%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW272+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:44 AM UTC 2025
% Result : Theorem 0.50s 0.70s
% Output : Proof 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 70 ( 32 ~; 24 |; 0 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 34 ( 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_pa_____type,type,
v_pa____: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Polynomial_Oorder_type,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(v_s_____type,type,
v_s____: $i ).
tff(1,plain,
( class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
<=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
tff(3,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_p: $i,T_a: $i] :
refl(( ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_p: $i,T_a: $i] :
rewrite(( ( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_p: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
<=> ! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_p: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
tff(10,plain,
! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( ~ ! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_p: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__0(T_a)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ( ( v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) )
<=> ( v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
~ ( ( v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(21,plain,
v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____) )
<=> ( v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s) ).
tff(26,plain,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
v_pa____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(transitivity,[status(thm)],[26,23,17]) ).
tff(28,plain,
( ( v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
<=> ( v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pne) ).
tff(30,plain,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW272+1 : TPTP v9.0.0. Released v5.2.0.
% 0.00/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.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 : Fri Jun 20 11:20:40 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.50/0.70 % SZS status Theorem
% 0.50/0.70 % SZS output start Proof
% See solution above
% 0.62/0.76 % E exiting
%------------------------------------------------------------------------------