TSTP Solution File: SWV598-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV598-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 15:23:43 EDT 2022
% Result : Unsatisfiable 0.69s 0.77s
% Output : Proof 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 45
% Syntax : Number of formulae : 95 ( 15 unt; 14 typ; 0 def)
% Number of atoms : 342 ( 109 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 451 ( 198 ~; 201 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 10 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 57 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Transcendental_Opi_type,type,
c_Transcendental_Opi: $i ).
tff(v_x_type,type,
v_x: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Transcendental_Osin_type,type,
c_Transcendental_Osin: $i > $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_Transcendental_Ocos_type,type,
c_Transcendental_Ocos: $i > $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(1,plain,
( class_Orderings_Olinorder(tc_RealDef_Oreal)
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
tff(3,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
<=> ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( $false
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) )
<=> ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(8,plain,
( ( c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> $true ),
inference(iff_true,[status(thm)],[7]) ).
tff(9,plain,
( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> $false ),
inference(transitivity,[status(thm)],[9,6]) ).
tff(11,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) )
<=> ( $false
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) )
<=> ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) ),
inference(transitivity,[status(thm)],[11,5]) ).
tff(13,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| $false )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_0_0) ).
tff(15,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal)
<=> $true ),
inference(iff_true,[status(thm)],[14]) ).
tff(16,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal)
<=> $false ),
inference(transitivity,[status(thm)],[16,6]) ).
tff(18,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| $false ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[18,13]) ).
tff(20,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,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(21,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,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(22,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,axiom,
( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_04) ).
tff(26,plain,
( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,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)],[25,24]) ).
tff(27,plain,
( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,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)],[26,20]) ).
tff(28,plain,
( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[27,19]) ).
tff(29,plain,
~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[28,12]) ).
tff(30,plain,
~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[29,4]) ).
tff(31,plain,
( ( v_x != c_Transcendental_Opi )
<=> ( v_x != c_Transcendental_Opi ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( $false
| ( v_x != c_Transcendental_Opi ) )
<=> ( v_x != c_Transcendental_Opi ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
c_Transcendental_Ocos(v_x) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(34,plain,
( ( c_Transcendental_Ocos(v_x) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
<=> $true ),
inference(iff_true,[status(thm)],[33]) ).
tff(35,plain,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
<=> $false ),
inference(transitivity,[status(thm)],[35,6]) ).
tff(37,plain,
( ( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) )
<=> ( $false
| ( v_x != c_Transcendental_Opi ) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) )
<=> ( v_x != c_Transcendental_Opi ) ),
inference(transitivity,[status(thm)],[37,32]) ).
tff(39,plain,
( ( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) )
<=> ( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).
tff(41,plain,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ),
inference(modus_ponens,[status(thm)],[41,39]) ).
tff(43,plain,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,plain,
v_x != c_Transcendental_Opi,
inference(modus_ponens,[status(thm)],[43,38]) ).
tff(45,plain,
v_x != c_Transcendental_Opi,
inference(modus_ponens,[status(thm)],[44,31]) ).
tff(46,plain,
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)
<=> ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ( $false
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ( $false
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(49,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ),
inference(transitivity,[status(thm)],[48,47]) ).
tff(50,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| $false
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(52,plain,
( c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
<=> $true ),
inference(iff_true,[status(thm)],[51]) ).
tff(53,plain,
( ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
<=> $false ),
inference(transitivity,[status(thm)],[53,6]) ).
tff(55,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| $false
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[55,50]) ).
tff(57,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
tff(60,plain,
( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(v_x,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),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[60,57]) ).
tff(62,plain,
( ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[61,56]) ).
tff(63,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[62,49]) ).
tff(64,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[63,46]) ).
tff(65,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(
( ( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
<=> ( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
trans(
monotonicity(
rewrite(
( ( ~ class_Orderings_Olinorder(T_a)
| ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
<=> ( ( V_x = V_y )
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) )),
( ( ~ class_Orderings_Olinorder(T_a)
| ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
<=> ( ( V_x = V_y )
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) )),
rewrite(
( ( ( V_x = V_y )
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
<=> ( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) )),
( ( ~ class_Orderings_Olinorder(T_a)
| ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
<=> ( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Olinorder(T_a)
| ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
tff(71,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
| c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)
| ( v_x = c_Transcendental_Opi )
| c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
| c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)
| ( v_x = c_Transcendental_Opi )
| c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ( ( v_x = c_Transcendental_Opi )
| c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ( c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)
| ( v_x = c_Transcendental_Opi )
| c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
| ( v_x = c_Transcendental_Opi )
| c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
| c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)
| ( v_x = c_Transcendental_Opi )
| c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
| ( v_x = c_Transcendental_Opi )
| c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
| c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)
| ( v_x = c_Transcendental_Opi )
| c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
| ( v_x = c_Transcendental_Opi )
| c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( ( V_x = V_y )
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) )
| c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal)
| ( v_x = c_Transcendental_Opi )
| c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
$false,
inference(unit_resolution,[status(thm)],[80,74,64,45,30,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWV598-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Sep 4 06:28:54 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.69/0.77 % SZS status Unsatisfiable
% 0.69/0.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------