TSTP Solution File: SWW231+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW231+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Thu Sep 29 20:57:59 EDT 2022
% Result : Theorem 8.00s 5.30s
% Output : Proof 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 104
% Syntax : Number of formulae : 233 ( 123 unt; 24 typ; 0 def)
% Number of atoms : 423 ( 291 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 320 ( 125 ~; 121 |; 0 &)
% ( 62 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 19 >; 11 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 5 con; 0-3 aty)
% Number of variables : 366 ( 328 !; 0 ?; 366 :)
% 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(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(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
tff(c_Transcendental_Ocos_type,type,
c_Transcendental_Ocos: $i > $i ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $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_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(22,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)],[21]) ).
tff(23,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(24,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(25,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)],[24,23]) ).
tff(26,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)],[25]) ).
tff(27,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)],[26,22]) ).
tff(28,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(29,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)],[28,27]) ).
tff(30,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)],[29]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,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)],[34,33]) ).
tff(36,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)],[35]) ).
tff(37,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)],[36,32]) ).
tff(38,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(39,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)],[38,37]) ).
tff(40,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Osin(v_a)) = c_Transcendental_Osin(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
inference(symmetry,[status(thm)],[39]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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(45,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)],[44,43]) ).
tff(46,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)],[45]) ).
tff(47,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)],[46,42]) ).
tff(48,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(49,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)],[48,47]) ).
tff(50,plain,
( class_Rings_Olinordered__idom(tc_RealDef_Oreal)
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
tff(52,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,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(54,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)],[53]) ).
tff(55,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(56,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(57,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)],[56]) ).
tff(58,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(59,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)],[58,57]) ).
tff(60,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)],[59,55]) ).
tff(61,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)],[60]) ).
tff(62,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)],[61,54]) ).
tff(63,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(64,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(65,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)],[64,63]) ).
tff(66,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)],[65,62,52]) ).
tff(67,plain,
c_NthRoot_Osqrt(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))) = c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_r)),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,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(69,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)],[68]) ).
tff(70,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(71,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(72,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)],[71,70]) ).
tff(73,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)],[72]) ).
tff(74,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)],[73,69]) ).
tff(75,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),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),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(76,plain,
c_NthRoot_Osqrt(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),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)],[75,74]) ).
tff(77,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_NthRoot_Osqrt(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(symmetry,[status(thm)],[76]) ).
tff(78,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,v_r),
inference(transitivity,[status(thm)],[77,67,49]) ).
tff(79,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,v_r)),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,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),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)],[79]) ).
tff(81,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(82,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)],[81]) ).
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)) ) )
<=> ! [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(84,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(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)) ) )
<=> ! [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)],[84]) ).
tff(86,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(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)) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
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)) ) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
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)) ) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,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)],[89,82]) ).
tff(91,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(92,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(93,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)],[92,91]) ).
tff(94,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)],[93,90,52]) ).
tff(95,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)],[94]) ).
tff(96,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)],[95]) ).
tff(97,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),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)],[96,80]) ).
tff(98,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_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(monotonicity,[status(thm)],[97,40]) ).
tff(99,plain,
( class_Rings_Oring(tc_RealDef_Oreal)
<=> class_Rings_Oring(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(100,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
tff(101,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,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(103,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)],[102]) ).
tff(104,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(105,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(106,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)],[105]) ).
tff(107,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(108,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)],[107,106]) ).
tff(109,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)],[108,104]) ).
tff(110,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)],[109]) ).
tff(111,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)],[110,103]) ).
tff(112,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_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_Osin(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_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_Osin(v_a))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,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_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_Osin(v_a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,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_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_Osin(v_a))) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,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_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_Osin(v_a))),
inference(unit_resolution,[status(thm)],[114,111,101]) ).
tff(116,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)],[95]) ).
tff(117,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)],[116]) ).
tff(118,plain,
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))) = 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)))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,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),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_Osin(v_a)),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,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(121,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)],[120,27]) ).
tff(122,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(123,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(124,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)],[123]) ).
tff(125,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(126,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(127,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)],[126,125]) ).
tff(128,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)],[127]) ).
tff(129,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)],[128,124]) ).
tff(130,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(131,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)],[130,129]) ).
tff(132,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)],[131]) ).
tff(133,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(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(transitivity,[status(thm)],[132,122,121,119,115,98,30]) ).
tff(134,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(135,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)],[134]) ).
tff(136,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(137,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(138,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)],[137,136]) ).
tff(139,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)],[138]) ).
tff(140,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)],[139,135]) ).
tff(141,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(142,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)],[141,140]) ).
tff(143,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)],[142]) ).
tff(144,plain,
( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(145,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
tff(146,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,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(148,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)],[147]) ).
tff(149,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(150,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(151,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)],[150]) ).
tff(152,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(153,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)],[152,151]) ).
tff(154,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)],[153,149]) ).
tff(155,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)],[154]) ).
tff(156,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)],[155,148]) ).
tff(157,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(158,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(159,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)],[158,157]) ).
tff(160,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)],[159,156,146]) ).
tff(161,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)],[160]) ).
tff(162,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(163,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)],[162]) ).
tff(164,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(165,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(166,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)],[165,164]) ).
tff(167,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)],[166]) ).
tff(168,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)],[167,163]) ).
tff(169,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(170,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)],[169,168]) ).
tff(171,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a)) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_a,c_Transcendental_Opi)),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Transcendental_Ocos(v_a)) = c_Transcendental_Ocos(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Opi,v_a)),
inference(transitivity,[status(thm)],[171,161]) ).
tff(173,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),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(monotonicity,[status(thm)],[97,172]) ).
tff(174,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(175,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(176,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)],[175,174]) ).
tff(177,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)],[176,111,101]) ).
tff(178,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(monotonicity,[status(thm)],[118]) ).
tff(179,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(180,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)],[179,140]) ).
tff(181,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(182,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(183,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)],[182]) ).
tff(184,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(185,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(186,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)],[185,184]) ).
tff(187,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)],[186]) ).
tff(188,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)],[187,183]) ).
tff(189,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(190,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)],[189,188]) ).
tff(191,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)],[190]) ).
tff(192,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(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(transitivity,[status(thm)],[191,181,180,178,177,173,143]) ).
tff(193,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_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_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)],[192,133]) ).
tff(194,plain,
c_Complex_Ocomplex_OComplex(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_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_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)],[193]) ).
tff(195,plain,
^ [V_z: $i] :
refl(
( ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
<=> ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ) )),
inference(bind,[status(th)],]) ).
tff(196,plain,
( ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
<=> ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ) ),
inference(quant_intro,[status(thm)],[195]) ).
tff(197,plain,
( ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
<=> ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ) ),
inference(rewrite,[status(thm)],]) ).
tff(198,axiom,
! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__surj) ).
tff(199,plain,
! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
inference(skolemize,[status(sab)],[199]) ).
tff(201,plain,
! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ),
inference(modus_ponens,[status(thm)],[200,196]) ).
tff(202,plain,
( ~ ! [V_z: $i] : ( c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z )
| ( c_Complex_Ocomplex_OComplex(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_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_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(quant_inst,[status(thm)],]) ).
tff(203,plain,
c_Complex_Ocomplex_OComplex(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_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_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(unit_resolution,[status(thm)],[202,201]) ).
tff(204,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_Ocomplex_OComplex(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_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)],[203]) ).
tff(205,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)],[204,194,20,10]) ).
tff(206,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(207,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(208,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)],[207,206]) ).
tff(209,plain,
$false,
inference(unit_resolution,[status(thm)],[208,205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.14 % Problem : SWW231+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.36 % Computer : n018.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 4 13:09:31 EDT 2022
% 0.12/0.36 % CPUTime :
% 0.12/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.37 Usage: tptp [options] [-file:]file
% 0.12/0.37 -h, -? prints this message.
% 0.12/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.37 -m, -model generate model.
% 0.12/0.37 -p, -proof generate proof.
% 0.12/0.37 -c, -core generate unsat core of named formulas.
% 0.12/0.37 -st, -statistics display statistics.
% 0.12/0.37 -t:timeout set timeout (in second).
% 0.12/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.37 -<param>:<value> configuration parameter and value.
% 0.12/0.37 -o:<output-file> file to place output in.
% 8.00/5.30 % SZS status Theorem
% 8.00/5.30 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------