TSTP Solution File: SWW224+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW224+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:57:58 EDT 2022
% Result : Theorem 174.52s 111.42s
% Output : Proof 174.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 87
% Syntax : Number of formulae : 177 ( 44 unt; 16 typ; 0 def)
% Number of atoms : 778 ( 90 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1008 ( 423 ~; 413 |; 0 &)
% ( 132 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 12 >; 9 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 437 ( 395 !; 0 ?; 437 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
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_x_type,type,
v_x: $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(v_e_type,type,
v_e: $i ).
tff(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(class_Groups_Oordered__ab__semigroup__add__imp__le_type,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(class_Groups_Ogroup__add_type,type,
class_Groups_Ogroup__add: $i > $o ).
tff(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_Groups_Oabs__class_Oabs_type,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(class_Groups_Oordered__ab__group__add_type,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(class_Groups_Oordered__ab__group__add__abs_type,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(1,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
tff(3,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
refl(
( ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
<=> ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
<=> ! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
<=> ! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
rewrite(
( ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
<=> ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
<=> ! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
tff(10,plain,
! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) )
<=> ( ~ ! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [V_b_2: $i,V_c_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
( class_Groups_Ogroup__add(tc_RealDef_Oreal)
<=> class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
tff(20,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) )
<=> ( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
rewrite(
( ( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) )
<=> ( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
tff(27,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) )
| ~ class_Groups_Ogroup__add(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m) = v_x ) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) )
| ~ class_Groups_Ogroup__add(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m) = v_x ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) )
| ~ class_Groups_Ogroup__add(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m) = v_x ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Groups_Ogroup__add(T_a)
| ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) )
| ~ class_Groups_Ogroup__add(tc_RealDef_Oreal)
| ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m) = v_x ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m) = v_x,
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
( class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
tff(37,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,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(39,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)],[38]) ).
tff(40,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(41,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(42,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)],[41]) ).
tff(43,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(44,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)],[43,42]) ).
tff(45,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)],[44,40]) ).
tff(46,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)],[45]) ).
tff(47,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)],[46,39]) ).
tff(48,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,v_e,v_m) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e) ) )
<=> ( ~ ! [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,v_e,v_m) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,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,v_e,v_m) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,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,v_e,v_m) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),
inference(unit_resolution,[status(thm)],[50,47,37]) ).
tff(52,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) ),
inference(monotonicity,[status(thm)],[51,34]) ).
tff(53,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m)) ),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x)
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m)) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(57,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e)),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( class_Orderings_Olinorder(tc_RealDef_Oreal)
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
tff(60,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,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(62,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)],[61]) ).
tff(63,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(64,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(65,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)],[64]) ).
tff(66,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(67,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)],[66,65]) ).
tff(68,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)],[67,63]) ).
tff(69,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)],[68]) ).
tff(70,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)],[69,62]) ).
tff(71,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(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) )
<=> ( ~ ! [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(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,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_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
| ~ 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(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,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_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
| ~ 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(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) ) ),
inference(transitivity,[status(thm)],[73,71]) ).
tff(75,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_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,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(tc_RealDef_Oreal,v_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_m,v_e),v_x),
inference(unit_resolution,[status(thm)],[76,70,60,57]) ).
tff(78,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m)),
inference(modus_ponens,[status(thm)],[77,54]) ).
tff(79,plain,
( class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)
<=> class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
tff(81,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
^ [V_b_2: $i,V_a_2: $i,T_a: $i] :
refl(
( ( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
<=> ( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
<=> ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
<=> ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
^ [V_b_2: $i,V_a_2: $i,T_a: $i] :
rewrite(
( ( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
<=> ( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
<=> ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
tff(88,plain,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)
| ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
<=> ( ~ ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)
| ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)
| ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [V_b_2: $i,V_a_2: $i,T_a: $i] :
( ~ class_Groups_Oordered__ab__group__add(T_a)
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)
| ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(unit_resolution,[status(thm)],[94,91,81]) ).
tff(96,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x) ),
inference(rewrite,[status(thm)],]) ).
tff(97,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(98,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,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(tc_RealDef_Oreal,v_x,v_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x) )
<=> ( ~ ! [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(tc_RealDef_Oreal,v_x,v_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,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,v_m,v_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
| ~ 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(tc_RealDef_Oreal,v_x,v_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,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,v_m,v_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
| ~ 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(tc_RealDef_Oreal,v_x,v_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,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,v_m,v_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,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(tc_RealDef_Oreal,v_x,v_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_m,v_x) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m),
inference(unit_resolution,[status(thm)],[104,70,60,98]) ).
tff(106,plain,
( ~ ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x,v_m)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(tautology,[status(thm)],]) ).
tff(107,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(unit_resolution,[status(thm)],[106,105,95]) ).
tff(108,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(109,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)],[108]) ).
tff(110,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(111,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(112,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)],[111]) ).
tff(113,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/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
tff(114,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)],[113,112]) ).
tff(115,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)],[114,110]) ).
tff(116,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)],[115]) ).
tff(117,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)],[116,109]) ).
tff(118,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) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) )
<=> ( ~ ! [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) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ 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) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ 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) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,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) )
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),
inference(unit_resolution,[status(thm)],[123,117,60,107]) ).
tff(125,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
<=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(126,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
tff(127,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
^ [V_a: $i,T_a: $i] :
trans(
monotonicity(
rewrite(
( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) )
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )),
( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ) )),
rewrite(
( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
( ( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [V_a: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) )
<=> ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,axiom,
! [V_a: $i,T_a: $i] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
tff(134,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ),
inference(modus_ponens,[status(thm)],[136,129]) ).
tff(138,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) )
<=> ( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ) ),
inference(transitivity,[status(thm)],[140,138]) ).
tff(142,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ),
inference(unit_resolution,[status(thm)],[143,137,127]) ).
tff(145,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),
inference(unit_resolution,[status(thm)],[144,124]) ).
tff(146,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ),
inference(symmetry,[status(thm)],[147]) ).
tff(149,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_x,v_m)),v_e)
<=> ~ 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_x,v_m)),v_e) ),
inference(rewrite,[status(thm)],]) ).
tff(150,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_x,v_m)),v_e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(151,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_x,v_m)),v_e),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,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(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))) )
<=> ( ~ ! [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(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,plain,
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)))
| 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_x,v_m)),v_e)
| ~ class_Orderings_Olinorder(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_x,v_m)),v_e)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(154,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_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)))
| 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_x,v_m)),v_e)
| ~ 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(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))) ) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,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_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)))
| 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_x,v_m)),v_e)
| ~ 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(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))) ) ),
inference(transitivity,[status(thm)],[154,152]) ).
tff(156,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_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)))
| 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_x,v_m)),v_e)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(157,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(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),v_e)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m))),
inference(unit_resolution,[status(thm)],[157,117,60,151]) ).
tff(159,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)),
inference(modus_ponens,[status(thm)],[158,148]) ).
tff(160,plain,
( ~ ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) )
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_e,v_m),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m),v_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v_x,v_m)) ),
inference(tautology,[status(thm)],]) ).
tff(161,plain,
$false,
inference(unit_resolution,[status(thm)],[160,159,78,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW224+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 12:59:38 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.
% 174.52/111.42 % SZS status Theorem
% 174.52/111.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------