%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW207+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:05 PM UTC 2026
% Result : Theorem 7.11s 1.49s
% Output : CNFRefutation 7.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 88 ( 48 unt; 0 def)
% Number of atoms : 147 ( 35 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 109 ( 50 ~; 39 |; 7 &)
% ( 3 <=>; 10 =>; 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 : 94 ( 2 sgn 48 !; 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,X9),X10))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(conj_0,conjecture,
? [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))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
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/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',fact_th) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',fact_rp) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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,X9),X10))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X9)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_23,plain,
! [X330,X331,X332] :
( ( ~ class_Orderings_Opreorder(X332)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X332,X331),X330))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X330),X331))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X331),X330)) )
& ( ~ class_Orderings_Opreorder(X332)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X332,X331),X330))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X330),X331)) )
& ( ~ class_Orderings_Opreorder(X332)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X332,X331),X330))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X332,X331),X330)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
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_Nat_Onat,c_RComplete_Onatfloor(X1072)),c_RComplete_Onatfloor(X1071)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1072),X1071)) ),
inference(fof_nnf,[status(thm)],[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(fof_nnf,[status(thm)],[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(tc_Nat_Onat,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(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_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]) ).
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] :
( ! [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))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X37)) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_43,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1)),c_RComplete_Onatfloor(X2))) ),
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_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_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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X326,X324),X325))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X326,X325),X324))
| ~ class_Orderings_Olinorder(X326) ),
inference(fof_nnf,[status(thm)],[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_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]) ).
fof(c_0_49,plain,
! [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)) ),
inference(fof_simplification,[status(thm)],[fact_gr0I]) ).
fof(c_0_50,negated_conjecture,
! [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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X2833)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
fof(c_0_51,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_52,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_53,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(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(X1))) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,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_45,c_0_46]) ).
cnf(c_0_55,plain,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c_0_57,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_48,c_0_38]) ).
fof(c_0_58,plain,
! [X701] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X701))
| X701 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])]) ).
cnf(c_0_59,negated_conjecture,
( ~ 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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,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_51]) ).
cnf(c_0_61,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_52]) ).
cnf(c_0_62,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_RealDef_Oreal,X1),hAPP(c_Complex_ORe,c_Complex_Oii))) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_63,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1),X2)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_64,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_57,c_0_46]) ).
cnf(c_0_65,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_66,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_67,negated_conjecture,
( ~ 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,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)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_36]),c_0_60]) ).
cnf(c_0_68,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_61,c_0_60]),c_0_38]) ).
cnf(c_0_69,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_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_OIm,c_Complex_Oii)),X1))
| c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
fof(c_0_71,plain,
! [X2074,X2075,X2076] :
( c_Groups_Ominus__class_Ominus(X2076,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2076),X2075),X2074),X2074) = X2075
| ~ class_Groups_Ogroup__add(X2076) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])])]) ).
cnf(c_0_72,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c_0_73,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_74,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_66]) ).
cnf(c_0_75,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_67,c_0_68]) ).
cnf(c_0_76,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Complex_ORe,c_Complex_Oii)),X1))
| c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3),X3) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(c_0_79,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_80,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2),X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_72]) ).
cnf(c_0_81,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_73,c_0_36]) ).
cnf(c_0_82,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_74,c_0_38]) ).
cnf(c_0_83,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_75,c_0_76]) ).
cnf(c_0_84,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_77,c_0_78]) ).
cnf(c_0_85,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_79,c_0_36]) ).
cnf(c_0_86,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_80,c_0_81]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_85]),c_0_86]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW207+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 09:40:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 7.11/1.49 % Version: 3.5.1
% 7.11/1.49 % Preprocessing class: FMLMSMSMSSSNFFN.
% 7.11/1.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.11/1.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.11/1.49 % Starting new_bool_3 with 300s (1) cores
% 7.11/1.49 % Starting new_bool_1 with 300s (1) cores
% 7.11/1.49 % Starting sh5l with 300s (1) cores
% 7.11/1.49 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 471835 completed with status 0
% 7.11/1.49 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 7.11/1.49 % Preprocessing class: FMLMSMSMSSSNFFN.
% 7.11/1.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.11/1.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.11/1.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.11/1.49 % No SInE strategy applied
% 7.11/1.49 % Search class: FGHSM-SSLM32-DFFFFFNN
% 7.11/1.49 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 7.11/1.49 % Starting SubtermCWHack with 136s (1) cores
% 7.11/1.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.11/1.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 7.11/1.49 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 7.11/1.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 7.11/1.49 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 471846 completed with status 0
% 7.11/1.49 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 7.11/1.49 % Preprocessing class: FMLMSMSMSSSNFFN.
% 7.11/1.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.11/1.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.11/1.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.11/1.49 % No SInE strategy applied
% 7.11/1.49 % Search class: FGHSM-SSLM32-DFFFFFNN
% 7.11/1.49 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 7.11/1.49 % Starting SubtermCWHack with 136s (1) cores
% 7.11/1.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.11/1.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 7.11/1.49 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 7.11/1.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 7.11/1.49 % Preprocessing time : 0.030 s
% 7.11/1.49 % Presaturation interreduction done
% 7.11/1.49
% 7.11/1.49 % Proof found!
% 7.11/1.49 % SZS status Theorem
% 7.11/1.49 % SZS output start CNFRefutation
% See solution above
% 7.11/1.50 % Parsed axioms : 1269
% 7.11/1.50 % Removed by relevancy pruning/SinE : 0
% 7.11/1.50 % Initial clauses : 1712
% 7.11/1.50 % Removed in clause preprocessing : 48
% 7.11/1.50 % Initial clauses in saturation : 1664
% 7.11/1.50 % Processed clauses : 6887
% 7.11/1.50 % ...of these trivial : 109
% 7.11/1.50 % ...subsumed : 2891
% 7.11/1.50 % ...remaining for further processing : 3887
% 7.11/1.50 % Other redundant clauses eliminated : 194
% 7.11/1.50 % Clauses deleted for lack of memory : 0
% 7.11/1.50 % Backward-subsumed : 47
% 7.11/1.50 % Backward-rewritten : 27
% 7.11/1.50 % Generated clauses : 18978
% 7.11/1.50 % ...of the previous two non-redundant : 15793
% 7.11/1.50 % ...aggressively subsumed : 0
% 7.11/1.50 % Contextual simplify-reflections : 2
% 7.11/1.50 % Paramodulations : 18780
% 7.11/1.50 % Factorizations : 10
% 7.11/1.50 % NegExts : 0
% 7.11/1.50 % Equation resolutions : 205
% 7.11/1.50 % Disequality decompositions : 0
% 7.11/1.50 % Total rewrite steps : 10885
% 7.11/1.50 % ...of those cached : 9582
% 7.11/1.50 % Propositional unsat checks : 0
% 7.11/1.50 % Propositional check models : 0
% 7.11/1.50 % Propositional check unsatisfiable : 0
% 7.11/1.50 % Propositional clauses : 0
% 7.11/1.50 % Propositional clauses after purity: 0
% 7.11/1.50 % Propositional unsat core size : 0
% 7.11/1.50 % Propositional preprocessing time : 0.000
% 7.11/1.50 % Propositional encoding time : 0.000
% 7.11/1.50 % Propositional solver time : 0.000
% 7.11/1.50 % Success case prop preproc time : 0.000
% 7.11/1.50 % Success case prop encoding time : 0.000
% 7.11/1.50 % Success case prop solver time : 0.000
% 7.11/1.50 % Current number of processed clauses : 2292
% 7.11/1.50 % Positive orientable unit clauses : 676
% 7.11/1.50 % Positive unorientable unit clauses: 14
% 7.11/1.50 % Negative unit clauses : 522
% 7.11/1.50 % Non-unit-clauses : 1080
% 7.11/1.50 % Current number of unprocessed clauses: 11896
% 7.11/1.50 % ...number of literals in the above : 23231
% 7.11/1.50 % Current number of archived formulas : 0
% 7.11/1.50 % Current number of archived clauses : 1466
% 7.11/1.50 % Clause-clause subsumption calls (NU) : 426736
% 7.11/1.50 % Rec. Clause-clause subsumption calls : 256862
% 7.11/1.50 % Non-unit clause-clause subsumptions : 751
% 7.11/1.50 % Unit Clause-clause subsumption calls : 32169
% 7.11/1.50 % Rewrite failures with RHS unbound : 0
% 7.11/1.50 % BW rewrite match attempts : 6974
% 7.11/1.50 % BW rewrite match successes : 243
% 7.11/1.50 % Condensation attempts : 0
% 7.11/1.50 % Condensation successes : 0
% 7.11/1.50 % Termbank termtop insertions : 565165
% 7.11/1.50 % Search garbage collected termcells : 19484
% 7.11/1.50
% 7.11/1.50 % -------------------------------------------------
% 7.11/1.50 % User time : 0.949 s
% 7.11/1.50 % System time : 0.050 s
% 7.11/1.50 % Total time : 0.999 s
% 7.11/1.50 % Maximum resident set size: 10800 pages
% 7.11/1.50
% 7.11/1.50 % -------------------------------------------------
% 7.11/1.50 % User time : 4.366 s
% 7.11/1.50 % System time : 0.221 s
% 7.11/1.50 % Total time : 4.587 s
% 7.11/1.50 % Maximum resident set size: 6144 pages
% 7.11/1.50 % E exiting
%------------------------------------------------------------------------------