TSTP Solution File: PUZ056-2.005 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PUZ056-2.005 : TPTP v8.1.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 : Mon Jul 18 18:27:25 EDT 2022
% Result : Unsatisfiable 0.46s 0.64s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 13
% Syntax : Number of clauses : 91 ( 39 unt; 0 nHn; 91 RR)
% Number of literals : 230 ( 0 equ; 141 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-5 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ p(u,v,w,x,y)
| p(z,v,w,x,y) ),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(2,axiom,
( ~ neq(u,v)
| ~ neq(u,w)
| ~ p(u,w,x,y,z)
| p(u,v,x,y,z) ),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(3,axiom,
( ~ neq(u,v)
| ~ neq(u,w)
| ~ neq(x,v)
| ~ neq(x,w)
| ~ p(x,u,w,y,z)
| p(x,u,v,y,z) ),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(4,axiom,
( ~ neq(u,v)
| ~ neq(u,w)
| ~ neq(x,v)
| ~ neq(x,w)
| ~ neq(y,v)
| ~ neq(y,w)
| ~ p(y,x,u,w,z)
| p(y,x,u,v,z) ),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(5,axiom,
( ~ neq(u,v)
| ~ neq(u,w)
| ~ neq(x,v)
| ~ neq(x,w)
| ~ neq(y,v)
| ~ neq(y,w)
| ~ neq(z,v)
| ~ neq(z,w)
| ~ p(z,y,x,u,w)
| p(z,y,x,u,v) ),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(7,axiom,
neq(s0,s1),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(8,axiom,
neq(s0,s2),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(9,axiom,
neq(s1,s0),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(11,axiom,
neq(s1,s2),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(12,axiom,
neq(s2,s0),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(13,axiom,
neq(s2,s1),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(15,axiom,
p(s0,s0,s0,s0,s0),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(16,axiom,
~ p(s2,s2,s2,s2,s2),
file('PUZ056-2.005.p',unknown),
[] ).
cnf(17,plain,
~ p(u,s2,s2,s2,s2),
inference(res,[status(thm),theory(equality)],[1,16]),
[iquote('0:Res:1.1,16.0')] ).
cnf(25,plain,
p(u,s0,s0,s0,s0),
inference(res,[status(thm),theory(equality)],[15,1]),
[iquote('0:Res:15.0,1.0')] ).
cnf(27,plain,
( ~ neq(u,v)
| ~ neq(u,s0)
| p(u,v,s0,s0,s0) ),
inference(res,[status(thm),theory(equality)],[25,2]),
[iquote('0:Res:25.0,2.2')] ).
cnf(29,plain,
( ~ neq(s2,s0)
| p(s2,s1,s0,s0,s0) ),
inference(res,[status(thm),theory(equality)],[13,27]),
[iquote('0:Res:13.0,27.0')] ).
cnf(35,plain,
p(s2,s1,s0,s0,s0),
inference(mrr,[status(thm)],[29,12]),
[iquote('0:MRR:29.0,12.0')] ).
cnf(37,plain,
p(u,s1,s0,s0,s0),
inference(res,[status(thm),theory(equality)],[35,1]),
[iquote('0:Res:35.0,1.0')] ).
cnf(49,plain,
( ~ neq(s1,u)
| ~ neq(s1,s0)
| ~ neq(v,u)
| ~ neq(v,s0)
| p(v,s1,u,s0,s0) ),
inference(res,[status(thm),theory(equality)],[37,3]),
[iquote('0:Res:37.0,3.4')] ).
cnf(50,plain,
( ~ neq(s1,u)
| ~ neq(v,u)
| ~ neq(v,s0)
| p(v,s1,u,s0,s0) ),
inference(mrr,[status(thm)],[49,9]),
[iquote('0:MRR:49.1,9.0')] ).
cnf(85,plain,
( ~ neq(u,s2)
| ~ neq(u,s0)
| p(u,s1,s2,s0,s0) ),
inference(res,[status(thm),theory(equality)],[11,50]),
[iquote('0:Res:11.0,50.0')] ).
cnf(91,plain,
( ~ neq(s1,s0)
| p(s1,s1,s2,s0,s0) ),
inference(res,[status(thm),theory(equality)],[11,85]),
[iquote('0:Res:11.0,85.0')] ).
cnf(93,plain,
p(s1,s1,s2,s0,s0),
inference(mrr,[status(thm)],[91,9]),
[iquote('0:MRR:91.0,9.0')] ).
cnf(94,plain,
p(u,s1,s2,s0,s0),
inference(res,[status(thm),theory(equality)],[93,1]),
[iquote('0:Res:93.0,1.0')] ).
cnf(105,plain,
( ~ neq(u,v)
| ~ neq(u,s1)
| p(u,v,s2,s0,s0) ),
inference(res,[status(thm),theory(equality)],[94,2]),
[iquote('0:Res:94.0,2.2')] ).
cnf(143,plain,
( ~ neq(s0,s1)
| p(s0,s2,s2,s0,s0) ),
inference(res,[status(thm),theory(equality)],[8,105]),
[iquote('0:Res:8.0,105.0')] ).
cnf(146,plain,
p(s0,s2,s2,s0,s0),
inference(mrr,[status(thm)],[143,7]),
[iquote('0:MRR:143.0,7.0')] ).
cnf(155,plain,
p(u,s2,s2,s0,s0),
inference(res,[status(thm),theory(equality)],[146,1]),
[iquote('0:Res:146.0,1.0')] ).
cnf(197,plain,
( ~ neq(s2,u)
| ~ neq(s2,s0)
| ~ neq(s2,u)
| ~ neq(s2,s0)
| ~ neq(v,u)
| ~ neq(v,s0)
| p(v,s2,s2,u,s0) ),
inference(res,[status(thm),theory(equality)],[155,4]),
[iquote('0:Res:155.0,4.6')] ).
cnf(199,plain,
( ~ neq(s2,u)
| ~ neq(s2,s0)
| ~ neq(v,u)
| ~ neq(v,s0)
| p(v,s2,s2,u,s0) ),
inference(obv,[status(thm),theory(equality)],[197]),
[iquote('0:Obv:197.1')] ).
cnf(200,plain,
( ~ neq(s2,u)
| ~ neq(v,u)
| ~ neq(v,s0)
| p(v,s2,s2,u,s0) ),
inference(mrr,[status(thm)],[199,12]),
[iquote('0:MRR:199.1,12.0')] ).
cnf(261,plain,
( ~ neq(u,s1)
| ~ neq(u,s0)
| p(u,s2,s2,s1,s0) ),
inference(res,[status(thm),theory(equality)],[13,200]),
[iquote('0:Res:13.0,200.0')] ).
cnf(264,plain,
( ~ neq(s2,s0)
| p(s2,s2,s2,s1,s0) ),
inference(res,[status(thm),theory(equality)],[13,261]),
[iquote('0:Res:13.0,261.0')] ).
cnf(266,plain,
p(s2,s2,s2,s1,s0),
inference(mrr,[status(thm)],[264,12]),
[iquote('0:MRR:264.0,12.0')] ).
cnf(270,plain,
p(u,s2,s2,s1,s0),
inference(res,[status(thm),theory(equality)],[266,1]),
[iquote('0:Res:266.0,1.0')] ).
cnf(281,plain,
( ~ neq(u,v)
| ~ neq(u,s2)
| p(u,v,s2,s1,s0) ),
inference(res,[status(thm),theory(equality)],[270,2]),
[iquote('0:Res:270.0,2.2')] ).
cnf(299,plain,
( ~ neq(s1,s2)
| p(s1,s0,s2,s1,s0) ),
inference(res,[status(thm),theory(equality)],[9,281]),
[iquote('0:Res:9.0,281.0')] ).
cnf(302,plain,
p(s1,s0,s2,s1,s0),
inference(mrr,[status(thm)],[299,11]),
[iquote('0:MRR:299.0,11.0')] ).
cnf(304,plain,
p(u,s0,s2,s1,s0),
inference(res,[status(thm),theory(equality)],[302,1]),
[iquote('0:Res:302.0,1.0')] ).
cnf(322,plain,
( ~ neq(s0,u)
| ~ neq(s0,s2)
| ~ neq(v,u)
| ~ neq(v,s2)
| p(v,s0,u,s1,s0) ),
inference(res,[status(thm),theory(equality)],[304,3]),
[iquote('0:Res:304.0,3.4')] ).
cnf(325,plain,
( ~ neq(s0,u)
| ~ neq(v,u)
| ~ neq(v,s2)
| p(v,s0,u,s1,s0) ),
inference(mrr,[status(thm)],[322,8]),
[iquote('0:MRR:322.1,8.0')] ).
cnf(453,plain,
( ~ neq(u,s1)
| ~ neq(u,s2)
| p(u,s0,s1,s1,s0) ),
inference(res,[status(thm),theory(equality)],[7,325]),
[iquote('0:Res:7.0,325.0')] ).
cnf(456,plain,
( ~ neq(s0,s2)
| p(s0,s0,s1,s1,s0) ),
inference(res,[status(thm),theory(equality)],[7,453]),
[iquote('0:Res:7.0,453.0')] ).
cnf(457,plain,
p(s0,s0,s1,s1,s0),
inference(mrr,[status(thm)],[456,8]),
[iquote('0:MRR:456.0,8.0')] ).
cnf(458,plain,
p(u,s0,s1,s1,s0),
inference(res,[status(thm),theory(equality)],[457,1]),
[iquote('0:Res:457.0,1.0')] ).
cnf(471,plain,
( ~ neq(u,v)
| ~ neq(u,s0)
| p(u,v,s1,s1,s0) ),
inference(res,[status(thm),theory(equality)],[458,2]),
[iquote('0:Res:458.0,2.2')] ).
cnf(479,plain,
( ~ neq(s2,s0)
| p(s2,s1,s1,s1,s0) ),
inference(res,[status(thm),theory(equality)],[13,471]),
[iquote('0:Res:13.0,471.0')] ).
cnf(485,plain,
p(s2,s1,s1,s1,s0),
inference(mrr,[status(thm)],[479,12]),
[iquote('0:MRR:479.0,12.0')] ).
cnf(487,plain,
p(u,s1,s1,s1,s0),
inference(res,[status(thm),theory(equality)],[485,1]),
[iquote('0:Res:485.0,1.0')] ).
cnf(512,plain,
( ~ neq(s1,u)
| ~ neq(s1,s0)
| ~ neq(s1,u)
| ~ neq(s1,s0)
| ~ neq(s1,u)
| ~ neq(s1,s0)
| ~ neq(v,u)
| ~ neq(v,s0)
| p(v,s1,s1,s1,u) ),
inference(res,[status(thm),theory(equality)],[487,5]),
[iquote('0:Res:487.0,5.8')] ).
cnf(514,plain,
( ~ neq(s1,u)
| ~ neq(s1,s0)
| ~ neq(v,u)
| ~ neq(v,s0)
| p(v,s1,s1,s1,u) ),
inference(obv,[status(thm),theory(equality)],[512]),
[iquote('0:Obv:512.3')] ).
cnf(515,plain,
( ~ neq(s1,u)
| ~ neq(v,u)
| ~ neq(v,s0)
| p(v,s1,s1,s1,u) ),
inference(mrr,[status(thm)],[514,9]),
[iquote('0:MRR:514.1,9.0')] ).
cnf(821,plain,
( ~ neq(u,s2)
| ~ neq(u,s0)
| p(u,s1,s1,s1,s2) ),
inference(res,[status(thm),theory(equality)],[11,515]),
[iquote('0:Res:11.0,515.0')] ).
cnf(824,plain,
( ~ neq(s1,s0)
| p(s1,s1,s1,s1,s2) ),
inference(res,[status(thm),theory(equality)],[11,821]),
[iquote('0:Res:11.0,821.0')] ).
cnf(826,plain,
p(s1,s1,s1,s1,s2),
inference(mrr,[status(thm)],[824,9]),
[iquote('0:MRR:824.0,9.0')] ).
cnf(827,plain,
p(u,s1,s1,s1,s2),
inference(res,[status(thm),theory(equality)],[826,1]),
[iquote('0:Res:826.0,1.0')] ).
cnf(837,plain,
( ~ neq(u,v)
| ~ neq(u,s1)
| p(u,v,s1,s1,s2) ),
inference(res,[status(thm),theory(equality)],[827,2]),
[iquote('0:Res:827.0,2.2')] ).
cnf(853,plain,
( ~ neq(s0,s1)
| p(s0,s2,s1,s1,s2) ),
inference(res,[status(thm),theory(equality)],[8,837]),
[iquote('0:Res:8.0,837.0')] ).
cnf(856,plain,
p(s0,s2,s1,s1,s2),
inference(mrr,[status(thm)],[853,7]),
[iquote('0:MRR:853.0,7.0')] ).
cnf(865,plain,
p(u,s2,s1,s1,s2),
inference(res,[status(thm),theory(equality)],[856,1]),
[iquote('0:Res:856.0,1.0')] ).
cnf(886,plain,
( ~ neq(s2,u)
| ~ neq(s2,s1)
| ~ neq(v,u)
| ~ neq(v,s1)
| p(v,s2,u,s1,s2) ),
inference(res,[status(thm),theory(equality)],[865,3]),
[iquote('0:Res:865.0,3.4')] ).
cnf(889,plain,
( ~ neq(s2,u)
| ~ neq(v,u)
| ~ neq(v,s1)
| p(v,s2,u,s1,s2) ),
inference(mrr,[status(thm)],[886,13]),
[iquote('0:MRR:886.1,13.0')] ).
cnf(1108,plain,
( ~ neq(u,s0)
| ~ neq(u,s1)
| p(u,s2,s0,s1,s2) ),
inference(res,[status(thm),theory(equality)],[12,889]),
[iquote('0:Res:12.0,889.0')] ).
cnf(1113,plain,
( ~ neq(s2,s1)
| p(s2,s2,s0,s1,s2) ),
inference(res,[status(thm),theory(equality)],[12,1108]),
[iquote('0:Res:12.0,1108.0')] ).
cnf(1115,plain,
p(s2,s2,s0,s1,s2),
inference(mrr,[status(thm)],[1113,13]),
[iquote('0:MRR:1113.0,13.0')] ).
cnf(1116,plain,
p(u,s2,s0,s1,s2),
inference(res,[status(thm),theory(equality)],[1115,1]),
[iquote('0:Res:1115.0,1.0')] ).
cnf(1127,plain,
( ~ neq(u,v)
| ~ neq(u,s2)
| p(u,v,s0,s1,s2) ),
inference(res,[status(thm),theory(equality)],[1116,2]),
[iquote('0:Res:1116.0,2.2')] ).
cnf(1197,plain,
( ~ neq(s1,s2)
| p(s1,s0,s0,s1,s2) ),
inference(res,[status(thm),theory(equality)],[9,1127]),
[iquote('0:Res:9.0,1127.0')] ).
cnf(1200,plain,
p(s1,s0,s0,s1,s2),
inference(mrr,[status(thm)],[1197,11]),
[iquote('0:MRR:1197.0,11.0')] ).
cnf(1210,plain,
p(u,s0,s0,s1,s2),
inference(res,[status(thm),theory(equality)],[1200,1]),
[iquote('0:Res:1200.0,1.0')] ).
cnf(1273,plain,
( ~ neq(s0,u)
| ~ neq(s0,s1)
| ~ neq(s0,u)
| ~ neq(s0,s1)
| ~ neq(v,u)
| ~ neq(v,s1)
| p(v,s0,s0,u,s2) ),
inference(res,[status(thm),theory(equality)],[1210,4]),
[iquote('0:Res:1210.0,4.6')] ).
cnf(1275,plain,
( ~ neq(s0,u)
| ~ neq(s0,s1)
| ~ neq(v,u)
| ~ neq(v,s1)
| p(v,s0,s0,u,s2) ),
inference(obv,[status(thm),theory(equality)],[1273]),
[iquote('0:Obv:1273.1')] ).
cnf(1276,plain,
( ~ neq(s0,u)
| ~ neq(v,u)
| ~ neq(v,s1)
| p(v,s0,s0,u,s2) ),
inference(mrr,[status(thm)],[1275,7]),
[iquote('0:MRR:1275.1,7.0')] ).
cnf(1467,plain,
( ~ neq(u,s2)
| ~ neq(u,s1)
| p(u,s0,s0,s2,s2) ),
inference(res,[status(thm),theory(equality)],[8,1276]),
[iquote('0:Res:8.0,1276.0')] ).
cnf(1477,plain,
( ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2) ),
inference(res,[status(thm),theory(equality)],[8,1467]),
[iquote('0:Res:8.0,1467.0')] ).
cnf(1478,plain,
p(s0,s0,s0,s2,s2),
inference(mrr,[status(thm)],[1477,7]),
[iquote('0:MRR:1477.0,7.0')] ).
cnf(1482,plain,
p(u,s0,s0,s2,s2),
inference(res,[status(thm),theory(equality)],[1478,1]),
[iquote('0:Res:1478.0,1.0')] ).
cnf(1492,plain,
( ~ neq(u,v)
| ~ neq(u,s0)
| p(u,v,s0,s2,s2) ),
inference(res,[status(thm),theory(equality)],[1482,2]),
[iquote('0:Res:1482.0,2.2')] ).
cnf(1541,plain,
( ~ neq(s2,s0)
| p(s2,s1,s0,s2,s2) ),
inference(res,[status(thm),theory(equality)],[13,1492]),
[iquote('0:Res:13.0,1492.0')] ).
cnf(1547,plain,
p(s2,s1,s0,s2,s2),
inference(mrr,[status(thm)],[1541,12]),
[iquote('0:MRR:1541.0,12.0')] ).
cnf(1549,plain,
p(u,s1,s0,s2,s2),
inference(res,[status(thm),theory(equality)],[1547,1]),
[iquote('0:Res:1547.0,1.0')] ).
cnf(1570,plain,
( ~ neq(s1,u)
| ~ neq(s1,s0)
| ~ neq(v,u)
| ~ neq(v,s0)
| p(v,s1,u,s2,s2) ),
inference(res,[status(thm),theory(equality)],[1549,3]),
[iquote('0:Res:1549.0,3.4')] ).
cnf(1573,plain,
( ~ neq(s1,u)
| ~ neq(v,u)
| ~ neq(v,s0)
| p(v,s1,u,s2,s2) ),
inference(mrr,[status(thm)],[1570,9]),
[iquote('0:MRR:1570.1,9.0')] ).
cnf(1821,plain,
( ~ neq(u,s2)
| ~ neq(u,s0)
| p(u,s1,s2,s2,s2) ),
inference(res,[status(thm),theory(equality)],[11,1573]),
[iquote('0:Res:11.0,1573.0')] ).
cnf(1826,plain,
( ~ neq(s1,s0)
| p(s1,s1,s2,s2,s2) ),
inference(res,[status(thm),theory(equality)],[11,1821]),
[iquote('0:Res:11.0,1821.0')] ).
cnf(1828,plain,
p(s1,s1,s2,s2,s2),
inference(mrr,[status(thm)],[1826,9]),
[iquote('0:MRR:1826.0,9.0')] ).
cnf(1829,plain,
p(u,s1,s2,s2,s2),
inference(res,[status(thm),theory(equality)],[1828,1]),
[iquote('0:Res:1828.0,1.0')] ).
cnf(1839,plain,
( ~ neq(u,v)
| ~ neq(u,s1)
| p(u,v,s2,s2,s2) ),
inference(res,[status(thm),theory(equality)],[1829,2]),
[iquote('0:Res:1829.0,2.2')] ).
cnf(2073,plain,
( ~ neq(s0,s1)
| p(s0,s2,s2,s2,s2) ),
inference(res,[status(thm),theory(equality)],[8,1839]),
[iquote('0:Res:8.0,1839.0')] ).
cnf(2076,plain,
$false,
inference(mrr,[status(thm)],[2073,7,17]),
[iquote('0:MRR:2073.0,2073.1,7.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : PUZ056-2.005 : TPTP v8.1.0. Released v3.5.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n026.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 : Sat May 28 23:09:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.46/0.64
% 0.46/0.64 SPASS V 3.9
% 0.46/0.64 SPASS beiseite: Proof found.
% 0.46/0.64 % SZS status Theorem
% 0.46/0.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.64 SPASS derived 1478 clauses, backtracked 0 clauses, performed 0 splits and kept 461 clauses.
% 0.46/0.64 SPASS allocated 64575 KBytes.
% 0.46/0.64 SPASS spent 0:00:00.28 on the problem.
% 0.46/0.64 0:00:00.03 for the input.
% 0.46/0.64 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.64 0:00:00.03 for inferences.
% 0.46/0.64 0:00:00.00 for the backtracking.
% 0.46/0.64 0:00:00.19 for the reduction.
% 0.46/0.64
% 0.46/0.64
% 0.46/0.64 Here is a proof with depth 52, length 91 :
% 0.46/0.64 % SZS output start Refutation
% See solution above
% 0.46/0.64 Formulae used in the proof : rule1 rule2 rule3 rule4 rule5 neq2 neq3 neq4 neq6 neq7 neq8 init goal
% 0.46/0.64
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