%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM622+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:28:13 EDT 2022
% Result : Theorem 81.00s 81.23s
% Output : Refutation 81.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of clauses : 35 ( 11 unt; 2 nHn; 35 RR)
% Number of literals : 77 ( 0 equ; 51 neg)
% Maximal clause size : 5 ( 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('NUM622+1.p',unknown),
[] ).
cnf(3,axiom,
isCountable0(szNzAzT0),
file('NUM622+1.p',unknown),
[] ).
cnf(16,axiom,
aElementOf0(sz00,szNzAzT0),
file('NUM622+1.p',unknown),
[] ).
cnf(28,axiom,
aElementOf0(xn,szNzAzT0),
file('NUM622+1.p',unknown),
[] ).
cnf(32,axiom,
aElementOf0(xm,szNzAzT0),
file('NUM622+1.p',unknown),
[] ).
cnf(57,axiom,
equal(sdtlpdtrp0(xe,xn),xp),
file('NUM622+1.p',unknown),
[] ).
cnf(59,axiom,
~ aElementOf0(xp,sdtlpdtrp0(xN,xm)),
file('NUM622+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ equal(u,slcrc0)
| aSet0(u) ),
file('NUM622+1.p',unknown),
[] ).
cnf(78,axiom,
aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
file('NUM622+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ aElementOf0(u,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,u)) ),
file('NUM622+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ isFinite0(u)
| ~ isCountable0(u)
| ~ aSet0(u) ),
file('NUM622+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ aSet0(u)
| ~ aSubsetOf0(v,u)
| aSet0(v) ),
file('NUM622+1.p',unknown),
[] ).
cnf(95,axiom,
( ~ aElementOf0(u,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0) ),
file('NUM622+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ aSet0(u)
| ~ aElementOf0(sbrdtbr0(u),szNzAzT0)
| isFinite0(u) ),
file('NUM622+1.p',unknown),
[] ).
cnf(105,axiom,
( ~ aSet0(u)
| ~ equal(u,slcrc0)
| equal(sbrdtbr0(u),sz00) ),
file('NUM622+1.p',unknown),
[] ).
cnf(113,axiom,
( ~ aElementOf0(u,szNzAzT0)
| equal(szmzizndt0(sdtlpdtrp0(xN,u)),sdtlpdtrp0(xe,u)) ),
file('NUM622+1.p',unknown),
[] ).
cnf(118,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,w)
| ~ aSubsetOf0(w,u)
| aElementOf0(v,u) ),
file('NUM622+1.p',unknown),
[] ).
cnf(130,axiom,
( ~ aSubsetOf0(u,szNzAzT0)
| ~ equal(v,szmzizndt0(u))
| aElementOf0(v,u)
| equal(u,slcrc0) ),
file('NUM622+1.p',unknown),
[] ).
cnf(223,plain,
( ~ equal(u,slcrc0)
| equal(sbrdtbr0(u),sz00) ),
inference(mrr,[status(thm)],[105,60]),
[iquote('0:MRR:105.0,60.1')] ).
cnf(249,plain,
( ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(u,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xp,u) ),
inference(res,[status(thm),theory(equality)],[118,59]),
[iquote('0:Res:118.3,59.0')] ).
cnf(393,plain,
( ~ aSet0(szNzAzT0)
| ~ aElementOf0(u,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,u)) ),
inference(res,[status(thm),theory(equality)],[95,89]),
[iquote('0:Res:95.1,89.1')] ).
cnf(398,plain,
( ~ aElementOf0(u,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,u)) ),
inference(ssi,[status(thm)],[393,3,2]),
[iquote('0:SSi:393.0,3.0,2.0')] ).
cnf(409,plain,
( ~ aSet0(u)
| ~ equal(u,slcrc0)
| ~ aElementOf0(sz00,szNzAzT0)
| isFinite0(u) ),
inference(spl,[status(thm),theory(equality)],[223,98]),
[iquote('0:SpL:223.1,98.1')] ).
cnf(415,plain,
( ~ equal(u,slcrc0)
| isFinite0(u) ),
inference(mrr,[status(thm)],[409,60,16]),
[iquote('0:MRR:409.0,409.2,60.1,16.0')] ).
cnf(420,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(sdtlpdtrp0(xN,u),slcrc0)
| ~ equal(sdtlpdtrp0(xN,u),slcrc0) ),
inference(ems,[status(thm)],[88,415,84,60]),
[iquote('0:EmS:88.0,88.1,88.2,415.1,84.1,60.1')] ).
cnf(436,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(sdtlpdtrp0(xN,u),slcrc0) ),
inference(obv,[status(thm),theory(equality)],[420]),
[iquote('0:Obv:420.1')] ).
cnf(1283,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,u),szNzAzT0)
| ~ equal(v,sdtlpdtrp0(xe,u))
| aElementOf0(v,sdtlpdtrp0(xN,u))
| equal(sdtlpdtrp0(xN,u),slcrc0) ),
inference(spl,[status(thm),theory(equality)],[113,130]),
[iquote('0:SpL:113.1,130.1')] ).
cnf(1286,plain,
( ~ aElementOf0(u,szNzAzT0)
| ~ equal(v,sdtlpdtrp0(xe,u))
| aElementOf0(v,sdtlpdtrp0(xN,u)) ),
inference(mrr,[status(thm)],[1283,95,436]),
[iquote('0:MRR:1283.1,1283.4,95.1,436.1')] ).
cnf(59546,plain,
( ~ aSubsetOf0(u,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xp,u)
| ~ aElementOf0(xm,szNzAzT0) ),
inference(sor,[status(thm)],[249,398]),
[iquote('0:SoR:249.0,398.1')] ).
cnf(59556,plain,
( ~ aSubsetOf0(u,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xp,u) ),
inference(mrr,[status(thm)],[59546,32]),
[iquote('0:MRR:59546.2,32.0')] ).
cnf(61648,plain,
~ aElementOf0(xp,sdtlpdtrp0(xN,xn)),
inference(res,[status(thm),theory(equality)],[78,59556]),
[iquote('0:Res:78.0,59556.0')] ).
cnf(61651,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ~ equal(sdtlpdtrp0(xe,xn),xp) ),
inference(res,[status(thm),theory(equality)],[1286,61648]),
[iquote('0:Res:1286.2,61648.0')] ).
cnf(61652,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ~ equal(xp,xp) ),
inference(rew,[status(thm),theory(equality)],[57,61651]),
[iquote('0:Rew:57.0,61651.1')] ).
cnf(61653,plain,
~ aElementOf0(xn,szNzAzT0),
inference(obv,[status(thm),theory(equality)],[61652]),
[iquote('0:Obv:61652.1')] ).
cnf(61654,plain,
$false,
inference(mrr,[status(thm)],[61653,28]),
[iquote('0:MRR:61653.0,28.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM622+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n026.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 : Wed Jul 6 12:34:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 81.00/81.23
% 81.00/81.23 SPASS V 3.9
% 81.00/81.23 SPASS beiseite: Proof found.
% 81.00/81.23 % SZS status Theorem
% 81.00/81.23 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.00/81.23 SPASS derived 48460 clauses, backtracked 21373 clauses, performed 154 splits and kept 41644 clauses.
% 81.00/81.23 SPASS allocated 136550 KBytes.
% 81.00/81.23 SPASS spent 0:1:18.02 on the problem.
% 81.00/81.23 0:00:00.04 for the input.
% 81.00/81.23 0:00:00.25 for the FLOTTER CNF translation.
% 81.00/81.23 0:00:00.79 for inferences.
% 81.00/81.23 0:00:02.22 for the backtracking.
% 81.00/81.23 0:1:13.90 for the reduction.
% 81.00/81.23
% 81.00/81.23
% 81.00/81.23 Here is a proof with depth 4, length 35 :
% 81.00/81.23 % SZS output start Refutation
% See solution above
% 81.00/81.23 Formulae used in the proof : mNATSet mZeroNum m__5309 m__5389 m__ mDefEmp m__5461 m__3671 mCountNFin mDefSub mCardNum mCardEmpty m__4660 mDefMin
% 81.00/81.23
%------------------------------------------------------------------------------