TSTP Solution File: NUM604+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM604+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Mon Jul 18 14:28:00 EDT 2022
% Result : Theorem 0.88s 1.12s
% Output : Refutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of clauses : 33 ( 11 unt; 3 nHn; 33 RR)
% Number of literals : 70 ( 0 equ; 41 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aSet0(szNzAzT0),
file('NUM604+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM604+1.p',unknown),
[] ).
cnf(15,axiom,
aElementOf0(sz00,szNzAzT0),
file('NUM604+1.p',unknown),
[] ).
cnf(17,axiom,
aSubsetOf0(xS,szNzAzT0),
file('NUM604+1.p',unknown),
[] ).
cnf(21,axiom,
aElementOf0(xi,szNzAzT0),
file('NUM604+1.p',unknown),
[] ).
cnf(22,axiom,
~ aElementOf0(xx,xS),
file('NUM604+1.p',unknown),
[] ).
cnf(41,axiom,
equal(sdtlpdtrp0(xe,xi),xx),
file('NUM604+1.p',unknown),
[] ).
cnf(42,axiom,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('NUM604+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ equal(u,slcrc0)
| aSet0(u) ),
file('NUM604+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ aElementOf0(u,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,u)) ),
file('NUM604+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ isFinite0(u)
| ~ isCountable0(u)
| ~ aSet0(u) ),
file('NUM604+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM604+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0) ),
file('NUM604+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sbrdtbr0(u),szNzAzT0)
| isFinite0(u) ),
file('NUM604+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ aSet0(u)
| ~ equal(u,slcrc0)
| equal(sbrdtbr0(u),sz00) ),
file('NUM604+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ aElementOf0(u,szNzAzT0)
| equal(szmzizndt0(sdtlpdtrp0(xN,u)),sdtlpdtrp0(xe,u)) ),
file('NUM604+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,w)
| ~ aSubsetOf0(w,u)
| aElementOf0(v,u) ),
file('NUM604+1.p',unknown),
[] ).
cnf(107,axiom,
( ~ aSubsetOf0(u,szNzAzT0)
| ~ equal(v,szmzizndt0(u))
| aElementOf0(v,u)
| equal(u,slcrc0) ),
file('NUM604+1.p',unknown),
[] ).
cnf(199,plain,
( ~ equal(u,slcrc0)
| equal(sbrdtbr0(u),sz00) ),
inference(mrr,[status(thm)],[82,43]),
[iquote('0:MRR:82.0,43.1')] ).
cnf(225,plain,
( ~ aSet0(xS)
| ~ aSubsetOf0(u,xS)
| ~ aElementOf0(xx,u) ),
inference(res,[status(thm),theory(equality)],[95,22]),
[iquote('0:Res:95.3,22.0')] ).
cnf(330,plain,
( ~ aSet0(szNzAzT0)
| aSet0(xS) ),
inference(res,[status(thm),theory(equality)],[17,67]),
[iquote('0:Res:17.0,67.1')] ).
cnf(336,plain,
aSet0(xS),
inference(ssi,[status(thm)],[330,3,2]),
[iquote('0:SSi:330.0,3.0,2.0')] ).
cnf(337,plain,
( ~ aSubsetOf0(u,xS)
| ~ aElementOf0(xx,u) ),
inference(mrr,[status(thm)],[225,336]),
[iquote('0:MRR:225.0,336.0')] ).
cnf(353,plain,
( ~ aSet0(u)
| ~ equal(u,slcrc0)
| ~ aElementOf0(sz00,szNzAzT0)
| isFinite0(u) ),
inference(spl,[status(thm),theory(equality)],[199,75]),
[iquote('0:SpL:199.1,75.1')] ).
cnf(357,plain,
( ~ equal(u,slcrc0)
| isFinite0(u) ),
inference(mrr,[status(thm)],[353,43,15]),
[iquote('0:MRR:353.0,353.2,43.1,15.0')] ).
cnf(363,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(sdtlpdtrp0(xN,u),slcrc0)
| ~ equal(sdtlpdtrp0(xN,u),slcrc0) ),
inference(ems,[status(thm)],[66,357,62,43]),
[iquote('0:EmS:66.0,66.1,66.2,357.1,62.1,43.1')] ).
cnf(382,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(sdtlpdtrp0(xN,u),slcrc0) ),
inference(obv,[status(thm),theory(equality)],[363]),
[iquote('0:Obv:363.1')] ).
cnf(454,plain,
~ aElementOf0(xx,sdtlpdtrp0(xN,xi)),
inference(res,[status(thm),theory(equality)],[42,337]),
[iquote('0:Res:42.0,337.0')] ).
cnf(1238,plain,
( ~ aSubsetOf0(u,szNzAzT0)
| aElementOf0(szmzizndt0(u),u)
| equal(u,slcrc0) ),
inference(eqr,[status(thm),theory(equality)],[107]),
[iquote('0:EqR:107.1')] ).
cnf(2825,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,u),sdtlpdtrp0(xN,u))
| equal(sdtlpdtrp0(xN,u),slcrc0) ),
inference(spr,[status(thm),theory(equality)],[90,1238]),
[iquote('0:SpR:90.1,1238.1')] ).
cnf(2849,plain,
( ~ aElementOf0(u,szNzAzT0)
| aElementOf0(sdtlpdtrp0(xe,u),sdtlpdtrp0(xN,u)) ),
inference(mrr,[status(thm)],[2825,73,382]),
[iquote('0:MRR:2825.1,2825.3,73.1,382.1')] ).
cnf(2868,plain,
( ~ aElementOf0(xi,szNzAzT0)
| aElementOf0(xx,sdtlpdtrp0(xN,xi)) ),
inference(spr,[status(thm),theory(equality)],[41,2849]),
[iquote('0:SpR:41.0,2849.1')] ).
cnf(2875,plain,
$false,
inference(mrr,[status(thm)],[2868,21,454]),
[iquote('0:MRR:2868.0,2868.1,21.0,454.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM604+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jul 7 09:39:29 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.88/1.12
% 0.88/1.12 SPASS V 3.9
% 0.88/1.12 SPASS beiseite: Proof found.
% 0.88/1.12 % SZS status Theorem
% 0.88/1.12 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.88/1.12 SPASS derived 1941 clauses, backtracked 189 clauses, performed 8 splits and kept 1205 clauses.
% 0.88/1.12 SPASS allocated 101079 KBytes.
% 0.88/1.12 SPASS spent 0:00:00.74 on the problem.
% 0.88/1.12 0:00:00.04 for the input.
% 0.88/1.12 0:00:00.29 for the FLOTTER CNF translation.
% 0.88/1.12 0:00:00.04 for inferences.
% 0.88/1.12 0:00:00.00 for the backtracking.
% 0.88/1.12 0:00:00.32 for the reduction.
% 0.88/1.12
% 0.88/1.12
% 0.88/1.12 Here is a proof with depth 3, length 33 :
% 0.88/1.12 % SZS output start Refutation
% See solution above
% 0.88/1.12 Formulae used in the proof : mNATSet mZeroNum m__3435 m__5034 m__ m__5045 mDefEmp m__3671 mCountNFin mDefSub mCardNum mCardEmpty m__4660 mDefMin
% 0.88/1.12
%------------------------------------------------------------------------------