TSTP Solution File: SWW208+1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 20:08:48 EDT 2023
% Result : Theorem 4.94s 1.41s
% Output : CNFRefutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 59 ( 31 unt; 0 def)
% Number of atoms : 110 ( 25 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 93 ( 42 ~; 34 |; 8 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 70 ( 5 sgn; 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_less__le__not__le,axiom,
! [X21,X13,X6] :
( class_Orderings_Opreorder(X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X13),X21))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X13),X21))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X21),X13)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_less__le__not__le) ).
fof(fact_real__le__trans,axiom,
! [X17,X18,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19),X17)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_real__le__trans) ).
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.ddB6U9IdRp/E---3.1_17247.p',fact_rp) ).
fof(conj_0,conjecture,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
& ! [X4] : 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____,X4)))))),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.ddB6U9IdRp/E---3.1_17247.p',conj_0) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(fact_real__le__linear,axiom,
! [X12,X11] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11),X12))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_real__le__linear) ).
fof(fact_less__add__one,axiom,
! [X8,X6] :
( class_Rings_Olinordered__semidom(X6)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6),X8),c_Groups_Oone__class_Oone(X6)))) ),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_less__add__one) ).
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.ddB6U9IdRp/E---3.1_17247.p',fact_real__norm__def) ).
fof(fact_th,axiom,
! [X4] : 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,X4)))),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.ddB6U9IdRp/E---3.1_17247.p',fact_th) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(fact_Zero__neq__Suc,axiom,
! [X29] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X29),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_Zero__neq__Suc) ).
fof(fact_Suc__eq__plus1,axiom,
! [X25] : c_Nat_OSuc(X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_Suc__eq__plus1) ).
fof(fact_natfloor__add__one,axiom,
! [X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X5))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X5),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X5)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_natfloor__add__one) ).
fof(fact_nat__add__commute,axiom,
! [X25,X29] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X29),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_nat__add__commute) ).
fof(fact_less__eq__real__def,axiom,
! [X21,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X13),X21))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13),X21))
| X13 = X21 ) ),
file('/export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p',fact_less__eq__real__def) ).
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.ddB6U9IdRp/E---3.1_17247.p',fact_natfloor__zero) ).
fof(c_0_16,plain,
! [X21,X13,X6] :
( class_Orderings_Opreorder(X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X6,X13),X21))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X13),X21))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X6,X21),X13)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_17,plain,
! [X180,X181,X182] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X182),X181))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X181),X180))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X182),X180)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(c_0_18,plain,
! [X503,X504,X505] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X504),X503))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X505,X504),X503))
| ~ class_Orderings_Opreorder(X505) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X503),X504))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X505,X504),X503))
| ~ class_Orderings_Opreorder(X505) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X504),X503))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X505,X503),X504))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X505,X504),X503))
| ~ class_Orderings_Opreorder(X505) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_19,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,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]) ).
fof(c_0_21,negated_conjecture,
~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
& ! [X4] : 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____,X4)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_22,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_18]) ).
cnf(c_0_23,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(c_0_25,plain,
! [X183,X184] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X184),X183))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X183),X184)) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(c_0_26,plain,
! [X326,X327] :
( ~ class_Rings_Olinordered__semidom(X327)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X327,X326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X327),X326),c_Groups_Oone__class_Oone(X327)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(c_0_27,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ 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_0)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_28,plain,
! [X361] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X361) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X361),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_29,plain,
! [X113] : 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,X113)))),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_30,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_31,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c_0_34,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ 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_0)))))),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_27]) ).
cnf(c_0_35,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_28]) ).
cnf(c_0_36,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_29]) ).
fof(c_0_37,plain,
! [X1557] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1557),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_38,plain,
! [X1623] : c_Nat_OSuc(X1623) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1623),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_39,plain,
! [X1393] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1393))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1393),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1393)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add__one])]) ).
fof(c_0_40,plain,
! [X1198,X1199] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1199),X1198) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1198),X1199),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(c_0_41,plain,
! [X266,X267] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X267),X266))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X267),X266))
| X267 = X266 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X267),X266))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X267),X266)) )
& ( X267 != X266
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X267),X266)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
cnf(c_0_42,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_43,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_44,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_0)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_45,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),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(rw,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_46,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,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_38]) ).
cnf(c_0_48,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
cnf(c_0_53,plain,
c_Groups_Ozero__class_Ozero(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_46,c_0_47]) ).
cnf(c_0_54,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_56,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_57,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_53,c_0_49]) ).
cnf(c_0_58,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_20])]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.22/0.22 % Problem : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% 0.22/0.23 % Command : run_E %s %d THM
% 0.22/0.44 % Computer : n004.cluster.edu
% 0.22/0.44 % Model : x86_64 x86_64
% 0.22/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.44 % Memory : 8042.1875MB
% 0.22/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.22/0.44 % CPULimit : 2400
% 0.22/0.44 % WCLimit : 300
% 0.22/0.44 % DateTime : Mon Oct 2 22:09:00 EDT 2023
% 0.22/0.44 % CPUTime :
% 0.41/0.67 Running first-order theorem proving
% 0.41/0.67 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.ddB6U9IdRp/E---3.1_17247.p
% 4.94/1.41 # Version: 3.1pre001
% 4.94/1.41 # Preprocessing class: FMLMSMSMSSSNFFN.
% 4.94/1.41 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.94/1.41 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.94/1.41 # Starting new_bool_3 with 300s (1) cores
% 4.94/1.41 # Starting new_bool_1 with 300s (1) cores
% 4.94/1.41 # Starting sh5l with 300s (1) cores
% 4.94/1.41 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 17334 completed with status 0
% 4.94/1.41 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 4.94/1.41 # Preprocessing class: FMLMSMSMSSSNFFN.
% 4.94/1.41 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.94/1.41 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.94/1.41 # No SInE strategy applied
% 4.94/1.41 # Search class: FGHSM-SSLM32-DFFFFFNN
% 4.94/1.41 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 4.94/1.41 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 4.94/1.41 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.94/1.41 # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 4.94/1.41 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 4.94/1.41 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 113s (1) cores
% 4.94/1.41 # G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 17345 completed with status 0
% 4.94/1.41 # Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 4.94/1.41 # Preprocessing class: FMLMSMSMSSSNFFN.
% 4.94/1.41 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.94/1.41 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.94/1.41 # No SInE strategy applied
% 4.94/1.41 # Search class: FGHSM-SSLM32-DFFFFFNN
% 4.94/1.41 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 4.94/1.41 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 4.94/1.41 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.94/1.41 # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 4.94/1.41 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 4.94/1.41 # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 113s (1) cores
% 4.94/1.41 # Preprocessing time : 0.023 s
% 4.94/1.41 # Presaturation interreduction done
% 4.94/1.41
% 4.94/1.41 # Proof found!
% 4.94/1.41 # SZS status Theorem
% 4.94/1.41 # SZS output start CNFRefutation
% See solution above
% 4.94/1.41 # Parsed axioms : 1269
% 4.94/1.41 # Removed by relevancy pruning/SinE : 0
% 4.94/1.41 # Initial clauses : 1712
% 4.94/1.41 # Removed in clause preprocessing : 48
% 4.94/1.41 # Initial clauses in saturation : 1664
% 4.94/1.41 # Processed clauses : 5171
% 4.94/1.41 # ...of these trivial : 86
% 4.94/1.41 # ...subsumed : 2050
% 4.94/1.41 # ...remaining for further processing : 3035
% 4.94/1.41 # Other redundant clauses eliminated : 223
% 4.94/1.41 # Clauses deleted for lack of memory : 0
% 4.94/1.41 # Backward-subsumed : 25
% 4.94/1.41 # Backward-rewritten : 41
% 4.94/1.41 # Generated clauses : 10855
% 4.94/1.41 # ...of the previous two non-redundant : 9246
% 4.94/1.41 # ...aggressively subsumed : 0
% 4.94/1.41 # Contextual simplify-reflections : 5
% 4.94/1.41 # Paramodulations : 10629
% 4.94/1.41 # Factorizations : 6
% 4.94/1.41 # NegExts : 0
% 4.94/1.41 # Equation resolutions : 236
% 4.94/1.41 # Total rewrite steps : 7716
% 4.94/1.41 # Propositional unsat checks : 0
% 4.94/1.41 # Propositional check models : 0
% 4.94/1.41 # Propositional check unsatisfiable : 0
% 4.94/1.41 # Propositional clauses : 0
% 4.94/1.41 # Propositional clauses after purity: 0
% 4.94/1.41 # Propositional unsat core size : 0
% 4.94/1.41 # Propositional preprocessing time : 0.000
% 4.94/1.41 # Propositional encoding time : 0.000
% 4.94/1.41 # Propositional solver time : 0.000
% 4.94/1.41 # Success case prop preproc time : 0.000
% 4.94/1.41 # Success case prop encoding time : 0.000
% 4.94/1.41 # Success case prop solver time : 0.000
% 4.94/1.41 # Current number of processed clauses : 1453
% 4.94/1.41 # Positive orientable unit clauses : 545
% 4.94/1.41 # Positive unorientable unit clauses: 23
% 4.94/1.41 # Negative unit clauses : 235
% 4.94/1.41 # Non-unit-clauses : 650
% 4.94/1.41 # Current number of unprocessed clauses: 7099
% 4.94/1.41 # ...number of literals in the above : 13241
% 4.94/1.41 # Current number of archived formulas : 0
% 4.94/1.41 # Current number of archived clauses : 1454
% 4.94/1.41 # Clause-clause subsumption calls (NU) : 178148
% 4.94/1.41 # Rec. Clause-clause subsumption calls : 105018
% 4.94/1.41 # Non-unit clause-clause subsumptions : 693
% 4.94/1.41 # Unit Clause-clause subsumption calls : 9149
% 4.94/1.41 # Rewrite failures with RHS unbound : 1776
% 4.94/1.41 # BW rewrite match attempts : 4255
% 4.94/1.41 # BW rewrite match successes : 551
% 4.94/1.41 # Condensation attempts : 0
% 4.94/1.41 # Condensation successes : 0
% 4.94/1.41 # Termbank termtop insertions : 428223
% 4.94/1.41
% 4.94/1.41 # -------------------------------------------------
% 4.94/1.41 # User time : 0.624 s
% 4.94/1.41 # System time : 0.031 s
% 4.94/1.41 # Total time : 0.655 s
% 4.94/1.41 # Maximum resident set size: 8696 pages
% 4.94/1.41
% 4.94/1.41 # -------------------------------------------------
% 4.94/1.41 # User time : 2.779 s
% 4.94/1.41 # System time : 0.112 s
% 4.94/1.41 # Total time : 2.892 s
% 4.94/1.41 # Maximum resident set size: 3236 pages
% 4.94/1.41 % E---3.1 exiting
% 5.47/1.41 % E---3.1 exiting
%------------------------------------------------------------------------------