%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW223+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:36:38 AM UTC 2025
% Result : Theorem 15.25s 15.43s
% Output : Proof 15.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 41
% Syntax : Number of formulae : 92 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 507 ( 25 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 708 ( 325 ~; 282 |; 0 &)
% ( 55 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 265 ( 239 !; 0 ?; 265 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(v_e2_____type,type,
v_e2____: $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(v_m_____type,type,
v_m____: $i ).
tff(v_b_____type,type,
v_b____: $i ).
tff(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
tff(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
tff(c_Int_OPls_type,type,
c_Int_OPls: $i ).
tff(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
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_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
tff(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(1,plain,
( class_Int_Onumber__ring(tc_RealDef_Oreal)
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
tff(3,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_z: $i,T_a: $i] :
refl(( ( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) )
<=> ! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) )
<=> ! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_z: $i,T_a: $i] :
rewrite(( ( class_Int_Onumber__ring(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) )
<=> ( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_z: $i,T_a: $i] :
( class_Int_Onumber__ring(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) )
<=> ! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_z: $i,T_a: $i] :
( class_Int_Onumber__ring(T_a)
=> ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).
tff(10,plain,
! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____) ) )
<=> ( ~ ! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [V_z: $i,T_a: $i] :
( ~ class_Int_Onumber__ring(T_a)
| ( c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) )
| ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),
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_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____)) ),
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,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____)) ),
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,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____))
<=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____)) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____)) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(24,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____)),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( class_Orderings_Olinorder(tc_RealDef_Oreal)
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
tff(27,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [V_x: $i,V_y: $i,T_a: $i] :
refl(( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
<=> ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
<=> ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [V_x: $i,V_y: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) )),
( ( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) )
<=> ( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) )),
rewrite(( ( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) )),
( ( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [V_x: $i,V_y: $i,T_a: $i] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) )
<=> ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [V_x: $i,V_y: $i,T_a: $i] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
tff(34,plain,
! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____)) )
<=> ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____)) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____)) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [V_x: $i,V_y: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,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,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),v_e2____)),
inference(unit_resolution,[status(thm)],[43,37,27,24]) ).
tff(45,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,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____)),
inference(modus_ponens,[status(thm)],[44,21]) ).
tff(46,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(48,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( class_Orderings_Opreorder(tc_RealDef_Oreal)
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
tff(51,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
refl(( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
^ [V_y: $i,V_x: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )),
( ( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ( class_Orderings_Opreorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) )),
rewrite(( ( class_Orderings_Opreorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) )),
( ( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [V_y: $i,V_x: $i,T_a: $i] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) )
<=> ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
tff(58,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [V_y: $i,V_x: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) )
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_a____,v_e2____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____),
inference(unit_resolution,[status(thm)],[67,61,51,48]) ).
tff(69,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(71,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal)
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
tff(74,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
^ [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(( ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
<=> ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
<=> ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
^ [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) )),
( ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) )
<=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) )),
rewrite(( ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )),
( ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )),
( ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) )
<=> ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) ) )),
rewrite(( ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ) )),
( ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) )
<=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) )
<=> ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
tff(81,plain,
! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
( ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____)) )
<=> ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) )
<=> ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) )
<=> ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____)) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) )
<=> ( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____)) ) ),
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,plain,
( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
( ~ ! [V_d: $i,V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_e2____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_a____,v_e2____)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____)) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,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,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_b____,v_m____)),v_a____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e2____,v_e2____)),
inference(unit_resolution,[status(thm)],[90,84,74,71,68]) ).
tff(92,plain,
$false,
inference(unit_resolution,[status(thm)],[91,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW223+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 11:20:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 15.25/15.43 % SZS status Theorem
% 15.25/15.43 % SZS output start Proof
% See solution above
% 15.31/15.53 % E exiting
%------------------------------------------------------------------------------