TSTP Solution File: SYO844+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYO844+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 : Thu Jul 21 19:56:18 EDT 2022
% Result : CounterSatisfiable 0.56s 0.75s
% Output : Saturation 0.60s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 1260)
% Comments :
%------------------------------------------------------------------------------
cnf(2283,plain,
( ~ aal4(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))),a3)
| ain(aun(v,u),asing(asing(a2)))
| ain(aun(v,u),apow(a3)) ),
inference(res,[status(thm),theory(equality)],[1539,1908]),
[iquote('21:Res:1539.4,1908.0')] ).
cnf(2281,plain,
( ~ aal4(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))))
| ~ asubq(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))),a3)
| ain(asm(asm(apow(a2),a2),asing(a2)),asing(asing(a2)))
| ain(asm(asm(apow(a2),a2),asing(a2)),apow(a3)) ),
inference(res,[status(thm),theory(equality)],[1540,1908]),
[iquote('21:Res:1540.2,1908.0')] ).
cnf(2563,plain,
( ~ aal4(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))))
| ~ asubq(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))),a3)
| ain(asing(apow(a2)),asing(asing(a2)))
| ain(asing(apow(a2)),apow(a3)) ),
inference(res,[status(thm),theory(equality)],[2302,1908]),
[iquote('25:Res:2302.2,1908.0')] ).
cnf(2284,plain,
( ~ aal4(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))))
| ~ asubq(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))),a3)
| ain(asm(a3,a3),asing(asing(a2))) ),
inference(mrr,[status(thm)],[2280,1425]),
[iquote('21:MRR:2280.3,1425.0')] ).
cnf(1994,plain,
( ~ aal4(aun(asing(a2),aun(apow(asing(a2)),asing(apow(a2)))))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(asing(a2),aun(apow(asing(a2)),asing(apow(a2)))),a3)
| ~ ain(aun(v,u),asing(apow(a2)))
| ~ ain(aun(v,u),aun(asing(a3),aun(asing(asing(a2)),a4))) ),
inference(res,[status(thm),theory(equality)],[1539,219]),
[iquote('17:Res:1539.4,219.1')] ).
cnf(1637,plain,
( ~ aal4(aun(asing(a2),aun(apow(asing(a2)),asing(apow(a2)))))
| ~ asubq(aun(asing(a2),aun(apow(asing(a2)),asing(apow(a2)))),a3)
| ~ ain(asm(asm(apow(a2),a2),asing(a2)),asing(apow(a2)))
| ~ ain(asm(asm(apow(a2),a2),asing(a2)),aun(asing(a3),aun(asing(asing(a2)),a4))) ),
inference(res,[status(thm),theory(equality)],[1540,219]),
[iquote('17:Res:1540.2,219.1')] ).
cnf(1980,plain,
( ~ aal4(asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3)))))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3)))),a3)
| ain(aun(v,u),asing(a2))
| ain(aun(v,u),aun(asing(a3),asing(asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[1539,1013]),
[iquote('17:Res:1539.4,1013.0')] ).
cnf(1998,plain,
( ~ aal4(aun(asm(apow(a2),apow(asing(a2))),a3))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(asm(apow(a2),apow(asing(a2))),a3),a3)
| ain(aun(v,u),asing(a2))
| ain(aun(v,u),aun(aun(a3,asing(a3)),a3)) ),
inference(res,[status(thm),theory(equality)],[1539,1361]),
[iquote('17:Res:1539.4,1361.0')] ).
cnf(2471,plain,
( ~ aal4(aun(asing(a2),aun(apow(asing(a2)),asing(apow(a2)))))
| ~ asubq(aun(asing(a2),aun(apow(asing(a2)),asing(apow(a2)))),a3)
| ~ ain(asing(apow(a2)),asing(apow(a2)))
| ~ ain(asing(apow(a2)),aun(asing(a3),aun(asing(asing(a2)),a4))) ),
inference(res,[status(thm),theory(equality)],[2302,219]),
[iquote('25:Res:2302.2,219.1')] ).
cnf(1581,plain,
( ~ aal4(aun(asing(a2),aun(apow(asing(a2)),asing(apow(a2)))))
| ~ asubq(aun(asing(a2),aun(apow(asing(a2)),asing(apow(a2)))),a3)
| ~ ain(asm(a3,a3),asing(apow(a2)))
| ~ ain(asm(a3,a3),aun(asing(a3),aun(asing(asing(a2)),a4))) ),
inference(res,[status(thm),theory(equality)],[1537,219]),
[iquote('17:Res:1537.2,219.1')] ).
cnf(1999,plain,
( ~ aal4(aun(asm(apow(a2),apow(asing(a2))),a3))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(asm(apow(a2),apow(asing(a2))),a3),a3)
| ain(aun(v,u),asing(asing(a3)))
| ain(aun(v,u),apow(a2)) ),
inference(res,[status(thm),theory(equality)],[1539,1328]),
[iquote('17:Res:1539.4,1328.0')] ).
cnf(2429,plain,
( ~ aal4(asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3)))))
| ~ asubq(asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3)))),a3)
| ain(asing(apow(a2)),asing(a2))
| ain(asing(apow(a2)),aun(asing(a3),asing(asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[2302,1013]),
[iquote('25:Res:2302.2,1013.0')] ).
cnf(1569,plain,
( ~ aal4(asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3)))))
| ~ asubq(asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3)))),a3)
| ain(asm(a3,a3),asing(a2))
| ain(asm(a3,a3),aun(asing(a3),asing(asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[1537,1013]),
[iquote('17:Res:1537.2,1013.0')] ).
cnf(2614,plain,
( ~ aal4(asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3)))))
| ~ asubq(asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3)))),a3)
| ain(asm(asm(apow(a2),a2),asing(a2)),aun(asing(a3),asing(asing(a3)))) ),
inference(mrr,[status(thm)],[1625,2610]),
[iquote('28:MRR:1625.2,2610.0')] ).
cnf(1990,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ~ ain(aun(v,u),asing(aun(a3,asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[1539,1115]),
[iquote('17:Res:1539.4,1115.0')] ).
cnf(2446,plain,
( ~ aal4(aun(asm(apow(a2),apow(asing(a2))),a3))
| ~ asubq(aun(asm(apow(a2),apow(asing(a2))),a3),a3)
| ain(asing(apow(a2)),asing(a2))
| ain(asing(apow(a2)),aun(aun(a3,asing(a3)),a3)) ),
inference(res,[status(thm),theory(equality)],[2302,1361]),
[iquote('25:Res:2302.2,1361.0')] ).
cnf(1583,plain,
( ~ aal4(aun(asm(apow(a2),apow(asing(a2))),a3))
| ~ asubq(aun(asm(apow(a2),apow(asing(a2))),a3),a3)
| ain(asm(a3,a3),asing(a2))
| ain(asm(a3,a3),aun(aun(a3,asing(a3)),a3)) ),
inference(res,[status(thm),theory(equality)],[1537,1361]),
[iquote('17:Res:1537.2,1361.0')] ).
cnf(1974,plain,
( ~ aal4(asm(a4,asing(a2)))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(asm(a4,asing(a2)),a3)
| ~ ain(aun(v,u),apow(a3))
| ain(aun(v,u),asing(a3)) ),
inference(res,[status(thm),theory(equality)],[1539,1008]),
[iquote('17:Res:1539.4,1008.0')] ).
cnf(1991,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ain(aun(v,u),apow(aun(a3,asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[1539,1114]),
[iquote('17:Res:1539.4,1114.0')] ).
cnf(1975,plain,
( ~ aal4(asm(a4,asing(a2)))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(asm(a4,asing(a2)),a3)
| ain(aun(v,u),asing(a3))
| ain(aun(v,u),apow(a2)) ),
inference(res,[status(thm),theory(equality)],[1539,1007]),
[iquote('17:Res:1539.4,1007.0')] ).
cnf(1995,plain,
( ~ aal4(aun(aun(a3,asing(a3)),a3))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(aun(a3,asing(a3)),a3),a3)
| ~ ain(aun(v,u),apow(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[1539,1649]),
[iquote('17:Res:1539.4,1649.0')] ).
cnf(2613,plain,
( ~ aal4(aun(asm(apow(a2),apow(asing(a2))),a3))
| ~ asubq(aun(asm(apow(a2),apow(asing(a2))),a3),a3)
| ain(asm(asm(apow(a2),a2),asing(a2)),aun(aun(a3,asing(a3)),a3)) ),
inference(mrr,[status(thm)],[1640,2610]),
[iquote('28:MRR:1640.2,2610.0')] ).
cnf(2225,plain,
( ~ aal4(asing(apow(a2)))
| ~ aal4(u)
| ~ asubq(v,asing(a3))
| ~ asubq(w,asing(a3))
| ~ asubq(asing(apow(a2)),a3)
| ~ asubq(u,apow(a3))
| ain(aun(w,v),u) ),
inference(res,[status(thm),theory(equality)],[1539,2220]),
[iquote('23:Res:1539.4,2220.1')] ).
cnf(1992,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ~ ain(aun(v,u),asing(a2)) ),
inference(res,[status(thm),theory(equality)],[1539,1015]),
[iquote('17:Res:1539.4,1015.1')] ).
cnf(1997,plain,
( ~ aal4(aun(aun(a3,asing(a3)),a3))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(aun(a3,asing(a3)),a3),a3)
| ~ ain(aun(v,u),asing(a2)) ),
inference(res,[status(thm),theory(equality)],[1539,1335]),
[iquote('17:Res:1539.4,1335.1')] ).
cnf(2447,plain,
( ~ aal4(aun(asm(apow(a2),apow(asing(a2))),a3))
| ~ asubq(aun(asm(apow(a2),apow(asing(a2))),a3),a3)
| ain(asing(apow(a2)),asing(asing(a3)))
| ain(asing(apow(a2)),apow(a2)) ),
inference(res,[status(thm),theory(equality)],[2302,1328]),
[iquote('25:Res:2302.2,1328.0')] ).
cnf(1978,plain,
( ~ aal4(asm(a4,a3))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(asm(a4,a3),a3)
| equal(aun(v,u),a2)
| ain(aun(v,u),asm(a4,a2)) ),
inference(res,[status(thm),theory(equality)],[1539,563]),
[iquote('17:Res:1539.4,563.0')] ).
cnf(1996,plain,
( ~ aal4(aun(aun(a3,asing(a3)),a3))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(aun(a3,asing(a3)),a3),a3)
| ain(aun(v,u),apow(a2)) ),
inference(res,[status(thm),theory(equality)],[1539,1648]),
[iquote('17:Res:1539.4,1648.0')] ).
cnf(1989,plain,
( ~ aal4(aun(u,v))
| ~ asubq(w,asing(a3))
| ~ asubq(x,asing(a3))
| ~ asubq(aun(u,v),a3)
| ain(aun(x,w),v)
| ain(aun(x,w),u) ),
inference(res,[status(thm),theory(equality)],[1539,53]),
[iquote('17:Res:1539.4,53.0')] ).
cnf(1976,plain,
( ~ aal4(asm(a4,asing(a2)))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(asm(a4,asing(a2)),a3)
| ~ ain(aun(v,u),apow(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[1539,542]),
[iquote('17:Res:1539.4,542.1')] ).
cnf(1633,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ~ ain(asm(asm(apow(a2),a2),asing(a2)),asing(aun(a3,asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[1540,1115]),
[iquote('17:Res:1540.2,1115.0')] ).
cnf(1623,plain,
( ~ aal4(asm(a4,a3))
| ~ asubq(asm(a4,a3),a3)
| equal(asm(asm(apow(a2),a2),asing(a2)),a2)
| ain(asm(asm(apow(a2),a2),asing(a2)),asm(a4,a2)) ),
inference(res,[status(thm),theory(equality)],[1540,563]),
[iquote('17:Res:1540.2,563.0')] ).
cnf(1634,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ain(asm(asm(apow(a2),a2),asing(a2)),apow(aun(a3,asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[1540,1114]),
[iquote('17:Res:1540.2,1114.0')] ).
cnf(2611,plain,
( ~ ain(asm(asm(apow(a2),a2),asing(a2)),apow(a3))
| ain(asm(asm(apow(a2),a2),asing(a2)),asing(a3)) ),
inference(mrr,[status(thm)],[1481,2609]),
[iquote('28:MRR:1481.0,2609.0')] ).
cnf(2610,plain,
~ ain(asm(asm(apow(a2),a2),asing(a2)),asing(a2)),
inference(mrr,[status(thm)],[1483,2609]),
[iquote('28:MRR:1483.0,2609.0')] ).
cnf(2609,plain,
ain(asm(asm(apow(a2),a2),asing(a2)),a4),
inference(mrr,[status(thm)],[1460,2600]),
[iquote('28:MRR:1460.0,2600.0')] ).
cnf(2612,plain,
( ~ aal4(asm(a4,a2))
| ~ asubq(asm(a4,a2),a3) ),
inference(mrr,[status(thm)],[1756,2610]),
[iquote('28:MRR:1756.2,2610.0')] ).
cnf(2600,plain,
asubq(asm(asm(apow(a2),a2),asing(a2)),a2),
inference(res,[status(thm),theory(equality)],[2599,20]),
[iquote('28:Res:2599.0,20.0')] ).
cnf(2599,plain,
ain(asm(asm(apow(a2),a2),asing(a2)),apow(a2)),
inference(spt,[],[1482]),
[iquote('28:Spt:1482.2')] ).
cnf(1707,plain,
( ~ asubq(u,a2)
| ~ asubq(v,a2)
| ~ ain(aun(v,u),a4)
| ain(aun(v,u),a3)
| equal(aun(v,u),a2)
| equal(aun(v,u),a3) ),
inference(res,[status(thm),theory(equality)],[54,1689]),
[iquote('15:Res:54.2,1689.1')] ).
cnf(1698,plain,
( ~ ain(aun(u,v),a4)
| ~ ain(aun(u,v),apow(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(u,asing(a3))
| ain(aun(u,v),asing(a3)) ),
inference(res,[status(thm),theory(equality)],[1096,1462]),
[iquote('15:Res:1096.3,1462.2')] ).
cnf(1632,plain,
( ~ aal4(aun(u,v))
| ~ asubq(aun(u,v),a3)
| ain(asm(asm(apow(a2),a2),asing(a2)),v)
| ain(asm(asm(apow(a2),a2),asing(a2)),u) ),
inference(res,[status(thm),theory(equality)],[1540,53]),
[iquote('17:Res:1540.2,53.0')] ).
cnf(1654,plain,
( ~ aal4(aun(aun(a3,asing(a3)),a3))
| ~ asubq(aun(aun(a3,asing(a3)),a3),a3)
| ~ ain(asm(asm(apow(a2),a2),asing(a2)),apow(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[1540,1649]),
[iquote('17:Res:1540.2,1649.0')] ).
cnf(1657,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,a2)
| ~ asubq(u,a2)
| ain(aun(u,v),a2)
| equal(aun(u,v),a3)
| ain(a1,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,1545]),
[iquote('17:Res:54.2,1545.1')] ).
cnf(1699,plain,
( ~ ain(aun(u,v),a4)
| ~ asubq(v,asing(a3))
| ~ asubq(u,asing(a3))
| ain(aun(u,v),asing(a3))
| ain(aun(u,v),apow(a2)) ),
inference(res,[status(thm),theory(equality)],[1034,1462]),
[iquote('15:Res:1034.3,1462.2')] ).
cnf(1988,plain,
( ~ aal4(asing(asing(a2)))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(asing(asing(a2)),a3)
| ~ ain(aun(v,u),apow(a3)) ),
inference(res,[status(thm),theory(equality)],[1539,1911]),
[iquote('21:Res:1539.4,1911.0')] ).
cnf(2222,plain,
( ~ aal4(asing(apow(a2)))
| ~ aal4(u)
| ~ asubq(asing(apow(a2)),a3)
| ~ asubq(u,apow(a3))
| ain(asm(asm(apow(a2),a2),asing(a2)),u) ),
inference(res,[status(thm),theory(equality)],[1540,2220]),
[iquote('23:Res:1540.2,2220.1')] ).
cnf(1972,plain,
( ~ aal4(asm(u,v))
| ~ asubq(w,asing(a3))
| ~ asubq(x,asing(a3))
| ~ asubq(asm(u,v),a3)
| ~ ain(aun(x,w),v) ),
inference(res,[status(thm),theory(equality)],[1539,40]),
[iquote('17:Res:1539.4,40.1')] ).
cnf(2508,plain,
( ~ aal4(apow(a2))
| ~ aal4(u)
| ~ asubq(apow(a2),a3)
| ~ asubq(u,apow(a3))
| ain(asing(apow(a2)),a4)
| ain(asing(apow(a2)),u) ),
inference(res,[status(thm),theory(equality)],[2302,2238]),
[iquote('25:Res:2302.2,2238.1')] ).
cnf(2577,plain,
( ~ asubq(asing(asm(apow(a2),a2)),apow(a3))
| ~ asubq(u,a2)
| ain(u,a2)
| equal(u,a3)
| ain(u,aun(a3,asing(asm(apow(a2),a2)))) ),
inference(mrr,[status(thm)],[2576,1835]),
[iquote('23:MRR:2576.1,1835.0')] ).
cnf(2439,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ~ ain(asing(apow(a2)),asing(aun(a3,asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[2302,1115]),
[iquote('25:Res:2302.2,1115.0')] ).
cnf(1577,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ~ ain(asm(a3,a3),asing(aun(a3,asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[1537,1115]),
[iquote('17:Res:1537.2,1115.0')] ).
cnf(1960,plain,
( ~ aal4(asm(u,v))
| ~ asubq(w,asing(a3))
| ~ asubq(x,asing(a3))
| ~ asubq(asm(u,v),a3)
| ain(aun(x,w),u) ),
inference(res,[status(thm),theory(equality)],[1539,32]),
[iquote('17:Res:1539.4,32.0')] ).
cnf(2519,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,apow(a3))
| ~ asubq(u,apow(a3))
| ~ asubq(w,a2)
| ain(w,a2)
| equal(w,a3)
| ain(w,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,2510]),
[iquote('23:Res:54.2,2510.2')] ).
cnf(2423,plain,
( ~ aal4(asm(a4,asing(a2)))
| ~ asubq(asm(a4,asing(a2)),a3)
| ~ ain(asing(apow(a2)),apow(a3))
| ain(asing(apow(a2)),asing(a3)) ),
inference(res,[status(thm),theory(equality)],[2302,1008]),
[iquote('25:Res:2302.2,1008.0')] ).
cnf(2440,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ain(asing(apow(a2)),apow(aun(a3,asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[2302,1114]),
[iquote('25:Res:2302.2,1114.0')] ).
cnf(2574,plain,
( ~ asubq(asing(asm(apow(a2),a2)),apow(a3))
| ~ asubq(u,a2)
| ain(u,asing(asm(apow(a2),a2)))
| ain(u,a3) ),
inference(obv,[status(thm),theory(equality)],[2572]),
[iquote('23:Obv:2572.2')] ).
cnf(2571,plain,
( ~ asubq(asing(asm(apow(a2),a2)),apow(a3))
| ~ asubq(u,a2)
| ain(u,a3)
| ain(u,aun(a3,asing(asm(apow(a2),a2)))) ),
inference(mrr,[status(thm)],[2570,1835]),
[iquote('23:MRR:2570.1,1835.0')] ).
cnf(2275,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,apow(a3))
| ~ asubq(u,apow(a3))
| ~ asubq(w,a2)
| ain(w,a3)
| ain(w,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,2267]),
[iquote('23:Res:54.2,2267.2')] ).
cnf(1578,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ain(asm(a3,a3),apow(aun(a3,asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[1537,1114]),
[iquote('17:Res:1537.2,1114.0')] ).
cnf(2568,plain,
( ~ asubq(asing(asm(apow(a2),a2)),apow(a3))
| ~ asubq(u,a2)
| ain(u,a4)
| ain(u,asing(asm(apow(a2),a2))) ),
inference(mrr,[status(thm)],[2566,1236]),
[iquote('23:MRR:2566.4,1236.0')] ).
cnf(2565,plain,
( ~ asubq(asing(asm(apow(a2),a2)),apow(a3))
| ~ asubq(u,a2)
| ain(u,a4)
| ain(u,aun(a3,asing(asm(apow(a2),a2)))) ),
inference(mrr,[status(thm)],[2564,1835]),
[iquote('23:MRR:2564.1,1835.0')] ).
cnf(2424,plain,
( ~ aal4(asm(a4,asing(a2)))
| ~ asubq(asm(a4,asing(a2)),a3)
| ain(asing(apow(a2)),asing(a3))
| ain(asing(apow(a2)),apow(a2)) ),
inference(res,[status(thm),theory(equality)],[2302,1007]),
[iquote('25:Res:2302.2,1007.0')] ).
cnf(2263,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,apow(a3))
| ~ asubq(u,apow(a3))
| ~ asubq(w,a2)
| ain(w,a4)
| ain(w,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,2255]),
[iquote('23:Res:54.2,2255.2')] ).
cnf(2443,plain,
( ~ aal4(aun(aun(a3,asing(a3)),a3))
| ~ asubq(aun(aun(a3,asing(a3)),a3),a3)
| ~ ain(asing(apow(a2)),apow(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[2302,1649]),
[iquote('25:Res:2302.2,1649.0')] ).
cnf(1621,plain,
( ~ aal4(asm(a4,asing(a2)))
| ~ asubq(asm(a4,asing(a2)),a3)
| ~ ain(asm(asm(apow(a2),a2),asing(a2)),apow(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[1540,542]),
[iquote('17:Res:1540.2,542.1')] ).
cnf(1653,plain,
( ~ aal4(aun(aun(a3,asing(a3)),a3))
| ~ asubq(aun(aun(a3,asing(a3)),a3),a3)
| ~ ain(asm(a3,a3),apow(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[1537,1649]),
[iquote('17:Res:1537.2,1649.0')] ).
cnf(2557,plain,
( ~ asubq(asing(asm(apow(a2),a2)),apow(a3))
| ~ asubq(u,a3)
| ain(u,asing(asm(apow(a2),a2))) ),
inference(mrr,[status(thm)],[2555,1226]),
[iquote('23:MRR:2555.3,1226.1')] ).
cnf(1908,plain,
( ~ ain(u,aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))))
| ain(u,asing(asing(a2)))
| ain(u,apow(a3)) ),
inference(spr,[status(thm),theory(equality)],[1904,52]),
[iquote('21:SpR:1904.0,52.2')] ).
cnf(2554,plain,
( ~ asubq(asing(asm(apow(a2),a2)),apow(a3))
| ~ asubq(u,a3)
| ain(u,aun(a3,asing(asm(apow(a2),a2)))) ),
inference(mrr,[status(thm)],[2553,1835]),
[iquote('23:MRR:2553.1,1835.0')] ).
cnf(2248,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,apow(a3))
| ~ asubq(u,apow(a3))
| ~ asubq(w,a3)
| ain(w,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,2233]),
[iquote('23:Res:54.2,2233.2')] ).
cnf(1491,plain,
( ~ asubq(u,a2)
| ~ asubq(v,a2)
| ~ ain(aun(v,u),a4)
| ain(aun(v,u),a2)
| equal(aun(v,u),a3) ),
inference(res,[status(thm),theory(equality)],[54,1484]),
[iquote('15:Res:54.2,1484.0')] ).
cnf(1961,plain,
( ~ aal4(apow(u))
| ~ asubq(v,asing(a3))
| ~ asubq(w,asing(a3))
| ~ asubq(apow(u),a3)
| asubq(aun(w,v),u) ),
inference(res,[status(thm),theory(equality)],[1539,20]),
[iquote('17:Res:1539.4,20.0')] ).
cnf(1107,plain,
( ~ aal5(asm(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))),a3))
| ~ ain(a1,apow(asing(a2))) ),
inference(spl,[status(thm),theory(equality)],[162,87]),
[iquote('2:SpL:162.0,87.0')] ).
cnf(2008,plain,
( ~ aal4(apow(a2))
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(apow(a2),a3)
| ain(aun(v,u),a4) ),
inference(mrr,[status(thm)],[1970,1455]),
[iquote('17:MRR:1970.5,1455.2')] ).
cnf(2221,plain,
( ~ aal4(asing(apow(a2)))
| ~ aal4(u)
| ~ asubq(asing(apow(a2)),a3)
| ~ asubq(u,apow(a3))
| ain(asm(a3,a3),u) ),
inference(res,[status(thm),theory(equality)],[1537,2220]),
[iquote('23:Res:1537.2,2220.1')] ).
cnf(2441,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ~ ain(asing(apow(a2)),asing(a2)) ),
inference(res,[status(thm),theory(equality)],[2302,1015]),
[iquote('25:Res:2302.2,1015.1')] ).
cnf(2445,plain,
( ~ aal4(aun(aun(a3,asing(a3)),a3))
| ~ asubq(aun(aun(a3,asing(a3)),a3),a3)
| ~ ain(asing(apow(a2)),asing(a2)) ),
inference(res,[status(thm),theory(equality)],[2302,1335]),
[iquote('25:Res:2302.2,1335.1')] ).
cnf(1910,plain,
( ~ ain(u,apow(a3))
| ain(u,aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2)))))) ),
inference(spl,[status(thm),theory(equality)],[1904,32]),
[iquote('21:SpL:1904.0,32.0')] ).
cnf(1579,plain,
( ~ aal4(aun(asing(a3),asing(asing(a3))))
| ~ asubq(aun(asing(a3),asing(asing(a3))),a3)
| ~ ain(asm(a3,a3),asing(a2)) ),
inference(res,[status(thm),theory(equality)],[1537,1015]),
[iquote('17:Res:1537.2,1015.1')] ).
cnf(1582,plain,
( ~ aal4(aun(aun(a3,asing(a3)),a3))
| ~ asubq(aun(aun(a3,asing(a3)),a3),a3)
| ~ ain(asm(a3,a3),asing(a2)) ),
inference(res,[status(thm),theory(equality)],[1537,1335]),
[iquote('17:Res:1537.2,1335.1')] ).
cnf(1603,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,a2)
| ~ asubq(u,a2)
| ain(aun(u,v),a4)
| ain(a1,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,1547]),
[iquote('17:Res:54.2,1547.1')] ).
cnf(1598,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,a2)
| ~ asubq(u,a2)
| ain(aun(u,v),a3)
| ain(a1,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,1546]),
[iquote('17:Res:54.2,1546.1')] ).
cnf(1904,plain,
equal(asm(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))),asing(asing(a2))),apow(a3)),
inference(spt,[],[1882]),
[iquote('21:Spt:1882.3')] ).
cnf(1948,plain,
( ~ asubq(u,a2)
| ~ asubq(v,a2)
| ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ain(aun(v,u),a4) ),
inference(res,[status(thm),theory(equality)],[54,1532]),
[iquote('15:Res:54.2,1532.0')] ).
cnf(1700,plain,
( ~ ain(aun(u,v),a4)
| ~ ain(aun(u,v),asing(a2))
| ~ asubq(v,asing(a3))
| ~ asubq(u,asing(a3)) ),
inference(res,[status(thm),theory(equality)],[546,1462]),
[iquote('15:Res:546.2,1462.2')] ).
cnf(2427,plain,
( ~ aal4(asm(a4,a3))
| ~ asubq(asm(a4,a3),a3)
| equal(asing(apow(a2)),a2)
| ain(asing(apow(a2)),asm(a4,a2)) ),
inference(res,[status(thm),theory(equality)],[2302,563]),
[iquote('25:Res:2302.2,563.0')] ).
cnf(2444,plain,
( ~ aal4(aun(aun(a3,asing(a3)),a3))
| ~ asubq(aun(aun(a3,asing(a3)),a3),a3)
| ain(asing(apow(a2)),apow(a2)) ),
inference(res,[status(thm),theory(equality)],[2302,1648]),
[iquote('25:Res:2302.2,1648.0')] ).
cnf(1110,plain,
( ~ asubq(asing(apow(a2)),aun(a4,asing(apow(a2))))
| ~ asubq(a4,aun(a4,asing(apow(a2))))
| ~ asubq(asing(asing(a2)),aun(a4,asing(apow(a2)))) ),
inference(res,[status(thm),theory(equality)],[54,497]),
[iquote('0:Res:54.2,497.0')] ).
cnf(2522,plain,
( ~ aal4(a1)
| ~ asubq(u,a2)
| ain(u,a2)
| equal(u,a3)
| ain(u,a1) ),
inference(mrr,[status(thm)],[2518,1295]),
[iquote('23:MRR:2518.1,1295.0')] ).
cnf(2510,plain,
( ~ aal4(u)
| ~ asubq(v,a2)
| ~ asubq(u,apow(a3))
| ain(v,a2)
| equal(v,a3)
| ain(v,u) ),
inference(res,[status(thm),theory(equality)],[19,2237]),
[iquote('23:Res:19.1,2237.1')] ).
cnf(2237,plain,
( ~ aal4(u)
| ~ ain(v,apow(a2))
| ~ asubq(u,apow(a3))
| ain(v,a2)
| equal(v,a3)
| ain(v,u) ),
inference(res,[status(thm),theory(equality)],[609,2223]),
[iquote('23:Res:609.3,2223.1')] ).
cnf(2438,plain,
( ~ aal4(aun(u,v))
| ~ asubq(aun(u,v),a3)
| ain(asing(apow(a2)),v)
| ain(asing(apow(a2)),u) ),
inference(res,[status(thm),theory(equality)],[2302,53]),
[iquote('25:Res:2302.2,53.0')] ).
cnf(997,plain,
( ~ aal4(asm(a3,a3))
| ~ ain(u,asing(apow(a2)))
| aal3(a4)
| aal3(asing(apow(a2)))
| ain(u,asm(a3,a3)) ),
inference(res,[status(thm),theory(equality)],[195,81]),
[iquote('2:Res:195.0,81.2')] ).
cnf(2425,plain,
( ~ aal4(asm(a4,asing(a2)))
| ~ asubq(asm(a4,asing(a2)),a3)
| ~ ain(asing(apow(a2)),apow(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[2302,542]),
[iquote('25:Res:2302.2,542.1')] ).
cnf(2238,plain,
( ~ aal4(u)
| ~ ain(v,apow(a2))
| ~ asubq(u,apow(a3))
| ain(v,a4)
| ain(v,u) ),
inference(res,[status(thm),theory(equality)],[494,2223]),
[iquote('23:Res:494.1,2223.1')] ).
cnf(2239,plain,
( ~ aal4(u)
| ~ ain(v,apow(a2))
| ~ asubq(u,apow(a3))
| ain(v,a3)
| ain(v,u) ),
inference(res,[status(thm),theory(equality)],[469,2223]),
[iquote('23:Res:469.2,2223.1')] ).
cnf(2419,plain,
( ~ aal4(apow(a2))
| ~ asubq(apow(a2),a3)
| ain(asing(apow(a2)),a4)
| asubq(asing(apow(a2)),a3) ),
inference(res,[status(thm),theory(equality)],[2302,498]),
[iquote('25:Res:2302.2,498.0')] ).
cnf(497,plain,
( ~ asubq(aun(a4,asing(apow(a2))),aun(a4,asing(apow(a2))))
| ~ asubq(asing(asing(a2)),aun(a4,asing(apow(a2)))) ),
inference(res,[status(thm),theory(equality)],[54,69]),
[iquote('0:Res:54.2,69.0')] ).
cnf(2255,plain,
( ~ aal4(u)
| ~ asubq(v,a2)
| ~ asubq(u,apow(a3))
| ain(v,a4)
| ain(v,u) ),
inference(res,[status(thm),theory(equality)],[19,2238]),
[iquote('23:Res:19.1,2238.1')] ).
cnf(2267,plain,
( ~ aal4(u)
| ~ asubq(v,a2)
| ~ asubq(u,apow(a3))
| ain(v,a3)
| ain(v,u) ),
inference(res,[status(thm),theory(equality)],[19,2239]),
[iquote('23:Res:19.1,2239.1')] ).
cnf(2234,plain,
( ~ aal4(u)
| ~ ain(asing(a3),apow(a2))
| ~ asubq(u,apow(a3))
| ain(asing(a3),u) ),
inference(res,[status(thm),theory(equality)],[1143,2223]),
[iquote('23:Res:1143.1,2223.1')] ).
cnf(2437,plain,
( ~ aal4(asing(asing(a2)))
| ~ asubq(asing(asing(a2)),a3)
| ~ ain(asing(apow(a2)),apow(a3)) ),
inference(res,[status(thm),theory(equality)],[2302,1911]),
[iquote('25:Res:2302.2,1911.0')] ).
cnf(87,axiom,
( ~ aal5(asm(aint(aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2)))),aun(asing(asing(a2)),aun(a4,asing(apow(a2))))),asing(u)))
| ~ ain(u,apow(asing(a2))) ),
file('SYO844+1.p',unknown),
[] ).
cnf(2479,plain,
( ~ asubq(asing(asm(apow(a2),a2)),apow(a3))
| ain(a2,asing(asm(apow(a2),a2))) ),
inference(mrr,[status(thm)],[2478,557]),
[iquote('23:MRR:2478.2,557.0')] ).
cnf(2289,plain,
( ~ asubq(asing(asm(apow(a2),a2)),apow(a3))
| ain(a2,aun(a3,asing(asm(apow(a2),a2)))) ),
inference(mrr,[status(thm)],[2288,1835]),
[iquote('23:MRR:2288.1,1835.0')] ).
cnf(2421,plain,
( ~ aal4(asm(u,v))
| ~ asubq(asm(u,v),a3)
| ~ ain(asing(apow(a2)),v) ),
inference(res,[status(thm),theory(equality)],[2302,40]),
[iquote('25:Res:2302.2,40.1')] ).
cnf(2220,plain,
( ~ aal4(u)
| ~ ain(v,asing(apow(a2)))
| ~ asubq(u,apow(a3))
| ain(v,u) ),
inference(spt,[],[1851]),
[iquote('23:Spt:1851.0,1851.1,1851.2,1851.5')] ).
cnf(219,plain,
( ~ ain(u,asing(apow(a2)))
| ~ ain(u,aun(asing(a2),aun(apow(asing(a2)),asing(apow(a2)))))
| ~ ain(u,aun(asing(a3),aun(asing(asing(a2)),a4))) ),
inference(rew,[status(thm),theory(equality)],[162,84]),
[iquote('2:Rew:162.0,84.2')] ).
cnf(2252,plain,
( ~ aal4(u)
| ~ asubq(asing(a3),a2)
| ~ asubq(u,apow(a3))
| ain(asing(a3),u) ),
inference(res,[status(thm),theory(equality)],[19,2234]),
[iquote('23:Res:19.1,2234.1')] ).
cnf(485,plain,
( ain(a1,aun(apow(asing(a2)),asing(apow(a2))))
| ain(a1,asm(apow(a2),apow(asing(a2)))) ),
inference(res,[status(thm),theory(equality)],[68,53]),
[iquote('0:Res:68.0,53.0')] ).
cnf(2410,plain,
( ~ aal4(asm(u,v))
| ~ asubq(asm(u,v),a3)
| ain(asing(apow(a2)),u) ),
inference(res,[status(thm),theory(equality)],[2302,32]),
[iquote('25:Res:2302.2,32.0')] ).
cnf(74,axiom,
aex4(aint(aun(apow(a2),asing(asing(a2))),aun(asing(asing(a2)),aun(a4,asing(apow(a2)))))),
file('SYO844+1.p',unknown),
[] ).
cnf(1268,plain,
( ~ ain(u,apow(asing(a2)))
| ain(u,asing(asing(a2)))
| ain(u,asing(apow(a2))) ),
inference(mrr,[status(thm)],[635,1267]),
[iquote('14:MRR:635.3,1267.0')] ).
cnf(69,axiom,
~ asubq(aun(asing(asing(a2)),aun(a4,asing(apow(a2)))),aun(a4,asing(apow(a2)))),
file('SYO844+1.p',unknown),
[] ).
cnf(68,axiom,
ain(a1,aun(asm(apow(a2),apow(asing(a2))),aun(apow(asing(a2)),asing(apow(a2))))),
file('SYO844+1.p',unknown),
[] ).
cnf(2411,plain,
( ~ aal4(apow(u))
| ~ asubq(apow(u),a3)
| asubq(asing(apow(a2)),u) ),
inference(res,[status(thm),theory(equality)],[2302,20]),
[iquote('25:Res:2302.2,20.0')] ).
cnf(1836,plain,
( ~ ain(u,apow(asing(a2)))
| ain(u,asing(asing(a2)))
| ain(u,apow(a3)) ),
inference(rew,[status(thm),theory(equality)],[1834,77]),
[iquote('19:Rew:1834.0,77.2')] ).
cnf(1839,plain,
( ~ asubq(asing(apow(a2)),u)
| ~ asubq(a3,u)
| asubq(apow(a3),u) ),
inference(spr,[status(thm),theory(equality)],[1834,54]),
[iquote('19:SpR:1834.0,54.2')] ).
cnf(1866,plain,
( ~ aal4(asing(apow(a2)))
| ~ adisjoint(a3,asing(apow(a2)))
| aal6(apow(a3)) ),
inference(mrr,[status(thm)],[1841,1864]),
[iquote('20:MRR:1841.1,1864.0')] ).
cnf(2302,plain,
( ~ aal4(u)
| ~ asubq(u,a3)
| ain(asing(apow(a2)),u) ),
inference(res,[status(thm),theory(equality)],[2290,1536]),
[iquote('25:Res:2290.0,1536.1')] ).
cnf(1857,plain,
( ~ ain(u,apow(a3))
| ain(u,asing(apow(a2))) ),
inference(mrr,[status(thm)],[1850,1213]),
[iquote('19:MRR:1850.2,1213.1')] ).
cnf(1190,plain,
ain(a1,aun(a3,aun(asing(asing(a2)),asing(apow(a2))))),
inference(rew,[status(thm),theory(equality)],[1172,208]),
[iquote('14:Rew:1172.0,208.0')] ).
cnf(180,plain,
aex3(aun(asing(asing(a3)),aun(a1,asing(apow(a2))))),
inference(rew,[status(thm),theory(equality)],[162,50]),
[iquote('2:Rew:162.0,50.0')] ).
cnf(2316,plain,
( ~ ain(apow(a3),a4)
| ain(apow(a3),asing(a2)) ),
inference(res,[status(thm),theory(equality)],[2311,548]),
[iquote('26:Res:2311.0,548.0')] ).
cnf(38,axiom,
aex4(asm(aun(a4,asing(apow(a2))),asing(a3))),
file('SYO844+1.p',unknown),
[] ).
cnf(1834,plain,
equal(aun(a3,asing(apow(a2))),apow(a3)),
inference(spt,[],[1156]),
[iquote('19:Spt:1156.5')] ).
cnf(195,plain,
asubq(asm(a3,a3),aun(a4,asing(apow(a2)))),
inference(rew,[status(thm),theory(equality)],[162,45]),
[iquote('2:Rew:162.0,45.0')] ).
cnf(2377,plain,
~ equal(asing(apow(a2)),a3),
inference(spt,[],[2362,2301,2321]),
[iquote('27:Spt:2362.0,2301.1,2321.0')] ).
cnf(10,axiom,
aex3(aun(a2,asing(apow(a2)))),
file('SYO844+1.p',unknown),
[] ).
cnf(989,plain,
ain(a1,asing(apow(a2))),
inference(spt,[],[983]),
[iquote('9:Spt:983.0')] ).
cnf(2290,plain,
ain(asing(apow(a2)),a3),
inference(spt,[],[1867]),
[iquote('25:Spt:1867.3')] ).
cnf(2378,plain,
ain(asing(apow(a2)),a2),
inference(spt,[],[2362,2301]),
[iquote('27:Spt:2362.0,2301.0')] ).
cnf(2314,plain,
~ ain(apow(a3),apow(a2)),
inference(res,[status(thm),theory(equality)],[2311,1382]),
[iquote('26:Res:2311.0,1382.0')] ).
cnf(2315,plain,
~ ain(apow(a3),a3),
inference(res,[status(thm),theory(equality)],[2311,1277]),
[iquote('26:Res:2311.0,1277.0')] ).
cnf(2313,plain,
~ asubq(apow(a3),a2),
inference(res,[status(thm),theory(equality)],[2311,1669]),
[iquote('26:Res:2311.0,1669.1')] ).
cnf(2312,plain,
~ asubq(a3,asing(a3)),
inference(mrr,[status(thm)],[2295,2311]),
[iquote('26:MRR:2295.1,2311.0')] ).
cnf(2311,plain,
asubq(apow(a3),asing(a2)),
inference(spt,[],[1869]),
[iquote('26:Spt:1869.4')] ).
cnf(2243,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,apow(a3))
| ~ asubq(u,apow(a3))
| ain(a2,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,2240]),
[iquote('23:Res:54.2,2240.1')] ).
cnf(2286,plain,
( ~ asubq(asing(asm(apow(a2),a2)),apow(a3))
| ain(a1,aun(a3,asing(asm(apow(a2),a2)))) ),
inference(mrr,[status(thm)],[2285,1835]),
[iquote('23:MRR:2285.1,1835.0')] ).
cnf(2227,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,apow(a3))
| ~ asubq(u,apow(a3))
| ain(a1,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,2224]),
[iquote('23:Res:54.2,2224.1')] ).
cnf(2279,plain,
( ~ aal4(a1)
| ~ asubq(u,a2)
| ain(u,a3)
| ain(u,a1) ),
inference(mrr,[status(thm)],[2274,1295]),
[iquote('23:MRR:2274.1,1295.0')] ).
cnf(2266,plain,
( ~ aal4(a1)
| ~ asubq(u,a2)
| ain(u,a4)
| ain(u,a1) ),
inference(mrr,[status(thm)],[2262,1295]),
[iquote('23:MRR:2262.1,1295.0')] ).
cnf(2251,plain,
( ~ aal4(a1)
| ~ asubq(u,a3)
| ain(u,a1) ),
inference(mrr,[status(thm)],[2247,1295]),
[iquote('23:MRR:2247.1,1295.0')] ).
cnf(2233,plain,
( ~ aal4(u)
| ~ asubq(v,a3)
| ~ asubq(u,apow(a3))
| ain(v,u) ),
inference(res,[status(thm),theory(equality)],[19,2223]),
[iquote('23:Res:19.1,2223.1')] ).
cnf(2246,plain,
~ aal4(a3),
inference(mrr,[status(thm)],[2245,557]),
[iquote('23:MRR:2245.1,557.0')] ).
cnf(2240,plain,
( ~ aal4(u)
| ~ asubq(u,apow(a3))
| ain(a2,u) ),
inference(res,[status(thm),theory(equality)],[1295,2223]),
[iquote('23:Res:1295.0,2223.1')] ).
cnf(2223,plain,
( ~ aal4(u)
| ~ ain(v,apow(a3))
| ~ asubq(u,apow(a3))
| ain(v,u) ),
inference(res,[status(thm),theory(equality)],[1857,2220]),
[iquote('23:Res:1857.1,2220.1')] ).
cnf(2232,plain,
aal3(a3),
inference(spt,[],[1862]),
[iquote('24:Spt:1862.2')] ).
cnf(2231,plain,
( ~ aal4(a1)
| ain(a1,a1) ),
inference(mrr,[status(thm)],[2226,1295]),
[iquote('23:MRR:2226.1,1295.0')] ).
cnf(2230,plain,
~ aal4(apow(a3)),
inference(mrr,[status(thm)],[2228,165]),
[iquote('23:MRR:2228.1,165.0')] ).
cnf(2224,plain,
( ~ aal4(u)
| ~ asubq(u,apow(a3))
| ain(a1,u) ),
inference(res,[status(thm),theory(equality)],[989,2220]),
[iquote('23:Res:989.0,2220.1')] ).
cnf(1134,plain,
( ~ ain(u,apow(aun(a3,asing(a3))))
| ain(u,asing(aun(a3,asing(a3))))
| ain(u,asing(a2))
| ain(u,aun(asing(a3),asing(asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[52,1013]),
[iquote('7:Res:52.2,1013.0')] ).
cnf(1390,plain,
( ~ ain(u,a4)
| ~ ain(u,apow(a3))
| ~ ain(u,apow(a2))
| ain(u,asing(a3)) ),
inference(res,[status(thm),theory(equality)],[1096,1382]),
[iquote('15:Res:1096.3,1382.0')] ).
cnf(2082,plain,
( ~ asubq(asing(asing(a3)),apow(a3))
| ~ asubq(asing(a3),apow(a3))
| ~ ain(a2,aun(asing(a3),asing(asing(a3)))) ),
inference(mrr,[status(thm)],[1158,2080]),
[iquote('22:MRR:1158.3,2080.0')] ).
cnf(1023,plain,
( ~ ain(u,a4)
| ~ ain(u,apow(a3))
| ain(u,apow(asing(a2)))
| ain(u,asing(a3)) ),
inference(res,[status(thm),theory(equality)],[540,1008]),
[iquote('7:Res:540.2,1008.0')] ).
cnf(1338,plain,
( ~ ain(u,apow(a2))
| ain(u,asing(a2))
| ain(u,a3)
| ain(u,aun(a3,asing(a3))) ),
inference(rew,[status(thm),theory(equality)],[1323,1149]),
[iquote('15:Rew:1323.0,1149.2')] ).
cnf(1673,plain,
( ~ ain(u,a4)
| ~ ain(u,apow(a3))
| ~ asubq(u,a2)
| ain(u,asing(a3)) ),
inference(res,[status(thm),theory(equality)],[1096,1669]),
[iquote('15:Res:1096.3,1669.1')] ).
cnf(1096,plain,
( ~ ain(u,a4)
| ~ ain(u,apow(a3))
| ain(u,asing(a3))
| asubq(u,asing(a2)) ),
inference(res,[status(thm),theory(equality)],[1023,20]),
[iquote('7:Res:1023.2,20.0')] ).
cnf(1013,plain,
( ~ ain(u,asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3)))))
| ain(u,asing(a2))
| ain(u,aun(asing(a3),asing(asing(a3)))) ),
inference(spr,[status(thm),theory(equality)],[570,52]),
[iquote('7:SpR:570.0,52.2')] ).
cnf(1021,plain,
( ~ ain(u,a4)
| ~ ain(u,apow(a3))
| ain(u,asing(a2))
| ain(u,asing(a3)) ),
inference(res,[status(thm),theory(equality)],[52,1008]),
[iquote('7:Res:52.2,1008.0')] ).
cnf(1333,plain,
( ~ ain(u,apow(a2))
| ain(u,asing(a2))
| ain(u,aun(aun(a3,asing(a3)),a3)) ),
inference(rew,[status(thm),theory(equality)],[1323,1146]),
[iquote('15:Rew:1323.0,1146.2')] ).
cnf(1115,plain,
( ~ ain(u,aun(asing(a3),asing(asing(a3))))
| ~ ain(u,asing(aun(a3,asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[1014,40]),
[iquote('7:Res:1014.1,40.1')] ).
cnf(1114,plain,
( ~ ain(u,aun(asing(a3),asing(asing(a3))))
| ain(u,apow(aun(a3,asing(a3)))) ),
inference(res,[status(thm),theory(equality)],[1014,32]),
[iquote('7:Res:1014.1,32.0')] ).
cnf(1014,plain,
( ~ ain(u,aun(asing(a3),asing(asing(a3))))
| ain(u,asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3))))) ),
inference(spl,[status(thm),theory(equality)],[570,32]),
[iquote('7:SpL:570.0,32.0')] ).
cnf(1423,plain,
( ~ ain(u,a4)
| ~ ain(u,apow(a2))
| ain(u,a2)
| equal(u,a3) ),
inference(obv,[status(thm),theory(equality)],[1422]),
[iquote('15:Obv:1422.0')] ).
cnf(609,plain,
( ~ ain(u,apow(a2))
| ain(u,a2)
| equal(u,a3)
| ain(u,apow(a3)) ),
inference(mrr,[status(thm)],[608,494]),
[iquote('7:MRR:608.0,494.2')] ).
cnf(460,plain,
( ~ ain(u,apow(a2))
| ain(u,asing(a2))
| ain(u,a2)
| equal(u,a3) ),
inference(res,[status(thm),theory(equality)],[52,231]),
[iquote('2:Res:52.2,231.0')] ).
cnf(639,plain,
( ~ ain(u,apow(a2))
| ain(u,a2)
| equal(u,a3)
| asubq(u,a3) ),
inference(res,[status(thm),theory(equality)],[609,20]),
[iquote('7:Res:609.3,20.0')] ).
cnf(570,plain,
equal(asm(asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3)))),asing(a2)),aun(asing(a3),asing(asing(a3)))),
inference(rew,[status(thm),theory(equality)],[535,224]),
[iquote('7:Rew:535.0,224.0')] ).
cnf(1383,plain,
( ~ ain(u,a4)
| ~ ain(u,asing(a2))
| ~ ain(u,apow(a2)) ),
inference(mrr,[status(thm)],[1380,1264]),
[iquote('15:MRR:1380.3,1264.0')] ).
cnf(545,plain,
( ~ ain(u,apow(a2))
| ~ ain(u,asing(a2))
| ain(u,apow(a3)) ),
inference(rew,[status(thm),theory(equality)],[535,495]),
[iquote('7:Rew:535.0,495.1')] ).
cnf(1015,plain,
( ~ ain(u,asing(a2))
| ~ ain(u,aun(asing(a3),asing(asing(a3)))) ),
inference(spl,[status(thm),theory(equality)],[570,40]),
[iquote('7:SpL:570.0,40.1')] ).
cnf(118,plain,
( ain(a3,a4)
| ain(a3,asing(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[14,53]),
[iquote('0:Res:14.0,53.0')] ).
cnf(2080,plain,
~ equal(aun(asing(a3),asing(asing(a3))),apow(a3)),
inference(spt,[],[2079,1678,2021]),
[iquote('22:Spt:2079.0,1678.4,2021.0')] ).
cnf(1929,plain,
( ~ ain(a3,apow(a3))
| ain(a3,a4) ),
inference(res,[status(thm),theory(equality)],[118,1911]),
[iquote('21:Res:118.1,1911.0')] ).
cnf(199,plain,
ain(a3,aun(asing(a3),asing(asing(a3)))),
inference(rew,[status(thm),theory(equality)],[162,46]),
[iquote('2:Rew:162.0,46.0')] ).
cnf(2081,plain,
( ~ ain(a2,apow(aun(a3,asing(a3))))
| ~ asubq(asing(asing(a3)),apow(a3))
| ~ asubq(asing(a3),apow(a3))
| ain(a2,asing(aun(a3,asing(a3)))) ),
inference(spt,[],[2079,1678]),
[iquote('22:Spt:2079.0,1678.0,1678.1,1678.2,1678.3')] ).
cnf(1567,plain,
( ~ aal4(asm(a4,a3))
| ~ asubq(asm(a4,a3),a3)
| equal(asm(a3,a3),a2)
| ain(asm(a3,a3),asm(a4,a2)) ),
inference(res,[status(thm),theory(equality)],[1537,563]),
[iquote('17:Res:1537.2,563.0')] ).
cnf(1539,plain,
( ~ aal4(u)
| ~ asubq(v,asing(a3))
| ~ asubq(w,asing(a3))
| ~ asubq(u,a3)
| ain(aun(w,v),u) ),
inference(res,[status(thm),theory(equality)],[1377,1536]),
[iquote('17:Res:1377.2,1536.1')] ).
cnf(1926,plain,
( ~ aal4(asing(asing(a2)))
| ~ asubq(asing(asing(a2)),a3)
| ~ ain(asm(asm(apow(a2),a2),asing(a2)),apow(a3)) ),
inference(res,[status(thm),theory(equality)],[1540,1911]),
[iquote('21:Res:1540.2,1911.0')] ).
cnf(1894,plain,
( ~ ain(a3,aun(aun(a3,asing(a3)),a3))
| ~ asubq(asm(apow(a2),apow(asing(a2))),apow(a3))
| equal(aun(asm(apow(a2),apow(asing(a2))),a3),apow(a3)) ),
inference(mrr,[status(thm)],[1893,536]),
[iquote('19:MRR:1893.0,536.0')] ).
cnf(1576,plain,
( ~ aal4(aun(u,v))
| ~ asubq(aun(u,v),a3)
| ain(asm(a3,a3),v)
| ain(asm(a3,a3),u) ),
inference(res,[status(thm),theory(equality)],[1537,53]),
[iquote('17:Res:1537.2,53.0')] ).
cnf(1532,plain,
( ~ asubq(aun(u,v),a2)
| ~ asubq(v,asing(a3))
| ~ asubq(u,asing(a3))
| ain(aun(u,v),a4) ),
inference(res,[status(thm),theory(equality)],[506,1455]),
[iquote('15:Res:506.2,1455.2')] ).
cnf(1167,plain,
( ~ ain(u,apow(aun(a3,asing(a3))))
| ain(u,asing(aun(a3,asing(a3))))
| ain(u,asing(a2))
| ain(u,asing(asing(a3)))
| ain(u,asing(a3)) ),
inference(res,[status(thm),theory(equality)],[1134,53]),
[iquote('7:Res:1134.3,53.0')] ).
cnf(1935,plain,
( ~ asubq(asing(a2),a3)
| ain(asing(a2),a4) ),
inference(res,[status(thm),theory(equality)],[19,1924]),
[iquote('21:Res:19.1,1924.0')] ).
cnf(1924,plain,
( ~ ain(asing(a2),apow(a3))
| ain(asing(a2),a4) ),
inference(res,[status(thm),theory(equality)],[143,1911]),
[iquote('21:Res:143.1,1911.0')] ).
cnf(1911,plain,
( ~ ain(u,asing(asing(a2)))
| ~ ain(u,apow(a3)) ),
inference(spl,[status(thm),theory(equality)],[1904,40]),
[iquote('21:SpL:1904.0,40.1')] ).
cnf(1913,plain,
( ~ asubq(asing(a2),asing(a2))
| ~ aal5(apow(a3)) ),
inference(res,[status(thm),theory(equality)],[19,1909]),
[iquote('21:Res:19.1,1909.1')] ).
cnf(1918,plain,
( ~ ain(asing(a2),a4)
| ~ aal5(apow(a3)) ),
inference(mrr,[status(thm)],[1917,484]),
[iquote('21:MRR:1917.1,484.0')] ).
cnf(1909,plain,
( ~ aal5(apow(a3))
| ~ ain(asing(a2),apow(asing(a2))) ),
inference(spl,[status(thm),theory(equality)],[1904,87]),
[iquote('21:SpL:1904.0,87.0')] ).
cnf(1906,plain,
asubq(apow(a3),apow(a3)),
inference(rew,[status(thm),theory(equality)],[1904,1837]),
[iquote('21:Rew:1904.0,1837.0')] ).
cnf(1617,plain,
( ~ aal4(asm(u,v))
| ~ asubq(asm(u,v),a3)
| ~ ain(asm(asm(apow(a2),a2),asing(a2)),v) ),
inference(res,[status(thm),theory(equality)],[1540,40]),
[iquote('17:Res:1540.2,40.1')] ).
cnf(1864,plain,
aal2(a3),
inference(spt,[],[1846]),
[iquote('20:Spt:1846.2')] ).
cnf(1835,plain,
asubq(a3,apow(a3)),
inference(rew,[status(thm),theory(equality)],[1834,16]),
[iquote('19:Rew:1834.0,16.0')] ).
cnf(1565,plain,
( ~ aal4(asm(a4,asing(a2)))
| ~ asubq(asm(a4,asing(a2)),a3)
| ~ ain(asm(a3,a3),apow(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[1537,542]),
[iquote('17:Res:1537.2,542.1')] ).
cnf(1445,plain,
( ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ain(aun(v,u),a2)
| equal(aun(v,u),a3) ),
inference(res,[status(thm),theory(equality)],[1377,1237]),
[iquote('15:Res:1377.2,1237.0')] ).
cnf(1607,plain,
( ~ aal4(asm(u,v))
| ~ asubq(asm(u,v),a3)
| ain(asm(asm(apow(a2),a2),asing(a2)),u) ),
inference(res,[status(thm),theory(equality)],[1540,32]),
[iquote('17:Res:1540.2,32.0')] ).
cnf(1542,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,a3)
| ~ asubq(u,a3)
| ain(a1,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,1538]),
[iquote('17:Res:54.2,1538.1')] ).
cnf(1426,plain,
( ~ ain(u,a4)
| ~ ain(u,apow(a2))
| ain(u,a3)
| equal(u,a2)
| equal(u,a3) ),
inference(obv,[status(thm),theory(equality)],[1420]),
[iquote('15:Obv:1420.0')] ).
cnf(1608,plain,
( ~ aal4(apow(u))
| ~ asubq(apow(u),a3)
| asubq(asm(asm(apow(a2),a2),asing(a2)),u) ),
inference(res,[status(thm),theory(equality)],[1540,20]),
[iquote('17:Res:1540.2,20.0')] ).
cnf(1164,plain,
( ~ asubq(asing(asm(apow(a2),a2)),aun(u,v))
| ~ asubq(a3,aun(u,v))
| ~ ain(w,v)
| aal3(u)
| aal3(v)
| ain(w,aun(a3,asing(asm(apow(a2),a2)))) ),
inference(sor,[status(thm)],[996,29]),
[iquote('0:SoR:996.0,29.0')] ).
cnf(1540,plain,
( ~ aal4(u)
| ~ asubq(u,a3)
| ain(asm(asm(apow(a2),a2),asing(a2)),u) ),
inference(res,[status(thm),theory(equality)],[1378,1536]),
[iquote('17:Res:1378.0,1536.1')] ).
cnf(1463,plain,
~ asubq(asm(asm(apow(a2),a2),asing(a2)),asing(a2)),
inference(res,[status(thm),theory(equality)],[179,1451]),
[iquote('15:Res:179.0,1451.0')] ).
cnf(1754,plain,
~ equal(asm(asm(apow(a2),a2),asing(a2)),a3),
inference(spt,[],[1740,1385,1711]),
[iquote('18:Spt:1740.0,1385.1,1711.0')] ).
cnf(1456,plain,
~ asubq(asm(asm(apow(a2),a2),asing(a2)),a3),
inference(res,[status(thm),theory(equality)],[179,1450]),
[iquote('15:Res:179.0,1450.0')] ).
cnf(179,plain,
asubq(asm(asm(apow(a2),a2),asing(a2)),asing(a3)),
inference(rew,[status(thm),theory(equality)],[162,49]),
[iquote('2:Rew:162.0,49.0')] ).
cnf(1378,plain,
ain(asm(asm(apow(a2),a2),asing(a2)),a3),
inference(res,[status(thm),theory(equality)],[179,1364]),
[iquote('15:Res:179.0,1364.0')] ).
cnf(1755,plain,
ain(asm(asm(apow(a2),a2),asing(a2)),a2),
inference(spt,[],[1740,1385]),
[iquote('18:Spt:1740.0,1385.0')] ).
cnf(1689,plain,
( ~ ain(u,a4)
| ~ asubq(u,a2)
| ain(u,a3)
| equal(u,a2)
| equal(u,a3) ),
inference(obv,[status(thm),theory(equality)],[1685]),
[iquote('15:Obv:1685.0')] ).
cnf(1561,plain,
( ~ aal4(asm(u,v))
| ~ asubq(asm(u,v),a3)
| ~ ain(asm(a3,a3),v) ),
inference(res,[status(thm),theory(equality)],[1537,40]),
[iquote('17:Res:1537.2,40.1')] ).
cnf(1157,plain,
( ~ asubq(asing(a3),apow(a3))
| ~ asubq(apow(asing(a2)),apow(a3))
| ~ ain(a2,aun(apow(asing(a2)),asing(a3)))
| equal(aun(apow(asing(a2)),asing(a3)),apow(a3)) ),
inference(res,[status(thm),theory(equality)],[23,615]),
[iquote('7:Res:23.0,615.3')] ).
cnf(1462,plain,
( ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(v,u),asing(a2)) ),
inference(res,[status(thm),theory(equality)],[54,1451]),
[iquote('15:Res:54.2,1451.0')] ).
cnf(1672,plain,
( ~ ain(u,a4)
| ~ asubq(u,a2)
| ain(u,asing(a3))
| ain(u,a3) ),
inference(res,[status(thm),theory(equality)],[1309,1669]),
[iquote('15:Res:1309.3,1669.1')] ).
cnf(1675,plain,
( ~ ain(u,a4)
| ~ ain(u,asing(a2))
| ~ asubq(u,a2) ),
inference(res,[status(thm),theory(equality)],[546,1669]),
[iquote('15:Res:546.2,1669.1')] ).
cnf(1669,plain,
( ~ asubq(u,a2)
| ~ asubq(u,asing(a2)) ),
inference(con,[status(thm)],[1666]),
[iquote('15:Con:1666.1')] ).
cnf(1662,plain,
( ~ asubq(aun(u,v),a2)
| ~ asubq(v,asing(a2))
| ~ asubq(u,asing(a2)) ),
inference(res,[status(thm),theory(equality)],[19,1388]),
[iquote('15:Res:19.1,1388.2')] ).
cnf(1388,plain,
( ~ asubq(u,asing(a2))
| ~ asubq(v,asing(a2))
| ~ ain(aun(v,u),apow(a2)) ),
inference(res,[status(thm),theory(equality)],[54,1382]),
[iquote('15:Res:54.2,1382.0')] ).
cnf(1549,plain,
( ~ aal4(asm(u,v))
| ~ asubq(asm(u,v),a3)
| ain(asm(a3,a3),u) ),
inference(res,[status(thm),theory(equality)],[1537,32]),
[iquote('17:Res:1537.2,32.0')] ).
cnf(1545,plain,
( ~ aal4(u)
| ~ asubq(u,a2)
| ain(u,a2)
| equal(u,a3)
| ain(a1,u) ),
inference(res,[status(thm),theory(equality)],[953,1538]),
[iquote('17:Res:953.3,1538.1')] ).
cnf(1649,plain,
( ~ ain(u,aun(aun(a3,asing(a3)),a3))
| ~ ain(u,apow(asing(a2))) ),
inference(mrr,[status(thm)],[1647,1267]),
[iquote('15:MRR:1647.2,1267.0')] ).
cnf(1648,plain,
( ~ ain(u,aun(aun(a3,asing(a3)),a3))
| ain(u,apow(a2)) ),
inference(mrr,[status(thm)],[1646,101]),
[iquote('15:MRR:1646.1,101.0')] ).
cnf(1360,plain,
( ~ ain(u,aun(aun(a3,asing(a3)),a3))
| ain(u,a3)
| ain(u,asm(apow(a2),apow(asing(a2)))) ),
inference(rew,[status(thm),theory(equality)],[1323,1332]),
[iquote('15:Rew:1323.0,1332.1')] ).
cnf(1550,plain,
( ~ aal4(apow(u))
| ~ asubq(apow(u),a3)
| asubq(asm(a3,a3),u) ),
inference(res,[status(thm),theory(equality)],[1537,20]),
[iquote('17:Res:1537.2,20.0')] ).
cnf(1547,plain,
( ~ aal4(u)
| ~ asubq(u,a2)
| ain(u,a4)
| ain(a1,u) ),
inference(res,[status(thm),theory(equality)],[506,1538]),
[iquote('17:Res:506.2,1538.1')] ).
cnf(1546,plain,
( ~ aal4(u)
| ~ asubq(u,a2)
| ain(u,a3)
| ain(a1,u) ),
inference(res,[status(thm),theory(equality)],[475,1538]),
[iquote('17:Res:475.2,1538.1')] ).
cnf(1544,plain,
( ~ aal4(asing(a3))
| ~ asubq(asing(a3),a2)
| ain(a1,asing(a3)) ),
inference(res,[status(thm),theory(equality)],[1147,1538]),
[iquote('17:Res:1147.1,1538.1')] ).
cnf(1590,plain,
( ~ aal4(asing(asing(a3)))
| ~ asubq(asing(asing(a3)),a3) ),
inference(mrr,[status(thm)],[1575,1049]),
[iquote('17:MRR:1575.2,1049.0')] ).
cnf(1589,plain,
( ~ aal4(apow(asing(a2)))
| ~ asubq(apow(asing(a2)),a3) ),
inference(mrr,[status(thm)],[1554,1050]),
[iquote('17:MRR:1554.2,1050.0')] ).
cnf(1588,plain,
( ~ aal4(asing(a2))
| ~ asubq(asing(a2),a3) ),
inference(mrr,[status(thm)],[1571,1050]),
[iquote('17:MRR:1571.2,1050.0')] ).
cnf(1552,plain,
( ~ aal4(asing(a3))
| ~ asubq(asing(a3),a3) ),
inference(res,[status(thm),theory(equality)],[1537,194]),
[iquote('17:Res:1537.2,194.0')] ).
cnf(1537,plain,
( ~ aal4(u)
| ~ asubq(u,a3)
| ain(asm(a3,a3),u) ),
inference(res,[status(thm),theory(equality)],[1050,1536]),
[iquote('17:Res:1050.0,1536.1')] ).
cnf(1538,plain,
( ~ aal4(u)
| ~ asubq(u,a3)
| ain(a1,u) ),
inference(res,[status(thm),theory(equality)],[411,1536]),
[iquote('17:Res:411.0,1536.1')] ).
cnf(1536,plain,
( ~ aal4(u)
| ~ ain(v,a3)
| ~ asubq(u,a3)
| ain(v,u) ),
inference(spt,[],[1520]),
[iquote('17:Spt:1520.0,1520.1,1520.2,1520.4')] ).
cnf(1455,plain,
( ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ~ asubq(aun(v,u),a3) ),
inference(res,[status(thm),theory(equality)],[54,1450]),
[iquote('15:Res:54.2,1450.0')] ).
cnf(1340,plain,
( ~ ain(u,apow(a2))
| ain(u,a3)
| ain(u,asm(apow(a2),apow(asing(a2)))) ),
inference(rew,[status(thm),theory(equality)],[1323,990]),
[iquote('15:Rew:1323.0,990.1')] ).
cnf(1496,plain,
~ aal5(a3),
inference(rew,[status(thm),theory(equality)],[1495,1341]),
[iquote('16:Rew:1495.0,1341.0')] ).
cnf(1495,plain,
equal(aun(a3,a3),a3),
inference(spt,[],[1358]),
[iquote('16:Spt:1358.2')] ).
cnf(1484,plain,
( ~ asubq(u,a2)
| ~ ain(u,a4)
| ain(u,a2)
| equal(u,a3) ),
inference(res,[status(thm),theory(equality)],[19,1423]),
[iquote('15:Res:19.1,1423.1')] ).
cnf(1361,plain,
( ~ ain(u,aun(asm(apow(a2),apow(asing(a2))),a3))
| ain(u,asing(a2))
| ain(u,aun(aun(a3,asing(a3)),a3)) ),
inference(rew,[status(thm),theory(equality)],[1323,1326]),
[iquote('15:Rew:1323.0,1326.2')] ).
cnf(1472,plain,
( ain(a1,asing(a3))
| ain(a1,apow(a2)) ),
inference(mrr,[status(thm)],[1469,502]),
[iquote('15:MRR:1469.0,502.0')] ).
cnf(1471,plain,
~ ain(a1,asing(a2)),
inference(mrr,[status(thm)],[1470,502]),
[iquote('15:MRR:1470.0,502.0')] ).
cnf(1328,plain,
( ~ ain(u,aun(asm(apow(a2),apow(asing(a2))),a3))
| ain(u,asing(asing(a3)))
| ain(u,apow(a2)) ),
inference(rew,[status(thm),theory(equality)],[1323,525]),
[iquote('15:Rew:1323.0,525.0')] ).
cnf(1465,plain,
~ asubq(a1,asing(a2)),
inference(mrr,[status(thm)],[1461,1292]),
[iquote('15:MRR:1461.0,1292.0')] ).
cnf(1451,plain,
( ~ asubq(u,asing(a3))
| ~ asubq(u,asing(a2)) ),
inference(con,[status(thm)],[1447]),
[iquote('15:Con:1447.1')] ).
cnf(1450,plain,
( ~ asubq(u,asing(a3))
| ~ asubq(u,a3) ),
inference(con,[status(thm)],[1446]),
[iquote('15:Con:1446.1')] ).
cnf(1359,plain,
( ~ ain(u,aun(aun(a3,asing(a3)),a3))
| ain(u,aun(asm(apow(a2),apow(asing(a2))),a3)) ),
inference(rew,[status(thm),theory(equality)],[1323,1327]),
[iquote('15:Rew:1323.0,1327.0')] ).
cnf(1377,plain,
( ~ asubq(u,asing(a3))
| ~ asubq(v,asing(a3))
| ain(aun(v,u),a3) ),
inference(res,[status(thm),theory(equality)],[54,1364]),
[iquote('15:Res:54.2,1364.0')] ).
cnf(1329,plain,
( ~ ain(u,apow(a2))
| ain(u,aun(asm(apow(a2),apow(asing(a2))),a3)) ),
inference(rew,[status(thm),theory(equality)],[1323,527]),
[iquote('15:Rew:1323.0,527.1')] ).
cnf(1440,plain,
( ~ asubq(asing(a3),a2)
| ~ ain(asing(a3),a4) ),
inference(res,[status(thm),theory(equality)],[19,1416]),
[iquote('15:Res:19.1,1416.1')] ).
cnf(1416,plain,
( ~ ain(asing(a3),a4)
| ~ ain(asing(a3),apow(a2)) ),
inference(res,[status(thm),theory(equality)],[1142,1383]),
[iquote('15:Res:1142.0,1383.1')] ).
cnf(1331,plain,
equal(asm(aun(asm(apow(a2),apow(asing(a2))),a3),asing(a2)),aun(aun(a3,asing(a3)),a3)),
inference(rew,[status(thm),theory(equality)],[1323,229]),
[iquote('15:Rew:1323.0,229.0')] ).
cnf(1429,plain,
~ asubq(asm(a3,a3),a3),
inference(res,[status(thm),theory(equality)],[19,1425]),
[iquote('15:Res:19.1,1425.0')] ).
cnf(1425,plain,
~ ain(asm(a3,a3),apow(a3)),
inference(mrr,[status(thm)],[1418,1055,1049]),
[iquote('15:MRR:1418.1,1418.2,1055.0,1049.0')] ).
cnf(1335,plain,
( ~ ain(u,asing(a2))
| ~ ain(u,aun(aun(a3,asing(a3)),a3)) ),
inference(rew,[status(thm),theory(equality)],[1323,1030]),
[iquote('15:Rew:1323.0,1030.1')] ).
cnf(1325,plain,
equal(asm(aun(asm(apow(a2),apow(asing(a2))),a3),asing(asing(a3))),apow(a2)),
inference(rew,[status(thm),theory(equality)],[1323,217]),
[iquote('15:Rew:1323.0,217.0')] ).
cnf(1355,plain,
( ~ ain(u,apow(a2))
| ~ ain(u,apow(asing(a2))) ),
inference(mrr,[status(thm)],[1339,1267]),
[iquote('15:MRR:1339.2,1267.0')] ).
cnf(1403,plain,
~ asubq(asm(asm(apow(a2),a2),asing(a3)),a2),
inference(res,[status(thm),theory(equality)],[19,1393]),
[iquote('15:Res:19.1,1393.0')] ).
cnf(1393,plain,
~ ain(asm(asm(apow(a2),a2),asing(a3)),apow(a2)),
inference(res,[status(thm),theory(equality)],[176,1382]),
[iquote('15:Res:176.0,1382.0')] ).
cnf(1324,plain,
~ aal5(asm(aun(asm(apow(a2),apow(asing(a2))),a3),a3)),
inference(rew,[status(thm),theory(equality)],[1323,232]),
[iquote('15:Rew:1323.0,232.0')] ).
cnf(1382,plain,
( ~ asubq(u,asing(a2))
| ~ ain(u,apow(a2)) ),
inference(mrr,[status(thm)],[1381,1277]),
[iquote('15:MRR:1381.2,1277.1')] ).
cnf(1330,plain,
asubq(a3,aun(asm(apow(a2),apow(asing(a2))),a3)),
inference(rew,[status(thm),theory(equality)],[1323,1191]),
[iquote('15:Rew:1323.0,1191.0')] ).
cnf(1365,plain,
( ~ ain(u,a3)
| asubq(u,asing(a3)) ),
inference(spl,[status(thm),theory(equality)],[1323,20]),
[iquote('15:SpL:1323.0,20.0')] ).
cnf(1364,plain,
( ~ asubq(u,asing(a3))
| ain(u,a3) ),
inference(spr,[status(thm),theory(equality)],[1323,19]),
[iquote('15:SpR:1323.0,19.1')] ).
cnf(1352,plain,
~ asubq(a3,a3),
inference(obv,[status(thm),theory(equality)],[1347]),
[iquote('15:Obv:1347.0')] ).
cnf(1323,plain,
equal(apow(asing(a3)),a3),
inference(spt,[],[1260]),
[iquote('15:Spt:1260.3')] ).
cnf(1309,plain,
( ~ ain(u,a4)
| ain(u,asing(a3))
| ain(u,a3)
| asubq(u,asing(a2)) ),
inference(res,[status(thm),theory(equality)],[1290,20]),
[iquote('14:Res:1290.1,20.0')] ).
cnf(1290,plain,
( ~ ain(u,a4)
| ain(u,apow(asing(a2)))
| ain(u,asing(a3))
| ain(u,a3) ),
inference(res,[status(thm),theory(equality)],[540,1186]),
[iquote('14:Res:540.2,1186.0')] ).
cnf(1238,plain,
( ~ ain(aun(u,v),a3)
| ~ asubq(v,asing(a2))
| ~ asubq(u,asing(a2)) ),
inference(mrr,[status(thm)],[1133,1226]),
[iquote('14:MRR:1133.3,1226.0')] ).
cnf(1287,plain,
( ~ ain(u,a4)
| ain(u,asing(a2))
| ain(u,asing(a3))
| ain(u,a3) ),
inference(res,[status(thm),theory(equality)],[52,1186]),
[iquote('14:Res:52.2,1186.0')] ).
cnf(1250,plain,
( ~ asubq(u,a3)
| ~ asubq(v,a3)
| ~ ain(aun(v,u),a3) ),
inference(res,[status(thm),theory(equality)],[54,1226]),
[iquote('14:Res:54.2,1226.0')] ).
cnf(1237,plain,
( ~ ain(u,a3)
| ain(u,a2)
| equal(u,a3) ),
inference(mrr,[status(thm)],[954,1226]),
[iquote('14:MRR:954.3,1226.0')] ).
cnf(1295,plain,
ain(a2,apow(a3)),
inference(mrr,[status(thm)],[1293,536]),
[iquote('14:MRR:1293.0,536.0')] ).
cnf(1292,plain,
ain(a2,asing(a3)),
inference(mrr,[status(thm)],[1291,557]),
[iquote('14:MRR:1291.1,557.0')] ).
cnf(1186,plain,
( ~ ain(u,asm(a4,asing(a2)))
| ain(u,asing(a3))
| ain(u,a3) ),
inference(rew,[status(thm),theory(equality)],[1172,567]),
[iquote('14:Rew:1172.0,567.2')] ).
cnf(1277,plain,
( ~ asubq(u,asing(a2))
| ~ ain(u,a3) ),
inference(res,[status(thm),theory(equality)],[19,1267]),
[iquote('14:Res:19.1,1267.1')] ).
cnf(1267,plain,
( ~ ain(u,a3)
| ~ ain(u,apow(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[1187,542]),
[iquote('14:Res:1187.1,542.1')] ).
cnf(1239,plain,
~ ain(asm(asm(apow(a2),a2),asing(a3)),a3),
inference(mrr,[status(thm)],[1113,1226]),
[iquote('14:MRR:1113.1,1226.0')] ).
cnf(1264,plain,
( ~ ain(u,a3)
| ~ ain(u,asing(a2)) ),
inference(res,[status(thm),theory(equality)],[1187,40]),
[iquote('14:Res:1187.1,40.1')] ).
cnf(1187,plain,
( ~ ain(u,a3)
| ain(u,asm(a4,asing(a2))) ),
inference(rew,[status(thm),theory(equality)],[1172,541]),
[iquote('14:Rew:1172.0,541.0')] ).
cnf(1259,plain,
ain(asm(a3,a3),a2),
inference(mrr,[status(thm)],[1257,1050]),
[iquote('14:MRR:1257.0,1050.0')] ).
cnf(1226,plain,
( ~ asubq(u,a3)
| ~ ain(u,a3) ),
inference(res,[status(thm),theory(equality)],[19,1213]),
[iquote('14:Res:19.1,1213.0')] ).
cnf(1246,plain,
~ ain(asm(apow(a2),a2),a3),
inference(res,[status(thm),theory(equality)],[1236,12]),
[iquote('14:Res:1236.1,12.0')] ).
cnf(1236,plain,
( ~ ain(u,a3)
| ain(u,a4) ),
inference(mrr,[status(thm)],[507,1226]),
[iquote('14:MRR:507.2,1226.0')] ).
cnf(1241,plain,
~ ain(asing(a2),apow(a2)),
inference(mrr,[status(thm)],[205,1234]),
[iquote('14:MRR:205.1,1234.0')] ).
cnf(1240,plain,
~ asubq(asing(a2),a2),
inference(mrr,[status(thm)],[280,1234]),
[iquote('14:MRR:280.1,1234.0')] ).
cnf(1235,plain,
~ ain(asing(a3),a3),
inference(mrr,[status(thm)],[1148,1226]),
[iquote('14:MRR:1148.1,1226.0')] ).
cnf(1234,plain,
~ ain(asing(a2),a3),
inference(mrr,[status(thm)],[613,1226]),
[iquote('14:MRR:613.1,1226.0')] ).
cnf(1213,plain,
( ~ ain(u,apow(a3))
| ~ ain(u,a3) ),
inference(spl,[status(thm),theory(equality)],[1172,40]),
[iquote('14:SpL:1172.0,40.1')] ).
cnf(1184,plain,
equal(asm(asm(a4,asing(a2)),asing(a3)),a3),
inference(rew,[status(thm),theory(equality)],[1172,543]),
[iquote('14:Rew:1172.0,543.0')] ).
cnf(1175,plain,
asubq(a3,asm(a3,asing(a2))),
inference(rew,[status(thm),theory(equality)],[1172,550]),
[iquote('14:Rew:1172.0,550.0')] ).
cnf(1173,plain,
asubq(a3,a4),
inference(rew,[status(thm),theory(equality)],[1172,169]),
[iquote('14:Rew:1172.0,169.0')] ).
cnf(1172,plain,
equal(asm(apow(a2),apow(a3)),a3),
inference(spt,[],[958]),
[iquote('14:Spt:958.3')] ).
cnf(996,plain,
( ~ aal4(aun(u,v))
| ~ asubq(v,aun(w,x))
| ~ asubq(u,aun(w,x))
| ~ ain(y,x)
| aal3(w)
| aal3(x)
| ain(y,aun(u,v)) ),
inference(res,[status(thm),theory(equality)],[54,81]),
[iquote('0:Res:54.2,81.2')] ).
cnf(1159,plain,
( ~ asubq(a4,apow(a3))
| ~ asubq(asing(asing(a2)),apow(a3))
| equal(aun(asing(asing(a2)),a4),apow(a3)) ),
inference(mrr,[status(thm)],[1152,15]),
[iquote('7:MRR:1152.2,15.0')] ).
cnf(615,plain,
( ~ asubq(u,apow(a3))
| ~ asubq(v,apow(a3))
| ~ ain(a2,aun(v,u))
| ~ ain(a3,aun(v,u))
| equal(aun(v,u),apow(a3)) ),
inference(res,[status(thm),theory(equality)],[54,571]),
[iquote('7:Res:54.2,571.0')] ).
cnf(1147,plain,
( ~ asubq(asing(a3),a2)
| asubq(asing(a3),a3) ),
inference(res,[status(thm),theory(equality)],[19,1144]),
[iquote('13:Res:19.1,1144.0')] ).
cnf(1144,plain,
( ~ ain(asing(a3),apow(a2))
| asubq(asing(a3),a3) ),
inference(res,[status(thm),theory(equality)],[1143,20]),
[iquote('13:Res:1143.1,20.0')] ).
cnf(1143,plain,
( ~ ain(asing(a3),apow(a2))
| ain(asing(a3),apow(a3)) ),
inference(res,[status(thm),theory(equality)],[1142,545]),
[iquote('13:Res:1142.0,545.1')] ).
cnf(1142,plain,
ain(asing(a3),asing(a2)),
inference(spt,[],[1141]),
[iquote('13:Spt:1141.1')] ).
cnf(568,plain,
( ~ asubq(u,asing(a2))
| ~ asubq(v,asing(a2))
| ~ ain(aun(v,u),a4)
| ain(aun(v,u),asing(a2)) ),
inference(rew,[status(thm),theory(equality)],[535,157]),
[iquote('7:Rew:535.0,157.3')] ).
cnf(1118,plain,
~ ain(a3,asing(aun(a3,asing(a3)))),
inference(res,[status(thm),theory(equality)],[199,1115]),
[iquote('7:Res:199.0,1115.0')] ).
cnf(1116,plain,
ain(a3,apow(aun(a3,asing(a3)))),
inference(res,[status(thm),theory(equality)],[199,1114]),
[iquote('7:Res:199.0,1114.0')] ).
cnf(995,plain,
( ~ aal4(a1)
| ~ ain(a2,aun(u,v))
| ~ ain(w,v)
| aal3(u)
| aal3(v)
| ain(w,a1) ),
inference(res,[status(thm),theory(equality)],[552,81]),
[iquote('7:Res:552.1,81.2')] ).
cnf(569,plain,
( ~ ain(asm(asm(apow(a2),a2),asing(a3)),a4)
| ain(asm(asm(apow(a2),a2),asing(a3)),asing(a2)) ),
inference(rew,[status(thm),theory(equality)],[535,240]),
[iquote('7:Rew:535.0,240.1')] ).
cnf(242,plain,
( ~ asubq(u,aun(a3,asing(a3)))
| asubq(aun(asm(apow(a2),asing(a2)),u),aun(a3,asing(a3))) ),
inference(rew,[status(thm),theory(equality)],[162,226]),
[iquote('2:Rew:162.0,226.1')] ).
cnf(241,plain,
( ~ asubq(u,aun(a3,asing(a3)))
| asubq(aun(u,asm(apow(a2),asing(a2))),aun(a3,asing(a3))) ),
inference(rew,[status(thm),theory(equality)],[162,225]),
[iquote('2:Rew:162.0,225.1')] ).
cnf(222,plain,
asubq(asm(a3,a3),aint(aun(asing(a3),a4),aun(asing(a2),apow(asing(a2))))),
inference(rew,[status(thm),theory(equality)],[162,73]),
[iquote('2:Rew:162.0,73.0')] ).
cnf(221,plain,
equal(aint(aun(asing(asing(a2)),a4),asm(apow(a2),a3)),asm(a3,a3)),
inference(rew,[status(thm),theory(equality)],[162,71]),
[iquote('2:Rew:162.0,71.0')] ).
cnf(194,plain,
~ ain(asm(a3,a3),asing(a3)),
inference(rew,[status(thm),theory(equality)],[162,35]),
[iquote('2:Rew:162.0,35.0')] ).
cnf(1049,plain,
ain(asm(a3,a3),apow(a2)),
inference(spt,[],[1031]),
[iquote('10:Spt:1031.2')] ).
cnf(1050,plain,
ain(asm(a3,a3),a3),
inference(mrr,[status(thm)],[237,1049]),
[iquote('10:MRR:237.0,1049.0')] ).
cnf(1051,plain,
asubq(asm(a3,a3),a2),
inference(res,[status(thm),theory(equality)],[1049,20]),
[iquote('10:Res:1049.0,20.0')] ).
cnf(1055,plain,
ain(asm(a3,a3),a4),
inference(spt,[],[1054]),
[iquote('11:Spt:1054.0')] ).
cnf(1076,plain,
~ equal(asm(a3,a3),a3),
inference(spt,[],[1073,1052,1059]),
[iquote('12:Spt:1073.0,1052.1,1059.0')] ).
cnf(244,plain,
( ~ ain(u,a4)
| ~ ain(u,aun(aun(a3,asing(a3)),aun(apow(asing(a2)),asing(a3))))
| ain(u,a3)
| ain(u,aun(apow(asing(a2)),asing(a3))) ),
inference(rew,[status(thm),theory(equality)],[162,230]),
[iquote('2:Rew:162.0,230.2')] ).
cnf(1034,plain,
( ~ ain(u,a4)
| ain(u,asing(a3))
| ain(u,apow(a2))
| asubq(u,asing(a2)) ),
inference(res,[status(thm),theory(equality)],[1019,20]),
[iquote('7:Res:1019.1,20.0')] ).
cnf(1019,plain,
( ~ ain(u,a4)
| ain(u,apow(asing(a2)))
| ain(u,asing(a3))
| ain(u,apow(a2)) ),
inference(res,[status(thm),theory(equality)],[540,1007]),
[iquote('7:Res:540.2,1007.0')] ).
cnf(1017,plain,
( ~ ain(u,a4)
| ain(u,asing(a2))
| ain(u,asing(a3))
| ain(u,apow(a2)) ),
inference(res,[status(thm),theory(equality)],[52,1007]),
[iquote('7:Res:52.2,1007.0')] ).
cnf(1008,plain,
( ~ ain(u,asm(a4,asing(a2)))
| ~ ain(u,apow(a3))
| ain(u,asing(a3)) ),
inference(res,[status(thm),theory(equality)],[567,40]),
[iquote('7:Res:567.2,40.1')] ).
cnf(1007,plain,
( ~ ain(u,asm(a4,asing(a2)))
| ain(u,asing(a3))
| ain(u,apow(a2)) ),
inference(res,[status(thm),theory(equality)],[567,32]),
[iquote('7:Res:567.2,32.0')] ).
cnf(81,axiom,
( ~ aal4(u)
| ~ ain(v,w)
| ~ asubq(u,aun(x,w))
| aal3(x)
| aal3(w)
| ain(v,u) ),
file('SYO844+1.p',unknown),
[] ).
cnf(572,plain,
( ~ ain(u,a4)
| ain(u,a3)
| equal(u,a2)
| equal(u,a3)
| ain(u,asing(a2)) ),
inference(rew,[status(thm),theory(equality)],[535,531]),
[iquote('7:Rew:535.0,531.2')] ).
cnf(571,plain,
( ~ asubq(u,apow(a3))
| ~ ain(a2,u)
| ~ ain(a3,u)
| equal(u,apow(a3)) ),
inference(rew,[status(thm),theory(equality)],[535,239]),
[iquote('7:Rew:535.0,239.1')] ).
cnf(624,plain,
( ~ aal3(asm(asm(apow(a2),asing(a2)),a3))
| ~ ain(a1,asm(apow(a2),asing(a2))) ),
inference(spl,[status(thm),theory(equality)],[162,76]),
[iquote('2:SpL:162.0,76.0')] ).
cnf(228,plain,
asubq(aun(asm(apow(a2),asing(a2)),asm(apow(a2),asing(a2))),aun(a3,asing(a3))),
inference(rew,[status(thm),theory(equality)],[162,94]),
[iquote('2:Rew:162.0,94.0')] ).
cnf(562,plain,
( ~ ain(u,a4)
| ain(u,a3)
| equal(u,a2)
| ain(u,asm(a4,a2)) ),
inference(rew,[status(thm),theory(equality)],[535,463]),
[iquote('7:Rew:535.0,463.2')] ).
cnf(539,plain,
( ~ ain(u,apow(a2))
| ain(u,apow(a3))
| ain(u,asm(a4,asing(a2))) ),
inference(rew,[status(thm),theory(equality)],[535,464]),
[iquote('7:Rew:535.0,464.2')] ).
cnf(214,plain,
( ~ aal4(a4)
| ~ aal2(asing(apow(asing(a1))))
| ~ adisjoint(asing(apow(a3)),a4) ),
inference(rew,[status(thm),theory(equality)],[162,145]),
[iquote('2:Rew:162.0,145.2')] ).
cnf(213,plain,
( ~ aal2(a4)
| ~ aal4(asing(apow(asing(a1))))
| ~ adisjoint(asing(apow(a3)),a4) ),
inference(rew,[status(thm),theory(equality)],[162,153]),
[iquote('2:Rew:162.0,153.2')] ).
cnf(953,plain,
( ~ asubq(u,a2)
| ain(u,a2)
| equal(u,a3)
| asubq(u,a3) ),
inference(res,[status(thm),theory(equality)],[19,639]),
[iquote('7:Res:19.1,639.0')] ).
cnf(561,plain,
( ~ ain(u,a4)
| ~ ain(u,a2)
| ain(u,a3)
| equal(u,a2) ),
inference(rew,[status(thm),theory(equality)],[535,530]),
[iquote('7:Rew:535.0,530.3')] ).
cnf(133,plain,
( ~ ain(u,a4)
| ain(u,a2)
| equal(u,a3)
| ain(u,asing(a2)) ),
inference(res,[status(thm),theory(equality)],[52,56]),
[iquote('0:Res:52.2,56.0')] ).
cnf(215,plain,
( ~ ain(u,apow(a2))
| ~ ain(u,asing(a3))
| ain(u,apow(a3)) ),
inference(rew,[status(thm),theory(equality)],[162,149]),
[iquote('2:Rew:162.0,149.2')] ).
cnf(231,plain,
( ~ ain(u,asm(apow(a2),asing(a2)))
| ain(u,a2)
| equal(u,a3) ),
inference(rew,[status(thm),theory(equality)],[162,64]),
[iquote('2:Rew:162.0,64.2')] ).
cnf(563,plain,
( ~ ain(u,asm(a4,a3))
| equal(u,a2)
| ain(u,asm(a4,a2)) ),
inference(rew,[status(thm),theory(equality)],[535,207]),
[iquote('7:Rew:535.0,207.1')] ).
cnf(252,plain,
( ~ aal4(a4)
| ~ aal2(asing(apow(a3)))
| ~ adisjoint(asing(apow(a3)),a4) ),
inference(res,[status(thm),theory(equality)],[59,167]),
[iquote('2:Res:59.3,167.0')] ).
cnf(251,plain,
( ~ aal2(a4)
| ~ aal4(asing(apow(a3)))
| ~ adisjoint(asing(apow(a3)),a4) ),
inference(res,[status(thm),theory(equality)],[60,167]),
[iquote('2:Res:60.3,167.0')] ).
cnf(227,plain,
asubq(asm(asm(apow(a2),apow(asing(a2))),asing(a2)),aun(a3,asing(a3))),
inference(rew,[status(thm),theory(equality)],[162,70]),
[iquote('2:Rew:162.0,70.0')] ).
cnf(223,plain,
ain(asing(a3),asm(apow(aun(a3,asing(a3))),asing(aun(a3,asing(a3))))),
inference(rew,[status(thm),theory(equality)],[162,78]),
[iquote('2:Rew:162.0,78.0')] ).
cnf(56,axiom,
( ~ ain(u,asm(a4,a2))
| equal(u,a3)
| ain(u,asing(a2)) ),
file('SYO844+1.p',unknown),
[] ).
cnf(177,plain,
( ~ ain(u,apow(a2))
| ain(u,asing(a3))
| ain(u,a3) ),
inference(rew,[status(thm),theory(equality)],[162,111]),
[iquote('2:Rew:162.0,111.1')] ).
cnf(494,plain,
( ~ ain(u,apow(a2))
| ain(u,apow(a3))
| ain(u,a4) ),
inference(res,[status(thm),theory(equality)],[464,32]),
[iquote('2:Res:464.2,32.0')] ).
cnf(186,plain,
ain(asing(a2),asm(aun(asing(asing(a2)),a4),asm(apow(a2),a3))),
inference(rew,[status(thm),theory(equality)],[162,61]),
[iquote('2:Rew:162.0,61.0')] ).
cnf(469,plain,
( ~ ain(u,apow(a2))
| ain(u,a3)
| ain(u,apow(a3)) ),
inference(obv,[status(thm),theory(equality)],[467]),
[iquote('2:Obv:467.0')] ).
cnf(181,plain,
aex3(asm(aun(asing(a3),a4),aun(asing(a2),apow(asing(a2))))),
inference(rew,[status(thm),theory(equality)],[162,58]),
[iquote('2:Rew:162.0,58.0')] ).
cnf(185,plain,
ain(a1,asm(aun(asing(asing(a2)),a4),asm(apow(a2),a3))),
inference(rew,[status(thm),theory(equality)],[162,55]),
[iquote('2:Rew:162.0,55.0')] ).
cnf(472,plain,
( ~ ain(u,apow(a2))
| ain(u,a3)
| asubq(u,a3) ),
inference(res,[status(thm),theory(equality)],[469,20]),
[iquote('2:Res:469.2,20.0')] ).
cnf(498,plain,
( ~ ain(u,apow(a2))
| ain(u,a4)
| asubq(u,a3) ),
inference(res,[status(thm),theory(equality)],[494,20]),
[iquote('2:Res:494.1,20.0')] ).
cnf(528,plain,
( ~ ain(u,asing(asing(a3)))
| ~ ain(u,apow(a2)) ),
inference(spl,[status(thm),theory(equality)],[217,40]),
[iquote('2:SpL:217.0,40.1')] ).
cnf(475,plain,
( ~ asubq(u,a2)
| ain(u,a3)
| asubq(u,a3) ),
inference(res,[status(thm),theory(equality)],[19,472]),
[iquote('2:Res:19.1,472.0')] ).
cnf(506,plain,
( ~ asubq(u,a2)
| ain(u,a4)
| asubq(u,a3) ),
inference(res,[status(thm),theory(equality)],[19,498]),
[iquote('2:Res:19.1,498.0')] ).
cnf(176,plain,
asubq(asm(asm(apow(a2),a2),asing(a3)),asing(a2)),
inference(rew,[status(thm),theory(equality)],[162,48]),
[iquote('2:Rew:162.0,48.0')] ).
cnf(192,plain,
asubq(asm(apow(a2),asing(a2)),aun(a3,asing(a3))),
inference(rew,[status(thm),theory(equality)],[162,51]),
[iquote('2:Rew:162.0,51.0')] ).
cnf(178,plain,
( ~ ain(u,asing(a3))
| ~ ain(u,a3) ),
inference(rew,[status(thm),theory(equality)],[162,107]),
[iquote('2:Rew:162.0,107.0')] ).
cnf(459,plain,
~ ain(asing(a3),asing(aun(a3,asing(a3)))),
inference(res,[status(thm),theory(equality)],[223,40]),
[iquote('2:Res:223.0,40.1')] ).
cnf(101,plain,
( ~ ain(u,a3)
| ain(u,apow(a2)) ),
inference(spl,[status(thm),theory(equality)],[25,32]),
[iquote('0:SpL:25.0,32.0')] ).
cnf(560,plain,
~ ain(a2,aun(asing(a3),asing(a3))),
inference(rew,[status(thm),theory(equality)],[535,175]),
[iquote('7:Rew:535.0,175.0')] ).
cnf(620,plain,
( ~ ain(a3,a1)
| equal(apow(a3),a1) ),
inference(mrr,[status(thm)],[617,565]),
[iquote('7:MRR:617.0,565.0')] ).
cnf(458,plain,
ain(asing(a3),apow(aun(a3,asing(a3)))),
inference(res,[status(thm),theory(equality)],[223,32]),
[iquote('2:Res:223.0,32.0')] ).
cnf(188,plain,
~ ain(asing(a2),asm(apow(a2),a3)),
inference(rew,[status(thm),theory(equality)],[162,141]),
[iquote('2:Rew:162.0,141.0')] ).
cnf(29,axiom,
aal4(aun(a3,asing(asm(apow(a2),a2)))),
file('SYO844+1.p',unknown),
[] ).
cnf(106,plain,
( ~ ain(u,a3)
| asubq(u,a2) ),
inference(res,[status(thm),theory(equality)],[101,20]),
[iquote('0:Res:101.1,20.0')] ).
cnf(23,axiom,
ain(a3,aun(apow(asing(a2)),asing(a3))),
file('SYO844+1.p',unknown),
[] ).
cnf(881,plain,
ain(a1,a2),
inference(mrr,[status(thm)],[880,555]),
[iquote('8:MRR:880.0,555.0')] ).
cnf(167,plain,
~ aal6(aun(asing(apow(a3)),a4)),
inference(rew,[status(thm),theory(equality)],[162,28]),
[iquote('2:Rew:162.0,28.0')] ).
cnf(191,plain,
asubq(asing(a3),aun(a3,asing(a3))),
inference(rew,[status(thm),theory(equality)],[162,41]),
[iquote('2:Rew:162.0,41.0')] ).
cnf(187,plain,
~ ain(a1,asm(apow(a2),a3)),
inference(rew,[status(thm),theory(equality)],[162,125]),
[iquote('2:Rew:162.0,125.0')] ).
cnf(184,plain,
~ ain(a3,asm(apow(a2),a3)),
inference(rew,[status(thm),theory(equality)],[162,21]),
[iquote('2:Rew:162.0,21.0')] ).
cnf(174,plain,
equal(asm(apow(a2),asing(a3)),a3),
inference(rew,[status(thm),theory(equality)],[162,25]),
[iquote('2:Rew:162.0,25.0')] ).
cnf(168,plain,
asubq(a3,aun(a3,asing(apow(a3)))),
inference(rew,[status(thm),theory(equality)],[162,24]),
[iquote('2:Rew:162.0,24.0')] ).
cnf(14,axiom,
ain(a3,aun(asing(asing(a2)),a4)),
file('SYO844+1.p',unknown),
[] ).
cnf(9,axiom,
~ aal3(aun(a1,asing(a3))),
file('SYO844+1.p',unknown),
[] ).
cnf(559,plain,
ain(a2,aun(a1,asing(a3))),
inference(rew,[status(thm),theory(equality)],[535,8]),
[iquote('7:Rew:535.0,8.0')] ).
cnf(166,plain,
aex5(aun(asing(apow(a3)),a4)),
inference(rew,[status(thm),theory(equality)],[162,17]),
[iquote('2:Rew:162.0,17.0')] ).
cnf(193,plain,
asubq(a3,aun(a3,asing(a3))),
inference(rew,[status(thm),theory(equality)],[162,34]),
[iquote('2:Rew:162.0,34.0')] ).
cnf(173,plain,
~ ain(a3,asing(a2)),
inference(rew,[status(thm),theory(equality)],[162,5]),
[iquote('2:Rew:162.0,5.0')] ).
cnf(274,plain,
~ ain(a3,apow(a2)),
inference(mrr,[status(thm)],[200,272]),
[iquote('2:MRR:200.1,272.0')] ).
cnf(165,plain,
~ ain(a1,apow(a3)),
inference(rew,[status(thm),theory(equality)],[162,4]),
[iquote('2:Rew:162.0,4.0')] ).
cnf(164,plain,
~ equal(apow(a3),a3),
inference(rew,[status(thm),theory(equality)],[162,6]),
[iquote('2:Rew:162.0,6.0')] ).
cnf(558,plain,
ain(a2,asm(a4,a3)),
inference(rew,[status(thm),theory(equality)],[535,163]),
[iquote('7:Rew:535.0,163.0')] ).
cnf(275,plain,
~ asubq(a3,a2),
inference(mrr,[status(thm)],[262,272]),
[iquote('2:MRR:262.1,272.0')] ).
cnf(272,plain,
~ ain(a3,a3),
inference(res,[status(thm),theory(equality)],[154,178]),
[iquote('2:Res:154.0,178.0')] ).
cnf(189,plain,
~ asubq(a1,a3),
inference(rew,[status(thm),theory(equality)],[162,97]),
[iquote('2:Rew:162.0,97.0')] ).
cnf(860,plain,
~ equal(a3,a1),
inference(spt,[],[806,640,641]),
[iquote('8:Spt:806.0,640.2,641.0')] ).
cnf(162,plain,
equal(asing(a1),a3),
inference(spt,[],[159]),
[iquote('2:Spt:159.2')] ).
cnf(154,plain,
ain(a3,asing(a3)),
inference(spt,[],[151]),
[iquote('1:Spt:151.1')] ).
cnf(557,plain,
~ ain(a2,a3),
inference(rew,[status(thm),theory(equality)],[535,190]),
[iquote('7:Rew:535.0,190.0')] ).
cnf(411,plain,
ain(a1,a3),
inference(mrr,[status(thm)],[267,410]),
[iquote('4:MRR:267.0,410.0')] ).
cnf(556,plain,
~ equal(a3,a2),
inference(rew,[status(thm),theory(equality)],[535,408]),
[iquote('7:Rew:535.0,408.0')] ).
cnf(565,plain,
asubq(a2,a3),
inference(rew,[status(thm),theory(equality)],[535,477]),
[iquote('7:Rew:535.0,477.0')] ).
cnf(540,plain,
( ~ ain(u,a4)
| ain(u,apow(asing(a2)))
| ain(u,asm(a4,asing(a2))) ),
inference(rew,[status(thm),theory(equality)],[535,112]),
[iquote('7:Rew:535.0,112.2')] ).
cnf(549,plain,
( ~ ain(u,a4)
| ~ ain(u,apow(asing(a2)))
| ain(u,asing(a2)) ),
inference(rew,[status(thm),theory(equality)],[535,131]),
[iquote('7:Rew:535.0,131.2')] ).
cnf(76,axiom,
( ~ aal3(asm(asm(apow(a2),asing(a2)),asing(u)))
| ~ ain(u,asm(apow(a2),asing(a2))) ),
file('SYO844+1.p',unknown),
[] ).
cnf(547,plain,
( ~ ain(u,a4)
| ~ ain(u,asing(a2))
| ain(u,apow(asing(a2))) ),
inference(rew,[status(thm),theory(equality)],[535,487]),
[iquote('7:Rew:535.0,487.1')] ).
cnf(548,plain,
( ~ asubq(u,asing(a2))
| ~ ain(u,a4)
| ain(u,asing(a2)) ),
inference(rew,[status(thm),theory(equality)],[535,150]),
[iquote('7:Rew:535.0,150.2')] ).
cnf(546,plain,
( ~ ain(u,a4)
| ~ ain(u,asing(a2))
| asubq(u,asing(a2)) ),
inference(rew,[status(thm),theory(equality)],[535,489]),
[iquote('7:Rew:535.0,489.1')] ).
cnf(542,plain,
( ~ ain(u,apow(asing(a2)))
| ~ ain(u,asm(a4,asing(a2))) ),
inference(rew,[status(thm),theory(equality)],[535,108]),
[iquote('7:Rew:535.0,108.1')] ).
cnf(538,plain,
equal(asm(a4,apow(asing(a2))),asm(a4,asing(a2))),
inference(rew,[status(thm),theory(equality)],[535,44]),
[iquote('7:Rew:535.0,44.0')] ).
cnf(552,plain,
( ~ ain(a2,u)
| asubq(a1,u) ),
inference(rew,[status(thm),theory(equality)],[535,11]),
[iquote('7:Rew:535.0,11.0')] ).
cnf(537,plain,
ain(a2,asm(a4,asing(a2))),
inference(rew,[status(thm),theory(equality)],[535,88]),
[iquote('7:Rew:535.0,88.0')] ).
cnf(544,plain,
~ ain(a2,asing(a2)),
inference(rew,[status(thm),theory(equality)],[535,110]),
[iquote('7:Rew:535.0,110.0')] ).
cnf(564,plain,
ain(a2,a1),
inference(rew,[status(thm),theory(equality)],[535,471]),
[iquote('7:Rew:535.0,471.0')] ).
cnf(555,plain,
ain(a2,a2),
inference(rew,[status(thm),theory(equality)],[535,410]),
[iquote('7:Rew:535.0,410.0')] ).
cnf(553,plain,
asubq(a2,a2),
inference(rew,[status(thm),theory(equality)],[535,99]),
[iquote('7:Rew:535.0,99.0')] ).
cnf(536,plain,
ain(a2,apow(a2)),
inference(rew,[status(thm),theory(equality)],[535,2]),
[iquote('7:Rew:535.0,2.0')] ).
cnf(535,plain,
equal(a0,a2),
inference(spt,[],[533]),
[iquote('7:Spt:533.2')] ).
cnf(502,plain,
ain(a1,a4),
inference(mrr,[status(thm)],[501,411]),
[iquote('4:MRR:501.0,411.0')] ).
cnf(484,plain,
ain(asing(a2),asing(a2)),
inference(spt,[],[152]),
[iquote('6:Spt:152.1')] ).
cnf(60,axiom,
( ~ aal2(u)
| ~ aal4(v)
| ~ adisjoint(v,u)
| aal6(aun(v,u)) ),
file('SYO844+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ aal4(u)
| ~ aal2(v)
| ~ adisjoint(v,u)
| aal6(aun(v,u)) ),
file('SYO844+1.p',unknown),
[] ).
cnf(143,plain,
( ain(asing(a2),a4)
| ain(asing(a2),asing(asing(a2))) ),
inference(res,[status(thm),theory(equality)],[140,53]),
[iquote('0:Res:140.0,53.0')] ).
cnf(140,plain,
ain(asing(a2),aun(asing(asing(a2)),a4)),
inference(res,[status(thm),theory(equality)],[61,32]),
[iquote('0:Res:61.0,32.0')] ).
cnf(54,axiom,
( ~ asubq(u,v)
| ~ asubq(w,v)
| asubq(aun(w,u),v) ),
file('SYO844+1.p',unknown),
[] ).
cnf(132,plain,
~ asubq(a2,asing(a2)),
inference(res,[status(thm),theory(equality)],[19,130]),
[iquote('0:Res:19.1,130.0')] ).
cnf(130,plain,
~ ain(a2,apow(asing(a2))),
inference(res,[status(thm),theory(equality)],[88,108]),
[iquote('0:Res:88.0,108.1')] ).
cnf(124,plain,
ain(a1,aun(asing(asing(a2)),a4)),
inference(res,[status(thm),theory(equality)],[55,32]),
[iquote('0:Res:55.0,32.0')] ).
cnf(53,axiom,
( ~ ain(u,aun(v,w))
| ain(u,w)
| ain(u,v) ),
file('SYO844+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ ain(u,v)
| ain(u,w)
| ain(u,asm(v,w)) ),
file('SYO844+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ ain(u,v)
| ~ ain(u,asm(w,v)) ),
file('SYO844+1.p',unknown),
[] ).
cnf(43,axiom,
~ ain(apow(a2),aun(apow(a2),asing(asing(a2)))),
file('SYO844+1.p',unknown),
[] ).
cnf(103,plain,
ain(a2,a4),
inference(res,[status(thm),theory(equality)],[88,32]),
[iquote('0:Res:88.0,32.0')] ).
cnf(32,axiom,
( ~ ain(u,asm(v,w))
| ain(u,v) ),
file('SYO844+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ aal3(aun(u,v))
| aal2(v)
| aal2(u) ),
file('SYO844+1.p',unknown),
[] ).
cnf(36,axiom,
ain(asing(a2),aun(asing(a2),apow(asing(a2)))),
file('SYO844+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ ain(u,apow(v))
| asubq(u,v) ),
file('SYO844+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ asubq(u,v)
| ain(u,apow(v)) ),
file('SYO844+1.p',unknown),
[] ).
cnf(27,axiom,
~ aal4(asm(apow(a2),apow(asing(a2)))),
file('SYO844+1.p',unknown),
[] ).
cnf(22,axiom,
~ equal(asm(apow(a2),a2),apow(a2)),
file('SYO844+1.p',unknown),
[] ).
cnf(30,axiom,
aex5(aun(a4,asing(asm(apow(a2),a2)))),
file('SYO844+1.p',unknown),
[] ).
cnf(12,axiom,
~ ain(asm(apow(a2),a2),a4),
file('SYO844+1.p',unknown),
[] ).
cnf(15,axiom,
ain(a2,aun(asing(asing(a2)),a4)),
file('SYO844+1.p',unknown),
[] ).
cnf(3,axiom,
~ aal5(apow(a2)),
file('SYO844+1.p',unknown),
[] ).
cnf(1,axiom,
~ asubq(a2,a1),
file('SYO844+1.p',unknown),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO844+1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 17:31:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.56/0.75
% 0.56/0.75 SPASS V 3.9
% 0.56/0.75 SPASS beiseite: Completion found.
% 0.56/0.75 % SZS status CounterSatisfiable
% 0.56/0.75 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.75 SPASS derived 2188 clauses, backtracked 363 clauses, performed 28 splits and kept 1461 clauses.
% 0.56/0.75 SPASS allocated 99839 KBytes.
% 0.56/0.75 SPASS spent 0:00:00.41 on the problem.
% 0.56/0.75 0:00:00.03 for the input.
% 0.56/0.75 0:00:00.04 for the FLOTTER CNF translation.
% 0.56/0.75 0:00:00.05 for inferences.
% 0.56/0.75 0:00:00.00 for the backtracking.
% 0.56/0.75 0:00:00.25 for the reduction.
% 0.56/0.75
% 0.56/0.75
% 0.56/0.75 The saturated set of worked-off clauses is :
% 0.56/0.75 % SZS output start Saturation
% See solution above
%------------------------------------------------------------------------------