%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN080-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 2 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 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 : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 22 ( 20 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: $i > $i ).
tff(g_type,type,
g: $i > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ( g(b) = f(g(b)) )
<=> ( f(g(b)) = g(b) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
^ [Y: $i,X: $i] :
refl(( ( f(X) = g(Y) )
<=> ( f(X) = g(Y) ) )),
inference(bind,[status(th)],[]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( f(X) = g(Y) )
<=> ! [Y: $i,X: $i] : ( f(X) = g(Y) ) ),
inference(quant_intro,[status(thm)],[2]) ).
tff(4,plain,
( ! [Y: $i,X: $i] : ( f(X) = g(Y) )
<=> ! [Y: $i,X: $i] : ( f(X) = g(Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
! [Y: $i,X: $i] : ( f(X) = g(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(6,plain,
! [Y: $i,X: $i] : ( f(X) = g(Y) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( f(X) = g(Y) ),
inference(skolemize,[status(sab)],[6]) ).
tff(8,plain,
! [Y: $i,X: $i] : ( f(X) = g(Y) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
( ~ ! [Y: $i,X: $i] : ( f(X) = g(Y) )
| ( f(f(a)) = g(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(10,plain,
f(f(a)) = g(b),
inference(unit_resolution,[status(thm)],[9,8]) ).
tff(11,plain,
( ( f(f(a)) = f(g(b)) )
<=> ( g(b) = f(g(b)) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( f(f(a)) = f(g(b)) )
<=> ( f(g(b)) = g(b) ) ),
inference(transitivity,[status(thm)],[11,1]) ).
tff(13,plain,
( ( f(g(b)) = g(b) )
<=> ( f(f(a)) = f(g(b)) ) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( ~ ! [Y: $i,X: $i] : ( f(X) = g(Y) )
| ( f(g(b)) = g(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
f(g(b)) = g(b),
inference(unit_resolution,[status(thm)],[14,8]) ).
tff(16,plain,
f(f(a)) = f(g(b)),
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,plain,
( ( f(f(a)) != f(g(b)) )
<=> ( f(f(a)) != f(g(b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
f(f(a)) != f(g(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(19,plain,
f(f(a)) != f(g(b)),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN080-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:27:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------