TSTP Solution File: LDA002-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LDA002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 : Sun Jul 17 16:45:55 EDT 2022
% Result : Unsatisfiable 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 82 ( 82 unt; 0 nHn; 82 RR)
% Number of literals : 82 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(f(f(u,v),f(u,w)),f(u,f(v,w))),
file('LDA002-1.p',unknown),
[] ).
cnf(2,axiom,
equal(f(n1,n1),n2),
file('LDA002-1.p',unknown),
[] ).
cnf(3,axiom,
equal(f(n2,n1),n3),
file('LDA002-1.p',unknown),
[] ).
cnf(4,axiom,
equal(f(n2,n2),u__dfg),
file('LDA002-1.p',unknown),
[] ).
cnf(5,axiom,
equal(f(u__dfg,n1),u1),
file('LDA002-1.p',unknown),
[] ).
cnf(6,axiom,
equal(f(u__dfg,n2),u2),
file('LDA002-1.p',unknown),
[] ).
cnf(7,axiom,
equal(f(u__dfg,n3),u3),
file('LDA002-1.p',unknown),
[] ).
cnf(8,axiom,
equal(f(u__dfg,u__dfg),uu),
file('LDA002-1.p',unknown),
[] ).
cnf(9,axiom,
equal(f(f(n3,n2),u2),a),
file('LDA002-1.p',unknown),
[] ).
cnf(10,axiom,
equal(f(u1,u3),b),
file('LDA002-1.p',unknown),
[] ).
cnf(11,axiom,
equal(f(uu,uu),v__dfg),
file('LDA002-1.p',unknown),
[] ).
cnf(12,axiom,
~ equal(f(b,v__dfg),f(a,v__dfg)),
file('LDA002-1.p',unknown),
[] ).
cnf(27,plain,
equal(f(f(u__dfg,u),u3),f(u__dfg,f(u,n3))),
inference(spr,[status(thm),theory(equality)],[7,1]),
[iquote('0:SpR:7.0,1.0')] ).
cnf(28,plain,
equal(f(f(u__dfg,u),u2),f(u__dfg,f(u,n2))),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(30,plain,
equal(f(f(u__dfg,u),uu),f(u__dfg,f(u,u__dfg))),
inference(spr,[status(thm),theory(equality)],[8,1]),
[iquote('0:SpR:8.0,1.0')] ).
cnf(31,plain,
equal(f(f(n2,u),n3),f(n2,f(u,n1))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(32,plain,
equal(f(f(n2,u),u__dfg),f(n2,f(u,n2))),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(33,plain,
equal(f(f(uu,u),v__dfg),f(uu,f(u,uu))),
inference(spr,[status(thm),theory(equality)],[11,1]),
[iquote('0:SpR:11.0,1.0')] ).
cnf(34,plain,
equal(f(f(n1,u),n2),f(n1,f(u,n1))),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(41,plain,
equal(f(n3,f(n2,u)),f(n2,f(n1,u))),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(42,plain,
equal(f(u__dfg,f(n2,u)),f(n2,f(n2,u))),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(44,plain,
equal(f(n1,f(n1,u)),f(n2,f(n1,u))),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(45,plain,
equal(f(f(n3,n2),f(u2,u)),f(a,f(f(n3,n2),u))),
inference(spr,[status(thm),theory(equality)],[9,1]),
[iquote('0:SpR:9.0,1.0')] ).
cnf(64,plain,
equal(f(u__dfg,f(n1,n3)),f(u1,u3)),
inference(spr,[status(thm),theory(equality)],[5,27]),
[iquote('0:SpR:5.0,27.0')] ).
cnf(65,plain,
equal(f(u__dfg,f(u__dfg,n3)),f(uu,u3)),
inference(spr,[status(thm),theory(equality)],[8,27]),
[iquote('0:SpR:8.0,27.0')] ).
cnf(67,plain,
equal(f(u__dfg,f(n1,n3)),b),
inference(rew,[status(thm),theory(equality)],[10,64]),
[iquote('0:Rew:10.0,64.0')] ).
cnf(68,plain,
equal(f(uu,u3),f(u__dfg,u3)),
inference(rew,[status(thm),theory(equality)],[7,65]),
[iquote('0:Rew:7.0,65.0')] ).
cnf(95,plain,
equal(f(u__dfg,f(u__dfg,n2)),f(uu,u2)),
inference(spr,[status(thm),theory(equality)],[8,28]),
[iquote('0:SpR:8.0,28.0')] ).
cnf(99,plain,
equal(f(uu,u2),f(u__dfg,u2)),
inference(rew,[status(thm),theory(equality)],[6,95]),
[iquote('0:Rew:6.0,95.0')] ).
cnf(164,plain,
equal(f(u__dfg,f(n3,u__dfg)),f(u3,uu)),
inference(spr,[status(thm),theory(equality)],[7,30]),
[iquote('0:SpR:7.0,30.0')] ).
cnf(165,plain,
equal(f(u__dfg,f(n2,u__dfg)),f(u2,uu)),
inference(spr,[status(thm),theory(equality)],[6,30]),
[iquote('0:SpR:6.0,30.0')] ).
cnf(167,plain,
equal(f(u__dfg,f(u__dfg,u__dfg)),f(uu,uu)),
inference(spr,[status(thm),theory(equality)],[8,30]),
[iquote('0:SpR:8.0,30.0')] ).
cnf(172,plain,
equal(f(n2,f(n2,u__dfg)),f(u2,uu)),
inference(rew,[status(thm),theory(equality)],[42,165]),
[iquote('0:Rew:42.0,165.0')] ).
cnf(173,plain,
equal(f(u__dfg,uu),v__dfg),
inference(rew,[status(thm),theory(equality)],[8,167,11]),
[iquote('0:Rew:8.0,167.0,11.0,167.0')] ).
cnf(207,plain,
equal(f(n2,f(n1,n1)),f(n3,n3)),
inference(spr,[status(thm),theory(equality)],[3,31]),
[iquote('0:SpR:3.0,31.0')] ).
cnf(208,plain,
equal(f(n2,f(n2,n1)),f(u__dfg,n3)),
inference(spr,[status(thm),theory(equality)],[4,31]),
[iquote('0:SpR:4.0,31.0')] ).
cnf(211,plain,
equal(f(n3,n3),u__dfg),
inference(rew,[status(thm),theory(equality)],[4,207,2]),
[iquote('0:Rew:4.0,207.0,2.0,207.0')] ).
cnf(224,plain,
equal(f(n2,n3),u3),
inference(rew,[status(thm),theory(equality)],[3,208,7]),
[iquote('0:Rew:3.0,208.0,7.0,208.0')] ).
cnf(252,plain,
equal(f(u__dfg,f(n3,u)),f(n3,f(n3,u))),
inference(spr,[status(thm),theory(equality)],[211,1]),
[iquote('0:SpR:211.0,1.0')] ).
cnf(256,plain,
equal(f(n3,f(n3,u__dfg)),f(u3,uu)),
inference(rew,[status(thm),theory(equality)],[252,164]),
[iquote('0:Rew:252.0,164.0')] ).
cnf(285,plain,
equal(f(n2,f(n1,n2)),f(n3,u__dfg)),
inference(spr,[status(thm),theory(equality)],[3,32]),
[iquote('0:SpR:3.0,32.0')] ).
cnf(286,plain,
equal(f(n2,f(n2,n2)),f(u__dfg,u__dfg)),
inference(spr,[status(thm),theory(equality)],[4,32]),
[iquote('0:SpR:4.0,32.0')] ).
cnf(289,plain,
equal(f(n2,u__dfg),uu),
inference(rew,[status(thm),theory(equality)],[4,286,8]),
[iquote('0:Rew:4.0,286.0,8.0,286.0')] ).
cnf(290,plain,
equal(f(u2,uu),f(n2,uu)),
inference(rew,[status(thm),theory(equality)],[289,172]),
[iquote('0:Rew:289.0,172.0')] ).
cnf(306,plain,
equal(f(uu,f(n2,u)),f(n2,f(u__dfg,u))),
inference(spr,[status(thm),theory(equality)],[289,1]),
[iquote('0:SpR:289.0,1.0')] ).
cnf(369,plain,
equal(f(n1,f(n1,n1)),f(n2,n2)),
inference(spr,[status(thm),theory(equality)],[2,34]),
[iquote('0:SpR:2.0,34.0')] ).
cnf(370,plain,
equal(f(n1,n2),u__dfg),
inference(rew,[status(thm),theory(equality)],[2,369,4]),
[iquote('0:Rew:2.0,369.0,4.0,369.0')] ).
cnf(377,plain,
equal(f(n3,u__dfg),f(n2,u__dfg)),
inference(rew,[status(thm),theory(equality)],[370,285]),
[iquote('0:Rew:370.0,285.0')] ).
cnf(379,plain,
equal(f(n3,u__dfg),uu),
inference(rew,[status(thm),theory(equality)],[289,377]),
[iquote('0:Rew:289.0,377.0')] ).
cnf(385,plain,
equal(f(u3,uu),f(n3,uu)),
inference(rew,[status(thm),theory(equality)],[379,256]),
[iquote('0:Rew:379.0,256.0')] ).
cnf(407,plain,
equal(f(n1,f(n2,n1)),f(u__dfg,n2)),
inference(spr,[status(thm),theory(equality)],[370,34]),
[iquote('0:SpR:370.0,34.0')] ).
cnf(411,plain,
equal(f(n1,n3),u2),
inference(rew,[status(thm),theory(equality)],[3,407,6]),
[iquote('0:Rew:3.0,407.0,6.0,407.0')] ).
cnf(412,plain,
equal(f(u__dfg,u2),b),
inference(rew,[status(thm),theory(equality)],[411,67]),
[iquote('0:Rew:411.0,67.0')] ).
cnf(416,plain,
equal(f(uu,u2),b),
inference(rew,[status(thm),theory(equality)],[412,99]),
[iquote('0:Rew:412.0,99.0')] ).
cnf(443,plain,
equal(f(f(n3,u),uu),f(n3,f(u,u__dfg))),
inference(spr,[status(thm),theory(equality)],[379,1]),
[iquote('0:SpR:379.0,1.0')] ).
cnf(444,plain,
equal(f(uu,f(n3,u)),f(n3,f(u__dfg,u))),
inference(spr,[status(thm),theory(equality)],[379,1]),
[iquote('0:SpR:379.0,1.0')] ).
cnf(469,plain,
equal(f(uu,f(u2,uu)),f(b,v__dfg)),
inference(spr,[status(thm),theory(equality)],[416,33]),
[iquote('0:SpR:416.0,33.0')] ).
cnf(471,plain,
equal(f(uu,f(n2,uu)),f(b,v__dfg)),
inference(rew,[status(thm),theory(equality)],[290,469]),
[iquote('0:Rew:290.0,469.0')] ).
cnf(472,plain,
equal(f(n2,f(u__dfg,uu)),f(b,v__dfg)),
inference(rew,[status(thm),theory(equality)],[306,471]),
[iquote('0:Rew:306.0,471.0')] ).
cnf(473,plain,
equal(f(b,v__dfg),f(n2,v__dfg)),
inference(rew,[status(thm),theory(equality)],[173,472]),
[iquote('0:Rew:173.0,472.0')] ).
cnf(474,plain,
~ equal(f(a,v__dfg),f(n2,v__dfg)),
inference(rew,[status(thm),theory(equality)],[473,12]),
[iquote('0:Rew:473.0,12.0')] ).
cnf(547,plain,
equal(f(n2,f(n1,u__dfg)),f(n3,uu)),
inference(spr,[status(thm),theory(equality)],[289,41]),
[iquote('0:SpR:289.0,41.0')] ).
cnf(589,plain,
equal(f(u__dfg,u3),f(n2,u3)),
inference(spr,[status(thm),theory(equality)],[224,42]),
[iquote('0:SpR:224.0,42.0')] ).
cnf(590,plain,
equal(f(u__dfg,uu),f(n2,uu)),
inference(spr,[status(thm),theory(equality)],[289,42]),
[iquote('0:SpR:289.0,42.0')] ).
cnf(593,plain,
equal(f(uu,u3),f(n2,u3)),
inference(rew,[status(thm),theory(equality)],[589,68]),
[iquote('0:Rew:589.0,68.0')] ).
cnf(596,plain,
equal(f(n2,uu),v__dfg),
inference(rew,[status(thm),theory(equality)],[173,590]),
[iquote('0:Rew:173.0,590.0')] ).
cnf(597,plain,
equal(f(u2,uu),v__dfg),
inference(rew,[status(thm),theory(equality)],[596,290]),
[iquote('0:Rew:596.0,290.0')] ).
cnf(616,plain,
equal(f(f(n2,u),v__dfg),f(n2,f(u,uu))),
inference(spr,[status(thm),theory(equality)],[596,1]),
[iquote('0:SpR:596.0,1.0')] ).
cnf(647,plain,
equal(f(f(n2,u3),v__dfg),f(uu,f(u3,uu))),
inference(spr,[status(thm),theory(equality)],[593,33]),
[iquote('0:SpR:593.0,33.0')] ).
cnf(649,plain,
equal(f(f(n2,u3),v__dfg),f(uu,f(n3,uu))),
inference(rew,[status(thm),theory(equality)],[385,647]),
[iquote('0:Rew:385.0,647.0')] ).
cnf(650,plain,
equal(f(n3,f(u__dfg,uu)),f(n2,f(u3,uu))),
inference(rew,[status(thm),theory(equality)],[616,649,444]),
[iquote('0:Rew:616.0,649.0,444.0,649.0')] ).
cnf(651,plain,
equal(f(n2,f(n3,uu)),f(n3,v__dfg)),
inference(rew,[status(thm),theory(equality)],[173,650,385]),
[iquote('0:Rew:173.0,650.0,385.0,650.0')] ).
cnf(715,plain,
equal(f(n1,u__dfg),f(n2,u__dfg)),
inference(spr,[status(thm),theory(equality)],[370,44]),
[iquote('0:SpR:370.0,44.0')] ).
cnf(718,plain,
equal(f(n1,u__dfg),uu),
inference(rew,[status(thm),theory(equality)],[289,715]),
[iquote('0:Rew:289.0,715.0')] ).
cnf(723,plain,
equal(f(n3,uu),f(n2,uu)),
inference(rew,[status(thm),theory(equality)],[718,547]),
[iquote('0:Rew:718.0,547.0')] ).
cnf(725,plain,
equal(f(n3,uu),v__dfg),
inference(rew,[status(thm),theory(equality)],[596,723]),
[iquote('0:Rew:596.0,723.0')] ).
cnf(736,plain,
equal(f(n3,v__dfg),f(n2,v__dfg)),
inference(rew,[status(thm),theory(equality)],[725,651]),
[iquote('0:Rew:725.0,651.0')] ).
cnf(781,plain,
equal(f(f(n3,u),v__dfg),f(n3,f(u,uu))),
inference(spr,[status(thm),theory(equality)],[725,1]),
[iquote('0:SpR:725.0,1.0')] ).
cnf(967,plain,
equal(f(a,f(f(n3,n2),uu)),f(f(n3,n2),v__dfg)),
inference(spr,[status(thm),theory(equality)],[597,45]),
[iquote('0:SpR:597.0,45.0')] ).
cnf(974,plain,
equal(f(a,f(n3,f(n2,u__dfg))),f(n3,f(n2,uu))),
inference(rew,[status(thm),theory(equality)],[443,967,781]),
[iquote('0:Rew:443.0,967.0,781.0,967.0')] ).
cnf(975,plain,
equal(f(a,v__dfg),f(n2,v__dfg)),
inference(rew,[status(thm),theory(equality)],[725,974,289,736,596]),
[iquote('0:Rew:725.0,974.0,289.0,974.0,736.0,974.0,596.0,974.0')] ).
cnf(976,plain,
$false,
inference(mrr,[status(thm)],[975,474]),
[iquote('0:MRR:975.0,474.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LDA002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 02:53:13 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.19/0.53
% 0.19/0.53 SPASS V 3.9
% 0.19/0.53 SPASS beiseite: Proof found.
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.53 SPASS derived 692 clauses, backtracked 0 clauses, performed 0 splits and kept 460 clauses.
% 0.19/0.53 SPASS allocated 64137 KBytes.
% 0.19/0.53 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.53 0:00:00.04 for the input.
% 0.19/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.53 0:00:00.01 for inferences.
% 0.19/0.53 0:00:00.00 for the backtracking.
% 0.19/0.53 0:00:00.10 for the reduction.
% 0.19/0.53
% 0.19/0.53
% 0.19/0.53 Here is a proof with depth 4, length 82 :
% 0.19/0.53 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : a1 clause_2 clause_3 clause_4 clause_5 clause_6 clause_7 clause_8 clause_9 clause_10 clause_11 prove_equation
% 0.19/0.53
%------------------------------------------------------------------------------