%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN083-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:38:12 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 6 ~; 2 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 30 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(d_type,type,
d: $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( f(X,f(Y,Z)) = f(f(X,Y),Z) )
<=> ( f(X,f(Y,Z)) = f(f(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_is_associative) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) )
| ( f(a,f(b,f(c,d))) = f(f(a,b),f(c,d)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
f(a,f(b,f(c,d))) = f(f(a,b),f(c,d)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( f(a,f(b,f(c,d))) = f(f(f(a,b),c),d) )
<=> ( f(f(a,b),f(c,d)) = f(f(f(a,b),c),d) ) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ( f(f(a,b),f(c,d)) = f(f(f(a,b),c),d) )
<=> ( f(a,f(b,f(c,d))) = f(f(f(a,b),c),d) ) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) )
| ( f(f(a,b),f(c,d)) = f(f(f(a,b),c),d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
f(f(a,b),f(c,d)) = f(f(f(a,b),c),d),
inference(unit_resolution,[status(thm)],[12,7]) ).
tff(14,plain,
f(a,f(b,f(c,d))) = f(f(f(a,b),c),d),
inference(modus_ponens,[status(thm)],[13,11]) ).
tff(15,plain,
( ( f(a,f(b,f(c,d))) != f(f(f(a,b),c),d) )
<=> ( f(a,f(b,f(c,d))) != f(f(f(a,b),c),d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
f(a,f(b,f(c,d))) != f(f(f(a,b),c),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(17,plain,
f(a,f(b,f(c,d))) != f(f(f(a,b),c),d),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
$false,
inference(unit_resolution,[status(thm)],[17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN083-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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 : Fri Jun 20 12:27:57 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------