TSTP Solution File: LCL166-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL166-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 14:35:01 EDT 2022
% Result : Unsatisfiable 243.26s 243.59s
% Output : Refutation 246.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 3
% Syntax : Number of clauses : 75 ( 11 unt; 0 nHn; 75 RR)
% Number of literals : 198 ( 0 equ; 124 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(v) ),
file('LCL166-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,u),v)))),
file('LCL166-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
file('LCL166-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,w),equivalent(equivalent(w,u),v))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,w))
| is_a_theorem(equivalent(equivalent(w,u),v)) ),
inference(res,[status(thm),theory(equality)],[7,1]),
[iquote('0:Res:7.1,1.1')] ).
cnf(9,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(w,v),x),u),equivalent(x,w))) ),
inference(sor,[status(thm)],[8,7]),
[iquote('0:SoR:8.1,7.1')] ).
cnf(10,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(v,w),equivalent(equivalent(w,x),v)),u),x)) ),
inference(sor,[status(thm)],[8,2]),
[iquote('0:SoR:8.1,2.0')] ).
cnf(12,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(equivalent(v,w),equivalent(equivalent(w,x),v)),u))
| is_a_theorem(x) ),
inference(res,[status(thm),theory(equality)],[10,1]),
[iquote('0:Res:10.1,1.1')] ).
cnf(14,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| ~ is_a_theorem(equivalent(equivalent(equivalent(w,v),x),u))
| is_a_theorem(equivalent(x,w)) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.2,1.1')] ).
cnf(15,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(w)
| ~ is_a_theorem(equivalent(equivalent(u,x),equivalent(v,w)))
| is_a_theorem(x) ),
inference(sor,[status(thm)],[12,9]),
[iquote('0:SoR:12.1,9.2')] ).
cnf(16,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(v,u),w),x),equivalent(w,v)))
| is_a_theorem(x) ),
inference(sor,[status(thm)],[12,10]),
[iquote('0:SoR:12.1,10.1')] ).
cnf(17,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),w),x),equivalent(w,u)))
| ~ is_a_theorem(x)
| is_a_theorem(v) ),
inference(sor,[status(thm)],[12,7]),
[iquote('0:SoR:12.1,7.1')] ).
cnf(21,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(v,u),w))
| ~ is_a_theorem(x)
| is_a_theorem(equivalent(x,equivalent(w,v))) ),
inference(sor,[status(thm)],[14,10]),
[iquote('0:SoR:14.2,10.1')] ).
cnf(30,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(w,equivalent(equivalent(x,y),equivalent(equivalent(y,w),x))))) ),
inference(sor,[status(thm)],[21,10]),
[iquote('0:SoR:21.1,10.1')] ).
cnf(33,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(u,equivalent(w,equivalent(equivalent(x,y),equivalent(equivalent(y,w),x))))) ),
inference(obv,[status(thm),theory(equality)],[30]),
[iquote('0:Obv:30.0')] ).
cnf(34,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(u,equivalent(v,equivalent(equivalent(w,x),equivalent(equivalent(x,v),w))))) ),
inference(con,[status(thm)],[33]),
[iquote('0:Con:33.1')] ).
cnf(41,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,u),v))))
| ~ is_a_theorem(equivalent(equivalent(x,y),equivalent(equivalent(y,z),x)))
| is_a_theorem(z) ),
inference(sor,[status(thm)],[12,34]),
[iquote('0:SoR:12.1,34.1')] ).
cnf(42,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,u),v))))
| ~ is_a_theorem(x)
| ~ is_a_theorem(equivalent(equivalent(y,x),z))
| is_a_theorem(equivalent(z,y)) ),
inference(sor,[status(thm)],[14,34]),
[iquote('0:SoR:14.2,34.1')] ).
cnf(47,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(v,w),u)))
| is_a_theorem(w) ),
inference(ssi,[status(thm)],[41,2]),
[iquote('0:SSi:41.0,2.0')] ).
cnf(48,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(v,u),w))
| is_a_theorem(equivalent(w,v)) ),
inference(ssi,[status(thm)],[42,2]),
[iquote('0:SSi:42.0,2.0')] ).
cnf(60,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(equivalent(v,equivalent(w,x)),u)),w))
| is_a_theorem(x) ),
inference(sor,[status(thm)],[47,34]),
[iquote('0:SoR:47.0,34.1')] ).
cnf(64,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(equivalent(equivalent(u,v),w),w)) ),
inference(sor,[status(thm)],[48,7]),
[iquote('0:SoR:48.1,7.1')] ).
cnf(66,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(equivalent(v,w),equivalent(equivalent(w,equivalent(x,u)),v)),x)) ),
inference(sor,[status(thm)],[48,2]),
[iquote('0:SoR:48.1,2.0')] ).
cnf(73,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,w))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[17,64]),
[iquote('0:SoR:17.0,64.2')] ).
cnf(74,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| ~ is_a_theorem(equivalent(w,u))
| is_a_theorem(equivalent(v,w)) ),
inference(sor,[status(thm)],[16,64]),
[iquote('0:SoR:16.1,64.2')] ).
cnf(77,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| ~ is_a_theorem(v)
| ~ is_a_theorem(w)
| is_a_theorem(equivalent(u,w)) ),
inference(sor,[status(thm)],[14,64]),
[iquote('0:SoR:14.2,64.2')] ).
cnf(82,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| ~ is_a_theorem(w)
| is_a_theorem(equivalent(u,w)) ),
inference(obv,[status(thm),theory(equality)],[77]),
[iquote('0:Obv:77.1')] ).
cnf(83,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(u,v)) ),
inference(con,[status(thm)],[82]),
[iquote('0:Con:82.1')] ).
cnf(88,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),w))
| ~ is_a_theorem(equivalent(w,u))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[47,83]),
[iquote('0:SoR:47.0,83.2')] ).
cnf(91,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| ~ is_a_theorem(w)
| is_a_theorem(equivalent(equivalent(v,u),w)) ),
inference(sor,[status(thm)],[8,83]),
[iquote('0:SoR:8.1,83.2')] ).
cnf(119,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),w),w))
| ~ is_a_theorem(v)
| is_a_theorem(u) ),
inference(sor,[status(thm)],[88,7]),
[iquote('0:SoR:88.0,7.1')] ).
cnf(159,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(v,equivalent(equivalent(w,x),equivalent(equivalent(x,v),w))),y))
| ~ is_a_theorem(u)
| is_a_theorem(y) ),
inference(sor,[status(thm)],[73,34]),
[iquote('0:SoR:73.0,34.1')] ).
cnf(161,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,w))
| ~ is_a_theorem(v)
| ~ is_a_theorem(u)
| is_a_theorem(w) ),
inference(sor,[status(thm)],[73,83]),
[iquote('0:SoR:73.0,83.2')] ).
cnf(162,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(u)
| ~ is_a_theorem(w)
| is_a_theorem(v) ),
inference(obv,[status(thm),theory(equality)],[161]),
[iquote('0:Obv:161.0')] ).
cnf(163,plain,
( ~ is_a_theorem(equivalent(u,v))
| ~ is_a_theorem(u)
| is_a_theorem(v) ),
inference(con,[status(thm)],[162]),
[iquote('0:Con:162.2')] ).
cnf(164,plain,
( ~ is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,u),v))),x))
| ~ is_a_theorem(y)
| is_a_theorem(x) ),
inference(obv,[status(thm),theory(equality)],[159]),
[iquote('0:Obv:159.0')] ).
cnf(165,plain,
( ~ is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,w),equivalent(equivalent(w,u),v))),x))
| is_a_theorem(x) ),
inference(con,[status(thm)],[164]),
[iquote('0:Con:164.1')] ).
cnf(298,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| ~ is_a_theorem(equivalent(w,u))
| ~ is_a_theorem(v)
| is_a_theorem(w) ),
inference(sor,[status(thm)],[119,91]),
[iquote('0:SoR:119.0,91.3')] ).
cnf(312,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,u))
| ~ is_a_theorem(w)
| is_a_theorem(v) ),
inference(obv,[status(thm),theory(equality)],[298]),
[iquote('0:Obv:298.1')] ).
cnf(313,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(v,u))
| is_a_theorem(v) ),
inference(con,[status(thm)],[312]),
[iquote('0:Con:312.2')] ).
cnf(461,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),w),equivalent(v,x)),equivalent(w,u)))
| is_a_theorem(x) ),
inference(sor,[status(thm)],[60,10]),
[iquote('0:SoR:60.0,10.1')] ).
cnf(582,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(w,equivalent(equivalent(w,v),u)))) ),
inference(sor,[status(thm)],[461,66]),
[iquote('0:SoR:461.0,66.1')] ).
cnf(637,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(u,v),w)))
| ~ is_a_theorem(w)
| is_a_theorem(v) ),
inference(sor,[status(thm)],[313,582]),
[iquote('0:SoR:313.1,582.1')] ).
cnf(678,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),u),w))
| ~ is_a_theorem(w)
| is_a_theorem(v) ),
inference(sor,[status(thm)],[637,582]),
[iquote('0:SoR:637.0,582.1')] ).
cnf(775,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(v,w),v))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[678,83]),
[iquote('0:SoR:678.0,83.2')] ).
cnf(776,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(equivalent(equivalent(v,w),v))
| is_a_theorem(w) ),
inference(obv,[status(thm),theory(equality)],[775]),
[iquote('0:Obv:775.0')] ).
cnf(777,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),u))
| is_a_theorem(v) ),
inference(con,[status(thm)],[776]),
[iquote('0:Con:776.0')] ).
cnf(785,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,equivalent(equivalent(w,v),u)),w)) ),
inference(sor,[status(thm)],[777,66]),
[iquote('0:SoR:777.0,66.1')] ).
cnf(803,plain,
( ~ is_a_theorem(equivalent(equivalent(u,u),v))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[165,785]),
[iquote('0:SoR:165.0,785.1')] ).
cnf(804,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,v),u)) ),
inference(sor,[status(thm)],[777,785]),
[iquote('0:SoR:777.0,785.1')] ).
cnf(904,plain,
is_a_theorem(equivalent(equivalent(u,v),equivalent(equivalent(v,equivalent(w,w)),u))),
inference(sor,[status(thm)],[803,2]),
[iquote('0:SoR:803.0,2.0')] ).
cnf(944,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,equivalent(w,w))) ),
inference(sor,[status(thm)],[74,804]),
[iquote('0:SoR:74.2,804.1')] ).
cnf(946,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,v)) ),
inference(sor,[status(thm)],[313,804]),
[iquote('0:SoR:313.1,804.1')] ).
cnf(948,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(v,v)) ),
inference(obv,[status(thm),theory(equality)],[946]),
[iquote('0:Obv:946.0')] ).
cnf(957,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(v)
| is_a_theorem(equivalent(u,equivalent(w,w))) ),
inference(obv,[status(thm),theory(equality)],[944]),
[iquote('0:Obv:944.0')] ).
cnf(958,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(u,equivalent(v,v))) ),
inference(con,[status(thm)],[957]),
[iquote('0:Con:957.1')] ).
cnf(984,plain,
is_a_theorem(equivalent(u,u)),
inference(ems,[status(thm)],[948,2]),
[iquote('0:EmS:948.0,2.0')] ).
cnf(1156,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(u,v),u),equivalent(v,w)))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[461,958]),
[iquote('0:SoR:461.0,958.1')] ).
cnf(1517,plain,
is_a_theorem(equivalent(u,equivalent(u,equivalent(v,v)))),
inference(sor,[status(thm)],[1156,904]),
[iquote('0:SoR:1156.0,904.0')] ).
cnf(1519,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,equivalent(equivalent(w,v),w)),u)) ),
inference(sor,[status(thm)],[1156,582]),
[iquote('0:SoR:1156.0,582.1')] ).
cnf(1529,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,equivalent(w,u)),v)),w)),
inference(sor,[status(thm)],[1156,2]),
[iquote('0:SoR:1156.0,2.0')] ).
cnf(1537,plain,
( ~ is_a_theorem(equivalent(u,equivalent(u,v)))
| ~ is_a_theorem(equivalent(w,w))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[15,1517]),
[iquote('0:SoR:15.2,1517.0')] ).
cnf(1572,plain,
( ~ is_a_theorem(equivalent(u,equivalent(u,v)))
| is_a_theorem(v) ),
inference(ssi,[status(thm)],[1537,984]),
[iquote('0:SSi:1537.1,984.0')] ).
cnf(1696,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(v,u)),v)),
inference(sor,[status(thm)],[1572,2]),
[iquote('0:SoR:1572.0,2.0')] ).
cnf(1732,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),equivalent(w,equivalent(u,w))))
| is_a_theorem(v) ),
inference(sor,[status(thm)],[88,1696]),
[iquote('0:SoR:88.1,1696.0')] ).
cnf(4010,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(u,v),u),w),v))
| is_a_theorem(w) ),
inference(sor,[status(thm)],[47,1519]),
[iquote('0:SoR:47.0,1519.1')] ).
cnf(5095,plain,
is_a_theorem(equivalent(equivalent(u,equivalent(equivalent(v,equivalent(w,v)),w)),u)),
inference(sor,[status(thm)],[1732,1529]),
[iquote('0:SoR:1732.0,1529.0')] ).
cnf(5120,plain,
( ~ is_a_theorem(equivalent(u,equivalent(equivalent(v,equivalent(w,v)),w)))
| is_a_theorem(u) ),
inference(sor,[status(thm)],[163,5095]),
[iquote('0:SoR:163.0,5095.0')] ).
cnf(12300,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,equivalent(w,u)),equivalent(v,w))) ),
inference(sor,[status(thm)],[4010,66]),
[iquote('0:SoR:4010.0,66.1')] ).
cnf(17922,plain,
( ~ is_a_theorem(equivalent(equivalent(u,v),w))
| is_a_theorem(equivalent(v,equivalent(w,u))) ),
inference(sor,[status(thm)],[165,12300]),
[iquote('0:SoR:165.0,12300.1')] ).
cnf(17973,plain,
( ~ is_a_theorem(u)
| is_a_theorem(equivalent(equivalent(v,equivalent(w,v)),equivalent(w,u))) ),
inference(sor,[status(thm)],[5120,12300]),
[iquote('0:SoR:5120.0,12300.1')] ).
cnf(23054,plain,
( ~ is_a_theorem(equivalent(u,v))
| is_a_theorem(equivalent(v,u)) ),
inference(sor,[status(thm)],[1732,17973]),
[iquote('0:SoR:1732.0,17973.1')] ).
cnf(23294,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),equivalent(equivalent(v,w),u)),w)),
inference(sor,[status(thm)],[23054,2]),
[iquote('0:SoR:23054.0,2.0')] ).
cnf(29506,plain,
is_a_theorem(equivalent(equivalent(equivalent(u,v),w),equivalent(v,equivalent(w,u)))),
inference(sor,[status(thm)],[17922,23294]),
[iquote('0:SoR:17922.0,23294.0')] ).
cnf(29570,plain,
$false,
inference(unc,[status(thm)],[29506,3]),
[iquote('0:UnC:29506.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL166-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 13:07:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 243.26/243.59
% 243.26/243.59 SPASS V 3.9
% 243.26/243.59 SPASS beiseite: Proof found.
% 243.26/243.59 % SZS status Theorem
% 243.26/243.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 243.26/243.59 SPASS derived 27014 clauses, backtracked 0 clauses, performed 0 splits and kept 10436 clauses.
% 243.26/243.59 SPASS allocated 109022 KBytes.
% 243.26/243.59 SPASS spent 0:04:03.24 on the problem.
% 243.26/243.59 0:00:00.03 for the input.
% 243.26/243.59 0:00:00.00 for the FLOTTER CNF translation.
% 243.26/243.59 0:00:00.47 for inferences.
% 243.26/243.59 0:00:00.00 for the backtracking.
% 243.26/243.59 0:04:02.64 for the reduction.
% 243.26/243.59
% 243.26/243.59
% 243.26/243.59 Here is a proof with depth 29, length 75 :
% 243.26/243.59 % SZS output start Refutation
% See solution above
% 246.47/246.75 Formulae used in the proof : condensed_detachment xhn prove_um
% 246.47/246.75
%------------------------------------------------------------------------------