%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV032-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:09:01 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 19 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 57 ( 26 ~; 22 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 12 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(rd_level_type,type,
rd_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(fifo_length_type,type,
fifo_length: $i ).
tff(n0_type,type,
n0: $i ).
tff(p_Reset_type,type,
p_Reset: $i > $o ).
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/sandbox/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)
| ( rd_level(plus(X_t_37,n1)) = n0 ) )
<=> ( ~ p_Reset(X_t_37)
| ( rd_level(plus(X_t_37,n1)) = n0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( rd_level(plus(X_t_37,n1)) = n0 ) )
<=> ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( rd_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)
| ( rd_level(plus(X_t_37,n1)) = n0 ) )
<=> ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( rd_level(plus(X_t_37,n1)) = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( rd_level(plus(X_t_37,n1)) = n0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_28) ).
tff(8,plain,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( rd_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)
| ( rd_level(plus(X_t_37,n1)) = n0 ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( rd_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)
| ( rd_level(plus(X_t_37,n1)) = n0 ) )
| ~ p_Reset(t_139)
| ( rd_level(plus(t_139,n1)) = n0 ) )
<=> ( ~ ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( rd_level(plus(X_t_37,n1)) = n0 ) )
| ~ p_Reset(t_139)
| ( rd_level(plus(t_139,n1)) = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( rd_level(plus(X_t_37,n1)) = n0 ) )
| ~ p_Reset(t_139)
| ( rd_level(plus(t_139,n1)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( rd_level(plus(X_t_37,n1)) = n0 ) )
| ~ p_Reset(t_139)
| ( rd_level(plus(t_139,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
rd_level(plus(t_139,n1)) = n0,
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( gt(fifo_length,rd_level(plus(t_139,n1)))
<=> gt(fifo_length,n0) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( gt(fifo_length,n0)
<=> gt(fifo_length,rd_level(plus(t_139,n1))) ),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
( gt(fifo_length,n0)
<=> gt(fifo_length,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
gt(fifo_length,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_3) ).
tff(19,plain,
gt(fifo_length,n0),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
gt(fifo_length,rd_level(plus(t_139,n1))),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
( ~ gt(fifo_length,rd_level(plus(t_139,n1)))
<=> ~ gt(fifo_length,rd_level(plus(t_139,n1))) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
~ gt(fifo_length,rd_level(plus(t_139,n1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).
tff(23,plain,
~ gt(fifo_length,rd_level(plus(t_139,n1))),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : HWV032-1 : TPTP v9.0.0. Released v2.5.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.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 : Thu Jun 19 17:20:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------