%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG413-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:59:04 AM UTC 2025
% Result : Unsatisfiable 0.94s 1.11s
% Output : Proof 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 26
% Syntax : Number of formulae : 57 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 174 ( 98 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 211 ( 98 ~; 94 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 129 ( 117 !; 0 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_d_____type,type,
v_d____: $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(c_RealVector_Oof__real_type,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(v_x_____type,type,
v_x____: $i ).
tff(v_ds_____type,type,
v_ds____: $i ).
tff(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_RealVector_Oreal__normed__vector_type,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__0_type,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(1,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
tff(3,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_x: $i,T_a: $i] :
refl(( ( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) )
<=> ( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
tff(8,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
<=> ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(17,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
tff(20,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
refl(( ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
<=> ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
tff(25,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V_x: $i,V_a: $i,T_a: $i,V_p: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[30,27,20]) ).
tff(32,plain,
c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____,v_ds____,tc_Complex_Ocomplex),c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[32,17]) ).
tff(34,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
tff(36,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) )
<=> ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
rewrite(( ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) )
<=> ( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
tff(43,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
| ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(v_d____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[49,46,36,33]) ).
tff(51,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(v_d____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[52,14]) ).
tff(54,plain,
( ( c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex) )
<=> ( c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(56,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_ds____,c_RealVector_Oof__real(v_x____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(v_d____,tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ALG413-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 11:13:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.94/1.11 % SZS status Unsatisfiable
% 0.94/1.11 % SZS output start Proof
% See solution above
% 0.94/1.15 % E exiting
%------------------------------------------------------------------------------