TSTP Solution File: SWC191+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC191+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 22:02:22 EDT 2022
% Result : Theorem 19.85s 20.02s
% Output : Refutation 19.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 29
% Syntax : Number of clauses : 44 ( 22 unt; 0 nHn; 44 RR)
% Number of literals : 95 ( 0 equ; 54 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc13),
file('SWC191+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc12),
file('SWC191+1.p',unknown),
[] ).
cnf(3,axiom,
ssItem(skc11),
file('SWC191+1.p',unknown),
[] ).
cnf(4,axiom,
ssItem(skc10),
file('SWC191+1.p',unknown),
[] ).
cnf(6,axiom,
ssList(skc8),
file('SWC191+1.p',unknown),
[] ).
cnf(7,axiom,
equalelemsP(skc8),
file('SWC191+1.p',unknown),
[] ).
cnf(10,axiom,
ssList(nil),
file('SWC191+1.p',unknown),
[] ).
cnf(11,axiom,
cyclefreeP(nil),
file('SWC191+1.p',unknown),
[] ).
cnf(12,axiom,
totalorderP(nil),
file('SWC191+1.p',unknown),
[] ).
cnf(13,axiom,
strictorderP(nil),
file('SWC191+1.p',unknown),
[] ).
cnf(14,axiom,
totalorderedP(nil),
file('SWC191+1.p',unknown),
[] ).
cnf(15,axiom,
strictorderedP(nil),
file('SWC191+1.p',unknown),
[] ).
cnf(16,axiom,
duplicatefreeP(nil),
file('SWC191+1.p',unknown),
[] ).
cnf(17,axiom,
equalelemsP(nil),
file('SWC191+1.p',unknown),
[] ).
cnf(57,axiom,
~ equal(skc11,skc10),
file('SWC191+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC191+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC191+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC191+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC191+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC191+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC191+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC191+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC191+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC191+1.p',unknown),
[] ).
cnf(113,axiom,
equal(app(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc13),skc8),
file('SWC191+1.p',unknown),
[] ).
cnf(122,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC191+1.p',unknown),
[] ).
cnf(129,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| equal(app(cons(u,nil),v),cons(u,v)) ),
file('SWC191+1.p',unknown),
[] ).
cnf(161,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(w,v),u),app(w,app(v,u))) ),
file('SWC191+1.p',unknown),
[] ).
cnf(191,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssItem(x)
| ~ ssItem(y)
| ~ equalelemsP(u)
| ~ equal(app(w,cons(y,cons(x,v))),u)
| equal(y,x) ),
file('SWC191+1.p',unknown),
[] ).
cnf(2449,plain,
( ~ ssList(cons(u,nil))
| ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[122]),
[iquote('0:EqR:122.2')] ).
cnf(2452,plain,
( ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(ssi,[status(thm)],[2449,91,17,16,13,12,11,15,14,10,80,79,76,75,74,78,77]),
[iquote('0:SSi:2449.0,91.1,17.1,16.1,13.1,12.1,11.1,15.1,14.0,10.0,80.0,79.0,76.0,75.0,74.0,78.0,77.2')] ).
cnf(4366,plain,
( ~ ssList(skc13)
| ~ ssList(cons(skc11,nil))
| ~ ssList(app(skc12,cons(skc10,nil)))
| equal(app(app(skc12,cons(skc10,nil)),app(cons(skc11,nil),skc13)),skc8) ),
inference(spr,[status(thm),theory(equality)],[161,113]),
[iquote('0:SpR:161.3,113.0')] ).
cnf(4414,plain,
equal(app(app(skc12,cons(skc10,nil)),app(cons(skc11,nil),skc13)),skc8),
inference(ssi,[status(thm)],[4366,92,2,91,4,17,16,13,12,11,15,14,10,80,79,76,75,74,78,77,2452,3,1]),
[iquote('0:SSi:4366.2,4366.1,4366.0,92.0,2.0,91.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,80.1,4.0,79.1,4.0,76.1,4.0,75.0,4.0,74.0,4.0,78.0,4.0,77.0,4.0,2452.2,4.0,91.1,3.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,80.1,3.0,79.1,3.0,76.1,3.0,75.0,3.0,74.0,3.0,78.0,3.0,77.0,3.0,2452.2,3.0,1.2')] ).
cnf(9057,plain,
( ~ ssItem(skc11)
| ~ ssList(skc13)
| equal(app(app(skc12,cons(skc10,nil)),cons(skc11,skc13)),skc8) ),
inference(spr,[status(thm),theory(equality)],[129,4414]),
[iquote('0:SpR:129.2,4414.0')] ).
cnf(9071,plain,
equal(app(app(skc12,cons(skc10,nil)),cons(skc11,skc13)),skc8),
inference(ssi,[status(thm)],[9057,1,3]),
[iquote('0:SSi:9057.1,9057.0,1.0,3.0')] ).
cnf(9270,plain,
( ~ ssList(cons(skc11,skc13))
| ~ ssList(cons(skc10,nil))
| ~ ssList(skc12)
| equal(app(skc12,app(cons(skc10,nil),cons(skc11,skc13))),skc8) ),
inference(spr,[status(thm),theory(equality)],[9071,161]),
[iquote('0:SpR:9071.0,161.3')] ).
cnf(9302,plain,
equal(app(skc12,app(cons(skc10,nil),cons(skc11,skc13))),skc8),
inference(ssi,[status(thm)],[9270,2,91,4,17,16,13,12,11,15,14,10,80,79,76,75,74,78,77,2452,3,1]),
[iquote('0:SSi:9270.2,9270.1,9270.0,2.0,91.0,4.2,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,80.0,4.1,79.0,4.1,76.0,4.1,75.0,4.1,74.0,4.0,78.0,4.0,77.0,4.0,2452.0,4.0,91.0,3.2,1.0')] ).
cnf(25044,plain,
( ~ ssItem(skc10)
| ~ ssList(cons(skc11,skc13))
| equal(app(skc12,cons(skc10,cons(skc11,skc13))),skc8) ),
inference(spr,[status(thm),theory(equality)],[129,9302]),
[iquote('0:SpR:129.2,9302.0')] ).
cnf(25062,plain,
equal(app(skc12,cons(skc10,cons(skc11,skc13))),skc8),
inference(ssi,[status(thm)],[25044,91,3,1,4]),
[iquote('0:SSi:25044.1,25044.0,91.0,3.0,1.0,4.2')] ).
cnf(27316,plain,
( ~ ssList(u)
| ~ ssList(skc13)
| ~ ssList(skc12)
| ~ ssItem(skc11)
| ~ ssItem(skc10)
| ~ equalelemsP(u)
| ~ equal(skc8,u)
| equal(skc11,skc10) ),
inference(spl,[status(thm),theory(equality)],[25062,191]),
[iquote('0:SpL:25062.0,191.6')] ).
cnf(27327,plain,
( ~ ssList(u)
| ~ equalelemsP(u)
| ~ equal(skc8,u)
| equal(skc11,skc10) ),
inference(ssi,[status(thm)],[27316,4,3,2,1]),
[iquote('0:SSi:27316.4,27316.3,27316.2,27316.1,4.0,3.0,2.0,1.0')] ).
cnf(27328,plain,
( ~ ssList(u)
| ~ equalelemsP(u)
| ~ equal(skc8,u) ),
inference(mrr,[status(thm)],[27327,57]),
[iquote('0:MRR:27327.3,57.0')] ).
cnf(27955,plain,
~ equal(skc8,skc8),
inference(ems,[status(thm)],[27328,6,7]),
[iquote('0:EmS:27328.0,27328.1,6.0,7.0')] ).
cnf(27958,plain,
$false,
inference(obv,[status(thm),theory(equality)],[27955]),
[iquote('0:Obv:27955.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC191+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n013.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 10:23:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 19.85/20.02
% 19.85/20.02 SPASS V 3.9
% 19.85/20.02 SPASS beiseite: Proof found.
% 19.85/20.02 % SZS status Theorem
% 19.85/20.02 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.85/20.02 SPASS derived 18995 clauses, backtracked 3237 clauses, performed 33 splits and kept 9285 clauses.
% 19.85/20.02 SPASS allocated 121587 KBytes.
% 19.85/20.02 SPASS spent 0:0:17.30 on the problem.
% 19.85/20.02 0:00:00.04 for the input.
% 19.85/20.02 0:00:00.07 for the FLOTTER CNF translation.
% 19.85/20.02 0:00:00.24 for inferences.
% 19.85/20.02 0:00:00.44 for the backtracking.
% 19.85/20.02 0:0:16.17 for the reduction.
% 19.85/20.02
% 19.85/20.02
% 19.85/20.02 Here is a proof with depth 6, length 44 :
% 19.85/20.02 % SZS output start Refutation
% See solution above
% 19.85/20.02 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax16 ax26 ax4 ax2 ax81 ax82 ax14
% 19.85/20.02
%------------------------------------------------------------------------------