TSTP Solution File: SWW204+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW204+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Thu Sep 29 20:57:53 EDT 2022
% Result : Theorem 0.70s 0.80s
% Output : Proof 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 26
% Syntax : Number of formulae : 40 ( 11 unt; 11 typ; 0 def)
% Number of atoms : 195 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 268 ( 116 ~; 112 |; 0 &)
% ( 19 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 76 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i ) > $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
tff(v_s_type,type,
v_s: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(1,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
<=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( class_Orderings_Oorder(tc_RealDef_Oreal)
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
tff(6,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
refl(
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
<=> ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
<=> ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) )
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) )),
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) )
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) ) )),
rewrite(
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) )
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) )),
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) )
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) )),
( ( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) )
<=> ( class_Orderings_Oorder(T_a)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) ) )),
rewrite(
( ( class_Orderings_Oorder(T_a)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) )
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) )),
( ( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) )
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) )
<=> ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
tff(13,plain,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__0960_A_060_061_Acmod_A_Is_A0_J_096) ).
tff(19,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096cmod_A_Is_A0_J_A_060_061_Ar_096) ).
tff(22,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) )
<=> ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y)) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,22,19,16,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW204+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.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 : Sun Sep 4 12:40:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.70/0.80 % SZS status Theorem
% 0.70/0.80 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------