%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW194+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 03:10:03 PM UTC 2026
% Result : Theorem 0.29s 3.91s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 25
% Syntax : Number of formulae : 98 ( 69 unt; 0 def)
% Number of atoms : 140 ( 59 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 79 ( 37 ~; 29 |; 2 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 93 ( 2 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_Bit0__def,axiom,
! [X18] : c_Int_OBit0(X18) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X18] : c_Int_OBit1(X18) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_real__sqrt__abs,axiom,
! [X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs) ).
fof(fact_nat__1__add__1,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
fof(fact_add__Pls__right,axiom,
! [X18] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,c_Int_OPls) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_real__sqrt__power,axiom,
! [X18,X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5),X18)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5)),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__power) ).
fof(fact_real__sqrt__abs2,axiom,
! [X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X5)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).
fof(fact_real__mult__1,axiom,
! [X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_real__mult__commute,axiom,
! [X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_real__sqrt__one,axiom,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__one) ).
fof(fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096) ).
fof(fact_less__one__imp__sqr__less__one,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__one__imp__sqr__less__one) ).
fof(fact_mult__2__right,axiom,
! [X17,X9] :
( class_Int_Onumber__ring(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X17),c_Int_Onumber__class_Onumber__of(X9,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X9,X17,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2__right) ).
fof(fact_less__eq__real__def,axiom,
! [X26,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X26)
<=> ( X25 = X26
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X25,X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_abs__norm__cancel,axiom,
! [X8,X9] :
( class_RealVector_Oreal__normed__vector(X9)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X9,X8)) = c_RealVector_Onorm__class_Onorm(X9,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_real__norm__def,axiom,
! [X50] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X50) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X50),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_real__le__antisym,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X17)
=> X17 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_leI,axiom,
! [X24,X5,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ c_Orderings_Oord__class_Oless(X9,X5,X24)
=> c_Orderings_Oord__class_Oless__eq(X9,X24,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_power__one,axiom,
! [X4,X9] :
( class_Groups_Omonoid__mult(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),c_Groups_Oone__class_Oone(X9)),X4) = c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(fact_real__le__refl,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(c_0_25,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_26,plain,
! [X574] : c_Int_OBit0(X574) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X574,X574),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_27,plain,
! [X569] : c_Int_OBit1(X569) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X569),X569),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_28,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X897] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X897),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X897),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs]) ).
cnf(c_0_30,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_nat__1__add__1]) ).
cnf(c_0_31,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X570] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X570,c_Int_OPls) = X570,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(c_0_34,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_32]) ).
cnf(c_0_37,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_38,plain,
! [X563,X564] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X564),X563)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X564)),X563),
inference(variable_rename,[status(thm)],[fact_real__sqrt__power]) ).
fof(c_0_39,plain,
! [X685] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X685),X685)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X685),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs2]) ).
fof(c_0_40,plain,
! [X170] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X170) = X170,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
cnf(c_0_41,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_42,plain,
! [X157,X158] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X158),X157) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X157),X158),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
cnf(c_0_43,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_31]),c_0_32]),c_0_32]) ).
cnf(c_0_44,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_45,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)),X2),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__sqrt__one]) ).
cnf(c_0_49,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096]) ).
cnf(c_0_50,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_31]),c_0_31]),c_0_31]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_51,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_44]),c_0_45]) ).
cnf(c_0_53,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
fof(c_0_54,plain,
! [X2451] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2451),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2451),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__one__imp__sqr__less__one])])]) ).
cnf(c_0_55,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_31]),c_0_32]),c_0_32]) ).
fof(c_0_56,plain,
! [X333,X334] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X334),X333),c_Int_Onumber__class_Onumber__of(X334,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X334,X333,X333)
| ~ class_Int_Onumber__ring(X334) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])])]) ).
cnf(c_0_57,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_51]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_44]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_44]) ).
cnf(c_0_58,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_48]),c_0_53]) ).
fof(c_0_59,plain,
! [X1914,X1915] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1915,X1914)
| X1915 != X1914 )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1915,X1914)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1915,X1914) )
& ( X1915 = X1914
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1915,X1914)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1915,X1914) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])])]) ).
cnf(c_0_60,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_61,plain,
! [X1088,X1089] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1089,X1088)) = c_RealVector_Onorm__class_Onorm(X1089,X1088)
| ~ class_RealVector_Oreal__normed__vector(X1089) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])])]) ).
fof(c_0_62,plain,
! [X1003] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1003) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1003),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_63,plain,
! [X146,X147] :
( X147 = X146
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X146,X147)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X147,X146) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])])]) ).
cnf(c_0_64,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_37]),c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_65,plain,
( ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
fof(c_0_66,plain,
! [X24,X5,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ c_Orderings_Oord__class_Oless(X9,X5,X24)
=> c_Orderings_Oord__class_Oless__eq(X9,X24,X5) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
cnf(c_0_67,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_31]),c_0_32]),c_0_32]) ).
cnf(c_0_70,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_71,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_62]) ).
cnf(c_0_72,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(c_0_73,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_74,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_64,c_0_51]) ).
cnf(c_0_75,plain,
( ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_31]),c_0_32]),c_0_32]) ).
fof(c_0_76,plain,
! [X1998,X1999,X2000] :
( c_Orderings_Oord__class_Oless__eq(X2000,X1998,X1999)
| c_Orderings_Oord__class_Oless(X2000,X1999,X1998)
| ~ class_Orderings_Olinorder(X2000) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])]) ).
cnf(c_0_77,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_78,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_44]) ).
cnf(c_0_79,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_80,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,plain,
( ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_37]),c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_82,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
cnf(c_0_83,plain,
( ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_84,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c_0_85,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
fof(c_0_86,plain,
! [X362,X363] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X363),c_Groups_Oone__class_Oone(X363)),X362) = c_Groups_Oone__class_Oone(X363)
| ~ class_Groups_Omonoid__mult(X363) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])])]) ).
cnf(c_0_87,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x____,v_x____)))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x____,v_x____)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82])]) ).
cnf(c_0_88,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x____,v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_81]),c_0_82])]) ).
cnf(c_0_90,plain,
( ~ class_Groups_Omonoid__mult(X1)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2) = c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_91,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
fof(c_0_92,plain,
! [X153] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X153,X153),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
cnf(c_0_93,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x____,v_x____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_81]),c_0_82])]) ).
cnf(c_0_94,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x____,v_x____)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]) ).
cnf(c_0_95,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW194+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.50 % Computer : n019.cluster.edu
% 0.18/0.50 % Model : x86_64 x86_64
% 0.18/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.50 % Memory : 8046.5625MB
% 0.18/0.50 % OS : Linux 6.8.0-71-generic
% 0.18/0.50 % CPULimit : 300
% 0.18/0.50 % WCLimit : 300
% 0.18/0.50 % DateTime : Mon Sep 21 09:40:51 UTC 2026
% 0.18/0.51 % CPUTime :
% 0.18/0.51 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.58 Running first-order theorem proving
% 0.23/0.58 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/benchmark/theBenchmark.p
% 0.29/3.91 % Version: 3.5.1
% 0.29/3.91 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.29/3.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/3.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.29/3.91 % Starting new_bool_3 with 300s (1) cores
% 0.29/3.91 % Starting new_bool_1 with 300s (1) cores
% 0.29/3.91 % Starting sh5l with 300s (1) cores
% 0.29/3.91 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2262460 completed with status 0
% 0.29/3.91 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.29/3.91 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.29/3.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/3.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.29/3.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/3.91 % No SInE strategy applied
% 0.29/3.91 % Search class: FGHSM-SMLM31-DFFFFFNN
% 0.29/3.91 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/3.91 % Starting SubtermCWHack with 136s (1) cores
% 0.29/3.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.29/3.91 % Starting SAT001_MinMin_p005000_rr_RG with 148s (1) cores
% 0.29/3.91 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 0.29/3.91 % Starting G-E--_107_C45_F1_PI_AE_Q7_CS_SP_PS_S0Y with 136s (1) cores
% 0.29/3.91 % SAT001_MinMin_p005000_rr_RG with pid 2262469 completed with status 0
% 0.29/3.91 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.29/3.91 % Preprocessing class: FMLMSMSMSSSNFFN.
% 0.29/3.91 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/3.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.29/3.91 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/3.91 % No SInE strategy applied
% 0.29/3.91 % Search class: FGHSM-SMLM31-DFFFFFNN
% 0.29/3.91 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/3.91 % Starting SubtermCWHack with 136s (1) cores
% 0.29/3.91 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.29/3.91 % Starting SAT001_MinMin_p005000_rr_RG with 148s (1) cores
% 0.29/3.91 % Preprocessing time : 0.043 s
% 0.29/3.91 % Presaturation interreduction done
% 0.29/3.91
% 0.29/3.91 % Proof found!
% 0.29/3.91 % SZS status Theorem
% 0.29/3.91 % SZS output start CNFRefutation
% See solution above
% 0.29/3.91 % Parsed axioms : 1199
% 0.29/3.91 % Removed by relevancy pruning/SinE : 0
% 0.29/3.91 % Initial clauses : 1727
% 0.29/3.91 % Removed in clause preprocessing : 89
% 0.29/3.91 % Initial clauses in saturation : 1638
% 0.29/3.91 % Processed clauses : 11144
% 0.29/3.91 % ...of these trivial : 162
% 0.29/3.91 % ...subsumed : 7031
% 0.29/3.91 % ...remaining for further processing : 3951
% 0.29/3.91 % Other redundant clauses eliminated : 425
% 0.29/3.91 % Clauses deleted for lack of memory : 0
% 0.29/3.91 % Backward-subsumed : 353
% 0.29/3.91 % Backward-rewritten : 211
% 0.29/3.91 % Generated clauses : 65511
% 0.29/3.91 % ...of the previous two non-redundant : 57582
% 0.29/3.91 % ...aggressively subsumed : 0
% 0.29/3.91 % Contextual simplify-reflections : 13
% 0.29/3.91 % Paramodulations : 65091
% 0.29/3.91 % Factorizations : 10
% 0.29/3.91 % NegExts : 0
% 0.29/3.91 % Equation resolutions : 441
% 0.29/3.91 % Disequality decompositions : 0
% 0.29/3.91 % Total rewrite steps : 53983
% 0.29/3.91 % ...of those cached : 51421
% 0.29/3.91 % Propositional unsat checks : 0
% 0.29/3.91 % Propositional check models : 0
% 0.29/3.91 % Propositional check unsatisfiable : 0
% 0.29/3.91 % Propositional clauses : 0
% 0.29/3.91 % Propositional clauses after purity: 0
% 0.29/3.91 % Propositional unsat core size : 0
% 0.29/3.91 % Propositional preprocessing time : 0.000
% 0.29/3.91 % Propositional encoding time : 0.000
% 0.29/3.91 % Propositional solver time : 0.000
% 0.29/3.91 % Success case prop preproc time : 0.000
% 0.29/3.91 % Success case prop encoding time : 0.000
% 0.29/3.91 % Success case prop solver time : 0.000
% 0.29/3.91 % Current number of processed clauses : 2006
% 0.29/3.91 % Positive orientable unit clauses : 512
% 0.29/3.91 % Positive unorientable unit clauses: 18
% 0.29/3.91 % Negative unit clauses : 324
% 0.29/3.91 % Non-unit-clauses : 1152
% 0.29/3.91 % Current number of unprocessed clauses: 48887
% 0.29/3.91 % ...number of literals in the above : 154067
% 0.29/3.91 % Current number of archived formulas : 0
% 0.29/3.91 % Current number of archived clauses : 1801
% 0.29/3.91 % Clause-clause subsumption calls (NU) : 349821
% 0.29/3.91 % Rec. Clause-clause subsumption calls : 185718
% 0.29/3.91 % Non-unit clause-clause subsumptions : 2759
% 0.29/3.91 % Unit Clause-clause subsumption calls : 13457
% 0.29/3.91 % Rewrite failures with RHS unbound : 0
% 0.29/3.91 % BW rewrite match attempts : 3884
% 0.29/3.91 % BW rewrite match successes : 475
% 0.29/3.91 % Condensation attempts : 0
% 0.29/3.91 % Condensation successes : 0
% 0.29/3.91 % Termbank termtop insertions : 2033535
% 0.29/3.91 % Search garbage collected termcells : 19520
% 0.29/3.91
% 0.29/3.91 % -------------------------------------------------
% 0.29/3.91 % User time : 3.044 s
% 0.29/3.91 % System time : 0.100 s
% 0.29/3.91 % Total time : 3.144 s
% 0.29/3.91 % Maximum resident set size: 10068 pages
% 0.29/3.91
% 0.29/3.91 % -------------------------------------------------
% 0.29/3.91 % User time : 14.074 s
% 0.29/3.91 % System time : 0.483 s
% 0.29/3.91 % Total time : 14.557 s
% 0.29/3.91 % Maximum resident set size: 6144 pages
% 0.29/3.91 % E exiting
%------------------------------------------------------------------------------