TSTP Solution File: SYN063-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN063-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Thu Sep 29 23:53:27 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 49 ( 9 unt; 4 typ; 0 def)
% Number of atoms : 264 ( 0 equ)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 253 ( 72 ~; 139 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 38 ( 38 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 58 ( 50 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_p_type,type,
big_p: $i > $o ).
tff(b_type,type,
b: $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ~ big_p(b)
<=> ~ big_p(b) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( ~ big_p(b)
| $false )
<=> ~ big_p(b) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ big_p(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tff(4,plain,
( big_p(c)
<=> $false ),
inference(iff_false,[status(thm)],[3]) ).
tff(5,plain,
( ( ~ big_p(b)
| big_p(c) )
<=> ( ~ big_p(b)
| $false ) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( ( ~ big_p(b)
| big_p(c) )
<=> ~ big_p(b) ),
inference(transitivity,[status(thm)],[5,2]) ).
tff(7,plain,
( ( $false
| ~ big_p(b)
| big_p(c) )
<=> ( ~ big_p(b)
| big_p(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
big_p(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(10,plain,
( big_p(a)
<=> $true ),
inference(iff_true,[status(thm)],[9]) ).
tff(11,plain,
( ~ big_p(a)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ~ big_p(a)
<=> $false ),
inference(transitivity,[status(thm)],[11,8]) ).
tff(13,plain,
( ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) )
<=> ( $false
| ~ big_p(b)
| big_p(c) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) )
<=> ( ~ big_p(b)
| big_p(c) ) ),
inference(transitivity,[status(thm)],[13,7]) ).
tff(15,plain,
( ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) )
<=> ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) )
<=> ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(18,plain,
( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
( ~ big_p(b)
| big_p(c) ),
inference(modus_ponens,[status(thm)],[19,14]) ).
tff(21,plain,
~ big_p(b),
inference(modus_ponens,[status(thm)],[20,6]) ).
tff(22,plain,
~ big_p(b),
inference(modus_ponens,[status(thm)],[21,1]) ).
tff(23,plain,
^ [Y: $i,X: $i] :
refl(
( ( big_p(Y)
| big_p(X) )
<=> ( big_p(Y)
| big_p(X) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) )
<=> ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) )
<=> ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
iff_false(asserted(~ big_p(c)),
( big_p(c)
<=> $false )),
( ( big_p(c)
| big_p(Y)
| big_p(X) )
<=> ( $false
| big_p(Y)
| big_p(X) ) )),
rewrite(
( ( $false
| big_p(Y)
| big_p(X) )
<=> ( big_p(Y)
| big_p(X) ) )),
( ( big_p(c)
| big_p(Y)
| big_p(X) )
<=> ( big_p(Y)
| big_p(X) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [Y: $i,X: $i] :
( big_p(c)
| big_p(Y)
| big_p(X) )
<=> ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(asserted(big_p(a)),
( big_p(a)
<=> $true )),
( ~ big_p(a)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ big_p(a)
<=> $false )),
( ( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
<=> ( $false
| big_p(c)
| big_p(Y)
| big_p(X) ) )),
rewrite(
( ( $false
| big_p(c)
| big_p(Y)
| big_p(X) )
<=> ( big_p(c)
| big_p(Y)
| big_p(X) ) )),
( ( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
<=> ( big_p(c)
| big_p(Y)
| big_p(X) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) )
<=> ! [Y: $i,X: $i] :
( big_p(c)
| big_p(Y)
| big_p(X) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ big_p(a)
| big_p(X) )
<=> ( ~ big_p(a)
| big_p(X) ) )),
( ( ~ big_p(a)
| big_p(X)
| big_p(c) )
<=> ( ~ big_p(a)
| big_p(X)
| big_p(c) ) )),
rewrite(
( ( ~ big_p(a)
| big_p(X)
| big_p(c) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(X) ) )),
( ( ~ big_p(a)
| big_p(X)
| big_p(c) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(X) ) )),
( ( ~ big_p(a)
| big_p(X)
| big_p(c)
| big_p(Y) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(X)
| big_p(Y) ) )),
rewrite(
( ( ~ big_p(a)
| big_p(c)
| big_p(X)
| big_p(Y) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ) )),
( ( ~ big_p(a)
| big_p(X)
| big_p(c)
| big_p(Y) )
<=> ( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(X)
| big_p(c)
| big_p(Y) )
<=> ! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(X)
| big_p(c)
| big_p(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(33,plain,
! [Y: $i,X: $i] :
( ~ big_p(a)
| big_p(c)
| big_p(Y)
| big_p(X) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Y: $i,X: $i] :
( big_p(c)
| big_p(Y)
| big_p(X) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) ),
inference(modus_ponens,[status(thm)],[35,25]) ).
tff(37,plain,
! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) ),
inference(modus_ponens,[status(thm)],[37,24]) ).
tff(39,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) )
| big_p(b) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) )
| big_p(b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( big_p(b)
| big_p(b) )
<=> big_p(b) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) )
| big_p(b)
| big_p(b) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) )
| big_p(b) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) )
| big_p(b)
| big_p(b) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) )
| big_p(b) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) )
| big_p(b)
| big_p(b) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] :
( big_p(Y)
| big_p(X) )
| big_p(b) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,38,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN063-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 01:28:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------