%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN079+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:38:11 AM UTC 2025
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 25 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 157 ( 69 ~; 53 |; 16 &)
% ( 16 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 54 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_f_type,type,
big_f: ( $i * $i ) > $o ).
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
( ~ big_f(f(a,b),f(a,c))
<=> ~ big_f(f(a,b),f(a,c)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ big_f(f(a,b),f(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel57) ).
tff(3,plain,
~ big_f(f(a,b),f(a,c)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ! [X: $i,Y: $i,Z: $i] :
( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( big_f(X,Y)
& big_f(Y,Z) )
<=> ~ ( ~ big_f(X,Y)
| ~ big_f(Y,Z) ) )),
( ~ ( big_f(X,Y)
& big_f(Y,Z) )
<=> ~ ~ ( ~ big_f(X,Y)
| ~ big_f(Y,Z) ) )),
rewrite(( ~ ~ ( ~ big_f(X,Y)
| ~ big_f(Y,Z) )
<=> ( ~ big_f(X,Y)
| ~ big_f(Y,Z) ) )),
( ~ ( big_f(X,Y)
& big_f(Y,Z) )
<=> ( ~ big_f(X,Y)
| ~ big_f(Y,Z) ) )),
( ( ~ ( big_f(X,Y)
& big_f(Y,Z) )
| big_f(X,Z) )
<=> ( ~ big_f(X,Y)
| ~ big_f(Y,Z)
| big_f(X,Z) ) )),
rewrite(( ( ~ big_f(X,Y)
| ~ big_f(Y,Z)
| big_f(X,Z) )
<=> ( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) ) )),
( ( ~ ( big_f(X,Y)
& big_f(Y,Z) )
| big_f(X,Z) )
<=> ( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f(X,Y)
& big_f(Y,Z) )
| big_f(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f(X,Y)
& big_f(Y,Z) )
| big_f(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f(X,Y)
& big_f(Y,Z) )
| big_f(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( big_f(X,Y)
& big_f(Y,Z) )
=> big_f(X,Z) )
<=> ( ~ ( big_f(X,Y)
& big_f(Y,Z) )
| big_f(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( big_f(X,Y)
& big_f(Y,Z) )
=> big_f(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f(X,Y)
& big_f(Y,Z) )
| big_f(X,Z) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( big_f(X,Y)
& big_f(Y,Z) )
=> big_f(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel57_3) ).
tff(11,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f(X,Y)
& big_f(Y,Z) )
| big_f(X,Z) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f(X,Y)
& big_f(Y,Z) )
| big_f(X,Z) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( big_f(X,Y)
& big_f(Y,Z) )
| big_f(X,Z) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [X: $i,Y: $i,Z: $i] :
( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
! [X: $i,Y: $i,Z: $i] :
( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) ),
inference(modus_ponens,[status(thm)],[14,4]) ).
tff(16,plain,
( big_f(f(b,c),f(a,c))
<=> big_f(f(b,c),f(a,c)) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
big_f(f(b,c),f(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel57_2) ).
tff(18,plain,
big_f(f(b,c),f(a,c)),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( big_f(f(a,b),f(b,c))
<=> big_f(f(a,b),f(b,c)) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
big_f(f(a,b),f(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel57_1) ).
tff(21,plain,
big_f(f(a,b),f(b,c)),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) )
| big_f(f(a,b),f(a,c))
| ~ big_f(f(a,b),f(b,c))
| ~ big_f(f(b,c),f(a,c)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) )
| big_f(f(a,b),f(a,c))
| ~ big_f(f(a,b),f(b,c))
| ~ big_f(f(b,c),f(a,c)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) )
| big_f(f(a,b),f(a,c))
| ~ big_f(f(a,b),f(b,c))
| ~ big_f(f(b,c),f(a,c)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( big_f(X,Z)
| ~ big_f(X,Y)
| ~ big_f(Y,Z) )
| big_f(f(a,b),f(a,c))
| ~ big_f(f(a,b),f(b,c))
| ~ big_f(f(b,c),f(a,c)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
$false,
inference(unit_resolution,[status(thm)],[24,21,18,15,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN079+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.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 : Fri Jun 20 12:26:40 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % SZS output start Proof
% See solution above
% 0.14/0.39 % E exiting
%------------------------------------------------------------------------------