TSTP Solution File: SWW207+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SWW207+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 20:10:46 EDT 2023
% Result : Theorem 6.80s 1.48s
% Output : CNFRefutation 6.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 87 ( 48 unt; 0 def)
% Number of atoms : 145 ( 34 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 107 ( 49 ~; 39 |; 7 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 93 ( 2 sgn; 47 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_less__le__not__le,axiom,
! [X9,X10,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_less__le__not__le) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X27] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X27)),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_less__eq__Suc__le__raw) ).
fof(fact_Suc__eq__plus1,axiom,
! [X29] : c_Nat_OSuc(X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_Suc__eq__plus1) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(fact_natfloor__mono,axiom,
! [X12,X7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X7)),c_RComplete_Onatfloor(X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_natfloor__mono) ).
fof(fact_le__natfloor__eq__one,axiom,
! [X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X10)) ),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_le__natfloor__eq__one) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X29] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29) = X29,
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_plus__nat_Oadd__0) ).
fof(fact_natfloor__zero,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_natfloor__zero) ).
fof(fact_complex__Re__i,axiom,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_complex__Re__i) ).
fof(fact_complex__Im__i,axiom,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_complex__Im__i) ).
fof(fact_leI,axiom,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_leI) ).
fof(conj_0,conjecture,
? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X8)))))),X37)) ),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',conj_0) ).
fof(fact_real__norm__def,axiom,
! [X23] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X23) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X23),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_real__norm__def) ).
fof(fact_th,axiom,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X8)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_th) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_gr0I,axiom,
! [X29] :
( X29 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)) ),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_gr0I) ).
fof(fact_real__natfloor__gt__diff__one,axiom,
! [X7] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X7,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X7)))),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_real__natfloor__gt__diff__one) ).
fof(fact_add__diff__cancel,axiom,
! [X11,X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ominus__class_Ominus(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X11),X11) = X4 ),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_add__diff__cancel) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(fact_rp,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_rp) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p',fact_real__of__nat__zero) ).
fof(c_0_22,plain,
! [X9,X10,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X10),X9))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X9),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_23,plain,
! [X330,X331,X332] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X331),X330))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X332,X331),X330))
| ~ class_Orderings_Opreorder(X332) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X330),X331))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X332,X331),X330))
| ~ class_Orderings_Opreorder(X332) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X331),X330))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X330),X331))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X332,X331),X330))
| ~ class_Orderings_Opreorder(X332) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
fof(c_0_24,plain,
! [X1915] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1915) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1915)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(c_0_25,plain,
! [X1900] : c_Nat_OSuc(X1900) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1900),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
cnf(c_0_26,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
fof(c_0_28,plain,
! [X1071,X1072] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1072),X1071))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1072)),c_RComplete_Onatfloor(X1071))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__mono])]) ).
fof(c_0_29,plain,
! [X1342] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1342)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1342)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1342))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1342))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])]) ).
cnf(c_0_30,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
c_Nat_OSuc(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X629] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X629) = X629,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
cnf(c_0_33,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2),X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_natfloor__zero]) ).
cnf(c_0_36,plain,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_complex__Re__i]) ).
cnf(c_0_37,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_complex__Im__i]) ).
cnf(c_0_39,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_41,plain,
! [X12,X7,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X5,X7),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X12),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(c_0_42,negated_conjecture,
~ ? [X37] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37))
& ! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,X8)))))),X37)) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_43,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,plain,
c_RComplete_Onatfloor(hAPP(c_Complex_ORe,c_Complex_Oii)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1)) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_47,plain,
! [X324,X325,X326] :
( ~ class_Orderings_Olinorder(X326)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X326,X325),X324))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X326,X324),X325)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).
cnf(c_0_48,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_49,negated_conjecture,
! [X2833] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2833))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_1(X2833))))))),X2833)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
fof(c_0_50,plain,
! [X400] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X400) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X400),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_51,plain,
! [X362] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X362)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(variable_rename,[status(thm)],[fact_th]) ).
cnf(c_0_52,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1)) ),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_54,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c_0_56,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
inference(rw,[status(thm)],[c_0_48,c_0_38]) ).
fof(c_0_57,plain,
! [X701] :
( X701 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X701)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
cnf(c_0_58,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_1(X1))))))),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_59,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
inference(rw,[status(thm)],[c_0_56,c_0_46]) ).
cnf(c_0_64,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_65,plain,
! [X2414] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2414,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X2414)))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__gt__diff__one]) ).
cnf(c_0_66,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,esk72_1(X1))))))),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_36]),c_0_59]) ).
cnf(c_0_67,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,X1)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_59]),c_0_38]) ).
cnf(c_0_68,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,plain,
( c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
fof(c_0_70,plain,
! [X2074,X2075,X2076] :
( ~ class_Groups_Ogroup__add(X2076)
| c_Groups_Ominus__class_Ominus(X2076,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2076),X2075),X2074),X2074) = X2075 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
cnf(c_0_71,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c_0_72,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(split_conjunct,[status(thm)],[fact_rp]) ).
cnf(c_0_73,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)))),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii)))),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_75,plain,
( c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,plain,
( c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(c_0_78,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__of__nat__zero]) ).
cnf(c_0_79,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_71]) ).
cnf(c_0_80,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),v_r)),
inference(rw,[status(thm)],[c_0_72,c_0_36]) ).
cnf(c_0_81,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,hAPP(c_Complex_OIm,c_Complex_Oii))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X1)))),
inference(rw,[status(thm)],[c_0_73,c_0_38]) ).
cnf(c_0_82,negated_conjecture,
c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),hAPP(c_Complex_OIm,c_Complex_Oii))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_83,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),X2),X2) = X1,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_84,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Complex_ORe,c_Complex_Oii),
inference(rw,[status(thm)],[c_0_78,c_0_36]) ).
cnf(c_0_85,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),hAPP(c_Complex_ORe,c_Complex_Oii))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_84]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWW207+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n011.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 2400
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Oct 2 22:31:08 EDT 2023
% 0.16/0.31 % CPUTime :
% 0.16/0.54 Running first-order model finding
% 0.16/0.54 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.M6Ng3xzOvo/E---3.1_26853.p
% 6.80/1.48 # Version: 3.1pre001
% 6.80/1.48 # Preprocessing class: FMLMSMSMSSSNFFN.
% 6.80/1.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.80/1.48 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.80/1.48 # Starting new_bool_3 with 300s (1) cores
% 6.80/1.48 # Starting new_bool_1 with 300s (1) cores
% 6.80/1.48 # Starting sh5l with 300s (1) cores
% 6.80/1.48 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 26931 completed with status 0
% 6.80/1.48 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 6.80/1.48 # Preprocessing class: FMLMSMSMSSSNFFN.
% 6.80/1.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.80/1.48 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.80/1.48 # No SInE strategy applied
% 6.80/1.48 # Search class: FGHSM-SSLM32-DFFFFFNN
% 6.80/1.48 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 6.80/1.48 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 6.80/1.48 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.80/1.48 # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 6.80/1.48 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 6.80/1.48 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 113s (1) cores
% 6.80/1.48 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 26941 completed with status 0
% 6.80/1.48 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 6.80/1.48 # Preprocessing class: FMLMSMSMSSSNFFN.
% 6.80/1.48 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.80/1.48 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 6.80/1.48 # No SInE strategy applied
% 6.80/1.48 # Search class: FGHSM-SSLM32-DFFFFFNN
% 6.80/1.48 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 6.80/1.48 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 6.80/1.48 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.80/1.48 # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 6.80/1.48 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 6.80/1.48 # Preprocessing time : 0.022 s
% 6.80/1.48 # Presaturation interreduction done
% 6.80/1.48
% 6.80/1.48 # Proof found!
% 6.80/1.48 # SZS status Theorem
% 6.80/1.48 # SZS output start CNFRefutation
% See solution above
% 6.80/1.48 # Parsed axioms : 1269
% 6.80/1.48 # Removed by relevancy pruning/SinE : 0
% 6.80/1.48 # Initial clauses : 1712
% 6.80/1.48 # Removed in clause preprocessing : 48
% 6.80/1.48 # Initial clauses in saturation : 1664
% 6.80/1.48 # Processed clauses : 6865
% 6.80/1.48 # ...of these trivial : 110
% 6.80/1.48 # ...subsumed : 2873
% 6.80/1.48 # ...remaining for further processing : 3882
% 6.80/1.48 # Other redundant clauses eliminated : 194
% 6.80/1.48 # Clauses deleted for lack of memory : 0
% 6.80/1.48 # Backward-subsumed : 46
% 6.80/1.48 # Backward-rewritten : 27
% 6.80/1.48 # Generated clauses : 18922
% 6.80/1.48 # ...of the previous two non-redundant : 15742
% 6.80/1.48 # ...aggressively subsumed : 0
% 6.80/1.48 # Contextual simplify-reflections : 2
% 6.80/1.48 # Paramodulations : 18724
% 6.80/1.48 # Factorizations : 10
% 6.80/1.48 # NegExts : 0
% 6.80/1.48 # Equation resolutions : 205
% 6.80/1.48 # Total rewrite steps : 10848
% 6.80/1.48 # Propositional unsat checks : 0
% 6.80/1.48 # Propositional check models : 0
% 6.80/1.48 # Propositional check unsatisfiable : 0
% 6.80/1.48 # Propositional clauses : 0
% 6.80/1.48 # Propositional clauses after purity: 0
% 6.80/1.48 # Propositional unsat core size : 0
% 6.80/1.48 # Propositional preprocessing time : 0.000
% 6.80/1.48 # Propositional encoding time : 0.000
% 6.80/1.48 # Propositional solver time : 0.000
% 6.80/1.48 # Success case prop preproc time : 0.000
% 6.80/1.48 # Success case prop encoding time : 0.000
% 6.80/1.48 # Success case prop solver time : 0.000
% 6.80/1.48 # Current number of processed clauses : 2288
% 6.80/1.48 # Positive orientable unit clauses : 677
% 6.80/1.48 # Positive unorientable unit clauses: 14
% 6.80/1.48 # Negative unit clauses : 522
% 6.80/1.48 # Non-unit-clauses : 1075
% 6.80/1.48 # Current number of unprocessed clauses: 11876
% 6.80/1.48 # ...number of literals in the above : 23184
% 6.80/1.48 # Current number of archived formulas : 0
% 6.80/1.48 # Current number of archived clauses : 1465
% 6.80/1.48 # Clause-clause subsumption calls (NU) : 345492
% 6.80/1.48 # Rec. Clause-clause subsumption calls : 235549
% 6.80/1.48 # Non-unit clause-clause subsumptions : 752
% 6.80/1.48 # Unit Clause-clause subsumption calls : 24404
% 6.80/1.48 # Rewrite failures with RHS unbound : 0
% 6.80/1.48 # BW rewrite match attempts : 6971
% 6.80/1.48 # BW rewrite match successes : 242
% 6.80/1.48 # Condensation attempts : 0
% 6.80/1.48 # Condensation successes : 0
% 6.80/1.48 # Termbank termtop insertions : 542290
% 6.80/1.48
% 6.80/1.48 # -------------------------------------------------
% 6.80/1.48 # User time : 0.828 s
% 6.80/1.48 # System time : 0.028 s
% 6.80/1.48 # Total time : 0.856 s
% 6.80/1.48 # Maximum resident set size: 8704 pages
% 6.80/1.48
% 6.80/1.48 # -------------------------------------------------
% 6.80/1.48 # User time : 3.751 s
% 6.80/1.48 # System time : 0.116 s
% 6.80/1.48 # Total time : 3.867 s
% 6.80/1.48 # Maximum resident set size: 3236 pages
% 6.80/1.48 % E---3.1 exiting
%------------------------------------------------------------------------------