TSTP Solution File: SWC422-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC422-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 22:03:58 EDT 2022
% Result : Unsatisfiable 36.46s 36.69s
% Output : Refutation 36.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of clauses : 47 ( 13 unt; 4 nHn; 47 RR)
% Number of literals : 127 ( 0 equ; 91 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC422-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC422-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC422-1.p',unknown),
[] ).
cnf(7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('SWC422-1.p',unknown),
[] ).
cnf(11,axiom,
( ssList(sk6)
| neq(sk2,nil) ),
file('SWC422-1.p',unknown),
[] ).
cnf(12,axiom,
( ssList(sk7)
| neq(sk2,nil) ),
file('SWC422-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(app(w,cons(u,nil)),v),sk1)
| ~ neq(sk4,nil) ),
file('SWC422-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('SWC422-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('SWC422-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ neq(sk4,nil)
| equal(app(app(sk6,cons(sk5,nil)),sk7),sk4) ),
file('SWC422-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ neq(sk4,nil)
| equal(app(app(sk7,cons(sk5,nil)),sk6),sk3) ),
file('SWC422-1.p',unknown),
[] ).
cnf(67,axiom,
ssItem(skaf44(u)),
file('SWC422-1.p',unknown),
[] ).
cnf(92,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC422-1.p',unknown),
[] ).
cnf(105,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC422-1.p',unknown),
[] ).
cnf(106,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC422-1.p',unknown),
[] ).
cnf(177,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC422-1.p',unknown),
[] ).
cnf(199,axiom,
( ~ ssList(u)
| ~ duplicatefreeP(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssList(y)
| ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
file('SWC422-1.p',unknown),
[] ).
cnf(208,plain,
( ~ neq(sk2,nil)
| ssList(sk7) ),
inference(rew,[status(thm),theory(equality)],[5,18]),
[iquote('0:Rew:5.0,18.0')] ).
cnf(209,plain,
ssList(sk7),
inference(mrr,[status(thm)],[208,12]),
[iquote('0:MRR:208.0,12.1')] ).
cnf(210,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(rew,[status(thm),theory(equality)],[5,17]),
[iquote('0:Rew:5.0,17.0')] ).
cnf(211,plain,
ssList(sk6),
inference(mrr,[status(thm)],[210,11]),
[iquote('0:MRR:210.0,11.1')] ).
cnf(214,plain,
neq(sk2,nil),
inference(obv,[status(thm),theory(equality)],[7]),
[iquote('0:Obv:7.0')] ).
cnf(215,plain,
( ~ neq(sk2,nil)
| equal(app(app(sk7,cons(sk5,nil)),sk6),sk1) ),
inference(rew,[status(thm),theory(equality)],[6,20,5]),
[iquote('0:Rew:6.0,20.1,5.0,20.0')] ).
cnf(216,plain,
equal(app(app(sk7,cons(sk5,nil)),sk6),sk1),
inference(mrr,[status(thm)],[215,214]),
[iquote('0:MRR:215.0,214.0')] ).
cnf(217,plain,
( ~ neq(sk2,nil)
| equal(app(app(sk6,cons(sk5,nil)),sk7),sk2) ),
inference(rew,[status(thm),theory(equality)],[5,19]),
[iquote('0:Rew:5.0,19.1,5.0,19.0')] ).
cnf(218,plain,
equal(app(app(sk6,cons(sk5,nil)),sk7),sk2),
inference(mrr,[status(thm)],[217,214]),
[iquote('0:MRR:217.0,214.0')] ).
cnf(223,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(app(w,cons(u,nil)),v),sk1)
| ~ neq(sk2,nil) ),
inference(rew,[status(thm),theory(equality)],[5,15]),
[iquote('0:Rew:5.0,15.5')] ).
cnf(224,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(u,cons(w,nil)),v),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
inference(mrr,[status(thm)],[223,214]),
[iquote('0:MRR:223.5,214.0')] ).
cnf(536,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,106]),
[iquote('0:Res:1.0,106.1')] ).
cnf(575,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[92]),
[iquote('1:Spt:92.1')] ).
cnf(775,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(u,cons(w,nil)),v),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
inference(mrr,[status(thm)],[224,575]),
[iquote('1:MRR:224.2,575.0')] ).
cnf(17688,plain,
( ~ ssList(sk7)
| ~ ssList(sk6)
| ~ equal(sk1,sk1)
| ~ equal(app(app(sk6,cons(sk5,nil)),sk7),sk2) ),
inference(spl,[status(thm),theory(equality)],[216,775]),
[iquote('1:SpL:216.0,775.2')] ).
cnf(17690,plain,
( ~ ssList(sk7)
| ~ ssList(sk6)
| ~ equal(app(app(sk6,cons(sk5,nil)),sk7),sk2) ),
inference(obv,[status(thm),theory(equality)],[17688]),
[iquote('1:Obv:17688.2')] ).
cnf(17691,plain,
( ~ ssList(sk7)
| ~ ssList(sk6)
| ~ equal(sk2,sk2) ),
inference(rew,[status(thm),theory(equality)],[218,17690]),
[iquote('1:Rew:218.0,17690.2')] ).
cnf(17692,plain,
( ~ ssList(sk7)
| ~ ssList(sk6) ),
inference(obv,[status(thm),theory(equality)],[17691]),
[iquote('1:Obv:17691.2')] ).
cnf(17693,plain,
$false,
inference(ssi,[status(thm)],[17692,211,209]),
[iquote('1:SSi:17692.1,17692.0,211.0,209.0')] ).
cnf(17730,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[92]),
[iquote('1:Spt:17693.0,92.0,92.2')] ).
cnf(17866,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssList(y)
| ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
inference(mrr,[status(thm)],[199,17730]),
[iquote('1:MRR:199.1,17730.1')] ).
cnf(43017,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ ssList(cons(w,v))
| ~ ssList(u)
| ssList(cons(w,app(v,u))) ),
inference(spr,[status(thm),theory(equality)],[177,105]),
[iquote('0:SpR:177.3,105.2')] ).
cnf(43081,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[43017]),
[iquote('0:Obv:43017.0')] ).
cnf(43082,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[43081,106]),
[iquote('0:SSi:43081.2,106.2')] ).
cnf(45539,plain,
( ~ ssList(app(app(u,cons(v,w)),cons(v,x)))
| ~ ssItem(v)
| ~ ssList(u)
| ~ ssList(w)
| ~ ssList(x) ),
inference(eqr,[status(thm),theory(equality)],[17866]),
[iquote('1:EqR:17866.5')] ).
cnf(45564,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[45539,105,106]),
[iquote('1:SSi:45539.0,105.2,105.2,106.2,106.2')] ).
cnf(45565,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[43082,45564]),
[iquote('1:MRR:43082.3,45564.1')] ).
cnf(45568,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[45565]),
[iquote('1:Con:45565.2')] ).
cnf(45569,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[536,45568]),
[iquote('1:MRR:536.1,45568.0')] ).
cnf(45570,plain,
$false,
inference(unc,[status(thm)],[45569,67]),
[iquote('1:UnC:45569.0,67.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC422-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 17:37:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 36.46/36.69
% 36.46/36.69 SPASS V 3.9
% 36.46/36.69 SPASS beiseite: Proof found.
% 36.46/36.69 % SZS status Theorem
% 36.46/36.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.46/36.69 SPASS derived 30262 clauses, backtracked 11298 clauses, performed 119 splits and kept 23818 clauses.
% 36.46/36.69 SPASS allocated 108317 KBytes.
% 36.46/36.69 SPASS spent 0:0:27.14 on the problem.
% 36.46/36.69 0:00:00.04 for the input.
% 36.46/36.69 0:00:00.00 for the FLOTTER CNF translation.
% 36.46/36.69 0:00:00.32 for inferences.
% 36.46/36.69 0:00:01.41 for the backtracking.
% 36.46/36.69 0:0:24.99 for the reduction.
% 36.46/36.69
% 36.46/36.69
% 36.46/36.69 Here is a proof with depth 1, length 47 :
% 36.46/36.69 % SZS output start Refutation
% See solution above
% 36.46/36.69 Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_11 co1_12 co1_15 co1_17 co1_18 co1_19 co1_20 clause47 clause72 clause85 clause86 clause157 clause179
% 36.46/36.69
%------------------------------------------------------------------------------