TSTP Solution File: NUM543+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM543+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 14:27:19 EDT 2022
% Result : Theorem 0.74s 0.95s
% Output : Refutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 41 ( 9 unt; 8 nHn; 41 RR)
% Number of literals : 120 ( 0 equ; 81 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
aSet0(xS),
file('NUM543+2.p',unknown),
[] ).
cnf(5,axiom,
isFinite0(xS),
file('NUM543+2.p',unknown),
[] ).
cnf(7,axiom,
aSubsetOf0(xS,szNzAzT0),
file('NUM543+2.p',unknown),
[] ).
cnf(8,axiom,
aElementOf0(skf10(u),xS),
file('NUM543+2.p',unknown),
[] ).
cnf(21,axiom,
( ~ aElementOf0(u,xS)
| aElementOf0(u,szNzAzT0) ),
file('NUM543+2.p',unknown),
[] ).
cnf(22,axiom,
( ~ aElementOf0(u,v)
| ~ equal(v,slcrc0) ),
file('NUM543+2.p',unknown),
[] ).
cnf(24,axiom,
( ~ aElementOf0(u,szNzAzT0)
| aElementOf0(szszuzczcdt0(u),szNzAzT0) ),
file('NUM543+2.p',unknown),
[] ).
cnf(35,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(skf10(u),slbdtrb0(u)) ),
file('NUM543+2.p',unknown),
[] ).
cnf(45,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,slbdtrb0(u))
| aElementOf0(v,szNzAzT0) ),
file('NUM543+2.p',unknown),
[] ).
cnf(60,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| sdtlseqdt0(v,u)
| sdtlseqdt0(szszuzczcdt0(u),v) ),
file('NUM543+2.p',unknown),
[] ).
cnf(65,axiom,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(v),u)
| aElementOf0(v,slbdtrb0(u)) ),
file('NUM543+2.p',unknown),
[] ).
cnf(71,axiom,
( ~ equal(u,v)
| ~ aElementOf0(v,szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| aElementOf0(u,slbdtrb0(szszuzczcdt0(v))) ),
file('NUM543+2.p',unknown),
[] ).
cnf(75,axiom,
( ~ isFinite0(u)
| ~ aSubsetOf0(u,szNzAzT0)
| ~ equal(v,szmzazxdt0(u))
| aElementOf0(v,u)
| equal(u,slcrc0) ),
file('NUM543+2.p',unknown),
[] ).
cnf(76,axiom,
( ~ aElementOf0(u,slbdtrb0(v))
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| aElementOf0(u,slbdtrb0(szszuzczcdt0(v))) ),
file('NUM543+2.p',unknown),
[] ).
cnf(77,axiom,
( ~ sdtlseqdt0(u,v)
| ~ sdtlseqdt0(v,u)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| equal(v,u) ),
file('NUM543+2.p',unknown),
[] ).
cnf(93,axiom,
( ~ isFinite0(u)
| ~ equal(v,szmzazxdt0(u))
| ~ aSubsetOf0(u,szNzAzT0)
| ~ aElementOf0(w,u)
| sdtlseqdt0(w,v)
| equal(u,slcrc0) ),
file('NUM543+2.p',unknown),
[] ).
cnf(105,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,slbdtrb0(u))
| aElementOf0(v,slbdtrb0(szszuzczcdt0(u))) ),
inference(mrr,[status(thm)],[76,45]),
[iquote('0:MRR:76.1,45.2')] ).
cnf(110,plain,
( ~ isFinite0(u)
| ~ aElementOf0(v,u)
| ~ aSubsetOf0(u,szNzAzT0)
| ~ equal(w,szmzazxdt0(u))
| sdtlseqdt0(v,w) ),
inference(mrr,[status(thm)],[93,22]),
[iquote('0:MRR:93.5,22.1')] ).
cnf(114,plain,
aElementOf0(skf10(u),szNzAzT0),
inference(res,[status(thm),theory(equality)],[8,21]),
[iquote('0:Res:8.0,21.0')] ).
cnf(122,plain,
~ equal(xS,slcrc0),
inference(res,[status(thm),theory(equality)],[8,22]),
[iquote('0:Res:8.0,22.0')] ).
cnf(128,plain,
( ~ isFinite0(xS)
| ~ equal(u,szmzazxdt0(xS))
| ~ aSubsetOf0(xS,szNzAzT0)
| sdtlseqdt0(skf10(v),u) ),
inference(res,[status(thm),theory(equality)],[8,110]),
[iquote('0:Res:8.0,110.3')] ).
cnf(159,plain,
( ~ equal(u,szmzazxdt0(xS))
| sdtlseqdt0(skf10(v),u) ),
inference(mrr,[status(thm)],[128,5,7]),
[iquote('0:MRR:128.0,128.2,5.0,7.0')] ).
cnf(420,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(skf10(szszuzczcdt0(u)),slbdtrb0(u))
| ~ aElementOf0(szszuzczcdt0(u),szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[105,35]),
[iquote('0:Res:105.2,35.1')] ).
cnf(424,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(skf10(szszuzczcdt0(u)),slbdtrb0(u)) ),
inference(mrr,[status(thm)],[420,24]),
[iquote('0:MRR:420.2,24.1')] ).
cnf(1065,plain,
( ~ equal(skf10(szszuzczcdt0(u)),u)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(skf10(szszuzczcdt0(u)),szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(u),szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[71,35]),
[iquote('0:Res:71.3,35.1')] ).
cnf(1077,plain,
( ~ equal(skf10(szszuzczcdt0(u)),u)
| ~ aElementOf0(u,szNzAzT0) ),
inference(mrr,[status(thm)],[1065,114,24]),
[iquote('0:MRR:1065.2,1065.3,114.0,24.1')] ).
cnf(1107,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(v,u)
| aElementOf0(u,slbdtrb0(v)) ),
inference(res,[status(thm),theory(equality)],[60,65]),
[iquote('0:Res:60.3,65.2')] ).
cnf(1115,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(v,szNzAzT0)
| sdtlseqdt0(u,v)
| aElementOf0(v,slbdtrb0(u)) ),
inference(obv,[status(thm),theory(equality)],[1107]),
[iquote('0:Obv:1107.1')] ).
cnf(1352,plain,
( ~ isFinite0(u)
| ~ aSubsetOf0(u,szNzAzT0)
| aElementOf0(szmzazxdt0(u),u)
| equal(u,slcrc0) ),
inference(eqr,[status(thm),theory(equality)],[75]),
[iquote('0:EqR:75.2')] ).
cnf(2369,plain,
( ~ isFinite0(xS)
| ~ aSubsetOf0(xS,szNzAzT0)
| equal(xS,slcrc0)
| aElementOf0(szmzazxdt0(xS),szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[1352,21]),
[iquote('0:Res:1352.2,21.0')] ).
cnf(2378,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| equal(xS,slcrc0)
| aElementOf0(szmzazxdt0(xS),szNzAzT0) ),
inference(ssi,[status(thm)],[2369,5,4]),
[iquote('0:SSi:2369.0,5.0,4.0')] ).
cnf(2379,plain,
aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(mrr,[status(thm)],[2378,7,122]),
[iquote('0:MRR:2378.0,2378.1,7.0,122.0')] ).
cnf(2591,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(skf10(szszuzczcdt0(u)),szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(u,skf10(szszuzczcdt0(u))) ),
inference(res,[status(thm),theory(equality)],[1115,424]),
[iquote('0:Res:1115.3,424.1')] ).
cnf(2609,plain,
( ~ aElementOf0(skf10(szszuzczcdt0(u)),szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(u,skf10(szszuzczcdt0(u))) ),
inference(obv,[status(thm),theory(equality)],[2591]),
[iquote('0:Obv:2591.0')] ).
cnf(2610,plain,
( ~ aElementOf0(u,szNzAzT0)
| sdtlseqdt0(u,skf10(szszuzczcdt0(u))) ),
inference(mrr,[status(thm)],[2609,114]),
[iquote('0:MRR:2609.0,114.0')] ).
cnf(2639,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ sdtlseqdt0(skf10(szszuzczcdt0(u)),u)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(skf10(szszuzczcdt0(u)),szNzAzT0)
| equal(skf10(szszuzczcdt0(u)),u) ),
inference(res,[status(thm),theory(equality)],[2610,77]),
[iquote('0:Res:2610.1,77.0')] ).
cnf(2642,plain,
( ~ sdtlseqdt0(skf10(szszuzczcdt0(u)),u)
| ~ aElementOf0(u,szNzAzT0)
| ~ aElementOf0(skf10(szszuzczcdt0(u)),szNzAzT0)
| equal(skf10(szszuzczcdt0(u)),u) ),
inference(obv,[status(thm),theory(equality)],[2639]),
[iquote('0:Obv:2639.0')] ).
cnf(2643,plain,
( ~ sdtlseqdt0(skf10(szszuzczcdt0(u)),u)
| ~ aElementOf0(u,szNzAzT0) ),
inference(mrr,[status(thm)],[2642,114,1077]),
[iquote('0:MRR:2642.2,2642.3,114.0,1077.0')] ).
cnf(2677,plain,
( ~ equal(u,szmzazxdt0(xS))
| ~ aElementOf0(u,szNzAzT0) ),
inference(res,[status(thm),theory(equality)],[159,2643]),
[iquote('0:Res:159.1,2643.0')] ).
cnf(2696,plain,
~ equal(szmzazxdt0(xS),szmzazxdt0(xS)),
inference(res,[status(thm),theory(equality)],[2379,2677]),
[iquote('0:Res:2379.0,2677.1')] ).
cnf(2714,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2696]),
[iquote('0:Obv:2696.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM543+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 07:55:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.74/0.95
% 0.74/0.95 SPASS V 3.9
% 0.74/0.95 SPASS beiseite: Proof found.
% 0.74/0.95 % SZS status Theorem
% 0.74/0.95 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.74/0.95 SPASS derived 1910 clauses, backtracked 123 clauses, performed 2 splits and kept 1060 clauses.
% 0.74/0.95 SPASS allocated 99944 KBytes.
% 0.74/0.95 SPASS spent 0:00:00.59 on the problem.
% 0.74/0.95 0:00:00.04 for the input.
% 0.74/0.95 0:00:00.12 for the FLOTTER CNF translation.
% 0.74/0.95 0:00:00.03 for inferences.
% 0.74/0.95 0:00:00.00 for the backtracking.
% 0.74/0.95 0:00:00.37 for the reduction.
% 0.74/0.95
% 0.74/0.95
% 0.74/0.95 Here is a proof with depth 5, length 41 :
% 0.74/0.95 % SZS output start Refutation
% See solution above
% 0.74/0.95 Formulae used in the proof : m__1986 m__ mZeroNum mDefEmp mSuccNum mLessTotal mSegSucc mDefMax mLessASymm
% 0.74/0.95
%------------------------------------------------------------------------------