TSTP Solution File: SWC419+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC419+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 22:03:57 EDT 2022
% Result : Theorem 61.65s 61.84s
% Output : Refutation 61.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of clauses : 37 ( 16 unt; 0 nHn; 37 RR)
% Number of literals : 73 ( 0 equ; 42 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc9),
file('SWC419+1.p',unknown),
[] ).
cnf(2,axiom,
ssItem(skc8),
file('SWC419+1.p',unknown),
[] ).
cnf(4,axiom,
ssList(skc6),
file('SWC419+1.p',unknown),
[] ).
cnf(7,axiom,
ssList(nil),
file('SWC419+1.p',unknown),
[] ).
cnf(8,axiom,
cyclefreeP(nil),
file('SWC419+1.p',unknown),
[] ).
cnf(9,axiom,
totalorderP(nil),
file('SWC419+1.p',unknown),
[] ).
cnf(10,axiom,
strictorderP(nil),
file('SWC419+1.p',unknown),
[] ).
cnf(11,axiom,
totalorderedP(nil),
file('SWC419+1.p',unknown),
[] ).
cnf(12,axiom,
strictorderedP(nil),
file('SWC419+1.p',unknown),
[] ).
cnf(13,axiom,
duplicatefreeP(nil),
file('SWC419+1.p',unknown),
[] ).
cnf(14,axiom,
equalelemsP(nil),
file('SWC419+1.p',unknown),
[] ).
cnf(15,axiom,
neq(skc7,nil),
file('SWC419+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC419+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC419+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC419+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC419+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC419+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC419+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC419+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC419+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssList(u)
| equal(app(u,nil),u) ),
file('SWC419+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC419+1.p',unknown),
[] ).
cnf(96,axiom,
( ~ neq(skc7,nil)
| equal(app(cons(skc8,nil),skc9),skc7) ),
file('SWC419+1.p',unknown),
[] ).
cnf(97,axiom,
( ~ neq(skc7,nil)
| equal(app(skc9,cons(skc8,nil)),skc6) ),
file('SWC419+1.p',unknown),
[] ).
cnf(120,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC419+1.p',unknown),
[] ).
cnf(188,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(u,cons(w,nil)),v),skc6)
| ~ equal(app(app(v,cons(w,nil)),u),skc7) ),
file('SWC419+1.p',unknown),
[] ).
cnf(196,plain,
equal(app(skc9,cons(skc8,nil)),skc6),
inference(mrr,[status(thm)],[97,15]),
[iquote('0:MRR:97.0,15.0')] ).
cnf(197,plain,
equal(app(cons(skc8,nil),skc9),skc7),
inference(mrr,[status(thm)],[96,15]),
[iquote('0:MRR:96.0,15.0')] ).
cnf(279,plain,
equal(app(skc6,nil),skc6),
inference(res,[status(thm),theory(equality)],[4,80]),
[iquote('0:Res:4.0,80.0')] ).
cnf(3019,plain,
( ~ ssList(cons(u,nil))
| ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[120]),
[iquote('0:EqR:120.2')] ).
cnf(3022,plain,
( ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(ssi,[status(thm)],[3019,88,14,13,10,9,8,12,11,7,77,76,73,72,71,75,74]),
[iquote('0:SSi:3019.0,88.1,14.1,13.1,10.1,9.1,8.1,12.1,11.0,7.0,77.0,76.0,73.0,72.0,71.0,75.0,74.2')] ).
cnf(30967,plain,
( ~ ssList(skc9)
| ~ ssList(u)
| ~ ssItem(skc8)
| ~ equal(app(skc6,u),skc6)
| ~ equal(app(app(u,cons(skc8,nil)),skc9),skc7) ),
inference(spl,[status(thm),theory(equality)],[196,188]),
[iquote('0:SpL:196.0,188.3')] ).
cnf(30977,plain,
( ~ ssList(u)
| ~ equal(app(skc6,u),skc6)
| ~ equal(app(app(u,cons(skc8,nil)),skc9),skc7) ),
inference(ssi,[status(thm)],[30967,2,1]),
[iquote('0:SSi:30967.2,30967.0,2.0,1.0')] ).
cnf(48014,plain,
( ~ ssList(cons(skc8,nil))
| ~ ssList(nil)
| ~ equal(app(skc6,nil),skc6)
| ~ equal(app(cons(skc8,nil),skc9),skc7) ),
inference(spl,[status(thm),theory(equality)],[79,30977]),
[iquote('0:SpL:79.1,30977.2')] ).
cnf(48037,plain,
( ~ ssList(cons(skc8,nil))
| ~ ssList(nil)
| ~ equal(skc6,skc6)
| ~ equal(skc7,skc7) ),
inference(rew,[status(thm),theory(equality)],[197,48014,279]),
[iquote('0:Rew:197.0,48014.3,279.0,48014.2')] ).
cnf(48038,plain,
( ~ ssList(cons(skc8,nil))
| ~ ssList(nil) ),
inference(obv,[status(thm),theory(equality)],[48037]),
[iquote('0:Obv:48037.3')] ).
cnf(48039,plain,
$false,
inference(ssi,[status(thm)],[48038,14,13,10,9,8,12,11,7,88,2,77,76,73,72,71,75,74,3022]),
[iquote('0:SSi:48038.1,48038.0,14.0,13.1,10.0,9.1,8.0,12.1,11.0,7.1,88.0,2.1,14.0,13.1,10.0,9.1,8.0,12.1,11.0,7.0,77.0,2.0,76.0,2.0,73.0,2.0,72.0,2.2,71.0,2.0,75.0,2.0,74.0,2.0,3022.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC419+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n018.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 : Sat Jun 11 20:59:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 61.65/61.84
% 61.65/61.84 SPASS V 3.9
% 61.65/61.84 SPASS beiseite: Proof found.
% 61.65/61.84 % SZS status Theorem
% 61.65/61.84 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.65/61.84 SPASS derived 30098 clauses, backtracked 3030 clauses, performed 41 splits and kept 12325 clauses.
% 61.65/61.84 SPASS allocated 143645 KBytes.
% 61.65/61.84 SPASS spent 0:0:51.64 on the problem.
% 61.65/61.84 0:00:00.04 for the input.
% 61.65/61.84 0:00:00.07 for the FLOTTER CNF translation.
% 61.65/61.84 0:00:00.63 for inferences.
% 61.65/61.84 0:00:02.57 for the backtracking.
% 61.65/61.84 0:0:47.78 for the reduction.
% 61.65/61.84
% 61.65/61.84
% 61.65/61.84 Here is a proof with depth 2, length 37 :
% 61.65/61.84 % SZS output start Refutation
% See solution above
% 61.65/61.84 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax84 ax16 ax4
% 61.65/61.84
%------------------------------------------------------------------------------