%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV028-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:09:00 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.43s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 25
% Syntax : Number of formulae : 54 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 147 ( 33 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 171 ( 82 ~; 70 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 75 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(level_type,type,
level: $i > $i ).
tff(plus_type,type,
plus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(t_139_type,type,
t_139: $i ).
tff(int_level_type,type,
int_level: $i > $i ).
tff(p_Reset_type,type,
p_Reset: $i > $o ).
tff(fifo_length_type,type,
fifo_length: $i ).
tff(1,plain,
( p_Reset(t_139)
<=> p_Reset(t_139) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
p_Reset(t_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_1) ).
tff(3,plain,
p_Reset(t_139),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X_t_37: $i] :
refl(( ( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) )
<=> ( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) )
<=> ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) )
<=> ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_26) ).
tff(8,plain,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) )
| ~ p_Reset(t_139)
| ( int_level(plus(t_139,n1)) = n0 ) )
<=> ( ~ ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) )
| ~ p_Reset(t_139)
| ( int_level(plus(t_139,n1)) = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) )
| ~ p_Reset(t_139)
| ( int_level(plus(t_139,n1)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) )
| ~ p_Reset(t_139)
| ( int_level(plus(t_139,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
int_level(plus(t_139,n1)) = n0,
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,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(19,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,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(23,plain,
level(plus(t_139,n1)) = int_level(plus(t_139,n1)),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
level(plus(t_139,n1)) = n0,
inference(transitivity,[status(thm)],[23,14]) ).
tff(25,plain,
( gt(level(plus(t_139,n1)),n0)
<=> gt(n0,n0) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( gt(fifo_length,n0)
<=> gt(fifo_length,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
gt(fifo_length,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_3) ).
tff(28,plain,
gt(fifo_length,n0),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( gt(level(plus(t_139,n1)),fifo_length)
<=> gt(level(plus(t_139,n1)),fifo_length) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
gt(level(plus(t_139,n1)),fifo_length),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_2) ).
tff(31,plain,
gt(level(plus(t_139,n1)),fifo_length),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,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(33,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(34,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(35,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)],[34]) ).
tff(36,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/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_13) ).
tff(37,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)],[36,35]) ).
tff(38,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)],[37,33]) ).
tff(39,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)],[38]) ).
tff(40,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)],[39,32]) ).
tff(41,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(plus(t_139,n1)),n0)
| ~ gt(level(plus(t_139,n1)),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(fifo_length,n0)
| gt(level(plus(t_139,n1)),n0)
| ~ gt(level(plus(t_139,n1)),fifo_length) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,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(plus(t_139,n1)),n0)
| ~ gt(level(plus(t_139,n1)),fifo_length) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,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(plus(t_139,n1)),n0)
| ~ gt(level(plus(t_139,n1)),fifo_length) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
gt(level(plus(t_139,n1)),n0),
inference(unit_resolution,[status(thm)],[43,40,31,28]) ).
tff(45,plain,
gt(n0,n0),
inference(modus_ponens,[status(thm)],[44,25]) ).
tff(46,plain,
^ [X_28: $i] :
refl(( ~ gt(X_28,X_28)
<=> ~ gt(X_28,X_28) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [X_28: $i] : ~ gt(X_28,X_28)
<=> ! [X_28: $i] : ~ gt(X_28,X_28) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X_28: $i] : ~ gt(X_28,X_28)
<=> ! [X_28: $i] : ~ gt(X_28,X_28) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
! [X_28: $i] : ~ gt(X_28,X_28),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_17) ).
tff(50,plain,
! [X_28: $i] : ~ gt(X_28,X_28),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X_28: $i] : ~ gt(X_28,X_28),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [X_28: $i] : ~ gt(X_28,X_28),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [X_28: $i] : ~ gt(X_28,X_28)
| ~ gt(n0,n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
$false,
inference(unit_resolution,[status(thm)],[53,52,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : HWV028-1 : TPTP v9.0.0. Released v2.5.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 17:20:25 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.43 % SZS status Unsatisfiable
% 0.23/0.43 % SZS output start Proof
% See solution above
% 0.23/0.44 % E exiting
%------------------------------------------------------------------------------