TSTP Solution File: SWW233+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW233+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 20:58:00 EDT 2022
% Result : Theorem 0.86s 0.86s
% Output : Proof 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 47
% Syntax : Number of formulae : 91 ( 28 unt; 13 typ; 0 def)
% Number of atoms : 392 ( 25 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 485 ( 196 ~; 215 |; 0 &)
% ( 44 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 25 ( 25 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 9 >; 8 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 208 ( 187 !; 0 ?; 208 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(v_r_____type,type,
v_r____: $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(c_RealVector_Onorm__class_Onorm_type,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(v_z_____type,type,
v_z____: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(1,plain,
( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
tff(3,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_c: $i,V_a: $i,T_a: $i] :
rewrite(
( ( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_c: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
<=> ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_c: $i,V_a: $i,T_a: $i] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(10,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ) )
<=> ( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_c: $i,V_a: $i,T_a: $i] :
( ~ class_Rings_Ocomm__semiring__1(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) )
| ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r____) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r____)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r____)
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
^ [V_x: $i] :
refl(
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [V_x: $i] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)
<=> ! [V_x: $i] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [V_x: $i] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)
<=> ! [V_x: $i] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [V_x: $i] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
tff(26,plain,
! [V_x: $i] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [V_x: $i] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [V_x: $i] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [V_x: $i] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r____) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r____),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____),
inference(modus_ponens,[status(thm)],[30,21]) ).
tff(32,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(34,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( class_Orderings_Olinorder(tc_RealDef_Oreal)
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
tff(37,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
refl(
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) )),
( ( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) )
<=> ( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) )),
rewrite(
( ( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ) )),
( ( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) )
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
tff(44,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____),
inference(unit_resolution,[status(thm)],[53,47,37,34]) ).
tff(55,plain,
( class_Orderings_Oorder(tc_RealDef_Oreal)
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
tff(57,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
^ [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
refl(
( ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
<=> ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
<=> ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) )),
( ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) )),
rewrite(
( ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ) )),
( ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ) )),
( ( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) )
<=> ( class_Orderings_Oorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ) ) )),
rewrite(
( ( class_Orderings_Oorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ) )),
( ( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) )
<=> ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
tff(64,plain,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_h) ).
tff(70,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____) )
<=> ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) )
<=> ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) )
<=> ( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____) ) ),
inference(transitivity,[status(thm)],[73,71]) ).
tff(75,plain,
( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [V_z: $i,V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ class_Orderings_Oorder(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),v_r____),
inference(unit_resolution,[status(thm)],[76,70,67,57,54]) ).
tff(78,plain,
$false,
inference(unit_resolution,[status(thm)],[77,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW233+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 : n020.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 13:08:44 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.
% 0.86/0.86 % SZS status Theorem
% 0.86/0.86 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------