%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT073+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:11 AM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 50 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 384 ( 0 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 756 ( 444 ~; 248 |; 34 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 172 ( 146 !; 11 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
tff(in_closed_type,type,
in_closed: ( $i * $i * $i ) > $o ).
tff(n10_type,type,
n10: $i ).
tff(n5_type,type,
n5: $i ).
tff(tptp_fun_X_0_type,type,
tptp_fun_X_0: ( $i * $i * $i * $i ) > $i ).
tff(n0_type,type,
n0: $i ).
tff(axis_compatible_type,type,
axis_compatible: ( $i * $i * $i * $i ) > $o ).
tff(1,plain,
^ [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
refl(( ~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
<=> ~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
<=> ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
rewrite(( ~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
<=> ~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
<=> ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
<=> ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
trans(monotonicity(rewrite(( ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ( in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
& in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
<=> ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) ) )),
rewrite(( ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
~ ( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) )
<=> ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )),
( ( ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ( in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
& in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
& ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
~ ( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ) )
<=> ( ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
& ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ) )),
rewrite(( ( ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
& ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
<=> ~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ) )),
( ( ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ( in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
& in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
& ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
~ ( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ) )
<=> ~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
( ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ( in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
& in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
& ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
~ ( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ) )
<=> ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
( axis_compatible(I1lo,I1hi,I2lo,I2hi)
<=> ? [X: $i] :
( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) )
<=> ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
( axis_compatible(I1lo,I1hi,I2lo,I2hi)
<=> ? [X: $i] :
( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
( axis_compatible(I1lo,I1hi,I2lo,I2hi)
<=> ? [X: $i] :
( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+2.ax',axis_compatible_def) ).
tff(10,plain,
! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
( axis_compatible(I1lo,I1hi,I2lo,I2hi)
<=> ? [X: $i] :
( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
( ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ( in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
& in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
& ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
~ ( in_closed(X,I1lo,I1hi)
& in_closed(X,I2lo,I2hi) ) ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
| ~ ( ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )
| ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ) ) )
<=> ( ~ ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
| ~ ( ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )
| ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ( ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) )
| ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) ) )
<=> ~ ( ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )
| ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ( ~ ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
| ~ ( ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) )
| ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) ) ) )
<=> ( ~ ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
| ~ ( ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )
| ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ) ) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
| ~ ( ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) )
| ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) ) ) )
<=> ( ~ ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
| ~ ( ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )
| ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ) ) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ~ ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
| ~ ( ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) )
| ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [I1lo: $i,I1hi: $i,I2lo: $i,I2hi: $i] :
~ ( ~ ( ~ axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ~ ( ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I1lo,I1hi)
| ~ in_closed(tptp_fun_X_0(I2hi,I2lo,I1hi,I1lo),I2lo,I2hi) ) )
| ~ ( axis_compatible(I1lo,I1hi,I2lo,I2hi)
| ! [X: $i] :
( ~ in_closed(X,I1lo,I1hi)
| ~ in_closed(X,I2lo,I2hi) ) ) )
| ~ ( ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )
| ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ ( ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )
| ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ) ),
inference(unit_resolution,[status(thm)],[19,13]) ).
tff(21,plain,
( ~ ( axis_compatible(n0,n10,n5,n10)
| ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )
| ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) )
| ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ),
inference(tautology,[status(thm)],[]) ).
tff(22,plain,
( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
( axis_compatible(n0,n10,n5,n10)
<=> axis_compatible(n0,n10,n5,n10) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
axis_compatible(n0,n10,n5,n10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible_hyp) ).
tff(25,plain,
axis_compatible(n0,n10,n5,n10),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) )
| ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ),
inference(tautology,[status(thm)],[]) ).
tff(27,plain,
( ~ ( ~ axis_compatible(n0,n10,n5,n10)
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) )
| ~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
~ ( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ),
inference(unit_resolution,[status(thm)],[27,22]) ).
tff(29,plain,
( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10)
| in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ),
inference(tautology,[status(thm)],[]) ).
tff(30,plain,
in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10)
| in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10) ),
inference(tautology,[status(thm)],[]) ).
tff(32,plain,
in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10),
inference(unit_resolution,[status(thm)],[31,28]) ).
tff(33,plain,
^ [X: $i] :
refl(( ( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) )
<=> ( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) )
<=> ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( in_closed(X,n0,n10)
& in_closed(X,n5,n10) )
<=> ~ ( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )),
( ~ ( in_closed(X,n0,n10)
& in_closed(X,n5,n10) )
<=> ~ ~ ( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )),
rewrite(( ~ ~ ( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) )
<=> ( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )),
( ~ ( in_closed(X,n0,n10)
& in_closed(X,n5,n10) )
<=> ( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X: $i] :
~ ( in_closed(X,n0,n10)
& in_closed(X,n5,n10) )
<=> ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ~ ? [X: $i] :
( in_closed(X,n0,n10)
& in_closed(X,n5,n10) )
<=> ~ ? [X: $i] :
( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
~ ? [X: $i] :
( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_false_compatible) ).
tff(39,plain,
~ ? [X: $i] :
( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ ? [X: $i] :
( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ),
inference(modus_ponens,[status(thm)],[39,37]) ).
tff(41,plain,
~ ? [X: $i] :
( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
~ ? [X: $i] :
( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
^ [X: $i] :
refl($oeq(~ ( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ),
~ ( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ))),
inference(bind,[status(th)],[]) ).
tff(44,plain,
! [X: $i] :
~ ( in_closed(X,n0,n10)
& in_closed(X,n5,n10) ),
inference(nnf-neg,[status(sab)],[42,43]) ).
tff(45,plain,
! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ),
inference(modus_ponens,[status(thm)],[44,36]) ).
tff(46,plain,
! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) ),
inference(modus_ponens,[status(thm)],[45,34]) ).
tff(47,plain,
( ( ~ ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) )
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) )
<=> ( ~ ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) )
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) )
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [X: $i] :
( ~ in_closed(X,n0,n10)
| ~ in_closed(X,n5,n10) )
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n0,n10)
| ~ in_closed(tptp_fun_X_0(n10,n5,n10,n0),n5,n10) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,46,32,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT073+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.34 % Computer : n028.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 7 13:59:49 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% See solution above
% 0.13/0.43 % E exiting
%------------------------------------------------------------------------------