TSTP Solution File: SYN318-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN318-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 23:54:40 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 32 ( 11 unt; 3 typ; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 181 ( 86 ~; 79 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 31 ( 28 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: $i > $o ).
tff(b_type,type,
b: $i ).
tff(g_type,type,
g: $i > $o ).
tff(1,plain,
( ~ g(b)
<=> ~ g(b) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ g(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
tff(3,plain,
~ g(b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(
( ( ~ f(b)
| g(X)
| ~ f(X) )
<=> ( ~ f(b)
| g(X)
| ~ f(X) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) )
<=> ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) )
<=> ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ f(X)
| ~ f(b) )
<=> ( ~ f(b)
| ~ f(X) ) )),
( ( ~ f(X)
| ~ f(b)
| g(X) )
<=> ( ~ f(b)
| ~ f(X)
| g(X) ) )),
rewrite(
( ( ~ f(b)
| ~ f(X)
| g(X) )
<=> ( ~ f(b)
| g(X)
| ~ f(X) ) )),
( ( ~ f(X)
| ~ f(b)
| g(X) )
<=> ( ~ f(b)
| g(X)
| ~ f(X) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X: $i] :
( ~ f(X)
| ~ f(b)
| g(X) )
<=> ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X: $i] :
( ~ f(X)
| ~ f(b)
| g(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
tff(10,plain,
! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) )
| g(b)
| ~ f(b) )
<=> ( ~ ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) )
| g(b)
| ~ f(b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ( ~ f(b)
| g(b)
| ~ f(b) )
<=> ( g(b)
| ~ f(b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( ~ ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) )
| ~ f(b)
| g(b)
| ~ f(b) )
<=> ( ~ ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) )
| g(b)
| ~ f(b) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) )
| ~ f(b)
| g(b)
| ~ f(b) )
<=> ( ~ ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) )
| g(b)
| ~ f(b) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ~ ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) )
| ~ f(b)
| g(b)
| ~ f(b) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X: $i] :
( ~ f(b)
| g(X)
| ~ f(X) )
| g(b)
| ~ f(b) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ f(b),
inference(unit_resolution,[status(thm)],[19,13,3]) ).
tff(21,plain,
^ [X: $i] :
refl(
( f(X)
<=> f(X) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $i] : f(X)
<=> ! [X: $i] : f(X) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] : f(X)
<=> ! [X: $i] : f(X) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [X: $i] : f(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
tff(25,plain,
! [X: $i] : f(X),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] : f(X),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] : f(X),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i] : f(X)
| f(b) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,27,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN318-1 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n007.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 02:16:05 EDT 2022
% 0.12/0.34 % 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.
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------