%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV022-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:08:58 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 72
% Syntax : Number of formulae : 205 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 989 ( 225 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 1105 ( 371 ~; 628 |; 0 &)
% ( 106 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 50 ( 50 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 284 ( 261 !; 0 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(fifo_length_type,type,
fifo_length: $i ).
tff(int_level_type,type,
int_level: $i > $i ).
tff(t_139_type,type,
t_139: $i ).
tff(level_type,type,
level: $i > $i ).
tff(plus_type,type,
plus: ( $i * $i ) > $i ).
tff(n0_type,type,
n0: $i ).
tff(def_10_type,type,
def_10: ( $i * $i ) > $o ).
tff(p_Reset_type,type,
p_Reset: $i > $o ).
tff(p_Wr_type,type,
p_Wr: $i > $o ).
tff(p_Rd_type,type,
p_Rd: $i > $o ).
tff(1,plain,
^ [X_t_32: $i] :
refl(( ( level(X_t_32) = int_level(X_t_32) )
<=> ( level(X_t_32) = int_level(X_t_32) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
<=> ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
<=> ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_21) ).
tff(5,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
| ( level(t_139) = int_level(t_139) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
level(t_139) = int_level(t_139),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( n1 = plus(n0,n1) )
<=> ( n1 = plus(n0,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
n1 = plus(n0,n1),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_20) ).
tff(12,plain,
n1 = plus(n0,n1),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
plus(n0,n1) = n1,
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
plus(level(t_139),plus(n0,n1)) = plus(level(t_139),n1),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
plus(level(t_139),n1) = plus(level(t_139),plus(n0,n1)),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( ( plus(level(t_139),n1) = fifo_length )
<=> ( plus(level(t_139),n1) = fifo_length ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
plus(level(t_139),n1) = fifo_length,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_1) ).
tff(18,plain,
plus(level(t_139),n1) = fifo_length,
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
fifo_length = plus(level(t_139),n1),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
fifo_length = plus(level(t_139),plus(n0,n1)),
inference(transitivity,[status(thm)],[19,15]) ).
tff(21,plain,
( def_10(plus(n0,n1),fifo_length)
<=> def_10(plus(n0,n1),plus(level(t_139),plus(n0,n1))) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ~ def_10(plus(n0,n1),fifo_length)
<=> ~ def_10(plus(n0,n1),plus(level(t_139),plus(n0,n1))) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( gt(fifo_length,plus(n0,n1))
<=> gt(plus(level(t_139),n1),plus(n0,n1)) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(24,plain,
( gt(plus(level(t_139),n1),plus(n0,n1))
<=> gt(fifo_length,plus(n0,n1)) ),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( gt(fifo_length,level(t_139))
<=> gt(fifo_length,int_level(t_139)) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(26,plain,
( gt(fifo_length,int_level(t_139))
<=> gt(fifo_length,level(t_139)) ),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( ~ gt(fifo_length,int_level(t_139))
<=> ~ gt(fifo_length,level(t_139)) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
int_level(t_139) = level(t_139),
inference(symmetry,[status(thm)],[9]) ).
tff(29,plain,
plus(int_level(t_139),n1) = plus(level(t_139),n1),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
plus(int_level(t_139),n1) = fifo_length,
inference(transitivity,[status(thm)],[29,18]) ).
tff(31,plain,
( ~ ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
| ( level(plus(t_139,n1)) = int_level(plus(t_139,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
level(plus(t_139,n1)) = int_level(plus(t_139,n1)),
inference(unit_resolution,[status(thm)],[31,7]) ).
tff(33,plain,
int_level(plus(t_139,n1)) = level(plus(t_139,n1)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) )
<=> ( level(plus(t_139,n1)) = fifo_length ) ),
inference(monotonicity,[status(thm)],[33,30]) ).
tff(35,plain,
( ( level(plus(t_139,n1)) = fifo_length )
<=> ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) ),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ( level(plus(t_139,n1)) != fifo_length )
<=> ( int_level(plus(t_139,n1)) != plus(int_level(t_139),n1) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( level(plus(t_139,n1)) != fifo_length )
<=> ( level(plus(t_139,n1)) != fifo_length ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
level(plus(t_139,n1)) != fifo_length,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_5) ).
tff(39,plain,
level(plus(t_139,n1)) != fifo_length,
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
int_level(plus(t_139,n1)) != plus(int_level(t_139),n1),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
( ~ p_Reset(t_139)
<=> ~ p_Reset(t_139) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
~ p_Reset(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_4) ).
tff(43,plain,
~ p_Reset(t_139),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( p_Wr(t_139)
<=> p_Wr(t_139) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
p_Wr(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_3) ).
tff(46,plain,
p_Wr(t_139),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ p_Rd(t_139)
<=> ~ p_Rd(t_139) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
~ p_Rd(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).
tff(49,plain,
~ p_Rd(t_139),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
^ [X_t_42: $i] :
refl(( ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
^ [X_t_42: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42)) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42)) ) )),
rewrite(( ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42)) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42)) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42)) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42)) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ) )),
rewrite(( ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_35) ).
tff(57,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) ),
inference(modus_ponens,[status(thm)],[60,50]) ).
tff(62,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
| p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
| p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( p_Reset(t_139)
| p_Rd(t_139)
| ~ p_Wr(t_139)
| ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) )
<=> ( p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| p_Rd(t_139)
| ~ p_Wr(t_139)
| ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
| p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| p_Rd(t_139)
| ~ p_Wr(t_139)
| ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
| p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| p_Rd(t_139)
| ~ p_Wr(t_139)
| ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = plus(int_level(X_t_42),n1) ) )
| p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = plus(int_level(t_139),n1) ) ),
inference(unit_resolution,[status(thm)],[67,61,49,46,43]) ).
tff(69,plain,
~ gt(fifo_length,int_level(t_139)),
inference(unit_resolution,[status(thm)],[68,40]) ).
tff(70,plain,
~ gt(fifo_length,level(t_139)),
inference(modus_ponens,[status(thm)],[69,27]) ).
tff(71,plain,
( ( level(t_139) = fifo_length )
<=> ( int_level(t_139) = fifo_length ) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(72,plain,
( ( int_level(t_139) = fifo_length )
<=> ( level(t_139) = fifo_length ) ),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ( int_level(t_139) != fifo_length )
<=> ( level(t_139) != fifo_length ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
^ [X_t_42: $i] :
refl(( ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
^ [X_t_42: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| gt(fifo_length,int_level(X_t_42)) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42)) ) )),
rewrite(( ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42)) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42)) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| gt(fifo_length,int_level(X_t_42)) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42)) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
rewrite(( ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| p_Rd(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_44) ).
tff(80,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ( p_Reset(t_139)
| p_Rd(t_139)
| ~ p_Wr(t_139)
| gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
<=> ( p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Reset(t_139)
| p_Rd(t_139)
| ~ p_Wr(t_139)
| gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Reset(t_139)
| p_Rd(t_139)
| ~ p_Wr(t_139)
| gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ) ),
inference(transitivity,[status(thm)],[86,84]) ).
tff(88,plain,
( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Reset(t_139)
| p_Rd(t_139)
| ~ p_Wr(t_139)
| gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| gt(fifo_length,int_level(X_t_42))
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) )
| p_Rd(t_139)
| p_Reset(t_139)
| ~ p_Wr(t_139)
| gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
( gt(fifo_length,int_level(t_139))
| ( int_level(plus(t_139,n1)) = int_level(t_139) ) ),
inference(unit_resolution,[status(thm)],[89,83,49,46,43]) ).
tff(91,plain,
int_level(plus(t_139,n1)) = int_level(t_139),
inference(unit_resolution,[status(thm)],[90,69]) ).
tff(92,plain,
int_level(t_139) = int_level(plus(t_139,n1)),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
int_level(t_139) = level(plus(t_139,n1)),
inference(transitivity,[status(thm)],[92,33]) ).
tff(94,plain,
( ( int_level(t_139) = fifo_length )
<=> ( level(plus(t_139,n1)) = fifo_length ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( level(plus(t_139,n1)) = fifo_length )
<=> ( int_level(t_139) = fifo_length ) ),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
( ( level(plus(t_139,n1)) != fifo_length )
<=> ( int_level(t_139) != fifo_length ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
int_level(t_139) != fifo_length,
inference(modus_ponens,[status(thm)],[39,96]) ).
tff(98,plain,
level(t_139) != fifo_length,
inference(modus_ponens,[status(thm)],[97,73]) ).
tff(99,plain,
^ [Y_18: $i,X_17: $i] :
refl(( ( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) )
<=> ( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) )
<=> ! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) )
<=> ! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
^ [Y_18: $i,X_17: $i] :
trans(monotonicity(rewrite(( ( gt(Y_18,X_17)
| ( X_17 = Y_18 ) )
<=> ( ( X_17 = Y_18 )
| gt(Y_18,X_17) ) )),
( ( gt(Y_18,X_17)
| ( X_17 = Y_18 )
| gt(X_17,Y_18) )
<=> ( ( X_17 = Y_18 )
| gt(Y_18,X_17)
| gt(X_17,Y_18) ) )),
rewrite(( ( ( X_17 = Y_18 )
| gt(Y_18,X_17)
| gt(X_17,Y_18) )
<=> ( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) ) )),
( ( gt(Y_18,X_17)
| ( X_17 = Y_18 )
| gt(X_17,Y_18) )
<=> ( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [Y_18: $i,X_17: $i] :
( gt(Y_18,X_17)
| ( X_17 = Y_18 )
| gt(X_17,Y_18) )
<=> ! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [Y_18: $i,X_17: $i] :
( gt(Y_18,X_17)
| ( X_17 = Y_18 )
| gt(X_17,Y_18) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_12) ).
tff(105,plain,
! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
( ( ~ ! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) )
| gt(level(t_139),fifo_length)
| ( level(t_139) = fifo_length )
| gt(fifo_length,level(t_139)) )
<=> ( ~ ! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) )
| gt(level(t_139),fifo_length)
| ( level(t_139) = fifo_length )
| gt(fifo_length,level(t_139)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) )
| gt(level(t_139),fifo_length)
| ( level(t_139) = fifo_length )
| gt(fifo_length,level(t_139)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [Y_18: $i,X_17: $i] :
( gt(X_17,Y_18)
| ( X_17 = Y_18 )
| gt(Y_18,X_17) )
| gt(level(t_139),fifo_length)
| ( level(t_139) = fifo_length )
| gt(fifo_length,level(t_139)) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
( gt(level(t_139),fifo_length)
| ( level(t_139) = fifo_length )
| gt(fifo_length,level(t_139)) ),
inference(unit_resolution,[status(thm)],[111,108]) ).
tff(113,plain,
gt(level(t_139),fifo_length),
inference(unit_resolution,[status(thm)],[112,98,70]) ).
tff(114,plain,
( gt(fifo_length,n0)
<=> gt(plus(level(t_139),n1),n0) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(115,plain,
( gt(plus(level(t_139),n1),n0)
<=> gt(fifo_length,n0) ),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
^ [X_1: $i] :
refl(( gt(plus(X_1,n1),n0)
<=> gt(plus(X_1,n1),n0) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [X_1: $i] : gt(plus(X_1,n1),n0)
<=> ! [X_1: $i] : gt(plus(X_1,n1),n0) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [X_1: $i] : gt(plus(X_1,n1),n0)
<=> ! [X_1: $i] : gt(plus(X_1,n1),n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,axiom,
! [X_1: $i] : gt(plus(X_1,n1),n0),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_2) ).
tff(120,plain,
! [X_1: $i] : gt(plus(X_1,n1),n0),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
! [X_1: $i] : gt(plus(X_1,n1),n0),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [X_1: $i] : gt(plus(X_1,n1),n0),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
( ~ ! [X_1: $i] : gt(plus(X_1,n1),n0)
| gt(plus(level(t_139),n1),n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
gt(plus(level(t_139),n1),n0),
inference(unit_resolution,[status(thm)],[123,122]) ).
tff(125,plain,
gt(fifo_length,n0),
inference(modus_ponens,[status(thm)],[124,115]) ).
tff(126,plain,
( ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) )
<=> ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) )
<=> ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
^ [Z_21: $i,Y_20: $i,X_19: $i] :
rewrite(( ( ~ gt(Z_21,Y_20)
| gt(Z_21,X_19)
| ~ gt(Y_20,X_19) )
<=> ( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Z_21,Y_20)
| gt(Z_21,X_19)
| ~ gt(Y_20,X_19) )
<=> ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Z_21,Y_20)
| gt(Z_21,X_19)
| ~ gt(Y_20,X_19) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_13) ).
tff(131,plain,
! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) )
| gt(level(t_139),n0)
| ~ gt(fifo_length,n0)
| ~ gt(level(t_139),fifo_length) )
<=> ( ~ ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) )
| gt(level(t_139),n0)
| ~ gt(fifo_length,n0)
| ~ gt(level(t_139),fifo_length) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ( ~ gt(fifo_length,n0)
| gt(level(t_139),n0)
| ~ gt(level(t_139),fifo_length) )
<=> ( gt(level(t_139),n0)
| ~ gt(fifo_length,n0)
| ~ gt(level(t_139),fifo_length) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,plain,
( ( ~ ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) )
| ~ gt(fifo_length,n0)
| gt(level(t_139),n0)
| ~ gt(level(t_139),fifo_length) )
<=> ( ~ ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) )
| gt(level(t_139),n0)
| ~ gt(fifo_length,n0)
| ~ gt(level(t_139),fifo_length) ) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( ( ~ ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) )
| ~ gt(fifo_length,n0)
| gt(level(t_139),n0)
| ~ gt(level(t_139),fifo_length) )
<=> ( ~ ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) )
| gt(level(t_139),n0)
| ~ gt(fifo_length,n0)
| ~ gt(level(t_139),fifo_length) ) ),
inference(transitivity,[status(thm)],[137,135]) ).
tff(139,plain,
( ~ ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) )
| ~ gt(fifo_length,n0)
| gt(level(t_139),n0)
| ~ gt(level(t_139),fifo_length) ),
inference(quant_inst,[status(thm)],[]) ).
tff(140,plain,
( ~ ! [Z_21: $i,Y_20: $i,X_19: $i] :
( ~ gt(Y_20,X_19)
| gt(Z_21,X_19)
| ~ gt(Z_21,Y_20) )
| gt(level(t_139),n0)
| ~ gt(fifo_length,n0)
| ~ gt(level(t_139),fifo_length) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
gt(level(t_139),n0),
inference(unit_resolution,[status(thm)],[140,134,125,113]) ).
tff(142,plain,
^ [X_11: $i,Y_12: $i] :
refl(( ( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) )
<=> ( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) ) )),
inference(bind,[status(th)],[]) ).
tff(143,plain,
( ! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) )
<=> ! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
( ! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) )
<=> ! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,axiom,
! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_8) ).
tff(146,plain,
! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) ),
inference(skolemize,[status(sab)],[146]) ).
tff(148,plain,
! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) ),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
( ( ~ ! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) )
| ~ gt(level(t_139),n0)
| gt(plus(level(t_139),n1),plus(n0,n1)) )
<=> ( ~ ! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) )
| ~ gt(level(t_139),n0)
| gt(plus(level(t_139),n1),plus(n0,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
( ~ ! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) )
| ~ gt(level(t_139),n0)
| gt(plus(level(t_139),n1),plus(n0,n1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
( ~ ! [X_11: $i,Y_12: $i] :
( ~ gt(Y_12,X_11)
| gt(plus(Y_12,n1),plus(X_11,n1)) )
| ~ gt(level(t_139),n0)
| gt(plus(level(t_139),n1),plus(n0,n1)) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
( ~ gt(level(t_139),n0)
| gt(plus(level(t_139),n1),plus(n0,n1)) ),
inference(unit_resolution,[status(thm)],[151,148]) ).
tff(153,plain,
gt(plus(level(t_139),n1),plus(n0,n1)),
inference(unit_resolution,[status(thm)],[152,141]) ).
tff(154,plain,
gt(fifo_length,plus(n0,n1)),
inference(modus_ponens,[status(thm)],[153,24]) ).
tff(155,plain,
^ [Y_4: $i,X_3: $i] :
refl(( ( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) )
<=> ( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) ) )),
inference(bind,[status(th)],[]) ).
tff(156,plain,
( ! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) )
<=> ! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) )
<=> ! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,axiom,
! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_6) ).
tff(159,plain,
! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) ),
inference(skolemize,[status(sab)],[159]) ).
tff(161,plain,
! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
( ( ~ ! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) )
| ~ def_10(plus(n0,n1),fifo_length)
| ~ gt(fifo_length,plus(n0,n1)) )
<=> ( ~ ! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) )
| ~ def_10(plus(n0,n1),fifo_length)
| ~ gt(fifo_length,plus(n0,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,plain,
( ~ ! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) )
| ~ def_10(plus(n0,n1),fifo_length)
| ~ gt(fifo_length,plus(n0,n1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ~ gt(X_3,Y_4) )
| ~ def_10(plus(n0,n1),fifo_length)
| ~ gt(fifo_length,plus(n0,n1)) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
( ~ def_10(plus(n0,n1),fifo_length)
| ~ gt(fifo_length,plus(n0,n1)) ),
inference(unit_resolution,[status(thm)],[164,161]) ).
tff(166,plain,
~ def_10(plus(n0,n1),fifo_length),
inference(unit_resolution,[status(thm)],[165,154]) ).
tff(167,plain,
~ def_10(plus(n0,n1),plus(level(t_139),plus(n0,n1))),
inference(modus_ponens,[status(thm)],[166,22]) ).
tff(168,plain,
^ [Y_4: $i,Z_5: $i] :
refl(( ( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
<=> ( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) )),
inference(bind,[status(th)],[]) ).
tff(169,plain,
( ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
<=> ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(quant_intro,[status(thm)],[168]) ).
tff(170,plain,
( ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
<=> ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
( ! [Y_4: $i,Z_5: $i,X_3: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
<=> ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(172,plain,
( ! [Y_4: $i,Z_5: $i,X_3: $i] :
( def_10(Y_4,X_3)
| ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) )
<=> ! [Y_4: $i,Z_5: $i,X_3: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(173,plain,
( ! [Y_4: $i,Z_5: $i,X_3: $i] :
( def_10(Y_4,X_3)
| ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) )
<=> ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(transitivity,[status(thm)],[172,171]) ).
tff(174,plain,
^ [Y_4: $i,Z_5: $i,X_3: $i] :
trans(monotonicity(rewrite(( ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) )
<=> ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) ) )),
( ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) )
<=> ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) ) )),
rewrite(( ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) )
<=> ( def_10(Y_4,X_3)
| ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) ) )),
( ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) )
<=> ( def_10(Y_4,X_3)
| ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) ) )),
inference(bind,[status(th)],[]) ).
tff(175,plain,
( ! [Y_4: $i,Z_5: $i,X_3: $i] :
( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) )
<=> ! [Y_4: $i,Z_5: $i,X_3: $i] :
( def_10(Y_4,X_3)
| ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) ) ),
inference(quant_intro,[status(thm)],[174]) ).
tff(176,plain,
( ! [Y_4: $i,Z_5: $i,X_3: $i] :
( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) )
<=> ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(transitivity,[status(thm)],[175,173]) ).
tff(177,axiom,
! [Y_4: $i,Z_5: $i,X_3: $i] :
( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_5) ).
tff(178,plain,
! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,plain,
! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ),
inference(modus_ponens,[status(thm)],[178,170]) ).
tff(180,plain,
! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ),
inference(skolemize,[status(sab)],[179]) ).
tff(181,plain,
! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ),
inference(modus_ponens,[status(thm)],[180,169]) ).
tff(182,plain,
( ( ~ ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
| def_10(plus(n0,n1),plus(level(t_139),plus(n0,n1)))
| ( minus(plus(level(t_139),plus(n0,n1)),plus(n0,n1)) = level(t_139) ) )
<=> ( ~ ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
| def_10(plus(n0,n1),plus(level(t_139),plus(n0,n1)))
| ( minus(plus(level(t_139),plus(n0,n1)),plus(n0,n1)) = level(t_139) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(183,plain,
( ~ ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
| def_10(plus(n0,n1),plus(level(t_139),plus(n0,n1)))
| ( minus(plus(level(t_139),plus(n0,n1)),plus(n0,n1)) = level(t_139) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
( ~ ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
| def_10(plus(n0,n1),plus(level(t_139),plus(n0,n1)))
| ( minus(plus(level(t_139),plus(n0,n1)),plus(n0,n1)) = level(t_139) ) ),
inference(modus_ponens,[status(thm)],[183,182]) ).
tff(185,plain,
( def_10(plus(n0,n1),plus(level(t_139),plus(n0,n1)))
| ( minus(plus(level(t_139),plus(n0,n1)),plus(n0,n1)) = level(t_139) ) ),
inference(unit_resolution,[status(thm)],[184,181]) ).
tff(186,plain,
minus(plus(level(t_139),plus(n0,n1)),plus(n0,n1)) = level(t_139),
inference(unit_resolution,[status(thm)],[185,167]) ).
tff(187,plain,
minus(fifo_length,n1) = minus(plus(level(t_139),plus(n0,n1)),plus(n0,n1)),
inference(monotonicity,[status(thm)],[20,12]) ).
tff(188,plain,
minus(fifo_length,n1) = int_level(t_139),
inference(transitivity,[status(thm)],[187,186,9]) ).
tff(189,plain,
( gt(fifo_length,minus(fifo_length,n1))
<=> gt(fifo_length,int_level(t_139)) ),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
( gt(fifo_length,int_level(t_139))
<=> gt(fifo_length,minus(fifo_length,n1)) ),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ~ gt(fifo_length,int_level(t_139))
<=> ~ gt(fifo_length,minus(fifo_length,n1)) ),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
~ gt(fifo_length,minus(fifo_length,n1)),
inference(modus_ponens,[status(thm)],[69,191]) ).
tff(193,plain,
^ [X_2: $i] :
refl(( ( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) )
<=> ( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) ) )),
inference(bind,[status(th)],[]) ).
tff(194,plain,
( ! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) )
<=> ! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) ) ),
inference(quant_intro,[status(thm)],[193]) ).
tff(195,plain,
( ! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) )
<=> ! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,axiom,
! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_3) ).
tff(197,plain,
! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) ),
inference(skolemize,[status(sab)],[197]) ).
tff(199,plain,
! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) ),
inference(modus_ponens,[status(thm)],[198,194]) ).
tff(200,plain,
( ( ~ ! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) )
| ~ gt(fifo_length,n0)
| gt(fifo_length,minus(fifo_length,n1)) )
<=> ( ~ ! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) )
| ~ gt(fifo_length,n0)
| gt(fifo_length,minus(fifo_length,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,plain,
( ~ ! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) )
| ~ gt(fifo_length,n0)
| gt(fifo_length,minus(fifo_length,n1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
( ~ ! [X_2: $i] :
( ~ gt(X_2,n0)
| gt(X_2,minus(X_2,n1)) )
| ~ gt(fifo_length,n0)
| gt(fifo_length,minus(fifo_length,n1)) ),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
( ~ gt(fifo_length,n0)
| gt(fifo_length,minus(fifo_length,n1)) ),
inference(unit_resolution,[status(thm)],[202,199]) ).
tff(204,plain,
gt(fifo_length,minus(fifo_length,n1)),
inference(unit_resolution,[status(thm)],[203,125]) ).
tff(205,plain,
$false,
inference(unit_resolution,[status(thm)],[204,192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : HWV022-1 : TPTP v9.0.0. Released v2.5.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 17:19:38 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.40 % SZS status Unsatisfiable
% 0.11/0.40 % SZS output start Proof
% See solution above
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------