%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV629-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:35:51 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.50s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 29 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 59 ( 27 ~; 23 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 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 : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 36 ( 33 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_FFT__Mirabelle_Oroot_type,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(1,plain,
^ [V_n: $i] :
refl(( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__unity_0) ).
tff(5,plain,
! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_n: $i] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
tff(12,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
tff(17,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),
inference(unit_resolution,[status(thm)],[22,19,12]) ).
tff(24,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(transitivity,[status(thm)],[24,9]) ).
tff(26,plain,
( ( c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
<=> ( c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(28,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV629-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 10:31:55 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.50 % SZS status Unsatisfiable
% 0.22/0.50 % SZS output start Proof
% See solution above
% 0.22/0.52 % E exiting
%------------------------------------------------------------------------------