TSTP Solution File: SWV603-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV603-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 15:23:45 EDT 2022
% Result : Unsatisfiable 0.96s 0.98s
% Output : Proof 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 40
% Syntax : Number of formulae : 69 ( 19 unt; 17 typ; 0 def)
% Number of atoms : 227 ( 40 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 273 ( 119 ~; 123 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 12 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 67 ( 59 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_Transcendental_Osin_type,type,
c_Transcendental_Osin: $i > $i ).
tff(c_Transcendental_Opi_type,type,
c_Transcendental_Opi: $i ).
tff(c_HOL_Oabs__class_Oabs_type,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_Transcendental_Ocos_type,type,
c_Transcendental_Ocos: $i > $i ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(c_RealDef_Oreal_type,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(v_n_type,type,
v_n: $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_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(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(1,plain,
( ( c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
<=> ( c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
<=> ( c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(4,plain,
c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
tff(9,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
^ [V_x: $i,V_y: $i] :
refl(
( ( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
<=> ( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
^ [V_x: $i,V_y: $i] :
trans(
monotonicity(
rewrite(
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
<=> ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal) )),
rewrite(
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
<=> c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) )),
rewrite(
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
<=> ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )),
( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) ) )),
rewrite(
( ( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
<=> ( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) ) )),
( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [V_x: $i,V_y: $i] :
trans(
monotonicity(
rewrite(
( ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) )),
( ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) )),
rewrite(
( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) )),
( ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
tff(19,plain,
! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_x: $i,V_y: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[20,14]) ).
tff(22,plain,
! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[22,12]) ).
tff(24,plain,
( ( ~ ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
<=> ( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ( ~ ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ( ~ ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,plain,
( ~ ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
( ~ ! [V_x: $i,V_y: $i] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_y,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),V_x,tc_RealDef_Oreal) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[29,23,10]) ).
tff(31,plain,
^ [V_r: $i] :
refl(
( ( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
<=> ( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
<=> ! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
^ [V_r: $i] :
rewrite(
( ( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
tff(37,plain,
! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ( c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Osin(c_Transcendental_Opi) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
<=> ( ~ ! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ( c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Osin(c_Transcendental_Opi) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ ! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ( c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Osin(c_Transcendental_Opi) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [V_r: $i] :
( ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r )
| c_HOL_Oord__class_Oless(V_r,c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ( c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Osin(c_Transcendental_Opi) )
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(c_Transcendental_Opi),c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Osin(c_Transcendental_Opi),
inference(unit_resolution,[status(thm)],[43,40,30]) ).
tff(45,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(c_Transcendental_Opi),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(transitivity,[status(thm)],[45,5]) ).
tff(47,plain,
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
<=> ( c_Transcendental_Osin(c_Transcendental_Opi) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
<=> ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
tff(50,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
c_Transcendental_Osin(c_Transcendental_Opi) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[50,47]) ).
tff(52,plain,
$false,
inference(unit_resolution,[status(thm)],[51,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV603-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 06:20:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.96/0.98 % SZS status Unsatisfiable
% 0.96/0.98 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------