TSTP Solution File: SWC174+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC174+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 22:02:15 EDT 2022
% Result : Theorem 5.94s 6.10s
% Output : Refutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 32
% Syntax : Number of clauses : 50 ( 25 unt; 1 nHn; 50 RR)
% Number of literals : 110 ( 0 equ; 65 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(skc13),
file('SWC174+1.p',unknown),
[] ).
cnf(2,axiom,
ssList(skc12),
file('SWC174+1.p',unknown),
[] ).
cnf(3,axiom,
ssItem(skc11),
file('SWC174+1.p',unknown),
[] ).
cnf(4,axiom,
ssItem(skc10),
file('SWC174+1.p',unknown),
[] ).
cnf(6,axiom,
ssList(skc8),
file('SWC174+1.p',unknown),
[] ).
cnf(7,axiom,
singletonP(skc8),
file('SWC174+1.p',unknown),
[] ).
cnf(10,axiom,
ssList(nil),
file('SWC174+1.p',unknown),
[] ).
cnf(11,axiom,
cyclefreeP(nil),
file('SWC174+1.p',unknown),
[] ).
cnf(12,axiom,
totalorderP(nil),
file('SWC174+1.p',unknown),
[] ).
cnf(13,axiom,
strictorderP(nil),
file('SWC174+1.p',unknown),
[] ).
cnf(14,axiom,
totalorderedP(nil),
file('SWC174+1.p',unknown),
[] ).
cnf(15,axiom,
strictorderedP(nil),
file('SWC174+1.p',unknown),
[] ).
cnf(16,axiom,
duplicatefreeP(nil),
file('SWC174+1.p',unknown),
[] ).
cnf(17,axiom,
equalelemsP(nil),
file('SWC174+1.p',unknown),
[] ).
cnf(18,axiom,
ssItem(skf45(u)),
file('SWC174+1.p',unknown),
[] ).
cnf(56,axiom,
~ neq(skc10,skc11),
file('SWC174+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC174+1.p',unknown),
[] ).
cnf(74,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC174+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC174+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC174+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC174+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC174+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC174+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ssList(cons(u,v)) ),
file('SWC174+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(v,u)) ),
file('SWC174+1.p',unknown),
[] ).
cnf(105,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| neq(v,u)
| equal(v,u) ),
file('SWC174+1.p',unknown),
[] ).
cnf(106,axiom,
( ~ ssList(u)
| ~ singletonP(u)
| equal(cons(skf45(u),nil),u) ),
file('SWC174+1.p',unknown),
[] ).
cnf(112,axiom,
equal(app(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc13),skc8),
file('SWC174+1.p',unknown),
[] ).
cnf(121,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC174+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| equal(app(cons(u,nil),v),cons(u,v)) ),
file('SWC174+1.p',unknown),
[] ).
cnf(159,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(w,v),u),app(w,app(v,u))) ),
file('SWC174+1.p',unknown),
[] ).
cnf(192,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssItem(y)
| ~ ssItem(z)
| ~ duplicatefreeP(u)
| ~ equal(z,y)
| ~ equal(app(app(x,cons(z,w)),cons(y,v)),u) ),
file('SWC174+1.p',unknown),
[] ).
cnf(201,plain,
( ~ ssList(skc8)
| equal(cons(skf45(skc8),nil),skc8) ),
inference(res,[status(thm),theory(equality)],[7,106]),
[iquote('0:Res:7.0,106.0')] ).
cnf(544,plain,
equal(cons(skf45(skc8),nil),skc8),
inference(mrr,[status(thm)],[201,6]),
[iquote('0:MRR:201.0,6.0')] ).
cnf(1101,plain,
( ~ ssItem(skf45(skc8))
| duplicatefreeP(skc8) ),
inference(spr,[status(thm),theory(equality)],[544,78]),
[iquote('0:SpR:544.0,78.1')] ).
cnf(1927,plain,
duplicatefreeP(skc8),
inference(mrr,[status(thm)],[1101,18]),
[iquote('0:MRR:1101.0,18.0')] ).
cnf(2299,plain,
( ~ ssItem(skc11)
| ~ ssItem(skc10)
| equal(skc11,skc10) ),
inference(res,[status(thm),theory(equality)],[105,56]),
[iquote('0:Res:105.2,56.0')] ).
cnf(2300,plain,
equal(skc11,skc10),
inference(ssi,[status(thm)],[2299,4,3]),
[iquote('0:SSi:2299.1,2299.0,4.0,3.0')] ).
cnf(2303,plain,
equal(app(app(app(skc12,cons(skc10,nil)),cons(skc10,nil)),skc13),skc8),
inference(rew,[status(thm),theory(equality)],[2300,112]),
[iquote('0:Rew:2300.0,112.0')] ).
cnf(2759,plain,
( ~ ssList(cons(u,nil))
| ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[121]),
[iquote('0:EqR:121.2')] ).
cnf(2764,plain,
( ~ ssItem(u)
| singletonP(cons(u,nil)) ),
inference(ssi,[status(thm)],[2759,76,77,73,74,75,78,79,90,17,16,13,12,11,15,14,10]),
[iquote('0:SSi:2759.0,76.0,77.0,73.0,74.0,75.0,78.0,79.0,90.0,17.2,16.1,13.1,12.1,11.1,15.1,14.1,10.1')] ).
cnf(4598,plain,
( ~ ssList(skc13)
| ~ ssList(cons(skc10,nil))
| ~ ssList(app(skc12,cons(skc10,nil)))
| equal(app(app(skc12,cons(skc10,nil)),app(cons(skc10,nil),skc13)),skc8) ),
inference(spr,[status(thm),theory(equality)],[159,2303]),
[iquote('0:SpR:159.3,2303.0')] ).
cnf(4651,plain,
equal(app(app(skc12,cons(skc10,nil)),app(cons(skc10,nil),skc13)),skc8),
inference(ssi,[status(thm)],[4598,91,2,76,4,77,73,74,75,78,79,2764,90,17,16,13,12,11,15,14,10,1]),
[iquote('0:SSi:4598.2,4598.1,4598.0,91.0,2.0,76.0,4.0,77.0,4.0,73.0,4.0,74.0,4.0,75.2,4.0,78.1,4.0,79.1,4.0,2764.1,4.0,90.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,76.0,4.0,77.0,4.0,73.0,4.0,74.0,4.0,75.2,4.0,78.1,4.0,79.1,4.0,2764.1,4.0,90.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,1.2')] ).
cnf(8887,plain,
( ~ ssItem(skc10)
| ~ ssList(skc13)
| equal(app(app(skc12,cons(skc10,nil)),cons(skc10,skc13)),skc8) ),
inference(spr,[status(thm),theory(equality)],[128,4651]),
[iquote('0:SpR:128.2,4651.0')] ).
cnf(8901,plain,
equal(app(app(skc12,cons(skc10,nil)),cons(skc10,skc13)),skc8),
inference(ssi,[status(thm)],[8887,1,4]),
[iquote('0:SSi:8887.1,8887.0,1.0,4.0')] ).
cnf(9022,plain,
( ~ ssList(u)
| ~ ssList(skc13)
| ~ ssList(nil)
| ~ ssList(skc12)
| ~ ssItem(skc10)
| ~ ssItem(skc10)
| ~ duplicatefreeP(u)
| ~ equal(skc10,skc10)
| ~ equal(skc8,u) ),
inference(spl,[status(thm),theory(equality)],[8901,192]),
[iquote('0:SpL:8901.0,192.8')] ).
cnf(9045,plain,
( ~ ssList(u)
| ~ ssList(skc13)
| ~ ssList(nil)
| ~ ssList(skc12)
| ~ ssItem(skc10)
| ~ duplicatefreeP(u)
| ~ equal(skc8,u) ),
inference(obv,[status(thm),theory(equality)],[9022]),
[iquote('0:Obv:9022.7')] ).
cnf(9046,plain,
( ~ ssList(u)
| ~ duplicatefreeP(u)
| ~ equal(skc8,u) ),
inference(ssi,[status(thm)],[9045,4,2,17,16,13,12,11,15,14,10,1]),
[iquote('0:SSi:9045.4,9045.3,9045.2,9045.1,4.0,2.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,1.0')] ).
cnf(11156,plain,
~ equal(skc8,skc8),
inference(ems,[status(thm)],[9046,6,1927]),
[iquote('0:EmS:9046.0,9046.1,6.0,1927.0')] ).
cnf(11161,plain,
$false,
inference(obv,[status(thm),theory(equality)],[11156]),
[iquote('0:Obv:11156.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC174+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n027.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 : Sun Jun 12 16:34:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 5.94/6.10
% 5.94/6.10 SPASS V 3.9
% 5.94/6.10 SPASS beiseite: Proof found.
% 5.94/6.10 % SZS status Theorem
% 5.94/6.10 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.94/6.10 SPASS derived 7402 clauses, backtracked 734 clauses, performed 22 splits and kept 3965 clauses.
% 5.94/6.10 SPASS allocated 108305 KBytes.
% 5.94/6.10 SPASS spent 0:00:05.43 on the problem.
% 5.94/6.10 0:00:00.04 for the input.
% 5.94/6.10 0:00:00.07 for the FLOTTER CNF translation.
% 5.94/6.10 0:00:00.09 for inferences.
% 5.94/6.10 0:00:00.09 for the backtracking.
% 5.94/6.10 0:00:04.95 for the reduction.
% 5.94/6.10
% 5.94/6.10
% 5.94/6.10 Here is a proof with depth 4, length 50 :
% 5.94/6.10 % SZS output start Refutation
% See solution above
% 5.94/6.10 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax2 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax16 ax26 ax1 ax81 ax82 ax13
% 5.94/6.10
%------------------------------------------------------------------------------