%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG362-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:58:59 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 32
% Syntax : Number of formulae : 63 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 429 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 642 ( 305 ~; 299 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 165 ( 148 !; 0 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_HOL_Oabs__class_Oabs_type,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_Complex_ORe_type,type,
c_Complex_ORe: $i > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_n_____type,type,
v_n____: $i ).
tff(v_s_type,type,
v_s: $i ).
tff(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(class_Ring__and__Field_Oordered__semidom_type,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(1,plain,
( class_Orderings_Opreorder(tc_RealDef_Oreal)
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
tff(3,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal)
<=> c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
tff(6,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(9,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
refl(( ( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) )
<=> ( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
trans(monotonicity(rewrite(( ( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a) )
<=> ( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(V_x,V_z,T_a) ) )),
( ( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) )),
rewrite(( ( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ) )),
( ( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
tff(16,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_x: $i,V_z: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[22,19,9,6,3]) ).
tff(24,plain,
( class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
tff(26,plain,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [T_a: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) )
<=> ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) )
<=> ! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) )
<=> ! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
tff(31,plain,
! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) )
| ~ class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) )
| ~ class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) )
| ~ class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [T_a: $i] :
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) )
| ~ class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[36,33,26]) ).
tff(38,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
tff(40,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
tff(43,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(46,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ) )),
( ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) )),
rewrite(( ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) )),
( ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) )),
( ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a) )
<=> ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a) ) )),
rewrite(( ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a) )
<=> ( ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) )),
( ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a) )
<=> ( ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) )),
( ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) )
<=> ( ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) )),
rewrite(( ( ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) )
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) )),
( ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) )
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
tff(53,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) )
| c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,56,46,43,40,37,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG362-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 11:09:47 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.52 % SZS status Unsatisfiable
% 0.19/0.52 % SZS output start Proof
% See solution above
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------