TSTP Solution File: SWW225+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWW225+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Mar 6 15:09:39 EST 2011
% Result : Theorem 21.37s
% Output : CNFRefutation 21.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 93 ( 41 unt; 0 def)
% Number of atoms : 212 ( 41 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 201 ( 82 ~; 83 |; 25 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 134 ( 1 sgn 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(61,axiom,
! [X5,X21,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X21)) ),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_termination__basic__simps_I4_J) ).
fof(88,axiom,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_real__of__nat__def) ).
fof(137,axiom,
! [X2] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X2),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_less__irrefl__nat) ).
fof(221,axiom,
! [X16,X2,X9] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X2),X16) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X16)),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_nat__add__assoc) ).
fof(226,axiom,
! [X21,X5,X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X21)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X21)),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_nat__add__left__commute) ).
fof(281,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',arity_Nat__Onat__Orderings_Opreorder) ).
fof(331,axiom,
! [X2,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X9)
=> X9 = X2 ) ),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_le__antisym) ).
fof(407,axiom,
! [X19,X8,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X8,X19)
<=> ( c_Orderings_Oord__class_Oless__eq(X4,X8,X19)
& ~ c_Orderings_Oord__class_Oless__eq(X4,X19,X8) ) ) ),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_less__le__not__le) ).
fof(427,axiom,
! [X26,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X26)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X26)
& X7 != X26 ) ),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_nat__less__le) ).
fof(453,axiom,
! [X2] : c_Nat_OSuc(X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_Suc__eq__plus1) ).
fof(614,axiom,
! [X26,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Nat_OSuc(X26))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X26)
| X7 = c_Nat_OSuc(X26) ) ),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_le__Suc__eq) ).
fof(669,axiom,
! [X26,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Nat_OSuc(X26))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X26) ),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_less__Suc__eq__le) ).
fof(743,axiom,
! [X2,X9] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X9,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X9),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_nat__add__commute) ).
fof(767,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('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',conj_0) ).
fof(782,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) ).
fof(812,axiom,
! [X2,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X9) ),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_nat__le__linear) ).
fof(1148,axiom,
! [X37,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X37)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X37,X21) ),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_real__le__linear) ).
fof(1246,axiom,
! [X7,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X26),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X7))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X7) ),
file('/tmp/tmpiiCKZs/sel_SWW225+1.p_1',fact_real__of__nat__le__iff) ).
fof(1270,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(assume_negation,[status(cth)],[767]) ).
fof(1282,plain,
! [X2] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X2),
inference(fof_simplification,[status(thm)],[137,theory(equality)]) ).
fof(1301,plain,
! [X19,X8,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X8,X19)
<=> ( c_Orderings_Oord__class_Oless__eq(X4,X8,X19)
& ~ c_Orderings_Oord__class_Oless__eq(X4,X19,X8) ) ) ),
inference(fof_simplification,[status(thm)],[407,theory(equality)]) ).
fof(1321,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(fof_simplification,[status(thm)],[1270,theory(equality)]) ).
fof(1526,plain,
! [X5,X21,X6] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X21)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X21)) ),
inference(fof_nnf,[status(thm)],[61]) ).
fof(1527,plain,
! [X22,X23,X24] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X23)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X23)) ),
inference(variable_rename,[status(thm)],[1526]) ).
cnf(1528,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[1527]) ).
cnf(1614,plain,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[88]) ).
fof(1770,plain,
! [X3] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X3),
inference(variable_rename,[status(thm)],[1282]) ).
cnf(1771,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[1770]) ).
fof(2032,plain,
! [X17,X18,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18),X17) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17)),
inference(variable_rename,[status(thm)],[221]) ).
cnf(2033,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[2032]) ).
fof(2050,plain,
! [X22,X23,X24] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X22)),
inference(variable_rename,[status(thm)],[226]) ).
cnf(2051,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
inference(split_conjunct,[status(thm)],[2050]) ).
cnf(2253,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[281]) ).
fof(2399,plain,
! [X2,X9] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X9)
| X9 = X2 ),
inference(fof_nnf,[status(thm)],[331]) ).
fof(2400,plain,
! [X10,X11] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X10)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X11)
| X11 = X10 ),
inference(variable_rename,[status(thm)],[2399]) ).
cnf(2401,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[2400]) ).
fof(2593,plain,
! [X19,X8,X4] :
( ~ class_Orderings_Opreorder(X4)
| ( ( ~ c_Orderings_Oord__class_Oless(X4,X8,X19)
| ( c_Orderings_Oord__class_Oless__eq(X4,X8,X19)
& ~ c_Orderings_Oord__class_Oless__eq(X4,X19,X8) ) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4,X8,X19)
| c_Orderings_Oord__class_Oless__eq(X4,X19,X8)
| c_Orderings_Oord__class_Oless(X4,X8,X19) ) ) ),
inference(fof_nnf,[status(thm)],[1301]) ).
fof(2594,plain,
! [X20,X21,X22] :
( ~ class_Orderings_Opreorder(X22)
| ( ( ~ c_Orderings_Oord__class_Oless(X22,X21,X20)
| ( c_Orderings_Oord__class_Oless__eq(X22,X21,X20)
& ~ c_Orderings_Oord__class_Oless__eq(X22,X20,X21) ) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X22,X21,X20)
| c_Orderings_Oord__class_Oless__eq(X22,X20,X21)
| c_Orderings_Oord__class_Oless(X22,X21,X20) ) ) ),
inference(variable_rename,[status(thm)],[2593]) ).
fof(2595,plain,
! [X20,X21,X22] :
( ( c_Orderings_Oord__class_Oless__eq(X22,X21,X20)
| ~ c_Orderings_Oord__class_Oless(X22,X21,X20)
| ~ class_Orderings_Opreorder(X22) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X22,X20,X21)
| ~ c_Orderings_Oord__class_Oless(X22,X21,X20)
| ~ class_Orderings_Opreorder(X22) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X22,X21,X20)
| c_Orderings_Oord__class_Oless__eq(X22,X20,X21)
| c_Orderings_Oord__class_Oless(X22,X21,X20)
| ~ class_Orderings_Opreorder(X22) ) ),
inference(distribute,[status(thm)],[2594]) ).
cnf(2596,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[2595]) ).
fof(2656,plain,
! [X26,X7] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X26)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X26)
& X7 != X26 ) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X26)
| X7 = X26
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X26) ) ),
inference(fof_nnf,[status(thm)],[427]) ).
fof(2657,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X27)
| ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
& X28 != X27 ) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
| X28 = X27
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X27) ) ),
inference(variable_rename,[status(thm)],[2656]) ).
fof(2658,plain,
! [X27,X28] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X27) )
& ( X28 != X27
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X27) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
| X28 = X27
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X27) ) ),
inference(distribute,[status(thm)],[2657]) ).
cnf(2659,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[2658]) ).
fof(2735,plain,
! [X3] : c_Nat_OSuc(X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[453]) ).
cnf(2736,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[2735]) ).
fof(3198,plain,
! [X26,X7] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Nat_OSuc(X26))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X26)
| X7 = c_Nat_OSuc(X26) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X26)
& X7 != c_Nat_OSuc(X26) )
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,c_Nat_OSuc(X26)) ) ),
inference(fof_nnf,[status(thm)],[614]) ).
fof(3199,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,c_Nat_OSuc(X27))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
| X28 = c_Nat_OSuc(X27) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
& X28 != c_Nat_OSuc(X27) )
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,c_Nat_OSuc(X27)) ) ),
inference(variable_rename,[status(thm)],[3198]) ).
fof(3200,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,c_Nat_OSuc(X27))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
| X28 = c_Nat_OSuc(X27) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,c_Nat_OSuc(X27)) )
& ( X28 != c_Nat_OSuc(X27)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,c_Nat_OSuc(X27)) ) ),
inference(distribute,[status(thm)],[3199]) ).
cnf(3201,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[3200]) ).
fof(3362,plain,
! [X26,X7] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Nat_OSuc(X26))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X26) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X26)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,c_Nat_OSuc(X26)) ) ),
inference(fof_nnf,[status(thm)],[669]) ).
fof(3363,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,c_Nat_OSuc(X27))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,c_Nat_OSuc(X27)) ) ),
inference(variable_rename,[status(thm)],[3362]) ).
cnf(3365,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[3363]) ).
fof(3592,plain,
! [X10,X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X11),
inference(variable_rename,[status(thm)],[743]) ).
cnf(3593,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[3592]) ).
cnf(3653,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(split_conjunct,[status(thm)],[1321]) ).
cnf(3696,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(split_conjunct,[status(thm)],[782]) ).
fof(3776,plain,
! [X10,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11,X10)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X11) ),
inference(variable_rename,[status(thm)],[812]) ).
cnf(3777,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[3776]) ).
fof(4859,plain,
! [X38,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X39,X38)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X38,X39) ),
inference(variable_rename,[status(thm)],[1148]) ).
cnf(4860,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[4859]) ).
fof(5158,plain,
! [X7,X26] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X26),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X7))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X7) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X7)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X26),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X7)) ) ),
inference(fof_nnf,[status(thm)],[1246]) ).
fof(5159,plain,
! [X27,X28] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X28),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X27))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X28),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X27)) ) ),
inference(variable_rename,[status(thm)],[5158]) ).
cnf(5160,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[5159]) ).
cnf(5161,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2)) ),
inference(split_conjunct,[status(thm)],[5159]) ).
cnf(5345,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3201,2736,theory(equality)]),2736,theory(equality)]),
[unfolding] ).
cnf(5351,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[3365,2736,theory(equality)]),
[unfolding] ).
cnf(5486,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_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[3653,2736,theory(equality)]),2736,theory(equality)]),
[unfolding] ).
cnf(5490,negated_conjecture,
~ 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_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,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,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5486,1614,theory(equality)]),1614,theory(equality)]) ).
cnf(5718,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5161,1614,theory(equality)]),1614,theory(equality)]) ).
cnf(5763,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5160,1614,theory(equality)]),1614,theory(equality)]) ).
cnf(5844,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2) != X1 ),
inference(spm,[status(thm)],[5345,3593,theory(equality)]) ).
cnf(5945,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X1)) ),
inference(spm,[status(thm)],[5718,4860,theory(equality)]) ).
cnf(6523,plain,
( 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____)
| ~ c_Orderings_Oord__class_Oless__eq(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(spm,[status(thm)],[2401,3696,theory(equality)]) ).
cnf(8576,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(spm,[status(thm)],[5351,2033,theory(equality)]) ).
cnf(94948,negated_conjecture,
~ 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(rw,[status(thm)],[inference(rw,[status(thm)],[5490,2033,theory(equality)]),3593,theory(equality)]) ).
cnf(94951,negated_conjecture,
~ 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(spm,[status(thm)],[94948,5763,theory(equality)]) ).
cnf(94988,negated_conjecture,
~ 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))),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(spm,[status(thm)],[94951,1528,theory(equality)]) ).
cnf(95011,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(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____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(spm,[status(thm)],[94988,3777,theory(equality)]) ).
cnf(95829,negated_conjecture,
( 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))),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| 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____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Orderings_Opreorder(tc_Nat_Onat) ),
inference(spm,[status(thm)],[2596,95011,theory(equality)]) ).
cnf(95854,negated_conjecture,
( 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))),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| 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____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| $false ),
inference(rw,[status(thm)],[95829,2253,theory(equality)]) ).
cnf(95855,negated_conjecture,
( 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))),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| 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____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(cn,[status(thm)],[95854,theory(equality)]) ).
cnf(95856,negated_conjecture,
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____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(sr,[status(thm)],[95855,94988,theory(equality)]) ).
cnf(99984,negated_conjecture,
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_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(spm,[status(thm)],[94951,5844,theory(equality)]) ).
cnf(102327,negated_conjecture,
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),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____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(spm,[status(thm)],[94948,5945,theory(equality)]) ).
cnf(102456,negated_conjecture,
( 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_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_Orderings_Oord__class_Oless(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____))),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(spm,[status(thm)],[2659,102327,theory(equality)]) ).
cnf(102489,negated_conjecture,
c_Orderings_Oord__class_Oless(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____))),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(sr,[status(thm)],[102456,99984,theory(equality)]) ).
cnf(224658,negated_conjecture,
c_Orderings_Oord__class_Oless__eq(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(spm,[status(thm)],[8576,95856,theory(equality)]) ).
cnf(224818,plain,
( 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____)
| $false ),
inference(rw,[status(thm)],[6523,224658,theory(equality)]) ).
cnf(224819,plain,
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(cn,[status(thm)],[224818,theory(equality)]) ).
cnf(224943,negated_conjecture,
c_Orderings_Oord__class_Oless(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,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[102489,224819,theory(equality)]),2051,theory(equality)]),3593,theory(equality)]) ).
cnf(224944,negated_conjecture,
$false,
inference(sr,[status(thm)],[224943,1771,theory(equality)]) ).
cnf(224945,negated_conjecture,
$false,
224944,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW225+1.p
% --creating new selector for []
% -running prover on /tmp/tmpiiCKZs/sel_SWW225+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWW225+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW225+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW225+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------