TSTP Solution File: SCT164+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SCT164+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 : 300s
% DateTime : Thu Aug 31 14:17:53 EDT 2023
% Result : Theorem 223.35s 30.35s
% Output : CNFRefutation 223.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 84 ( 26 unt; 0 def)
% Number of atoms : 175 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 161 ( 70 ~; 53 |; 14 &)
% ( 11 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-4 aty)
% Number of variables : 172 ( 6 sgn; 116 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f170,axiom,
! [X34,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X34))
<=> ? [X52] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X52) = X34 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(f254,axiom,
! [X14,X12] :
( class_Finite__Set_Ofinite(X12)
=> c_Finite__Set_Ofinite(X12,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
fof(f259,axiom,
! [X12] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X12),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X12),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X12,c_Orderings_Otop__class_Otop(tc_fun(X12,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(f367,axiom,
! [X42,X43] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X43)),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(f373,axiom,
! [X34,X44] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X34))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34)),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(f398,axiom,
! [X44,X34] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X44))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34)),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(f400,axiom,
! [X34] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X34)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(f403,axiom,
! [X42] : hAPP(c_Nat_OSuc,X42) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(f432,axiom,
! [X65,X17,X27,X12] :
( c_Finite__Set_Ofinite(X12,X27)
=> c_Finite__Set_Ofinite(X17,c_Set_Oimage(X12,X17,X65,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(f444,axiom,
! [X17,X10,X1,X12] : hBOOL(hAPP(hAPP(c_member(X12),hAPP(X1,X10)),c_Set_Oimage(X17,X12,X1,c_Orderings_Otop__class_Otop(tc_fun(X17,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(f485,axiom,
! [X46] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X46)
<=> ? [X37] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(f517,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(f522,axiom,
! [X80] :
( class_Finite__Set_Ofinite(X80)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(f685,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
<=> ? [X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = X0 ),
inference(rectify,[],[f170]) ).
fof(f768,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(X1)
=> c_Finite__Set_Ofinite(X1,X0) ),
inference(rectify,[],[f254]) ).
fof(f772,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(rectify,[],[f259]) ).
fof(f880,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ),
inference(rectify,[],[f367]) ).
fof(f886,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),X1)) ),
inference(rectify,[],[f373]) ).
fof(f911,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X0)) ),
inference(rectify,[],[f398]) ).
fof(f912,plain,
! [X0] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),
inference(rectify,[],[f400]) ).
fof(f915,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,X0),
inference(rectify,[],[f403]) ).
fof(f941,plain,
! [X0,X1,X2,X3] :
( c_Finite__Set_Ofinite(X3,X2)
=> c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2)) ),
inference(rectify,[],[f432]) ).
fof(f953,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X0,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
inference(rectify,[],[f444]) ).
fof(f994,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ) ),
inference(rectify,[],[f485]) ).
fof(f1007,plain,
! [X0] :
( class_Finite__Set_Ofinite(X0)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f522]) ).
fof(f1350,plain,
! [X0,X1] :
( c_Finite__Set_Ofinite(X1,X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f768]) ).
fof(f1443,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X0)) ),
inference(ennf_transformation,[],[f880]) ).
fof(f1472,plain,
! [X0,X1,X2,X3] :
( c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(ennf_transformation,[],[f941]) ).
fof(f1527,plain,
! [X0] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) ),
inference(ennf_transformation,[],[f994]) ).
fof(f1546,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(ennf_transformation,[],[f1007]) ).
fof(f1651,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
| ! [X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X0 )
& ( ? [X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = X0
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ) ),
inference(nnf_transformation,[],[f685]) ).
fof(f1652,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
| ! [X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X0 )
& ( ? [X3] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) = X0
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ) ),
inference(rectify,[],[f1651]) ).
fof(f1653,plain,
! [X0,X1] :
( ? [X3] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) = X0
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),sK21(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f1654,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
| ! [X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X0 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),sK21(X0,X1)) = X0
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f1652,f1653]) ).
fof(f1684,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) )
& ( c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool))) ) ),
inference(nnf_transformation,[],[f772]) ).
fof(f1715,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),X1)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ) ),
inference(nnf_transformation,[],[f886]) ).
fof(f1741,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X0)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ),
inference(nnf_transformation,[],[f911]) ).
fof(f1773,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f1527]) ).
fof(f1774,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X3] :
! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(rectify,[],[f1773]) ).
fof(f1775,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK36(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK36(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1776,plain,
! [X0] :
( ? [X3] :
! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK37(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1777,plain,
! [X0] :
( ( c_Finite__Set_Ofinite(tc_Nat_Onat,X0)
| ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK36(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK36(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK37(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f1774,f1776,f1775]) ).
fof(f2073,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X0 ),
inference(cnf_transformation,[],[f1654]) ).
fof(f2191,plain,
! [X0,X1] :
( c_Finite__Set_Ofinite(X1,X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f1350]) ).
fof(f2196,plain,
! [X0] :
( c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f1684]) ).
fof(f2326,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X0)) ),
inference(cnf_transformation,[],[f1443]) ).
fof(f2333,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),X1)) ),
inference(cnf_transformation,[],[f1715]) ).
fof(f2381,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f1741]) ).
fof(f2384,plain,
! [X0] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),
inference(cnf_transformation,[],[f912]) ).
fof(f2388,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f915]) ).
fof(f2415,plain,
! [X2,X3,X0,X1] :
( c_Finite__Set_Ofinite(X1,c_Set_Oimage(X3,X1,X0,X2))
| ~ c_Finite__Set_Ofinite(X3,X2) ),
inference(cnf_transformation,[],[f1472]) ).
fof(f2433,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X0,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))))),
inference(cnf_transformation,[],[f953]) ).
fof(f2483,plain,
! [X0,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK37(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f1777]) ).
fof(f2522,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f517]) ).
fof(f2527,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(cnf_transformation,[],[f1546]) ).
fof(f2610,plain,
! [X2,X1] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(equality_resolution,[],[f2073]) ).
cnf(c_308,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1))),
inference(cnf_transformation,[],[f2610]) ).
cnf(c_418,plain,
( ~ class_Finite__Set_Ofinite(X0)
| c_Finite__Set_Ofinite(X0,X1) ),
inference(cnf_transformation,[],[f2191]) ).
cnf(c_424,plain,
( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X0),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(cnf_transformation,[],[f2196]) ).
cnf(c_551,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f2326]) ).
cnf(c_557,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ),
inference(cnf_transformation,[],[f2333]) ).
cnf(c_606,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)),X1)) ),
inference(cnf_transformation,[],[f2381]) ).
cnf(c_608,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X0)) = hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f2384]) ).
cnf(c_612,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f2388]) ).
cnf(c_639,plain,
( ~ c_Finite__Set_Ofinite(X0,X1)
| c_Finite__Set_Ofinite(X2,c_Set_Oimage(X0,X2,X3,X1)) ),
inference(cnf_transformation,[],[f2415]) ).
cnf(c_657,plain,
hBOOL(hAPP(hAPP(c_member(X0),hAPP(X1,X2)),c_Set_Oimage(X3,X0,X1,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))))),
inference(cnf_transformation,[],[f2433]) ).
cnf(c_708,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X0),X1))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),sK37(X1))) ),
inference(cnf_transformation,[],[f2483]) ).
cnf(c_745,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f2522]) ).
cnf(c_750,plain,
( ~ class_Finite__Set_Ofinite(X0)
| class_Finite__Set_Ofinite(tc_Option_Ooption(X0)) ),
inference(cnf_transformation,[],[f2527]) ).
cnf(c_1258,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X1)) ),
inference(prop_impl_just,[status(thm)],[c_606,c_557,c_551]) ).
cnf(c_1259,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ),
inference(renaming,[status(thm)],[c_1258]) ).
cnf(c_22501,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X1)) ),
inference(prop_impl_just,[status(thm)],[c_1259]) ).
cnf(c_22502,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X0)) ),
inference(renaming,[status(thm)],[c_22501]) ).
cnf(c_168541,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0),hAPP(c_Nat_OSuc,X0))),
inference(superposition,[status(thm)],[c_612,c_308]) ).
cnf(c_168549,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X0)))),
inference(superposition,[status(thm)],[c_608,c_168541]) ).
cnf(c_168553,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X0)))),X0)),
inference(superposition,[status(thm)],[c_168549,c_22502]) ).
cnf(c_168895,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X0))),X0)),
inference(demodulation,[status(thm)],[c_168553,c_608]) ).
cnf(c_168977,plain,
( ~ class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(superposition,[status(thm)],[c_418,c_424]) ).
cnf(c_172508,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,sK37(X0)))),X0))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X0) ),
inference(superposition,[status(thm)],[c_708,c_168895]) ).
cnf(c_213331,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X0,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))),
inference(superposition,[status(thm)],[c_657,c_172508]) ).
cnf(c_213356,plain,
~ c_Finite__Set_Ofinite(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(superposition,[status(thm)],[c_639,c_213331]) ).
cnf(c_213404,plain,
~ class_Finite__Set_Ofinite(tc_Option_Ooption(X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_168977,c_213356]) ).
cnf(c_213408,plain,
~ class_Finite__Set_Ofinite(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_750,c_213404]) ).
cnf(c_213409,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_745,c_213408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT164+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n002.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 : 300
% 0.13/0.34 % DateTime : Thu Aug 24 16:43:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 223.35/30.35 % SZS status Started for theBenchmark.p
% 223.35/30.35 % SZS status Theorem for theBenchmark.p
% 223.35/30.35
% 223.35/30.35 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 223.35/30.35
% 223.35/30.35 ------ iProver source info
% 223.35/30.35
% 223.35/30.35 git: date: 2023-05-31 18:12:56 +0000
% 223.35/30.35 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 223.35/30.35 git: non_committed_changes: false
% 223.35/30.35 git: last_make_outside_of_git: false
% 223.35/30.35
% 223.35/30.35 ------ Parsing...
% 223.35/30.35 ------ Clausification by vclausify_rel & Parsing by iProver...
% 223.35/30.35
% 223.35/30.35 ------ Preprocessing... sup_sim: 22 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 5 sf_s rm: 19 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe_e
% 223.35/30.35
% 223.35/30.35 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 223.35/30.35
% 223.35/30.35 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 223.35/30.35 ------ Proving...
% 223.35/30.35 ------ Problem Properties
% 223.35/30.35
% 223.35/30.35
% 223.35/30.35 clauses 441
% 223.35/30.35 conjectures 2
% 223.35/30.35 EPR 18
% 223.35/30.35 Horn 336
% 223.35/30.35 unary 111
% 223.35/30.35 binary 151
% 223.35/30.35 lits 1137
% 223.35/30.35 lits eq 244
% 223.35/30.35 fd_pure 0
% 223.35/30.35 fd_pseudo 0
% 223.35/30.35 fd_cond 11
% 223.35/30.35 fd_pseudo_cond 72
% 223.35/30.35 AC symbols 0
% 223.35/30.35
% 223.35/30.35 ------ Input Options Time Limit: Unbounded
% 223.35/30.35
% 223.35/30.35
% 223.35/30.35 ------
% 223.35/30.35 Current options:
% 223.35/30.35 ------
% 223.35/30.35
% 223.35/30.35
% 223.35/30.35
% 223.35/30.35
% 223.35/30.35 ------ Proving...
% 223.35/30.35
% 223.35/30.35
% 223.35/30.35 % SZS status Theorem for theBenchmark.p
% 223.35/30.35
% 223.35/30.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 223.35/30.35
% 223.35/30.36
%------------------------------------------------------------------------------