TSTP Solution File: NUM613+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM613+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 : Mon Jul 18 14:28:07 EDT 2022
% Result : Theorem 12.92s 13.15s
% Output : Refutation 12.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 35 ( 19 unt; 6 nHn; 35 RR)
% Number of literals : 68 ( 0 equ; 38 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(19,axiom,
aElementOf0(xK,szNzAzT0),
file('NUM613+3.p',unknown),
[] ).
cnf(21,axiom,
aElementOf0(xk,szNzAzT0),
file('NUM613+3.p',unknown),
[] ).
cnf(37,axiom,
equal(szszuzczcdt0(xk),xK),
file('NUM613+3.p',unknown),
[] ).
cnf(46,axiom,
equal(sbrdtbr0(xQ),xK),
file('NUM613+3.p',unknown),
[] ).
cnf(50,axiom,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
file('NUM613+3.p',unknown),
[] ).
cnf(51,axiom,
~ equal(sbrdtbr0(xP),xk),
file('NUM613+3.p',unknown),
[] ).
cnf(78,axiom,
equal(szszuzczcdt0(sbrdtbr0(xP)),sbrdtbr0(xQ)),
file('NUM613+3.p',unknown),
[] ).
cnf(100,axiom,
( ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(u,szszuzczcdt0(u)) ),
file('NUM613+3.p',unknown),
[] ).
cnf(113,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(szszuzczcdt0(u),u) ),
file('NUM613+3.p',unknown),
[] ).
cnf(185,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| sdtlseqdt0(v,u)
| sdtlseqdt0(szszuzczcdt0(u),v) ),
file('NUM613+3.p',unknown),
[] ).
cnf(250,axiom,
( ~ sdtlseqdt0(u,v)
| ~ sdtlseqdt0(v,u)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| equal(v,u) ),
file('NUM613+3.p',unknown),
[] ).
cnf(406,plain,
equal(szszuzczcdt0(sbrdtbr0(xP)),xK),
inference(rew,[status(thm),theory(equality)],[46,78]),
[iquote('0:Rew:46.0,78.0')] ).
cnf(497,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ~ sdtlseqdt0(sbrdtbr0(xP),xk)
| ~ sdtlseqdt0(xk,sbrdtbr0(xP))
| ~ aElementOf0(xk,szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[250,51]),
[iquote('0:Res:250.4,51.0')] ).
cnf(513,plain,
( ~ sdtlseqdt0(xk,sbrdtbr0(xP))
| ~ sdtlseqdt0(sbrdtbr0(xP),xk) ),
inference(mrr,[status(thm)],[497,50,21]),
[iquote('0:MRR:497.0,497.3,50.0,21.0')] ).
cnf(573,plain,
( ~ aElementOf0(xk,szNzAzT0)
| sdtlseqdt0(xk,xK) ),
inference(spr,[status(thm),theory(equality)],[37,100]),
[iquote('0:SpR:37.0,100.1')] ).
cnf(574,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| sdtlseqdt0(sbrdtbr0(xP),xK) ),
inference(spr,[status(thm),theory(equality)],[406,100]),
[iquote('0:SpR:406.0,100.1')] ).
cnf(576,plain,
sdtlseqdt0(xk,xK),
inference(mrr,[status(thm)],[573,21]),
[iquote('0:MRR:573.0,21.0')] ).
cnf(577,plain,
sdtlseqdt0(sbrdtbr0(xP),xK),
inference(mrr,[status(thm)],[574,50]),
[iquote('0:MRR:574.0,50.0')] ).
cnf(649,plain,
~ equal(szszuzczcdt0(xk),xk),
inference(res,[status(thm),theory(equality)],[21,113]),
[iquote('0:Res:21.0,113.0')] ).
cnf(652,plain,
~ equal(szszuzczcdt0(sbrdtbr0(xP)),sbrdtbr0(xP)),
inference(res,[status(thm),theory(equality)],[50,113]),
[iquote('0:Res:50.0,113.0')] ).
cnf(660,plain,
~ equal(xk,xK),
inference(rew,[status(thm),theory(equality)],[37,649]),
[iquote('0:Rew:37.0,649.0')] ).
cnf(661,plain,
~ equal(sbrdtbr0(xP),xK),
inference(rew,[status(thm),theory(equality)],[406,652]),
[iquote('0:Rew:406.0,652.0')] ).
cnf(2438,plain,
( ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(u,xk)
| sdtlseqdt0(xK,u) ),
inference(spr,[status(thm),theory(equality)],[37,185]),
[iquote('0:SpR:37.0,185.3')] ).
cnf(2442,plain,
( ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(u,xk)
| sdtlseqdt0(xK,u) ),
inference(mrr,[status(thm)],[2438,21]),
[iquote('0:MRR:2438.0,21.0')] ).
cnf(4189,plain,
( ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(u,sbrdtbr0(xP))
| sdtlseqdt0(xK,u) ),
inference(spr,[status(thm),theory(equality)],[406,185]),
[iquote('0:SpR:406.0,185.3')] ).
cnf(4203,plain,
( ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(u,sbrdtbr0(xP))
| sdtlseqdt0(xK,u) ),
inference(mrr,[status(thm)],[4189,50]),
[iquote('0:MRR:4189.0,50.0')] ).
cnf(6142,plain,
( ~ sdtlseqdt0(xK,xk)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aElementOf0(xK,szNzAzT0)
| equal(xk,xK) ),
inference(res,[status(thm),theory(equality)],[576,250]),
[iquote('0:Res:576.0,250.0')] ).
cnf(6144,plain,
( ~ sdtlseqdt0(xK,sbrdtbr0(xP))
| ~ aElementOf0(sbrdtbr0(xP),szNzAzT0)
| ~ aElementOf0(xK,szNzAzT0)
| equal(sbrdtbr0(xP),xK) ),
inference(res,[status(thm),theory(equality)],[577,250]),
[iquote('0:Res:577.0,250.0')] ).
cnf(6153,plain,
~ sdtlseqdt0(xK,xk),
inference(mrr,[status(thm)],[6142,21,19,660]),
[iquote('0:MRR:6142.1,6142.2,6142.3,21.0,19.0,660.0')] ).
cnf(6154,plain,
~ sdtlseqdt0(xK,sbrdtbr0(xP)),
inference(mrr,[status(thm)],[6144,50,19,661]),
[iquote('0:MRR:6144.1,6144.2,6144.3,50.0,19.0,661.0')] ).
cnf(8989,plain,
( sdtlseqdt0(sbrdtbr0(xP),xk)
| sdtlseqdt0(xK,sbrdtbr0(xP)) ),
inference(res,[status(thm),theory(equality)],[50,2442]),
[iquote('0:Res:50.0,2442.0')] ).
cnf(9030,plain,
sdtlseqdt0(sbrdtbr0(xP),xk),
inference(mrr,[status(thm)],[8989,6154]),
[iquote('0:MRR:8989.1,6154.0')] ).
cnf(9031,plain,
~ sdtlseqdt0(xk,sbrdtbr0(xP)),
inference(mrr,[status(thm)],[513,9030]),
[iquote('0:MRR:513.1,9030.0')] ).
cnf(24706,plain,
( ~ aElementOf0(xk,szNzAzT0)
| sdtlseqdt0(xK,xk) ),
inference(res,[status(thm),theory(equality)],[4203,9031]),
[iquote('0:Res:4203.1,9031.0')] ).
cnf(24707,plain,
$false,
inference(mrr,[status(thm)],[24706,21,6153]),
[iquote('0:MRR:24706.0,24706.1,21.0,6153.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM613+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 17:33:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 12.92/13.15
% 12.92/13.15 SPASS V 3.9
% 12.92/13.15 SPASS beiseite: Proof found.
% 12.92/13.15 % SZS status Theorem
% 12.92/13.15 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.92/13.15 SPASS derived 18620 clauses, backtracked 4422 clauses, performed 33 splits and kept 11460 clauses.
% 12.92/13.15 SPASS allocated 117243 KBytes.
% 12.92/13.15 SPASS spent 0:0:12.46 on the problem.
% 12.92/13.15 0:00:00.04 for the input.
% 12.92/13.15 0:00:00.71 for the FLOTTER CNF translation.
% 12.92/13.15 0:00:00.30 for inferences.
% 12.92/13.15 0:00:00.30 for the backtracking.
% 12.92/13.15 0:0:10.85 for the reduction.
% 12.92/13.15
% 12.92/13.15
% 12.92/13.15 Here is a proof with depth 2, length 35 :
% 12.92/13.15 % SZS output start Refutation
% See solution above
% 12.92/13.15 Formulae used in the proof : m__3418 m__3533 m__5078 m__5255 m__ mLessSucc mNatNSucc mLessTotal mLessASymm
% 12.92/13.15
%------------------------------------------------------------------------------