TSTP Solution File: SYN346-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN346-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 23:54:53 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of formulae : 26 ( 8 unt; 3 typ; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 100 ( 59 ~; 31 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 50 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $o ).
tff(z1_type,type,
z1: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [Y2: $i,Y1: $i] :
refl(
( f(b,z1(Y1,Y2))
<=> f(b,z1(Y1,Y2)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y2: $i,Y1: $i] : f(b,z1(Y1,Y2))
<=> ! [Y2: $i,Y1: $i] : f(b,z1(Y1,Y2)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y2: $i,Y1: $i] : f(b,z1(Y1,Y2))
<=> ! [Y2: $i,Y1: $i] : f(b,z1(Y1,Y2)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y2: $i,Y1: $i] : f(b,z1(Y1,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
tff(5,plain,
! [Y2: $i,Y1: $i] : f(b,z1(Y1,Y2)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y2: $i,Y1: $i] : f(b,z1(Y1,Y2)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y2: $i,Y1: $i] : f(b,z1(Y1,Y2)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y2: $i,Y1: $i] : f(b,z1(Y1,Y2))
| f(b,z1(b,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
f(b,z1(b,b)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y2: $i,Y1: $i] :
refl(
( ( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
<=> ( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
<=> ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
<=> ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
tff(14,plain,
! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
| ~ f(b,z1(b,b)) )
<=> ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
| ~ f(b,z1(b,b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( ~ f(b,z1(b,b))
| ~ f(b,z1(b,b)) )
<=> ~ f(b,z1(b,b)) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
| ~ f(b,z1(b,b))
| ~ f(b,z1(b,b)) )
<=> ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
| ~ f(b,z1(b,b)) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
| ~ f(b,z1(b,b))
| ~ f(b,z1(b,b)) )
<=> ( ~ ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
| ~ f(b,z1(b,b)) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
| ~ f(b,z1(b,b))
| ~ f(b,z1(b,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [Y2: $i,Y1: $i] :
( ~ f(Y1,z1(Y1,Y2))
| ~ f(Y2,z1(Y1,Y2)) )
| ~ f(b,z1(b,b)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,16,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN346-1 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 02:47:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------