%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC246-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 22:02:46 EDT 2022
% Result : Unsatisfiable 29.38s 29.58s
% Output : Refutation 29.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of clauses : 66 ( 27 unt; 2 nHn; 66 RR)
% Number of literals : 154 ( 0 equ; 97 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC246-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC246-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
file('SWC246-1.p',unknown),
[] ).
cnf(14,axiom,
ssList(sk7),
file('SWC246-1.p',unknown),
[] ).
cnf(20,axiom,
equalelemsP(nil),
file('SWC246-1.p',unknown),
[] ).
cnf(21,axiom,
duplicatefreeP(nil),
file('SWC246-1.p',unknown),
[] ).
cnf(22,axiom,
strictorderedP(nil),
file('SWC246-1.p',unknown),
[] ).
cnf(23,axiom,
totalorderedP(nil),
file('SWC246-1.p',unknown),
[] ).
cnf(24,axiom,
strictorderP(nil),
file('SWC246-1.p',unknown),
[] ).
cnf(25,axiom,
totalorderP(nil),
file('SWC246-1.p',unknown),
[] ).
cnf(26,axiom,
cyclefreeP(nil),
file('SWC246-1.p',unknown),
[] ).
cnf(27,axiom,
ssList(nil),
file('SWC246-1.p',unknown),
[] ).
cnf(31,axiom,
ssItem(skaf83(u)),
file('SWC246-1.p',unknown),
[] ).
cnf(32,axiom,
ssList(skaf82(u)),
file('SWC246-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC246-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC246-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC246-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC246-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC246-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC246-1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC246-1.p',unknown),
[] ).
cnf(90,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC246-1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC246-1.p',unknown),
[] ).
cnf(93,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC246-1.p',unknown),
[] ).
cnf(104,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC246-1.p',unknown),
[] ).
cnf(105,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC246-1.p',unknown),
[] ).
cnf(128,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC246-1.p',unknown),
[] ).
cnf(135,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC246-1.p',unknown),
[] ).
cnf(176,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC246-1.p',unknown),
[] ).
cnf(198,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('SWC246-1.p',unknown),
[] ).
cnf(360,plain,
( ~ ssItem(u)
| ssList(cons(u,sk7)) ),
inference(res,[status(thm),theory(equality)],[14,105]),
[iquote('0:Res:14.0,105.1')] ).
cnf(586,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[91]),
[iquote('1:Spt:91.1')] ).
cnf(591,plain,
~ memberP(nil,u),
inference(mrr,[status(thm)],[90,586]),
[iquote('1:MRR:90.0,586.0')] ).
cnf(592,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[89,586]),
[iquote('1:MRR:89.0,586.0')] ).
cnf(593,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[88,586]),
[iquote('1:MRR:88.0,586.0')] ).
cnf(594,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[87,586]),
[iquote('1:MRR:87.0,586.0')] ).
cnf(595,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[86,586]),
[iquote('1:MRR:86.0,586.0')] ).
cnf(596,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[85,586]),
[iquote('1:MRR:85.0,586.0')] ).
cnf(597,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[84,586]),
[iquote('1:MRR:84.0,586.0')] ).
cnf(598,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[83,586]),
[iquote('1:MRR:83.0,586.0')] ).
cnf(711,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[105,586]),
[iquote('1:MRR:105.1,586.0')] ).
cnf(716,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[135,586]),
[iquote('1:MRR:135.1,586.0')] ).
cnf(802,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
inference(mrr,[status(thm)],[176,586]),
[iquote('1:MRR:176.2,586.0')] ).
cnf(809,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[9,586]),
[iquote('1:MRR:9.2,586.0')] ).
cnf(2798,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[716]),
[iquote('1:EqR:716.1')] ).
cnf(2799,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[2798,711,20,21,26,25,24,23,22,27,592,593,594,595,596,597,598]),
[iquote('1:SSi:2798.0,711.0,20.0,21.0,26.0,25.0,24.0,23.0,22.0,27.0,592.0,593.0,594.0,595.0,596.0,597.0,598.1')] ).
cnf(6039,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ equal(app(cons(u,nil),v),sk1)
| memberP(nil,sk5(v,nil,u)) ),
inference(spl,[status(thm),theory(equality)],[93,809]),
[iquote('1:SpL:93.1,809.2')] ).
cnf(6053,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ equal(cons(u,v),sk1)
| memberP(nil,sk5(v,nil,u)) ),
inference(rew,[status(thm),theory(equality)],[93,6039,802]),
[iquote('1:Rew:93.1,6039.3,802.2,6039.3')] ).
cnf(6054,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[6053,20,21,26,25,24,23,22,27,711,592,593,594,595,596,597,598,2799]),
[iquote('1:SSi:6053.2,6053.0,20.0,21.0,26.0,25.0,24.0,23.0,22.0,27.0,711.0,20.0,21.0,26.0,25.0,24.0,23.0,22.0,27.1,592.0,593.0,594.0,595.0,596.0,597.0,598.0,2799.0')] ).
cnf(6055,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[6054,591]),
[iquote('1:MRR:6054.2,591.0')] ).
cnf(6073,plain,
( ~ ssList(u)
| ~ ssList(skaf82(u))
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(spl,[status(thm),theory(equality)],[128,6055]),
[iquote('1:SpL:128.2,6055.1')] ).
cnf(6088,plain,
( ~ ssList(u)
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(ssi,[status(thm)],[6073,32]),
[iquote('1:SSi:6073.1,32.0')] ).
cnf(9868,plain,
( ~ equal(sk1,sk1)
| equal(nil,sk1) ),
inference(ems,[status(thm)],[6088,1]),
[iquote('1:EmS:6088.0,1.0')] ).
cnf(9871,plain,
equal(nil,sk1),
inference(obv,[status(thm),theory(equality)],[9868]),
[iquote('1:Obv:9868.0')] ).
cnf(9872,plain,
$false,
inference(mrr,[status(thm)],[9871,7]),
[iquote('1:MRR:9871.0,7.0')] ).
cnf(9987,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[91]),
[iquote('1:Spt:9872.0,91.0,91.2')] ).
cnf(10019,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)],[198,9987]),
[iquote('1:MRR:198.1,9987.1')] ).
cnf(36884,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)],[176,104]),
[iquote('0:SpR:176.3,104.2')] ).
cnf(36913,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[36884]),
[iquote('0:Obv:36884.0')] ).
cnf(36914,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[36913,105]),
[iquote('0:SSi:36913.2,105.2')] ).
cnf(43672,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)],[10019]),
[iquote('1:EqR:10019.5')] ).
cnf(43698,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[43672,104,105]),
[iquote('1:SSi:43672.0,104.2,104.2,105.2,105.2')] ).
cnf(43700,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[36914,43698]),
[iquote('1:MRR:36914.3,43698.1')] ).
cnf(43703,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[43700]),
[iquote('1:Con:43700.2')] ).
cnf(43705,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[360,43703]),
[iquote('1:MRR:360.1,43703.0')] ).
cnf(43709,plain,
$false,
inference(unc,[status(thm)],[43705,31]),
[iquote('1:UnC:43705.0,31.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWC246-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 : Sun Jun 12 00:19:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 29.38/29.58
% 29.38/29.58 SPASS V 3.9
% 29.38/29.58 SPASS beiseite: Proof found.
% 29.38/29.58 % SZS status Theorem
% 29.38/29.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.38/29.58 SPASS derived 29293 clauses, backtracked 10855 clauses, performed 123 splits and kept 23556 clauses.
% 29.38/29.58 SPASS allocated 105725 KBytes.
% 29.38/29.58 SPASS spent 0:0:22.17 on the problem.
% 29.38/29.58 0:00:00.04 for the input.
% 29.38/29.58 0:00:00.00 for the FLOTTER CNF translation.
% 29.38/29.58 0:00:00.26 for inferences.
% 29.38/29.58 0:00:00.84 for the backtracking.
% 29.38/29.58 0:0:20.66 for the reduction.
% 29.38/29.58
% 29.38/29.58
% 29.38/29.58 Here is a proof with depth 3, length 66 :
% 29.38/29.58 % SZS output start Refutation
% See solution above
% 29.38/29.58 Formulae used in the proof : co1_1 co1_7 co1_9 co1_14 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause12 clause13 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause74 clause85 clause86 clause109 clause116 clause157 clause179
% 29.38/29.58
%------------------------------------------------------------------------------