%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV015-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:08:56 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 49 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 271 ( 63 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 362 ( 155 ~; 181 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 29 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(int_level_type,type,
int_level: $i > $i ).
tff(x_139_type,type,
x_139: $i ).
tff(level_type,type,
level: $i > $i ).
tff(plus_type,type,
plus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
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/sandbox2/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(x_139) = int_level(x_139) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
level(x_139) = int_level(x_139),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( gt(level(x_139),n0)
<=> gt(int_level(x_139),n0) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( gt(level(x_139),n0)
<=> gt(level(x_139),n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
gt(level(x_139),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_1) ).
tff(13,plain,
gt(level(x_139),n0),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
gt(int_level(x_139),n0),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
( ~ ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
| ( level(plus(x_139,n1)) = int_level(plus(x_139,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
level(plus(x_139,n1)) = int_level(plus(x_139,n1)),
inference(unit_resolution,[status(thm)],[15,7]) ).
tff(17,plain,
( ( level(plus(x_139,n1)) = level(x_139) )
<=> ( int_level(plus(x_139,n1)) = int_level(x_139) ) ),
inference(monotonicity,[status(thm)],[16,9]) ).
tff(18,plain,
( ( level(plus(x_139,n1)) != level(x_139) )
<=> ( int_level(plus(x_139,n1)) != int_level(x_139) ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( level(plus(x_139,n1)) != level(x_139) )
<=> ( level(plus(x_139,n1)) != level(x_139) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
level(plus(x_139,n1)) != level(x_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_5) ).
tff(21,plain,
level(plus(x_139,n1)) != level(x_139),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
int_level(plus(x_139,n1)) != int_level(x_139),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
( ~ p_Reset(x_139)
<=> ~ p_Reset(x_139) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
~ p_Reset(x_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_4) ).
tff(25,plain,
~ p_Reset(x_139),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( p_Wr(x_139)
<=> p_Wr(x_139) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
p_Wr(x_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_3) ).
tff(28,plain,
p_Wr(x_139),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( p_Rd(x_139)
<=> p_Rd(x_139) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
p_Rd(x_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_2) ).
tff(31,plain,
p_Rd(x_139),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [X_t_42: $i] :
refl(( ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,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(int_level(X_t_42),n0) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0) ) )),
rewrite(( ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( 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(int_level(X_t_42),n0)
| ( 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(int_level(X_t_42),n0)
| ( 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)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) ) )),
( ( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( 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)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( 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)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_53) ).
tff(38,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
| p_Reset(x_139)
| ~ p_Rd(x_139)
| ~ p_Wr(x_139)
| ~ gt(int_level(x_139),n0)
| ( int_level(plus(x_139,n1)) = int_level(x_139) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
| p_Reset(x_139)
| ~ p_Rd(x_139)
| ~ p_Wr(x_139)
| ~ gt(int_level(x_139),n0)
| ( int_level(plus(x_139,n1)) = int_level(x_139) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( p_Reset(x_139)
| ~ p_Rd(x_139)
| ~ p_Wr(x_139)
| ( int_level(plus(x_139,n1)) = int_level(x_139) )
| ~ gt(int_level(x_139),n0) )
<=> ( p_Reset(x_139)
| ~ p_Rd(x_139)
| ~ p_Wr(x_139)
| ~ gt(int_level(x_139),n0)
| ( int_level(plus(x_139,n1)) = int_level(x_139) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
| p_Reset(x_139)
| ~ p_Rd(x_139)
| ~ p_Wr(x_139)
| ( int_level(plus(x_139,n1)) = int_level(x_139) )
| ~ gt(int_level(x_139),n0) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
| p_Reset(x_139)
| ~ p_Rd(x_139)
| ~ p_Wr(x_139)
| ~ gt(int_level(x_139),n0)
| ( int_level(plus(x_139,n1)) = int_level(x_139) ) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
| p_Reset(x_139)
| ~ p_Rd(x_139)
| ~ p_Wr(x_139)
| ( int_level(plus(x_139,n1)) = int_level(x_139) )
| ~ gt(int_level(x_139),n0) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
| p_Reset(x_139)
| ~ p_Rd(x_139)
| ~ p_Wr(x_139)
| ~ gt(int_level(x_139),n0)
| ( int_level(plus(x_139,n1)) = int_level(x_139) ) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
| p_Reset(x_139)
| ~ p_Rd(x_139)
| ~ p_Wr(x_139)
| ( int_level(plus(x_139,n1)) = int_level(x_139) )
| ~ gt(int_level(x_139),n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| ( int_level(plus(X_t_42,n1)) = int_level(X_t_42) )
| ~ gt(int_level(X_t_42),n0) )
| p_Reset(x_139)
| ~ p_Rd(x_139)
| ~ p_Wr(x_139)
| ~ gt(int_level(x_139),n0)
| ( int_level(plus(x_139,n1)) = int_level(x_139) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ~ gt(int_level(x_139),n0)
| ( int_level(plus(x_139,n1)) = int_level(x_139) ) ),
inference(unit_resolution,[status(thm)],[47,41,31,28,25]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,22,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HWV015-1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Thu Jun 19 17:23:49 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% See solution above
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------