equal(product(eta(quotient(u,v)),u),difference(i(u),eta(v))),
inference(rew,[status(thm),theory(equality)],[2272,2480]),
[iquote('0:Rew:2272.0,2480.0')] ).
cnf(2482,plain,
equal(product(i(i(quotient(u,v))),v),difference(i(u),eta(v))),
inference(rew,[status(thm),theory(equality)],[2481,354]),
[iquote('0:Rew:2481.0,354.0')] ).
cnf(4610,plain,
equal(i(difference(eta(u),v)),difference(v,eta(u))),
inference(spr,[status(thm),theory(equality)],[2217,88]),
[iquote('0:SpR:2217.0,88.0')] ).
cnf(4630,plain,
equal(difference(difference(eta(u),v),j(w)),quotient(difference(v,eta(u)),w)),
inference(spr,[status(thm),theory(equality)],[2217,1411]),
[iquote('0:SpR:2217.0,1411.0')] ).
cnf(5151,plain,
equal(i(product(difference(eta(u),v),w)),difference(w,difference(v,eta(u)))),
inference(spr,[status(thm),theory(equality)],[4610,190]),
[iquote('0:SpR:4610.0,190.0')] ).
cnf(7712,plain,
equal(product(i(i(j(product(u,v)))),u),difference(i(j(v)),eta(u))),
inference(spr,[status(thm),theory(equality)],[120,2482]),
[iquote('0:SpR:120.0,2482.0')] ).
cnf(7743,plain,
equal(product(i(product(u,v)),u),difference(v,eta(u))),
inference(rew,[status(thm),theory(equality)],[88,7712]),
[iquote('0:Rew:88.0,7712.0,88.0,7712.0')] ).
cnf(11723,plain,
equal(product(difference(eta(u),v),w),difference(eta(u),product(v,w))),
inference(spr,[status(thm),theory(equality)],[653,4]),
[iquote('0:SpR:653.0,4.0')] ).
cnf(11734,plain,
equal(j(difference(product(difference(eta(u),v),w),j(u))),product(u,product(v,w))),
inference(spr,[status(thm),theory(equality)],[653,140]),
[iquote('0:SpR:653.0,140.0')] ).
cnf(11872,plain,
equal(i(difference(eta(u),product(v,w))),difference(w,difference(v,eta(u)))),
inference(rew,[status(thm),theory(equality)],[11723,5151]),
[iquote('0:Rew:11723.0,5151.0')] ).
cnf(11917,plain,
equal(difference(product(u,v),eta(w)),difference(v,difference(u,eta(w)))),
inference(rew,[status(thm),theory(equality)],[4610,11872]),
[iquote('0:Rew:4610.0,11872.0')] ).
cnf(11935,plain,
equal(j(quotient(difference(u,difference(v,eta(w))),w)),product(w,product(v,u))),
inference(rew,[status(thm),theory(equality)],[11917,11734,4630,11723]),
[iquote('0:Rew:11917.0,11734.0,4630.0,11734.0,11723.0,11734.0')] ).
cnf(54719,plain,
equal(difference(product(u,v),product(u,i(product(u,w)))),quotient(difference(v,difference(w,eta(u))),u)),
inference(spr,[status(thm),theory(equality)],[7743,1176]),
[iquote('0:SpR:7743.0,1176.0')] ).
cnf(54879,plain,
equal(quotient(difference(u,difference(v,eta(w))),w),i(product(t(w,v),product(w,u)))),
inference(rew,[status(thm),theory(equality)],[190,54719,19,198]),
[iquote('0:Rew:190.0,54719.0,19.0,54719.0,198.0,54719.0')] ).
cnf(54880,plain,
equal(j(i(product(t(u,v),product(u,w)))),product(u,product(v,w))),
inference(rew,[status(thm),theory(equality)],[54879,11935]),
[iquote('0:Rew:54879.0,11935.0')] ).
cnf(54881,plain,
equal(product(t(u,v),product(u,w)),product(u,product(v,w))),
inference(rew,[status(thm),theory(equality)],[107,54880]),
[iquote('0:Rew:107.0,54880.0')] ).
cnf(54882,plain,
$false,
inference(unc,[status(thm)],[54881,27]),
[iquote('0:UnC:54881.0,27.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP770-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n017.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 : Mon Jun 13 19:27:38 EDT 2022
% 0.14/0.35 % CPUTime :
% 19.77/19.96
% 19.77/19.96 SPASS V 3.9
% 19.77/19.96 SPASS beiseite: Proof found.
% 19.77/19.96 % SZS status Theorem
% 19.77/19.96 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.77/19.96 SPASS derived 28649 clauses, backtracked 0 clauses, performed 0 splits and kept 5531 clauses.
% 19.77/19.96 SPASS allocated 119496 KBytes.
% 19.77/19.96 SPASS spent 0:0:18.73 on the problem.
% 19.77/19.96 0:00:00.03 for the input.
% 19.77/19.96 0:00:00.00 for the FLOTTER CNF translation.
% 19.77/19.96 0:00:00.18 for inferences.
% 19.77/19.96 0:00:00.00 for the backtracking.
% 19.77/19.96 0:0:18.46 for the reduction.
% 19.77/19.96
% 19.77/19.96
% 19.77/19.96 Here is a proof with depth 6, length 89 :
% 19.77/19.96 % SZS output start Refutation
% See solution above
% 19.77/19.96 Formulae used in the proof : sos01 sos02 sos03 sos04 sos05 sos06 sos07 sos08 sos09 sos10 sos11 sos12 sos13 sos14 sos16 sos19 sos23 sos24 goals
% 19.77/19.96
%------------------------------------------------------------------------------