TSTP Solution File: HWV028-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV028-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 Sep 17 02:10:44 EDT 2022
% Result : Unsatisfiable 0.17s 0.40s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 34
% Syntax : Number of formulae : 67 ( 27 unt; 9 typ; 0 def)
% Number of atoms : 152 ( 35 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 173 ( 83 ~; 70 |; 0 &)
% ( 20 <=>; 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 : 7 ( 5 >; 2 *; 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,
^ [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(plus(t_139,n1)) = int_level(plus(t_139,n1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
level(plus(t_139,n1)) = int_level(plus(t_139,n1)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
int_level(plus(t_139,n1)) = level(plus(t_139,n1)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( p_Reset(t_139)
<=> p_Reset(t_139) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
p_Reset(t_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_1) ).
tff(13,plain,
p_Reset(t_139),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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(17,axiom,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_26) ).
tff(18,plain,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [X_t_37: $i] :
( ~ p_Reset(X_t_37)
| ( int_level(plus(X_t_37,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,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(22,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(23,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)],[22,21]) ).
tff(24,plain,
int_level(plus(t_139,n1)) = n0,
inference(unit_resolution,[status(thm)],[23,20,13]) ).
tff(25,plain,
n0 = int_level(plus(t_139,n1)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
n0 = level(plus(t_139,n1)),
inference(transitivity,[status(thm)],[25,10]) ).
tff(27,plain,
( gt(n0,n0)
<=> gt(level(plus(t_139,n1)),n0) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( gt(level(plus(t_139,n1)),n0)
<=> gt(n0,n0) ),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( gt(fifo_length,n0)
<=> gt(fifo_length,n0) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
gt(fifo_length,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_3) ).
tff(31,plain,
gt(fifo_length,n0),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( gt(level(plus(t_139,n1)),fifo_length)
<=> gt(level(plus(t_139,n1)),fifo_length) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
gt(level(plus(t_139,n1)),fifo_length),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).
tff(34,plain,
gt(level(plus(t_139,n1)),fifo_length),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,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(36,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(37,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(38,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)],[37]) ).
tff(39,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(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)],[39,38]) ).
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) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
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) ),
inference(skolemize,[status(sab)],[41]) ).
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) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,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(45,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(46,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)],[45,44]) ).
tff(47,plain,
gt(level(plus(t_139,n1)),n0),
inference(unit_resolution,[status(thm)],[46,43,34,31]) ).
tff(48,plain,
gt(n0,n0),
inference(modus_ponens,[status(thm)],[47,28]) ).
tff(49,plain,
^ [X_28: $i] :
refl(
( ~ gt(X_28,X_28)
<=> ~ gt(X_28,X_28) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [X_28: $i] : ~ gt(X_28,X_28)
<=> ! [X_28: $i] : ~ gt(X_28,X_28) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X_28: $i] : ~ gt(X_28,X_28)
<=> ! [X_28: $i] : ~ gt(X_28,X_28) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
! [X_28: $i] : ~ gt(X_28,X_28),
file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax',axiom_17) ).
tff(53,plain,
! [X_28: $i] : ~ gt(X_28,X_28),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X_28: $i] : ~ gt(X_28,X_28),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X_28: $i] : ~ gt(X_28,X_28),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [X_28: $i] : ~ gt(X_28,X_28)
| ~ gt(n0,n0) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
~ gt(n0,n0),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : HWV028-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n006.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 : Wed Aug 31 22:04:54 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.17/0.40 % SZS status Unsatisfiable
% 0.17/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------