TSTP Solution File: SWW225+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWW225+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n023.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 : Mon Jun 24 18:16:36 EDT 2024
% Result : Theorem 94.23s 13.69s
% Output : CNFRefutation 94.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 124 ( 61 unt; 0 def)
% Number of atoms : 208 ( 51 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 157 ( 73 ~; 59 |; 7 &)
% ( 11 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 205 ( 7 sgn 132 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
c_SEQ_Osubseq(v_f____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fz_I1_J) ).
fof(f66,axiom,
! [X14,X5,X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(f67,axiom,
! [X25,X22,X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X25)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(f68,axiom,
! [X5,X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f70,axiom,
! [X18,X1] :
( c_SEQ_Osubseq(X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,hAPP(X1,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_seq__suble) ).
fof(f73,axiom,
! [X25,X22,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X22)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(f229,axiom,
! [X5,X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5),X5) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(f230,axiom,
! [X6,X5] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6),X5) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(f241,axiom,
! [X18,X17] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(f308,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
<=> ? [X21] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X21)) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(f314,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(f315,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X18),X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(f323,axiom,
! [X5] : c_Nat_OSuc(X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f341,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(f445,axiom,
! [X5] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5)) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
fof(f457,axiom,
! [X9,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,c_RComplete_Onatfloor(X23))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X9),X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
fof(f595,axiom,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__eq__of__nat) ).
fof(f1269,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1270,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(negated_conjecture,[],[f1269]) ).
fof(f1333,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(rectify,[],[f66]) ).
fof(f1334,plain,
! [X0,X1,X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(rectify,[],[f67]) ).
fof(f1335,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(rectify,[],[f68]) ).
fof(f1337,plain,
! [X0,X1] :
( c_SEQ_Osubseq(X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(X1,X0)) ),
inference(rectify,[],[f70]) ).
fof(f1340,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) ),
inference(rectify,[],[f73]) ).
fof(f1494,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
inference(rectify,[],[f229]) ).
fof(f1495,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
inference(rectify,[],[f230]) ).
fof(f1506,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
inference(rectify,[],[f241]) ).
fof(f1573,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = X0 ),
inference(rectify,[],[f308]) ).
fof(f1579,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f314]) ).
fof(f1580,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(rectify,[],[f315]) ).
fof(f1588,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(rectify,[],[f323]) ).
fof(f1603,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)),
inference(rectify,[],[f341]) ).
fof(f1701,plain,
! [X0] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
inference(rectify,[],[f445]) ).
fof(f1711,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_RComplete_Onatfloor(X1))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),X1) ) ),
inference(rectify,[],[f457]) ).
fof(f2289,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(flattening,[],[f1270]) ).
fof(f2361,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(X1,X0))
| ~ c_SEQ_Osubseq(X1) ),
inference(ennf_transformation,[],[f1337]) ).
fof(f2363,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f1340]) ).
fof(f2720,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_RComplete_Onatfloor(X1))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),X1) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(ennf_transformation,[],[f1711]) ).
fof(f3474,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1506]) ).
fof(f3500,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
& ( ? [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1573]) ).
fof(f3501,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
& ( ? [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f3500]) ).
fof(f3502,plain,
! [X0,X1] :
( ? [X3] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = X0
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK32(X0,X1))) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3503,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) != X0 )
& ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK32(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f3501,f3502]) ).
fof(f3506,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f1579]) ).
fof(f3507,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f1580]) ).
fof(f3576,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_RComplete_Onatfloor(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_RComplete_Onatfloor(X1)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(nnf_transformation,[],[f2720]) ).
fof(f3824,plain,
c_SEQ_Osubseq(v_f____),
inference(cnf_transformation,[],[f2]) ).
fof(f3906,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f1333]) ).
fof(f3907,plain,
! [X2,X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)),
inference(cnf_transformation,[],[f1334]) ).
fof(f3908,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(cnf_transformation,[],[f1335]) ).
fof(f3911,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(X1,X0))
| ~ c_SEQ_Osubseq(X1) ),
inference(cnf_transformation,[],[f2361]) ).
fof(f3914,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2363]) ).
fof(f4147,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0) = X1,
inference(cnf_transformation,[],[f1494]) ).
fof(f4148,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1) = X0,
inference(cnf_transformation,[],[f1495]) ).
fof(f4161,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f4162,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) ),
inference(cnf_transformation,[],[f3474]) ).
fof(f4253,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK32(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3503]) ).
fof(f4262,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f3506]) ).
fof(f4263,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3506]) ).
fof(f4264,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3507]) ).
fof(f4277,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1588]) ).
fof(f4307,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f1603]) ).
fof(f4450,plain,
! [X0] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
inference(cnf_transformation,[],[f1701]) ).
fof(f4466,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_RComplete_Onatfloor(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(cnf_transformation,[],[f3576]) ).
fof(f4661,plain,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f595]) ).
fof(f5542,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(cnf_transformation,[],[f2289]) ).
fof(f5595,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(definition_unfolding,[],[f4162,f4277]) ).
fof(f5596,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4161,f4277]) ).
fof(f5621,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK32(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4253,f4277]) ).
fof(f5629,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4263,f4277]) ).
fof(f5630,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)) ),
inference(definition_unfolding,[],[f4262,f4277]) ).
fof(f5632,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(definition_unfolding,[],[f4264,f4277]) ).
fof(f5733,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(definition_unfolding,[],[f5542,f4277,f4277]) ).
cnf(c_50,plain,
c_SEQ_Osubseq(v_f____),
inference(cnf_transformation,[],[f3824]) ).
cnf(c_122,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(cnf_transformation,[],[f3906]) ).
cnf(c_123,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X2)),
inference(cnf_transformation,[],[f3907]) ).
cnf(c_124,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),
inference(cnf_transformation,[],[f3908]) ).
cnf(c_127,plain,
( ~ c_SEQ_Osubseq(X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f3911]) ).
cnf(c_130,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(cnf_transformation,[],[f3914]) ).
cnf(c_350,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X1) = X0,
inference(cnf_transformation,[],[f4147]) ).
cnf(c_351,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),X0) = X1,
inference(cnf_transformation,[],[f4148]) ).
cnf(c_364,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f5595]) ).
cnf(c_365,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f5596]) ).
cnf(c_457,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,sK32(X1,X0))) = X1 ),
inference(cnf_transformation,[],[f5621]) ).
cnf(c_465,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f5629]) ).
cnf(c_466,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[],[f5630]) ).
cnf(c_468,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),X1) ),
inference(cnf_transformation,[],[f5632]) ).
cnf(c_509,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f4307]) ).
cnf(c_649,plain,
c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
inference(cnf_transformation,[],[f4450]) ).
cnf(c_666,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_RComplete_Onatfloor(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),X1) ),
inference(cnf_transformation,[],[f4466]) ).
cnf(c_854,plain,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f4661]) ).
cnf(c_1721,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(cnf_transformation,[],[f5733]) ).
cnf(c_2608,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_465,c_364]) ).
cnf(c_2609,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(renaming,[status(thm)],[c_2608]) ).
cnf(c_2784,plain,
( ~ c_SEQ_Osubseq(X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(X0,X1)) ),
inference(prop_impl_just,[status(thm)],[c_127]) ).
cnf(c_2910,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_365,c_130,c_466]) ).
cnf(c_2911,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(renaming,[status(thm)],[c_2910]) ).
cnf(c_13096,plain,
c_RComplete_Onatfloor(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_649,c_854]) ).
cnf(c_13106,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X0)),
inference(light_normalisation,[status(thm)],[c_509,c_854]) ).
cnf(c_15523,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_RComplete_Onatfloor(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_666,c_854]) ).
cnf(c_17406,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(light_normalisation,[status(thm)],[c_1721,c_854]) ).
cnf(c_17407,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(demodulation,[status(thm)],[c_17406,c_123,c_124]) ).
cnf(c_20796,plain,
( X0 != v_f____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_50,c_2784]) ).
cnf(c_20797,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(v_f____,X0)),
inference(unflattening,[status(thm)],[c_20796]) ).
cnf(c_102933,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_2609]) ).
cnf(c_102934,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(renaming,[status(thm)],[c_102933]) ).
cnf(c_103203,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_2911]) ).
cnf(c_103204,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(renaming,[status(thm)],[c_103203]) ).
cnf(c_156464,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_RComplete_Onatfloor(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
inference(superposition,[status(thm)],[c_15523,c_17407]) ).
cnf(c_156465,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_RComplete_Onatfloor(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),
inference(forward_subsumption_resolution,[status(thm)],[c_156464,c_13106]) ).
cnf(c_156466,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(demodulation,[status(thm)],[c_156465,c_13096]) ).
cnf(c_157352,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X0),X0),
inference(superposition,[status(thm)],[c_20797,c_102934]) ).
cnf(c_158563,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(superposition,[status(thm)],[c_103204,c_156466]) ).
cnf(c_186111,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1),
inference(superposition,[status(thm)],[c_122,c_350]) ).
cnf(c_235459,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK32(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(superposition,[status(thm)],[c_158563,c_457]) ).
cnf(c_236500,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK32(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ),
inference(superposition,[status(thm)],[c_235459,c_468]) ).
cnf(c_236552,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK32(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_235459,c_351]) ).
cnf(c_250522,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),sK32(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),
inference(demodulation,[status(thm)],[c_236552,c_186111]) ).
cnf(c_250584,plain,
sK32(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(superposition,[status(thm)],[c_250522,c_351]) ).
cnf(c_250780,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),
inference(demodulation,[status(thm)],[c_250522,c_250584]) ).
cnf(c_252784,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ),
inference(light_normalisation,[status(thm)],[c_236500,c_250584,c_250780]) ).
cnf(c_252820,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(superposition,[status(thm)],[c_252784,c_156466]) ).
cnf(c_253045,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),
inference(superposition,[status(thm)],[c_365,c_252820]) ).
cnf(c_253054,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_253045,c_157352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW225+1 : TPTP v8.2.0. Released v5.2.0.
% 0.04/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n023.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
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Wed Jun 19 05:49:09 EDT 2024
% 0.18/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 94.23/13.69 % SZS status Started for theBenchmark.p
% 94.23/13.69 % SZS status Theorem for theBenchmark.p
% 94.23/13.69
% 94.23/13.69 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 94.23/13.69
% 94.23/13.69 ------ iProver source info
% 94.23/13.69
% 94.23/13.69 git: date: 2024-06-12 09:56:46 +0000
% 94.23/13.69 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 94.23/13.69 git: non_committed_changes: false
% 94.23/13.69
% 94.23/13.69 ------ Parsing...
% 94.23/13.69 ------ Clausification by vclausify_rel & Parsing by iProver...
% 94.23/13.69
% 94.23/13.69 ------ Preprocessing... sup_sim: 282 sf_s rm: 7 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 37 sf_s rm: 8 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe_e
% 94.23/13.69
% 94.23/13.69 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 94.23/13.69
% 94.23/13.69 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 94.23/13.69 ------ Proving...
% 94.23/13.69 ------ Problem Properties
% 94.23/13.69
% 94.23/13.69
% 94.23/13.69 clauses 1413
% 94.23/13.69 conjectures 0
% 94.23/13.69 EPR 248
% 94.23/13.69 Horn 1167
% 94.23/13.69 unary 426
% 94.23/13.69 binary 499
% 94.23/13.69 lits 3142
% 94.23/13.69 lits eq 663
% 94.23/13.69 fd_pure 0
% 94.23/13.69 fd_pseudo 0
% 94.23/13.69 fd_cond 86
% 94.23/13.69 fd_pseudo_cond 63
% 94.23/13.69 AC symbols 0
% 94.23/13.69
% 94.23/13.69 ------ Schedule dynamic 5 is on
% 94.23/13.69
% 94.23/13.69 ------ no conjectures: strip conj schedule
% 94.23/13.69
% 94.23/13.69 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 94.23/13.69
% 94.23/13.69
% 94.23/13.69 ------
% 94.23/13.69 Current options:
% 94.23/13.69 ------
% 94.23/13.69
% 94.23/13.69
% 94.23/13.69
% 94.23/13.69
% 94.23/13.69 ------ Proving...
% 94.23/13.69
% 94.23/13.69
% 94.23/13.69 % SZS status Theorem for theBenchmark.p
% 94.23/13.69
% 94.23/13.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 94.23/13.69
% 94.23/13.70
%------------------------------------------------------------------------------