TSTP Solution File: SYN073+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN073+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 23:53:33 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 36 ( 15 unt; 3 typ; 0 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 79 ( 31 ~; 37 |; 0 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 83 ( 67 !; 13 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_f_type,type,
big_f: ( $i * $i ) > $o ).
tff(tptp_fun_Y1_0_type,type,
tptp_fun_Y1_0: $i > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1)
<=> ~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ ( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
=> ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1) )
<=> ~ ( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ ( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
=> ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel50) ).
tff(4,plain,
~ ( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(modus_ponens,[status(thm)],[7,1]) ).
tff(9,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(modus_ponens,[status(thm)],[8,1]) ).
tff(10,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(modus_ponens,[status(thm)],[9,1]) ).
tff(11,plain,
~ ? [X1: $i] :
! [Y1: $i] : big_f(X1,Y1),
inference(modus_ponens,[status(thm)],[10,1]) ).
tff(12,plain,
^ [X1: $i] :
sk(
$oeq(
~ ! [Y1: $i] : big_f(X1,Y1),
~ big_f(X1,tptp_fun_Y1_0(X1)))),
inference(bind,[status(th)],]) ).
tff(13,plain,
! [X1: $i] : ~ big_f(X1,tptp_fun_Y1_0(X1)),
inference(nnf-neg,[status(sab)],[11,12]) ).
tff(14,plain,
( ~ ! [X1: $i] : ~ big_f(X1,tptp_fun_Y1_0(X1))
| ~ big_f(tptp_fun_Y1_0(a),tptp_fun_Y1_0(tptp_fun_Y1_0(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
~ big_f(tptp_fun_Y1_0(a),tptp_fun_Y1_0(tptp_fun_Y1_0(a))),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ ! [X1: $i] : ~ big_f(X1,tptp_fun_Y1_0(X1))
| ~ big_f(a,tptp_fun_Y1_0(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(17,plain,
~ big_f(a,tptp_fun_Y1_0(a)),
inference(unit_resolution,[status(thm)],[16,13]) ).
tff(18,plain,
^ [X: $i] :
refl(
( ( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [X: $i] :
rewrite(
( ( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) ),
inference(transitivity,[status(thm)],[21,19]) ).
tff(23,plain,
( ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
<=> ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ),
inference(or_elim,[status(thm)],[4]) ).
tff(25,plain,
! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| big_f(a,tptp_fun_Y1_0(a))
| ! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y) )
<=> ( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| big_f(a,tptp_fun_Y1_0(a))
| ! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| big_f(a,tptp_fun_Y1_0(a))
| ! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [X: $i] :
( big_f(a,X)
| ! [Y: $i] : big_f(X,Y) )
| big_f(a,tptp_fun_Y1_0(a))
| ! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y),
inference(unit_resolution,[status(thm)],[30,27,17]) ).
tff(32,plain,
( ~ ! [Y: $i] : big_f(tptp_fun_Y1_0(a),Y)
| big_f(tptp_fun_Y1_0(a),tptp_fun_Y1_0(tptp_fun_Y1_0(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
$false,
inference(unit_resolution,[status(thm)],[32,31,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN073+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.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 01:47:33 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.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------