%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV598-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:35:47 AM UTC 2025
% Result : Unsatisfiable 0.52s 0.69s
% Output : Proof 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 63 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 279 ( 92 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 354 ( 146 ~; 183 |; 0 &)
% ( 25 <=>; 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 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/sandbox2/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_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
<=> ( c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(6,plain,
c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( 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_x,tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
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_0_0) ).
tff(9,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,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(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)
| ~ 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(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_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(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)
| ~ 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)],[12]) ).
tff(14,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)],[13,11]) ).
tff(15,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/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_04) ).
tff(16,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)],[15,14]) ).
tff(17,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)],[16,10]) ).
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) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
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) ),
inference(modus_ponens,[status(thm)],[18,10]) ).
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) ),
inference(modus_ponens,[status(thm)],[19,10]) ).
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) ),
inference(unit_resolution,[status(thm)],[20,9]) ).
tff(22,plain,
~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[21,6]) ).
tff(23,plain,
( ( c_Transcendental_Ocos(v_x) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
<=> ( c_Transcendental_Ocos(v_x) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
c_Transcendental_Ocos(v_x) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(25,plain,
c_Transcendental_Ocos(v_x) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,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(27,axiom,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).
tff(28,plain,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ),
inference(modus_ponens,[status(thm)],[28,26]) ).
tff(30,plain,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ),
inference(modus_ponens,[status(thm)],[29,26]) ).
tff(31,plain,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( v_x != c_Transcendental_Opi ) ),
inference(modus_ponens,[status(thm)],[31,26]) ).
tff(33,plain,
v_x != c_Transcendental_Opi,
inference(unit_resolution,[status(thm)],[32,25]) ).
tff(34,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)
<=> 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) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,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/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
tff(36,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),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,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(38,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(39,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/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
tff(40,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)],[39,38]) ).
tff(41,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)],[40,37]) ).
tff(42,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)],[41,37]) ).
tff(43,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)],[42,37]) ).
tff(44,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)],[43,37]) ).
tff(45,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(unit_resolution,[status(thm)],[44,36]) ).
tff(46,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,v_x,tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[45,6]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,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(51,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)],[50]) ).
tff(52,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
tff(53,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)],[52,51]) ).
tff(54,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)],[53,49]) ).
tff(55,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)],[54]) ).
tff(56,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)],[55,48]) ).
tff(57,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(58,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(59,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)],[58]) ).
tff(60,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)],[59,57]) ).
tff(61,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(62,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)],[61,60]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,56,46,33,22,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV598-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 10:27:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.52/0.69 % SZS status Unsatisfiable
% 0.52/0.69 % SZS output start Proof
% See solution above
% 0.59/0.76 % E exiting
%------------------------------------------------------------------------------