TSTP Solution File: CAT003-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Tue Sep 6 17:29:37 EDT 2022
% Result : Unsatisfiable 0.85s 0.76s
% Output : Proof 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 40
% Syntax : Number of formulae : 86 ( 27 unt; 7 typ; 0 def)
% Number of atoms : 434 ( 423 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 652 ( 313 ~; 298 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 164 ( 153 !; 0 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(g_type,type,
g: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(h_type,type,
h: $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(codomain_type,type,
codomain: $i > $i ).
tff(1,plain,
( ( compose(b,h) = compose(b,g) )
<=> ( compose(b,h) = compose(b,g) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
compose(b,h) = compose(b,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bh_equals_bg) ).
tff(3,plain,
compose(b,h) = compose(b,g),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( ( codomain(b) = domain(h) )
<=> ( codomain(b) = domain(h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
codomain(b) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_h) ).
tff(7,plain,
codomain(b) = domain(h),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
( ( codomain(a) = domain(b) )
<=> ( codomain(a) = domain(b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
tff(10,plain,
codomain(a) = domain(b),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
<=> ( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( ( codomain(X) != domain(Y) )
| ( codomain(Y) != domain(Z) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) )
<=> ( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(Y) != domain(Z) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(Y) != domain(Z) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',star_property) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(b) != domain(h) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(a) != domain(b) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(b) != domain(h) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(a) != domain(b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ( codomain(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(b) != domain(h) ) )
<=> ( ( codomain(b) != domain(h) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(a) != domain(b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(b) != domain(h) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(b) != domain(h) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(a) != domain(b) ) ) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(b) != domain(h) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(b) != domain(h) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(a) != domain(b) ) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(b) != domain(h) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(b) != domain(h) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(a) != domain(b) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
inference(unit_resolution,[status(thm)],[26,20,10,7]) ).
tff(28,plain,
compose(compose(a,b),h) = compose(a,compose(b,h)),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
compose(compose(a,b),h) = compose(a,compose(b,g)),
inference(transitivity,[status(thm)],[28,4]) ).
tff(30,plain,
( ( codomain(b) = domain(g) )
<=> ( domain(h) = domain(g) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( codomain(b) = domain(g) )
<=> ( codomain(b) = domain(g) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
codomain(b) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_g) ).
tff(33,plain,
codomain(b) = domain(g),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
domain(h) = domain(g),
inference(modus_ponens,[status(thm)],[33,30]) ).
tff(35,plain,
codomain(b) = domain(g),
inference(transitivity,[status(thm)],[7,34]) ).
tff(36,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(b) != domain(g) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(b) != domain(g) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ( codomain(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) )
| ( codomain(b) != domain(g) ) )
<=> ( ( codomain(b) != domain(g) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) )
| ( codomain(b) != domain(g) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(b) != domain(g) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) ) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) )
| ( codomain(b) != domain(g) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(b) != domain(g) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) ) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) )
| ( codomain(b) != domain(g) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( codomain(Y) != domain(Z) ) )
| ( codomain(b) != domain(g) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
compose(a,compose(b,g)) = compose(compose(a,b),g),
inference(unit_resolution,[status(thm)],[41,20,10,35]) ).
tff(43,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ( codomain(compose(a,b)) = domain(h) )
<=> ( codomain(compose(a,b)) = domain(g) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(45,plain,
( ( codomain(compose(a,b)) = domain(g) )
<=> ( codomain(compose(a,b)) = domain(h) ) ),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
^ [Y: $i,X: $i] :
refl(
( ( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) )
<=> ( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) )
<=> ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) )
<=> ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_domain2) ).
tff(50,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) )
| ( codomain(a) != domain(b) )
| ( codomain(compose(a,b)) = codomain(b) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) )
| ( codomain(a) != domain(b) )
| ( codomain(compose(a,b)) = codomain(b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) )
| ( codomain(a) != domain(b) )
| ( codomain(compose(a,b)) = codomain(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) )
| ( codomain(a) != domain(b) )
| ( codomain(compose(a,b)) = codomain(b) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
codomain(compose(a,b)) = codomain(b),
inference(unit_resolution,[status(thm)],[55,52,10]) ).
tff(57,plain,
codomain(compose(a,b)) = domain(g),
inference(transitivity,[status(thm)],[56,7,34]) ).
tff(58,plain,
codomain(compose(a,b)) = domain(h),
inference(modus_ponens,[status(thm)],[57,45]) ).
tff(59,plain,
( ( h = g )
<=> ( g = h ) ),
inference(commutativity,[status(thm)],]) ).
tff(60,plain,
( ( g = h )
<=> ( h = g ) ),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ( g != h )
<=> ( h != g ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( g != h )
<=> ( g != h ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,axiom,
g != h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_g_equals_h) ).
tff(64,plain,
g != h,
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
h != g,
inference(modus_ponens,[status(thm)],[64,61]) ).
tff(66,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( codomain(compose(a,b)) != domain(X) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(Z) ) )
<=> ( ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) ) )),
( ( ( codomain(compose(a,b)) != domain(X) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),Z) != Y ) )
<=> ( ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) )
| ( compose(compose(a,b),Z) != Y ) ) )),
rewrite(
( ( ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) )
| ( compose(compose(a,b),Z) != Y ) )
<=> ( ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) ) )),
( ( ( codomain(compose(a,b)) != domain(X) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),Z) != Y ) )
<=> ( ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) ) )),
( ( ( codomain(compose(a,b)) != domain(X) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),Z) != Y )
| ( X = Z ) )
<=> ( ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) )
| ( X = Z ) ) )),
rewrite(
( ( ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) )
| ( X = Z ) )
<=> ( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) ) )),
( ( ( codomain(compose(a,b)) != domain(X) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),Z) != Y )
| ( X = Z ) )
<=> ( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( codomain(compose(a,b)) != domain(X) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),Z) != Y )
| ( X = Z ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( codomain(compose(a,b)) != domain(X) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),Z) != Y )
| ( X = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',endomorphism) ).
tff(70,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) )
| ( codomain(compose(a,b)) != domain(g) )
| ( h = g )
| ( codomain(compose(a,b)) != domain(h) )
| ( compose(compose(a,b),g) != compose(a,compose(b,g)) )
| ( compose(compose(a,b),h) != compose(a,compose(b,g)) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) )
| ( codomain(compose(a,b)) != domain(g) )
| ( h = g )
| ( codomain(compose(a,b)) != domain(h) )
| ( compose(compose(a,b),g) != compose(a,compose(b,g)) )
| ( compose(compose(a,b),h) != compose(a,compose(b,g)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ( h = g )
| ( compose(compose(a,b),g) != compose(a,compose(b,g)) )
| ( codomain(compose(a,b)) != domain(g) )
| ( compose(compose(a,b),h) != compose(a,compose(b,g)) )
| ( codomain(compose(a,b)) != domain(h) ) )
<=> ( ( codomain(compose(a,b)) != domain(g) )
| ( h = g )
| ( codomain(compose(a,b)) != domain(h) )
| ( compose(compose(a,b),g) != compose(a,compose(b,g)) )
| ( compose(compose(a,b),h) != compose(a,compose(b,g)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) )
| ( h = g )
| ( compose(compose(a,b),g) != compose(a,compose(b,g)) )
| ( codomain(compose(a,b)) != domain(g) )
| ( compose(compose(a,b),h) != compose(a,compose(b,g)) )
| ( codomain(compose(a,b)) != domain(h) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) )
| ( codomain(compose(a,b)) != domain(g) )
| ( h = g )
| ( codomain(compose(a,b)) != domain(h) )
| ( compose(compose(a,b),g) != compose(a,compose(b,g)) )
| ( compose(compose(a,b),h) != compose(a,compose(b,g)) ) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) )
| ( h = g )
| ( compose(compose(a,b),g) != compose(a,compose(b,g)) )
| ( codomain(compose(a,b)) != domain(g) )
| ( compose(compose(a,b),h) != compose(a,compose(b,g)) )
| ( codomain(compose(a,b)) != domain(h) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) )
| ( codomain(compose(a,b)) != domain(g) )
| ( h = g )
| ( codomain(compose(a,b)) != domain(h) )
| ( compose(compose(a,b),g) != compose(a,compose(b,g)) )
| ( compose(compose(a,b),h) != compose(a,compose(b,g)) ) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) )
| ( h = g )
| ( compose(compose(a,b),g) != compose(a,compose(b,g)) )
| ( codomain(compose(a,b)) != domain(g) )
| ( compose(compose(a,b),h) != compose(a,compose(b,g)) )
| ( codomain(compose(a,b)) != domain(h) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(compose(a,b),Z) != Y )
| ( codomain(compose(a,b)) != domain(Z) )
| ( compose(compose(a,b),X) != Y )
| ( codomain(compose(a,b)) != domain(X) ) )
| ( codomain(compose(a,b)) != domain(g) )
| ( h = g )
| ( codomain(compose(a,b)) != domain(h) )
| ( compose(compose(a,b),g) != compose(a,compose(b,g)) )
| ( compose(compose(a,b),h) != compose(a,compose(b,g)) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,72,57,65,58,43,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : CAT003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 30 06:00:42 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 0.85/0.76 % SZS status Unsatisfiable
% 0.85/0.76 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------