%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW231+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:36:39 AM UTC 2025
% Result : Theorem 21.17s 21.37s
% Output : Proof 21.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 149
% Syntax : Number of formulae : 414 ( 218 unt; 0 typ; 0 def)
% Number of atoms : 1028 ( 579 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 979 ( 407 ~; 403 |; 0 &)
% ( 125 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 5 con; 0-3 aty)
% Number of variables : 821 ( 735 !; 0 ?; 821 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Complex_Orcis_type,type,
c_Complex_Orcis: ( $i * $i ) > $i ).
tff(v_a_type,type,
v_a: $i ).
tff(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(v_r_type,type,
v_r: $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Transcendental_Opi_type,type,
c_Transcendental_Opi: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_NthRoot_Osqrt_type,type,
c_NthRoot_Osqrt: $i > $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(c_Complex_Ocis_type,type,
c_Complex_Ocis: $i > $i ).
tff(c_RealVector_Oof__real_type,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Complex_Ocomplex_OComplex_type,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(c_Complex_ORe_type,type,
c_Complex_ORe: $i > $i ).
tff(c_Complex_OIm_type,type,
c_Complex_OIm: $i > $i ).
tff(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Transcendental_Osin_type,type,
c_Transcendental_Osin: $i > $i ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(c_Groups_Osgn__class_Osgn_type,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__idom_type,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
tff(class_Rings_Ocomm__ring__1_type,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(c_Transcendental_Ocos_type,type,
c_Transcendental_Ocos: $i > $i ).
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(class_Rings_Olinordered__ring_type,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(class_Groups_Oordered__ab__group__add__abs_type,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(1,plain,
^ [V_a: $i,V_r: $i] :
refl(( ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) )
<=> ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) )
<=> ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) )
<=> ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rcis__def) ).
tff(5,plain,
! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) )
| ( c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)) = c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [V_y: $i,V_x: $i] :
refl(( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) )
<=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) )
<=> ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) )
<=> ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mult__def) ).
tff(15,plain,
! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))))),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [V_y: $i,V_x: $i] :
refl(( ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) )
<=> ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) )
<=> ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) )
<=> ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Im__mult) ).
tff(25,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) )
| ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_Orcis(V_r,V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_r)),c_Complex_Ocis(V_a)) )
| ( c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))) = c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
^ [V_a: $i,V_r: $i] :
refl(( ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) )
<=> ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) )
<=> ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) )
<=> ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Im__rcis) ).
tff(39,plain,
! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) )
| ( c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = c_Complex_OIm(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
^ [V_x: $i] :
refl(( ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) )
<=> ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) )
<=> ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) )
<=> ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sin__periodic__pi2) ).
tff(49,plain,
! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [V_x: $i] : ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)) )
| ( c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
tff(58,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
tff(65,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
inference(unit_resolution,[status(thm)],[71,68,58]) ).
tff(73,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( class_Rings_Olinordered__idom(tc_RealDef_Oreal)
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
tff(76,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
^ [V_k: $i,T_a: $i] :
refl(( ( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
<=> ( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
<=> ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
<=> ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
^ [V_k: $i,T_a: $i] :
rewrite(( ( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
<=> ( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [V_k: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
<=> ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,axiom,
! [V_k: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sgn) ).
tff(83,plain,
! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ),
inference(modus_ponens,[status(thm)],[85,78]) ).
tff(87,plain,
( ( ~ ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) )
<=> ( ~ ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [V_k: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),
inference(unit_resolution,[status(thm)],[89,86,76]) ).
tff(91,plain,
^ [V_x: $i] :
refl(( ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
<=> ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
<=> ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
<=> ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,axiom,
! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).
tff(95,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
( ~ ! [V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) )
| ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),
inference(unit_resolution,[status(thm)],[102,68,58]) ).
tff(104,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),
inference(symmetry,[status(thm)],[90]) ).
tff(105,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) )
<=> ( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
^ [V_x: $i,T_a: $i] :
rewrite(( ( class_Rings_Olinordered__idom(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) )
<=> ( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ) )),
inference(bind,[status(th)],[]) ).
tff(111,plain,
( ! [V_x: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,axiom,
! [V_x: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).
tff(113,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ),
inference(modus_ponens,[status(thm)],[113,109]) ).
tff(115,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ),
inference(skolemize,[status(sab)],[114]) ).
tff(116,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ),
inference(modus_ponens,[status(thm)],[115,108]) ).
tff(117,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = v_r ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = v_r ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = v_r ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = v_r ) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = v_r,
inference(unit_resolution,[status(thm)],[119,116,76]) ).
tff(121,plain,
v_r = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
v_r = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),
inference(transitivity,[status(thm)],[121,106,103]) ).
tff(123,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
^ [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) )
<=> ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) )
<=> ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
^ [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) )
<=> ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
tff(131,plain,
! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) ) )
<=> ( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [V_ry: $i,V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(unit_resolution,[status(thm)],[137,134,58]) ).
tff(139,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r),
inference(transitivity,[status(thm)],[138,124]) ).
tff(140,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))) = c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r)),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(symmetry,[status(thm)],[138]) ).
tff(142,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
<=> ( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(143,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( class_Rings_Olinordered__idom(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
<=> ( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(146,plain,
( ! [V_a: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,axiom,
! [V_a: $i,T_a: $i] :
( class_Rings_Olinordered__idom(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__self) ).
tff(148,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ),
inference(modus_ponens,[status(thm)],[148,144]) ).
tff(150,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ),
inference(modus_ponens,[status(thm)],[150,143]) ).
tff(152,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__idom(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) )
| ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r) ) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r),
inference(unit_resolution,[status(thm)],[154,151,76]) ).
tff(156,plain,
( class_Rings_Oring(tc_RealDef_Oreal)
<=> class_Rings_Oring(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
tff(158,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
<=> ( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ) )),
inference(bind,[status(th)],[]) ).
tff(160,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( class_Rings_Oring(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
<=> ( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ) )),
inference(bind,[status(th)],[]) ).
tff(163,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Oring(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Oring(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
tff(165,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ),
inference(modus_ponens,[status(thm)],[165,161]) ).
tff(167,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ),
inference(skolemize,[status(sab)],[166]) ).
tff(168,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ),
inference(modus_ponens,[status(thm)],[167,160]) ).
tff(169,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) ) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
inference(unit_resolution,[status(thm)],[171,168,158]) ).
tff(173,plain,
( class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
<=> class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
tff(175,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
<=> ( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ) )),
inference(bind,[status(th)],[]) ).
tff(177,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ) ),
inference(quant_intro,[status(thm)],[176]) ).
tff(178,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(179,plain,
^ [V_x: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__ring__1(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
<=> ( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ) )),
inference(bind,[status(th)],[]) ).
tff(180,plain,
( ! [V_x: $i,T_a: $i] :
( class_Rings_Ocomm__ring__1(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ) ),
inference(quant_intro,[status(thm)],[179]) ).
tff(181,axiom,
! [V_x: $i,T_a: $i] :
( class_Rings_Ocomm__ring__1(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
tff(182,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ),
inference(modus_ponens,[status(thm)],[182,178]) ).
tff(184,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ),
inference(skolemize,[status(sab)],[183]) ).
tff(185,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ),
inference(modus_ponens,[status(thm)],[184,177]) ).
tff(186,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(188,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) ) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
inference(unit_resolution,[status(thm)],[188,185,175]) ).
tff(190,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(monotonicity,[status(thm)],[191,190]) ).
tff(193,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(transitivity,[status(thm)],[192,172,155,123,141]) ).
tff(194,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
^ [V_y: $i,V_x: $i] :
refl(( ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) )
<=> ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ) )),
inference(bind,[status(th)],[]) ).
tff(196,plain,
( ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) )
<=> ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ) ),
inference(quant_intro,[status(thm)],[195]) ).
tff(197,plain,
( ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) )
<=> ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(198,axiom,
! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__mult) ).
tff(199,plain,
! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ),
inference(skolemize,[status(sab)],[199]) ).
tff(201,plain,
! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ),
inference(modus_ponens,[status(thm)],[200,196]) ).
tff(202,plain,
( ~ ! [V_y: $i,V_x: $i] : ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) )
| ( c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
inference(unit_resolution,[status(thm)],[202,201]) ).
tff(204,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(monotonicity,[status(thm)],[190]) ).
tff(206,plain,
c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
^ [V_x: $i] :
refl(( ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) )
<=> ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) ) )),
inference(bind,[status(th)],[]) ).
tff(208,plain,
( ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) )
<=> ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) ) ),
inference(quant_intro,[status(thm)],[207]) ).
tff(209,plain,
( ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) )
<=> ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(210,axiom,
! [V_x: $i] : ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__minus) ).
tff(211,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) ),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) ),
inference(skolemize,[status(sab)],[211]) ).
tff(213,plain,
! [V_x: $i] : ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) ),
inference(modus_ponens,[status(thm)],[212,208]) ).
tff(214,plain,
( ~ ! [V_x: $i] : ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x)) )
| ( c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(215,plain,
c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(unit_resolution,[status(thm)],[214,213]) ).
tff(216,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_NthRoot_Osqrt(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(transitivity,[status(thm)],[216,206]) ).
tff(218,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(transitivity,[status(thm)],[205,215]) ).
tff(219,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
inference(monotonicity,[status(thm)],[220,217]) ).
tff(222,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(223,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(224,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) ),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(unit_resolution,[status(thm)],[224,168,158]) ).
tff(226,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)),
inference(transitivity,[status(thm)],[226,221,204,194,140,99,90]) ).
tff(228,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
inference(symmetry,[status(thm)],[228]) ).
tff(230,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(231,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(232,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a)) ) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a)),
inference(unit_resolution,[status(thm)],[232,185,175]) ).
tff(234,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(236,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Rings_Ocomm__ring__1(T_a)
| ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) )
| ~ class_Rings_Ocomm__ring__1(tc_RealDef_Oreal)
| ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(modus_ponens,[status(thm)],[236,235]) ).
tff(238,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(unit_resolution,[status(thm)],[237,185,175]) ).
tff(239,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a)),
inference(monotonicity,[status(thm)],[240]) ).
tff(242,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)),
inference(transitivity,[status(thm)],[241,234]) ).
tff(243,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a))),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
^ [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ) )),
inference(bind,[status(th)],[]) ).
tff(248,plain,
( ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) )
<=> ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ) ),
inference(quant_intro,[status(thm)],[247]) ).
tff(249,plain,
( ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) )
<=> ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(250,plain,
^ [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ) )),
inference(bind,[status(th)],[]) ).
tff(251,plain,
( ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) )
<=> ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ) ),
inference(quant_intro,[status(thm)],[250]) ).
tff(252,axiom,
! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
tff(253,plain,
! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ),
inference(modus_ponens,[status(thm)],[252,251]) ).
tff(254,plain,
! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ),
inference(modus_ponens,[status(thm)],[253,249]) ).
tff(255,plain,
! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ),
inference(skolemize,[status(sab)],[254]) ).
tff(256,plain,
! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ),
inference(modus_ponens,[status(thm)],[255,248]) ).
tff(257,plain,
( ( ~ ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) ) )
<=> ( ~ ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(258,plain,
( ~ ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(259,plain,
( ~ ! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) ) ),
inference(modus_ponens,[status(thm)],[258,257]) ).
tff(260,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)),
inference(unit_resolution,[status(thm)],[259,256,58]) ).
tff(261,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Transcendental_Osin(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(symmetry,[status(thm)],[240]) ).
tff(263,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(monotonicity,[status(thm)],[262,90]) ).
tff(264,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
inference(symmetry,[status(thm)],[263]) ).
tff(265,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
inference(transitivity,[status(thm)],[264,190]) ).
tff(266,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Osin(v_a)),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Osin(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Osin(v_a)),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_OIm(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) )
| ( c_Complex_OIm(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Osin(v_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(270,plain,
c_Complex_OIm(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Osin(v_a)),
inference(unit_resolution,[status(thm)],[269,41]) ).
tff(271,plain,
c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Complex_OIm(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)),
inference(monotonicity,[status(thm)],[10]) ).
tff(272,plain,
( ~ ! [V_y: $i,V_x: $i] : ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y))) )
| ( c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(273,plain,
c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a)))),
inference(unit_resolution,[status(thm)],[272,27]) ).
tff(274,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a)))) = c_Complex_OIm(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))),
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))))),
inference(transitivity,[status(thm)],[274,271,270,268,261,246,229,73,55,44,34,29]) ).
tff(276,plain,
^ [V_y: $i,V_x: $i] :
refl(( ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) )
<=> ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ) )),
inference(bind,[status(th)],[]) ).
tff(277,plain,
( ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) )
<=> ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ) ),
inference(quant_intro,[status(thm)],[276]) ).
tff(278,plain,
( ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) )
<=> ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(279,axiom,
! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__Re__mult) ).
tff(280,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ),
inference(modus_ponens,[status(thm)],[279,278]) ).
tff(281,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ),
inference(skolemize,[status(sab)],[280]) ).
tff(282,plain,
! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) ),
inference(modus_ponens,[status(thm)],[281,277]) ).
tff(283,plain,
( ~ ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) )
| ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(284,plain,
c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))))),
inference(unit_resolution,[status(thm)],[283,282]) ).
tff(285,plain,
c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))) = c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
inference(monotonicity,[status(thm)],[32]) ).
tff(286,plain,
c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
^ [V_a: $i,V_r: $i] :
refl(( ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) )
<=> ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(288,plain,
( ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) )
<=> ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ) ),
inference(quant_intro,[status(thm)],[287]) ).
tff(289,plain,
( ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) )
<=> ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(290,axiom,
! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Re__rcis) ).
tff(291,plain,
! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ),
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,plain,
! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ),
inference(skolemize,[status(sab)],[291]) ).
tff(293,plain,
! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ),
inference(modus_ponens,[status(thm)],[292,288]) ).
tff(294,plain,
( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) )
| ( c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
inference(unit_resolution,[status(thm)],[294,293]) ).
tff(296,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = c_Complex_ORe(c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
^ [V_y: $i,V_x: $i] :
refl(( ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) )
<=> ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ) )),
inference(bind,[status(th)],[]) ).
tff(298,plain,
( ! [V_y: $i,V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) )
<=> ! [V_y: $i,V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ) ),
inference(quant_intro,[status(thm)],[297]) ).
tff(299,plain,
( ! [V_y: $i,V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) )
<=> ! [V_y: $i,V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(300,axiom,
! [V_y: $i,V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__add) ).
tff(301,plain,
! [V_y: $i,V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ),
inference(modus_ponens,[status(thm)],[300,299]) ).
tff(302,plain,
! [V_y: $i,V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ),
inference(skolemize,[status(sab)],[301]) ).
tff(303,plain,
! [V_y: $i,V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ),
inference(modus_ponens,[status(thm)],[302,298]) ).
tff(304,plain,
( ~ ! [V_y: $i,V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) )
| ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),c_Transcendental_Ocos(v_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),c_Transcendental_Osin(v_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(305,plain,
c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),c_Transcendental_Ocos(v_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),c_Transcendental_Osin(v_a))),
inference(unit_resolution,[status(thm)],[304,303]) ).
tff(306,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
inference(monotonicity,[status(thm)],[104]) ).
tff(307,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(symmetry,[status(thm)],[306]) ).
tff(308,plain,
( class_Rings_Olinordered__ring(tc_RealDef_Oreal)
<=> class_Rings_Olinordered__ring(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(309,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
tff(310,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[309,308]) ).
tff(311,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) )
<=> ( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(312,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ) ),
inference(quant_intro,[status(thm)],[311]) ).
tff(313,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(314,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( class_Rings_Olinordered__ring(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) )
<=> ( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ) )),
inference(bind,[status(th)],[]) ).
tff(315,plain,
( ! [V_a: $i,T_a: $i] :
( class_Rings_Olinordered__ring(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ) ),
inference(quant_intro,[status(thm)],[314]) ).
tff(316,axiom,
! [V_a: $i,T_a: $i] :
( class_Rings_Olinordered__ring(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
tff(317,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ),
inference(modus_ponens,[status(thm)],[316,315]) ).
tff(318,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ),
inference(modus_ponens,[status(thm)],[317,313]) ).
tff(319,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ),
inference(skolemize,[status(sab)],[318]) ).
tff(320,plain,
! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ),
inference(modus_ponens,[status(thm)],[319,312]) ).
tff(321,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) )
| ~ class_Rings_Olinordered__ring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) )
| ~ class_Rings_Olinordered__ring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(322,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) )
| ~ class_Rings_Olinordered__ring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(323,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_Rings_Olinordered__ring(T_a)
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) )
| ~ class_Rings_Olinordered__ring(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) ),
inference(modus_ponens,[status(thm)],[322,321]) ).
tff(324,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
inference(unit_resolution,[status(thm)],[323,320,310]) ).
tff(325,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
<=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(326,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
tff(327,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[326,325]) ).
tff(328,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
inference(bind,[status(th)],[]) ).
tff(329,plain,
( ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(quant_intro,[status(thm)],[328]) ).
tff(330,plain,
( ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(331,plain,
^ [V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )),
( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ) )),
rewrite(( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
inference(bind,[status(th)],[]) ).
tff(332,plain,
( ! [V_a: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(quant_intro,[status(thm)],[331]) ).
tff(333,axiom,
! [V_a: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
tff(334,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[333,332]) ).
tff(335,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[334,330]) ).
tff(336,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(skolemize,[status(sab)],[335]) ).
tff(337,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[336,329]) ).
tff(338,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(339,plain,
( ( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(340,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) ) ),
inference(monotonicity,[status(thm)],[339]) ).
tff(341,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) ) ),
inference(transitivity,[status(thm)],[340,338]) ).
tff(342,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(343,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) ) ),
inference(modus_ponens,[status(thm)],[342,341]) ).
tff(344,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(unit_resolution,[status(thm)],[343,337,327,324]) ).
tff(345,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r),
inference(transitivity,[status(thm)],[344,226,221,204,194,140,99]) ).
tff(346,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
inference(monotonicity,[status(thm)],[345]) ).
tff(347,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),
inference(symmetry,[status(thm)],[344]) ).
tff(348,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),
inference(monotonicity,[status(thm)],[347]) ).
tff(349,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),
inference(transitivity,[status(thm)],[348,346,307]) ).
tff(350,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),c_Transcendental_Ocos(v_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),c_Transcendental_Osin(v_a)))),
inference(monotonicity,[status(thm)],[349,305]) ).
tff(351,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),c_Transcendental_Ocos(v_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),c_Transcendental_Osin(v_a)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))),
inference(symmetry,[status(thm)],[350]) ).
tff(352,plain,
^ [V_x: $i] :
refl(( ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) )
<=> ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ) )),
inference(bind,[status(th)],[]) ).
tff(353,plain,
( ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) )
<=> ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ) ),
inference(quant_intro,[status(thm)],[352]) ).
tff(354,plain,
( ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) )
<=> ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(355,axiom,
! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__periodic__pi) ).
tff(356,plain,
! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ),
inference(modus_ponens,[status(thm)],[355,354]) ).
tff(357,plain,
! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ),
inference(skolemize,[status(sab)],[356]) ).
tff(358,plain,
! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) ),
inference(modus_ponens,[status(thm)],[357,353]) ).
tff(359,plain,
( ~ ! [V_x: $i] : ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) )
| ( c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(360,plain,
c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a)),
inference(unit_resolution,[status(thm)],[359,358]) ).
tff(361,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(362,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
inference(quant_intro,[status(thm)],[361]) ).
tff(363,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(364,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(365,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
inference(quant_intro,[status(thm)],[364]) ).
tff(366,axiom,
! [V_c: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(367,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(modus_ponens,[status(thm)],[366,365]) ).
tff(368,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(modus_ponens,[status(thm)],[367,363]) ).
tff(369,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(skolemize,[status(sab)],[368]) ).
tff(370,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(modus_ponens,[status(thm)],[369,362]) ).
tff(371,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(372,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(373,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a) ) ),
inference(modus_ponens,[status(thm)],[372,371]) ).
tff(374,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a),
inference(unit_resolution,[status(thm)],[373,370,58]) ).
tff(375,plain,
c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi)) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
inference(monotonicity,[status(thm)],[374]) ).
tff(376,plain,
c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi)),
inference(symmetry,[status(thm)],[375]) ).
tff(377,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),c_Transcendental_Ocos(v_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),c_Transcendental_Osin(v_a))) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
inference(symmetry,[status(thm)],[305]) ).
tff(378,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),c_Transcendental_Ocos(v_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),c_Transcendental_Osin(v_a))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a)),
inference(transitivity,[status(thm)],[377,376,360]) ).
tff(379,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),c_Transcendental_Ocos(v_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),c_Transcendental_Osin(v_a)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))),
inference(monotonicity,[status(thm)],[378]) ).
tff(380,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),c_Transcendental_Ocos(v_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(c_Transcendental_Opi)),c_Transcendental_Osin(v_a)))),
inference(symmetry,[status(thm)],[379]) ).
tff(381,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
<=> ( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(382,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) ),
inference(quant_intro,[status(thm)],[381]) ).
tff(383,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(384,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( class_Rings_Oring(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
<=> ( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(385,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Oring(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) ),
inference(quant_intro,[status(thm)],[384]) ).
tff(386,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( class_Rings_Oring(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
tff(387,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
inference(modus_ponens,[status(thm)],[386,385]) ).
tff(388,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
inference(modus_ponens,[status(thm)],[387,383]) ).
tff(389,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
inference(skolemize,[status(sab)],[388]) ).
tff(390,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
inference(modus_ponens,[status(thm)],[389,382]) ).
tff(391,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(392,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(393,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Oring(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) )
| ~ class_Rings_Oring(tc_RealDef_Oreal)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))) ) ),
inference(modus_ponens,[status(thm)],[392,391]) ).
tff(394,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a))),
inference(unit_resolution,[status(thm)],[393,390,158]) ).
tff(395,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),
inference(monotonicity,[status(thm)],[104]) ).
tff(396,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),
inference(monotonicity,[status(thm)],[395]) ).
tff(397,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Ocos(v_a)),
inference(monotonicity,[status(thm)],[396]) ).
tff(398,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Ocos(v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,v_r)))),c_Transcendental_Ocos(v_a)),
inference(symmetry,[status(thm)],[397]) ).
tff(399,plain,
( ~ ! [V_a: $i,V_r: $i] : ( c_Complex_ORe(c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) )
| ( c_Complex_ORe(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Ocos(v_a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(400,plain,
c_Complex_ORe(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Transcendental_Ocos(v_a)),
inference(unit_resolution,[status(thm)],[399,293]) ).
tff(401,plain,
c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Complex_ORe(c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a)),
inference(monotonicity,[status(thm)],[10]) ).
tff(402,plain,
( ~ ! [V_y: $i,V_x: $i] : ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))) )
| ( c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(403,plain,
c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),
inference(unit_resolution,[status(thm)],[402,282]) ).
tff(404,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))) = c_Complex_ORe(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))),c_Complex_Ocis(v_a))),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))))),
inference(transitivity,[status(thm)],[404,401,400,398,394,380,351,296,286,284]) ).
tff(406,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))))) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))))),
inference(monotonicity,[status(thm)],[405,275]) ).
tff(407,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))))) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_OIm(c_Complex_Ocis(v_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_ORe(c_Complex_Ocis(v_a))))),
inference(symmetry,[status(thm)],[406]) ).
tff(408,plain,
( ~ ! [V_y: $i,V_x: $i] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_ORe(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_OIm(V_y))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(V_x)),c_Complex_OIm(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(V_x)),c_Complex_ORe(V_y)))) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(409,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))))),c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_ORe(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_OIm(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Complex_OIm(c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)))))),c_Complex_ORe(c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)))))),
inference(unit_resolution,[status(thm)],[408,17]) ).
tff(410,plain,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) = c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(transitivity,[status(thm)],[31,409,407,20,10]) ).
tff(411,plain,
( ( c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a) )
<=> ( c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(412,axiom,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(413,plain,
c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_NthRoot_Osqrt(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)) != c_Complex_Orcis(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r)),v_a),
inference(modus_ponens,[status(thm)],[412,411]) ).
tff(414,plain,
$false,
inference(unit_resolution,[status(thm)],[413,410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW231+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 11:20:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 21.17/21.37 % SZS status Theorem
% 21.17/21.37 % SZS output start Proof
% See solution above
% 21.25/21.49 % E exiting
%------------------------------------------------------------------------------