TSTP Solution File: SWC106+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC106+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 : Tue Jul 19 22:01:46 EDT 2022
% Result : Theorem 1.21s 1.39s
% Output : Refutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of clauses : 50 ( 21 unt; 13 nHn; 50 RR)
% Number of literals : 104 ( 0 equ; 50 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
ssList(skc4),
file('SWC106+1.p',unknown),
[] ).
cnf(5,axiom,
ssList(nil),
file('SWC106+1.p',unknown),
[] ).
cnf(6,axiom,
cyclefreeP(nil),
file('SWC106+1.p',unknown),
[] ).
cnf(7,axiom,
totalorderP(nil),
file('SWC106+1.p',unknown),
[] ).
cnf(8,axiom,
strictorderP(nil),
file('SWC106+1.p',unknown),
[] ).
cnf(9,axiom,
totalorderedP(nil),
file('SWC106+1.p',unknown),
[] ).
cnf(10,axiom,
strictorderedP(nil),
file('SWC106+1.p',unknown),
[] ).
cnf(11,axiom,
duplicatefreeP(nil),
file('SWC106+1.p',unknown),
[] ).
cnf(12,axiom,
equalelemsP(nil),
file('SWC106+1.p',unknown),
[] ).
cnf(51,axiom,
ssList(skf46(u,v)),
file('SWC106+1.p',unknown),
[] ).
cnf(52,axiom,
ssItem(skf45(u,v)),
file('SWC106+1.p',unknown),
[] ).
cnf(60,axiom,
( skP0(u,v)
| neq(v,nil) ),
file('SWC106+1.p',unknown),
[] ).
cnf(69,axiom,
( ~ skP0(skc4,skc5)
| neq(skc5,nil) ),
file('SWC106+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ neq(skc5,nil)
| ~ skP0(skc4,skc5) ),
file('SWC106+1.p',unknown),
[] ).
cnf(86,axiom,
( skP0(u,v)
| equal(cons(skf45(u,v),nil),u) ),
file('SWC106+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC106+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC106+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ rearsegP(u,v)
| ~ neq(v,nil)
| skP0(v,u) ),
file('SWC106+1.p',unknown),
[] ).
cnf(108,axiom,
( ~ ssList(u)
| ~ ssList(v)
| neq(v,u)
| equal(v,u) ),
file('SWC106+1.p',unknown),
[] ).
cnf(110,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ equal(cons(u,v),nil) ),
file('SWC106+1.p',unknown),
[] ).
cnf(120,axiom,
( equal(app(skf46(u,v),cons(skf45(v,u),nil)),u)
| skP0(v,u) ),
file('SWC106+1.p',unknown),
[] ).
cnf(145,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(w,u),v)
| rearsegP(v,u) ),
file('SWC106+1.p',unknown),
[] ).
cnf(153,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ totalorderedP(cons(v,u))
| leq(v,hd(u))
| equal(nil,u) ),
file('SWC106+1.p',unknown),
[] ).
cnf(197,plain,
neq(skc5,nil),
inference(mrr,[status(thm)],[69,60]),
[iquote('0:MRR:69.0,60.1')] ).
cnf(198,plain,
~ skP0(skc4,skc5),
inference(mrr,[status(thm)],[79,197]),
[iquote('0:MRR:79.0,197.0')] ).
cnf(199,plain,
( skP0(u,v)
| equal(app(skf46(v,u),u),v) ),
inference(rew,[status(thm),theory(equality)],[86,120]),
[iquote('0:Rew:86.0,120.0')] ).
cnf(255,plain,
( ~ ssList(u)
| neq(skc4,u)
| equal(skc4,u) ),
inference(res,[status(thm),theory(equality)],[2,108]),
[iquote('0:Res:2.0,108.0')] ).
cnf(257,plain,
( ~ ssItem(u)
| ~ equal(cons(u,skc4),nil) ),
inference(res,[status(thm),theory(equality)],[2,110]),
[iquote('0:Res:2.0,110.0')] ).
cnf(310,plain,
( ~ ssItem(u)
| ~ totalorderedP(cons(u,skc4))
| leq(u,hd(skc4))
| equal(skc4,nil) ),
inference(res,[status(thm),theory(equality)],[2,153]),
[iquote('0:Res:2.0,153.1')] ).
cnf(1464,plain,
equal(skc4,nil),
inference(spt,[spt(split,[position(s1)])],[310]),
[iquote('1:Spt:310.3')] ).
cnf(1472,plain,
~ skP0(nil,skc5),
inference(rew,[status(thm),theory(equality)],[1464,198]),
[iquote('1:Rew:1464.0,198.0')] ).
cnf(1504,plain,
( ~ ssItem(u)
| ~ equal(cons(u,nil),nil) ),
inference(rew,[status(thm),theory(equality)],[1464,257]),
[iquote('1:Rew:1464.0,257.1')] ).
cnf(1806,plain,
( ~ ssItem(skf45(u,v))
| ~ ssList(nil)
| skP0(u,v)
| ssList(u) ),
inference(spr,[status(thm),theory(equality)],[86,90]),
[iquote('0:SpR:86.1,90.2')] ).
cnf(1808,plain,
( ~ ssItem(skf45(u,v))
| ~ equal(u,nil)
| skP0(u,v) ),
inference(spl,[status(thm),theory(equality)],[86,1504]),
[iquote('1:SpL:86.1,1504.1')] ).
cnf(1818,plain,
( ~ equal(u,nil)
| skP0(u,v) ),
inference(ssi,[status(thm)],[1808,52]),
[iquote('1:SSi:1808.0,52.0')] ).
cnf(1850,plain,
~ equal(nil,nil),
inference(res,[status(thm),theory(equality)],[1818,1472]),
[iquote('1:Res:1818.1,1472.0')] ).
cnf(1851,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1850]),
[iquote('1:Obv:1850.0')] ).
cnf(1852,plain,
~ equal(skc4,nil),
inference(spt,[spt(split,[position(sa)])],[1851,1464]),
[iquote('1:Spt:1851.0,310.3,1464.0')] ).
cnf(1853,plain,
( ~ ssItem(u)
| ~ totalorderedP(cons(u,skc4))
| leq(u,hd(skc4)) ),
inference(spt,[spt(split,[position(s2)])],[310]),
[iquote('1:Spt:1851.0,310.0,310.1,310.2')] ).
cnf(1867,plain,
( skP0(u,v)
| ssList(u) ),
inference(ssi,[status(thm)],[1806,12,11,8,7,6,10,9,5,52]),
[iquote('0:SSi:1806.1,1806.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0,52.0')] ).
cnf(4052,plain,
( ~ ssList(u)
| ~ ssList(app(v,u))
| ~ ssList(v)
| rearsegP(app(v,u),u) ),
inference(eqr,[status(thm),theory(equality)],[145]),
[iquote('0:EqR:145.3')] ).
cnf(4066,plain,
( ~ ssList(u)
| ~ ssList(v)
| rearsegP(app(v,u),u) ),
inference(ssi,[status(thm)],[4052,91]),
[iquote('0:SSi:4052.1,91.2')] ).
cnf(4151,plain,
( ~ ssList(u)
| ~ ssList(skf46(v,u))
| skP0(u,v)
| rearsegP(v,u) ),
inference(spr,[status(thm),theory(equality)],[199,4066]),
[iquote('0:SpR:199.1,4066.2')] ).
cnf(4162,plain,
( ~ ssList(u)
| skP0(u,v)
| rearsegP(v,u) ),
inference(ssi,[status(thm)],[4151,51]),
[iquote('0:SSi:4151.1,51.0')] ).
cnf(4163,plain,
( skP0(u,v)
| rearsegP(v,u) ),
inference(mrr,[status(thm)],[4162,1867]),
[iquote('0:MRR:4162.0,1867.1')] ).
cnf(4164,plain,
( ~ neq(u,nil)
| skP0(u,v) ),
inference(mrr,[status(thm)],[98,4163]),
[iquote('0:MRR:98.0,4163.1')] ).
cnf(4175,plain,
~ neq(skc4,nil),
inference(res,[status(thm),theory(equality)],[4164,198]),
[iquote('0:Res:4164.1,198.0')] ).
cnf(4176,plain,
( ~ ssList(nil)
| equal(skc4,nil) ),
inference(res,[status(thm),theory(equality)],[255,4175]),
[iquote('0:Res:255.1,4175.0')] ).
cnf(4179,plain,
equal(skc4,nil),
inference(ssi,[status(thm)],[4176,12,11,8,7,6,10,9,5]),
[iquote('0:SSi:4176.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0')] ).
cnf(4180,plain,
$false,
inference(mrr,[status(thm)],[4179,1852]),
[iquote('1:MRR:4179.0,1852.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWC106+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.10 % Command : run_spass %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Sun Jun 12 00:41:25 EDT 2022
% 0.09/0.28 % CPUTime :
% 1.21/1.39
% 1.21/1.39 SPASS V 3.9
% 1.21/1.39 SPASS beiseite: Proof found.
% 1.21/1.39 % SZS status Theorem
% 1.21/1.39 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.21/1.39 SPASS derived 2847 clauses, backtracked 670 clauses, performed 25 splits and kept 2093 clauses.
% 1.21/1.39 SPASS allocated 101262 KBytes.
% 1.21/1.39 SPASS spent 0:00:01.06 on the problem.
% 1.21/1.39 0:00:00.03 for the input.
% 1.21/1.39 0:00:00.04 for the FLOTTER CNF translation.
% 1.21/1.39 0:00:00.03 for inferences.
% 1.21/1.39 0:00:00.02 for the backtracking.
% 1.21/1.39 0:00:00.78 for the reduction.
% 1.21/1.39
% 1.21/1.39
% 1.21/1.39 Here is a proof with depth 3, length 50 :
% 1.21/1.39 % SZS output start Refutation
% See solution above
% 1.21/1.39 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax16 ax26 ax15 ax21 ax6 ax67
% 1.21/1.39
%------------------------------------------------------------------------------