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 : n010.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 : Unsatisfiable 7.47s 7.75s
% Output : Refutation 7.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of clauses : 48 ( 22 unt; 5 nHn; 48 RR)
% Number of literals : 88 ( 0 equ; 45 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC106-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC106-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC106-1.p',unknown),
[] ).
cnf(7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('SWC106-1.p',unknown),
[] ).
cnf(9,axiom,
( ssItem(sk5)
| neq(sk2,nil) ),
file('SWC106-1.p',unknown),
[] ).
cnf(10,axiom,
( ssList(sk6)
| neq(sk2,nil) ),
file('SWC106-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('SWC106-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('SWC106-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ neq(sk4,nil)
| equal(cons(sk5,nil),sk3) ),
file('SWC106-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ neq(sk4,nil)
| equal(app(sk6,cons(sk5,nil)),sk4) ),
file('SWC106-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ neq(sk1,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk4,nil) ),
file('SWC106-1.p',unknown),
[] ).
cnf(19,axiom,
equalelemsP(nil),
file('SWC106-1.p',unknown),
[] ).
cnf(20,axiom,
duplicatefreeP(nil),
file('SWC106-1.p',unknown),
[] ).
cnf(21,axiom,
strictorderedP(nil),
file('SWC106-1.p',unknown),
[] ).
cnf(22,axiom,
totalorderedP(nil),
file('SWC106-1.p',unknown),
[] ).
cnf(23,axiom,
strictorderP(nil),
file('SWC106-1.p',unknown),
[] ).
cnf(24,axiom,
totalorderP(nil),
file('SWC106-1.p',unknown),
[] ).
cnf(25,axiom,
cyclefreeP(nil),
file('SWC106-1.p',unknown),
[] ).
cnf(26,axiom,
ssList(nil),
file('SWC106-1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssList(u)
| rearsegP(u,u) ),
file('SWC106-1.p',unknown),
[] ).
cnf(117,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,u),u) ),
file('SWC106-1.p',unknown),
[] ).
cnf(118,axiom,
( ~ ssList(u)
| ~ ssList(v)
| equal(u,v)
| neq(u,v) ),
file('SWC106-1.p',unknown),
[] ).
cnf(154,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ rearsegP(u,v)
| rearsegP(app(w,u),v) ),
file('SWC106-1.p',unknown),
[] ).
cnf(206,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(rew,[status(thm),theory(equality)],[5,15]),
[iquote('0:Rew:5.0,15.0')] ).
cnf(207,plain,
ssList(sk6),
inference(mrr,[status(thm)],[206,10]),
[iquote('0:MRR:206.0,10.1')] ).
cnf(208,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(rew,[status(thm),theory(equality)],[5,14]),
[iquote('0:Rew:5.0,14.0')] ).
cnf(209,plain,
ssItem(sk5),
inference(mrr,[status(thm)],[208,9]),
[iquote('0:MRR:208.0,9.1')] ).
cnf(210,plain,
neq(sk2,nil),
inference(obv,[status(thm),theory(equality)],[7]),
[iquote('0:Obv:7.0')] ).
cnf(211,plain,
( ~ neq(sk2,nil)
| equal(cons(sk5,nil),sk1) ),
inference(rew,[status(thm),theory(equality)],[6,16,5]),
[iquote('0:Rew:6.0,16.1,5.0,16.0')] ).
cnf(212,plain,
equal(cons(sk5,nil),sk1),
inference(mrr,[status(thm)],[211,210]),
[iquote('0:MRR:211.0,210.0')] ).
cnf(213,plain,
( ~ neq(sk2,nil)
| equal(app(sk6,sk1),sk2) ),
inference(rew,[status(thm),theory(equality)],[212,17,5]),
[iquote('0:Rew:212.0,17.1,5.0,17.1,5.0,17.0')] ).
cnf(214,plain,
equal(app(sk6,sk1),sk2),
inference(mrr,[status(thm)],[213,210]),
[iquote('0:MRR:213.0,210.0')] ).
cnf(215,plain,
( ~ neq(sk1,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk2,nil) ),
inference(rew,[status(thm),theory(equality)],[5,18]),
[iquote('0:Rew:5.0,18.2')] ).
cnf(216,plain,
( ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(mrr,[status(thm)],[215,210]),
[iquote('0:MRR:215.2,210.0')] ).
cnf(477,plain,
rearsegP(sk1,sk1),
inference(res,[status(thm),theory(equality)],[1,77]),
[iquote('0:Res:1.0,77.0')] ).
cnf(526,plain,
( ~ ssItem(u)
| ~ equal(cons(u,sk1),sk1) ),
inference(res,[status(thm),theory(equality)],[1,117]),
[iquote('0:Res:1.0,117.1')] ).
cnf(527,plain,
( ~ ssList(u)
| equal(sk1,u)
| neq(sk1,u) ),
inference(res,[status(thm),theory(equality)],[1,118]),
[iquote('0:Res:1.0,118.1')] ).
cnf(4447,plain,
( ~ ssList(sk1)
| ~ ssList(u)
| ~ ssList(sk6)
| ~ rearsegP(sk1,u)
| rearsegP(sk2,u) ),
inference(spr,[status(thm),theory(equality)],[214,154]),
[iquote('0:SpR:214.0,154.4')] ).
cnf(7306,plain,
( ~ ssList(u)
| ~ rearsegP(sk1,u)
| rearsegP(sk2,u) ),
inference(ssi,[status(thm)],[4447,207,1]),
[iquote('0:SSi:4447.2,4447.0,207.0,1.0')] ).
cnf(9407,plain,
( ~ ssList(sk1)
| ~ rearsegP(sk1,sk1)
| ~ neq(sk1,nil) ),
inference(res,[status(thm),theory(equality)],[7306,216]),
[iquote('0:Res:7306.2,216.0')] ).
cnf(9758,plain,
( ~ rearsegP(sk1,sk1)
| ~ neq(sk1,nil) ),
inference(ssi,[status(thm)],[9407,1]),
[iquote('0:SSi:9407.0,1.0')] ).
cnf(9759,plain,
~ neq(sk1,nil),
inference(mrr,[status(thm)],[9758,477]),
[iquote('0:MRR:9758.0,477.0')] ).
cnf(12708,plain,
( ~ ssList(nil)
| equal(nil,sk1) ),
inference(res,[status(thm),theory(equality)],[527,9759]),
[iquote('0:Res:527.2,9759.0')] ).
cnf(12709,plain,
equal(nil,sk1),
inference(ssi,[status(thm)],[12708,26,25,24,23,22,21,20,19]),
[iquote('0:SSi:12708.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0')] ).
cnf(12732,plain,
equal(cons(sk5,sk1),sk1),
inference(rew,[status(thm),theory(equality)],[12709,212]),
[iquote('0:Rew:12709.0,212.0')] ).
cnf(13773,plain,
( ~ ssItem(sk5)
| ~ equal(sk1,sk1) ),
inference(spl,[status(thm),theory(equality)],[12732,526]),
[iquote('0:SpL:12732.0,526.1')] ).
cnf(13774,plain,
~ ssItem(sk5),
inference(obv,[status(thm),theory(equality)],[13773]),
[iquote('0:Obv:13773.1')] ).
cnf(13775,plain,
$false,
inference(ssi,[status(thm)],[13774,209]),
[iquote('0:SSi:13774.0,209.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC106-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 11 22:44:10 EDT 2022
% 0.13/0.33 % CPUTime :
% 7.47/7.75
% 7.47/7.75 SPASS V 3.9
% 7.47/7.75 SPASS beiseite: Proof found.
% 7.47/7.75 % SZS status Theorem
% 7.47/7.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.47/7.75 SPASS derived 8722 clauses, backtracked 5680 clauses, performed 80 splits and kept 9788 clauses.
% 7.47/7.75 SPASS allocated 85603 KBytes.
% 7.47/7.75 SPASS spent 0:00:06.68 on the problem.
% 7.47/7.75 0:00:00.04 for the input.
% 7.47/7.75 0:00:00.00 for the FLOTTER CNF translation.
% 7.47/7.75 0:00:00.06 for inferences.
% 7.47/7.75 0:00:00.20 for the backtracking.
% 7.47/7.75 0:00:06.16 for the reduction.
% 7.47/7.75
% 7.47/7.75
% 7.47/7.75 Here is a proof with depth 3, length 48 :
% 7.47/7.75 % SZS output start Refutation
% See solution above
% 7.47/7.75 Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_9 co1_10 co1_14 co1_15 co1_16 co1_17 co1_18 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause59 clause99 clause100 clause136
% 7.47/7.75
%------------------------------------------------------------------------------