%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL664+1.001 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Sep 18 04:57:36 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 19 ( 2 unt; 7 typ; 0 def)
% Number of atoms : 552 ( 0 equ)
% Maximal formula atoms : 17 ( 46 avg)
% Number of connectives : 897 ( 427 ~; 427 |; 0 &)
% ( 43 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 70 ( 70 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 7 >; 1 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 2 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 253 ( 240 !; 9 ?; 253 :)
% Comments :
%------------------------------------------------------------------------------
tff(p11_type,type,
p11: $i > $o ).
tff(r1_type,type,
r1: ( $i * $i ) > $o ).
tff(p12_type,type,
p12: $i > $o ).
tff(p13_type,type,
p13: $i > $o ).
tff(p15_type,type,
p15: $i > $o ).
tff(p14_type,type,
p14: $i > $o ).
tff(p16_type,type,
p16: $i > $o ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $false
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ? [X: $i] : $false
<=> $false ),
inference(elim_unused_vars,[status(thm)],]) ).
tff(4,plain,
^ [X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
<=> ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) ) )),
rewrite(
( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
<=> ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) ) )),
rewrite(
( ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) ) )),
rewrite(
( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
<=> ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) ) ) )),
rewrite(
( ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) ) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) ) ) )),
rewrite(
( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
<=> ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) ) )),
rewrite(
( ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) ) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) ) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
rewrite(
( ( ~ r1(X,Y)
| p15(Y) )
<=> ( p15(Y)
| ~ r1(X,Y) ) ))),
( ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
<=> ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) ) ) )),
rewrite(
( ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) ) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) ) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
rewrite(
( ( ~ r1(X,Y)
| p13(Y) )
<=> ( p13(Y)
| ~ r1(X,Y) ) ))),
( ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
<=> ! [Y: $i] :
( p13(Y)
| ~ r1(X,Y) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p13(Y)
| ~ r1(X,Y) ) ) )),
rewrite(
( ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p13(Y)
| ~ r1(X,Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p13(Y)
| ~ r1(X,Y) ) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p13(Y)
| ~ r1(X,Y) ) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
rewrite(
( ( ~ r1(X,Y)
| p12(Y) )
<=> ( p12(Y)
| ~ r1(X,Y) ) ))),
( ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
<=> ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) ) )
<=> ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p13(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) ) )),
rewrite(
( ( ~ ! [Y: $i] :
( p16(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) )
| ~ ! [Y: $i] :
( p14(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p15(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p13(Y)
| ~ r1(X,Y) )
| ! [Y: $i] :
( p12(Y)
| ~ r1(X,Y) ) )
<=> $true )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) ) )
<=> $true )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> ( $true
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) ) )),
rewrite(
( ( $true
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> $true )),
( ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> $true )),
( ~ ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> $false )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> ? [X: $i] : $false ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> $false ),
inference(transitivity,[status(thm)],[5,3]) ).
tff(7,plain,
( ~ ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> ~ $false ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ~ ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> $true ),
inference(transitivity,[status(thm)],[7,2]) ).
tff(9,plain,
( ~ ~ ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ~ ~ ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) )
<=> $false ),
inference(transitivity,[status(thm)],[9,1]) ).
tff(11,axiom,
~ ~ ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ r1(X,Y)
| p16(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p14(Y) )
| ~ ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p15(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p13(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p12(Y) )
| ! [Y: $i] :
( ~ r1(X,Y)
| p11(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
tff(12,plain,
$false,
inference(modus_ponens,[status(thm)],[11,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL664+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % 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 : Thu Sep 1 23:19:03 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.
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------