TSTP Solution File: SYN356+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN356+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 23:54:57 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 26
% Syntax : Number of formulae : 60 ( 11 unt; 4 typ; 0 def)
% Number of atoms : 238 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 375 ( 196 ~; 121 |; 33 &)
% ( 19 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 96 ( 90 !; 0 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_q_type,type,
big_q: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(big_r_type,type,
big_r: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) )
<=> ( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) )
<=> ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( ~ big_r(X,Y)
| ( big_r(Y,X)
& big_q(X,Y) ) )
<=> ( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ( big_r(Y,X)
& big_q(X,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ( big_r(Y,X)
& big_q(X,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ( big_r(Y,X)
& big_q(X,Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ~ ( ( big_r(a,b)
& ! [X: $i,Y: $i] :
( big_r(X,Y)
=> ( big_r(Y,X)
& big_q(X,Y) ) )
& ! [U: $i,V: $i] :
( big_q(U,V)
=> big_q(U,U) ) )
=> ( big_q(a,a)
& big_q(b,b) ) )
<=> ~ ( ~ ( big_r(a,b)
& ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ( big_r(Y,X)
& big_q(X,Y) ) )
& ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) ) )
| ( big_q(a,a)
& big_q(b,b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
~ ( ( big_r(a,b)
& ! [X: $i,Y: $i] :
( big_r(X,Y)
=> ( big_r(Y,X)
& big_q(X,Y) ) )
& ! [U: $i,V: $i] :
( big_q(U,V)
=> big_q(U,U) ) )
=> ( big_q(a,a)
& big_q(b,b) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2107) ).
tff(8,plain,
~ ( ~ ( big_r(a,b)
& ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ( big_r(Y,X)
& big_q(X,Y) ) )
& ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) ) )
| ( big_q(a,a)
& big_q(b,b) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
( big_r(a,b)
& ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ( big_r(Y,X)
& big_q(X,Y) ) )
& ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) ) ),
inference(or_elim,[status(thm)],[8]) ).
tff(10,plain,
! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ( big_r(Y,X)
& big_q(X,Y) ) ),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ( big_r(Y,X)
& big_q(X,Y) ) ),
inference(modus_ponens,[status(thm)],[10,5]) ).
tff(12,plain,
! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ( big_r(Y,X)
& big_q(X,Y) ) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) ),
inference(modus_ponens,[status(thm)],[12,4]) ).
tff(14,plain,
! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) ),
inference(modus_ponens,[status(thm)],[13,2]) ).
tff(15,plain,
( big_r(a,b)
<=> big_r(a,b) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
big_r(a,b),
inference(and_elim,[status(thm)],[9]) ).
tff(17,plain,
big_r(a,b),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) )
| ~ big_r(a,b)
| ~ ( ~ big_q(a,b)
| ~ big_r(b,a) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) )
| ~ big_r(a,b)
| ~ ( ~ big_q(a,b)
| ~ big_r(b,a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) )
| ~ big_r(a,b)
| ~ ( ~ big_q(a,b)
| ~ big_r(b,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
( ~ ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) )
| ~ big_r(a,b)
| ~ ( ~ big_q(a,b)
| ~ big_r(b,a) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
~ ( ~ big_q(a,b)
| ~ big_r(b,a) ),
inference(unit_resolution,[status(thm)],[20,17,14]) ).
tff(22,plain,
( ~ big_q(a,b)
| ~ big_r(b,a)
| big_q(a,b) ),
inference(tautology,[status(thm)],]) ).
tff(23,plain,
big_q(a,b),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
^ [U: $i,V: $i] :
refl(
( ( ~ big_q(U,V)
| big_q(U,U) )
<=> ( ~ big_q(U,V)
| big_q(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) )
<=> ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) )
<=> ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) ),
inference(and_elim,[status(thm)],[9]) ).
tff(28,plain,
! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) )
| ~ big_q(a,b)
| big_q(a,a) )
<=> ( ~ ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) )
| ~ big_q(a,b)
| big_q(a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) )
| ~ big_q(a,b)
| big_q(a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) )
| ~ big_q(a,b)
| big_q(a,a) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
big_q(a,a),
inference(unit_resolution,[status(thm)],[33,30,23]) ).
tff(35,plain,
( ~ big_q(a,b)
| ~ big_r(b,a)
| big_r(b,a) ),
inference(tautology,[status(thm)],]) ).
tff(36,plain,
big_r(b,a),
inference(unit_resolution,[status(thm)],[35,21]) ).
tff(37,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) )
| ~ big_r(b,a)
| ~ ( ~ big_q(b,a)
| ~ big_r(a,b) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) )
| ~ big_r(b,a)
| ~ ( ~ big_q(b,a)
| ~ big_r(a,b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) )
| ~ big_r(b,a)
| ~ ( ~ big_q(b,a)
| ~ big_r(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X: $i,Y: $i] :
( ~ big_r(X,Y)
| ~ ( ~ big_q(X,Y)
| ~ big_r(Y,X) ) )
| ~ big_r(b,a)
| ~ ( ~ big_q(b,a)
| ~ big_r(a,b) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ big_r(b,a)
| ~ ( ~ big_q(b,a)
| ~ big_r(a,b) ) ),
inference(unit_resolution,[status(thm)],[39,14]) ).
tff(41,plain,
~ ( ~ big_q(b,a)
| ~ big_r(a,b) ),
inference(unit_resolution,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ big_q(b,a)
| ~ big_r(a,b)
| big_q(b,a) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
big_q(b,a),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) )
| ~ big_q(b,a)
| big_q(b,b) )
<=> ( ~ ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) )
| ~ big_q(b,a)
| big_q(b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) )
| ~ big_q(b,a)
| big_q(b,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [U: $i,V: $i] :
( ~ big_q(U,V)
| big_q(U,U) )
| ~ big_q(b,a)
| big_q(b,b) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
big_q(b,b),
inference(unit_resolution,[status(thm)],[46,30,43]) ).
tff(48,plain,
( ~ ~ ( ~ big_q(a,a)
| ~ big_q(b,b) )
<=> ( ~ big_q(a,a)
| ~ big_q(b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( big_q(a,a)
& big_q(b,b) )
<=> ~ ( ~ big_q(a,a)
| ~ big_q(b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ( big_q(a,a)
& big_q(b,b) )
<=> ~ ~ ( ~ big_q(a,a)
| ~ big_q(b,b) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ~ ( big_q(a,a)
& big_q(b,b) )
<=> ( ~ big_q(a,a)
| ~ big_q(b,b) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ( big_q(a,a)
& big_q(b,b) )
<=> ~ ( big_q(a,a)
& big_q(b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
~ ( big_q(a,a)
& big_q(b,b) ),
inference(or_elim,[status(thm)],[8]) ).
tff(54,plain,
~ ( big_q(a,a)
& big_q(b,b) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ big_q(a,a)
| ~ big_q(b,b) ),
inference(modus_ponens,[status(thm)],[54,51]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,47,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SYN356+1 : TPTP v8.1.0. Released v2.0.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 03:12:59 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------