TSTP Solution File: SYN291-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN291-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Thu Sep 29 23:54:33 EDT 2022
% Result : Unsatisfiable 0.18s 0.47s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 10 unt; 5 typ; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 100 ( 48 ~; 33 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(k0_type,type,
k0: $i > $o ).
tff(e_type,type,
e: $i ).
tff(s0_type,type,
s0: $i > $o ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ~ q1(d,X,Y)
<=> ~ q1(d,X,Y) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ~ q1(d,X,Y)
<=> ! [Y: $i,X: $i] : ~ q1(d,X,Y) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ~ q1(d,X,Y)
<=> ! [Y: $i,X: $i] : ~ q1(d,X,Y) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ~ q1(d,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(5,plain,
! [Y: $i,X: $i] : ~ q1(d,X,Y),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ~ q1(d,X,Y),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ~ q1(d,X,Y),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( q1(d,d,d)
<=> q1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( ( $false
| $false
| q1(d,d,d) )
<=> q1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
k0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(12,plain,
( k0(e)
<=> $true ),
inference(iff_true,[status(thm)],[11]) ).
tff(13,plain,
( ~ k0(e)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ k0(e)
<=> $false ),
inference(transitivity,[status(thm)],[13,10]) ).
tff(15,axiom,
s0(d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(16,plain,
( s0(d)
<=> $true ),
inference(iff_true,[status(thm)],[15]) ).
tff(17,plain,
( ~ s0(d)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ~ s0(d)
<=> $false ),
inference(transitivity,[status(thm)],[17,10]) ).
tff(19,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> ( $false
| $false
| q1(d,d,d) ) ),
inference(monotonicity,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> q1(d,d,d) ),
inference(transitivity,[status(thm)],[19,9]) ).
tff(21,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( q1(d,d,d)
| ~ k0(e) )
<=> ( ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,axiom,
( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_117) ).
tff(27,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[27,21]) ).
tff(29,plain,
q1(d,d,d),
inference(modus_ponens,[status(thm)],[28,20]) ).
tff(30,plain,
q1(d,d,d),
inference(modus_ponens,[status(thm)],[29,8]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] : ~ q1(d,X,Y)
| ~ q1(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,30,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN291-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n009.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
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Sep 5 02:19:50 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.47 % SZS status Unsatisfiable
% 0.18/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------