%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT001-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:00:18 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 39 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 98 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 109 ( 49 ~; 45 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 84 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(h_type,type,
h: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(g_type,type,
g: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',associativity_of_compose) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( compose(b,h) = compose(b,g) )
<=> ( compose(b,h) = compose(b,g) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
compose(b,h) = compose(b,g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bh_equals_bg) ).
tff(12,plain,
compose(b,h) = compose(b,g),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
compose(b,g) = compose(b,h),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
compose(a,compose(b,g)) = compose(a,compose(b,h)),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
compose(a,compose(b,g)) = compose(compose(a,b),g),
inference(unit_resolution,[status(thm)],[15,7]) ).
tff(17,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
compose(compose(a,b),g) = compose(compose(a,b),h),
inference(transitivity,[status(thm)],[17,14,9]) ).
tff(19,plain,
( ( h != g )
<=> ( h != g ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
tff(21,plain,
h != g,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [Z: $i,X: $i] :
refl(( ( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) )
<=> ( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) )
<=> ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) )
<=> ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) )
<=> ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(26,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( compose(compose(a,b),X) != Y ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(27,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( compose(compose(a,b),X) != Y ) )
<=> ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ) ),
inference(transitivity,[status(thm)],[26,25]) ).
tff(28,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( ( compose(compose(a,b),X) != Y )
| ( compose(compose(a,b),Z) != Y )
| ( X = Z ) )
<=> ( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( compose(compose(a,b),X) != Y ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( compose(compose(a,b),X) != Y )
| ( compose(compose(a,b),Z) != Y )
| ( X = Z ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( compose(compose(a,b),X) != Y ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( compose(compose(a,b),X) != Y )
| ( compose(compose(a,b),Z) != Y )
| ( X = Z ) )
<=> ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ) ),
inference(transitivity,[status(thm)],[29,27]) ).
tff(31,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( compose(compose(a,b),X) != Y )
| ( compose(compose(a,b),Z) != Y )
| ( X = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monomorphism) ).
tff(32,plain,
! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ),
inference(modus_ponens,[status(thm)],[32,24]) ).
tff(34,plain,
! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) ),
inference(modus_ponens,[status(thm)],[34,23]) ).
tff(36,plain,
( ( ~ ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) )
| ( h = g )
| ( compose(compose(a,b),g) != compose(compose(a,b),h) ) )
<=> ( ~ ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) )
| ( h = g )
| ( compose(compose(a,b),g) != compose(compose(a,b),h) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) )
| ( h = g )
| ( compose(compose(a,b),g) != compose(compose(a,b),h) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [Z: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != compose(compose(a,b),X) ) )
| ( h = g )
| ( compose(compose(a,b),g) != compose(compose(a,b),h) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,35,21,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : CAT001-4 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 11:49:05 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------