%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV573-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:35:45 AM UTC 2025
% Result : Unsatisfiable 0.17s 0.53s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 32 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 45 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 63 ( 27 ~; 23 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 33 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Complex_Ocomplex_OComplex_type,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Nat_Osemiring__1__class_Oof__nat_type,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(v_n_type,type,
v_n: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_RealVector_Oof__real_type,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(class_RealVector_Oreal__algebra__1_type,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(1,plain,
( ( c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) )
<=> ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
^ [V_x: $i] :
refl(( ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) )
<=> ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ) )),
inference(bind,[status(th)],[]) ).
tff(3,plain,
( ! [V_x: $i] : ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) )
<=> ! [V_x: $i] : ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ) ),
inference(quant_intro,[status(thm)],[2]) ).
tff(4,plain,
( ! [V_x: $i] : ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) )
<=> ! [V_x: $i] : ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
! [V_x: $i] : ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__eq__cancel__iff2_2) ).
tff(6,plain,
! [V_x: $i] : ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
! [V_x: $i] : ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ),
inference(skolemize,[status(sab)],[6]) ).
tff(8,plain,
! [V_x: $i] : ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
( ~ ! [V_x: $i] : ( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) )
| ( c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(10,plain,
c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[9,8]) ).
tff(11,plain,
( ( c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) )
<=> ( c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) )
<=> ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) ) ),
inference(transitivity,[status(thm)],[11,1]) ).
tff(13,plain,
( ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) )
<=> ( c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
<=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
tff(16,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
^ [V_n: $i,T_a: $i] :
refl(( ( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) )
<=> ( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) )
<=> ! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) )
<=> ! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__of__nat__eq_0) ).
tff(21,plain,
! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ( ~ ! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V_n: $i,T_a: $i] :
( ~ class_RealVector_Oreal__algebra__1(T_a)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),T_a) = c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a) ) )
| ~ class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ( c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[26,23,16]) ).
tff(28,plain,
c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(modus_ponens,[status(thm)],[27,13]) ).
tff(29,plain,
( ( c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) )
<=> ( c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(31,plain,
c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV573-1 : TPTP v9.0.0. Released v4.1.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Jun 20 10:25:05 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.17/0.53 % SZS status Unsatisfiable
% 0.17/0.53 % SZS output start Proof
% See solution above
% 0.17/0.58 % E exiting
%------------------------------------------------------------------------------