TSTP Solution File: CAT004-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT004-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 17:29:38 EDT 2022
% Result : Unsatisfiable 1.13s 1.03s
% Output : Proof 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 67
% Syntax : Number of formulae : 171 ( 68 unt; 7 typ; 0 def)
% Number of atoms : 855 ( 829 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1248 ( 598 ~; 574 |; 0 &)
% ( 76 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 41 ( 41 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 305 ( 284 !; 0 ?; 305 :)
% Comments :
%------------------------------------------------------------------------------
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(g_type,type,
g: $i ).
tff(b_type,type,
b: $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(h_type,type,
h: $i ).
tff(a_type,type,
a: $i ).
tff(codomain_type,type,
codomain: $i > $i ).
tff(1,plain,
( ( compose(compose(a,b),h) = compose(compose(a,b),g) )
<=> ( compose(compose(a,b),h) = compose(compose(a,b),g) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
compose(compose(a,b),h) = compose(compose(a,b),g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_h_equals_ab_g) ).
tff(3,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( codomain(b) = codomain(compose(a,b)) )
<=> ( codomain(compose(a,b)) = codomain(b) ) ),
inference(commutativity,[status(thm)],]) ).
tff(5,plain,
( ( codomain(compose(a,b)) = domain(h) )
<=> ( codomain(compose(a,b)) = domain(g) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ( codomain(compose(a,b)) = domain(h) )
<=> ( codomain(compose(a,b)) = domain(h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
codomain(compose(a,b)) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_h) ).
tff(8,plain,
codomain(compose(a,b)) = domain(h),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
codomain(compose(a,b)) = domain(g),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
domain(g) = codomain(compose(a,b)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ( codomain(compose(a,b)) = domain(g) )
<=> ( domain(h) = domain(g) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( codomain(compose(a,b)) = domain(g) )
<=> ( codomain(compose(a,b)) = domain(g) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
codomain(compose(a,b)) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_g) ).
tff(14,plain,
codomain(compose(a,b)) = domain(g),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
domain(h) = domain(g),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
domain(h) = codomain(compose(a,b)),
inference(transitivity,[status(thm)],[15,10]) ).
tff(17,plain,
( ( codomain(b) = domain(h) )
<=> ( codomain(b) = codomain(compose(a,b)) ) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ( codomain(b) = domain(h) )
<=> ( codomain(compose(a,b)) = codomain(b) ) ),
inference(transitivity,[status(thm)],[17,4]) ).
tff(19,plain,
( ( codomain(compose(a,b)) = codomain(b) )
<=> ( codomain(b) = domain(h) ) ),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ( codomain(a) = domain(b) )
<=> ( codomain(a) = domain(b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
tff(22,plain,
codomain(a) = domain(b),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,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(24,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)],[23]) ).
tff(25,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(26,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(27,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,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(31,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(32,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)],[31,30]) ).
tff(33,plain,
codomain(compose(a,b)) = codomain(b),
inference(unit_resolution,[status(thm)],[32,29,22]) ).
tff(34,plain,
codomain(b) = domain(h),
inference(modus_ponens,[status(thm)],[33,19]) ).
tff(35,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(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) ) )
<=> ! [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)],[35]) ).
tff(37,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(38,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(39,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)],[38]) ).
tff(40,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(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) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,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)],[41,37]) ).
tff(43,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)],[42]) ).
tff(44,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)],[43,36]) ).
tff(45,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(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(b) != domain(h) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,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(47,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(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(b) != domain(h) ) ),
inference(unit_resolution,[status(thm)],[47,44,22]) ).
tff(49,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
inference(unit_resolution,[status(thm)],[48,34]) ).
tff(50,plain,
^ [X: $i] :
refl(
( ( compose(domain(X),X) = X )
<=> ( compose(domain(X),X) = X ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X: $i] : ( compose(domain(X),X) = X )
<=> ! [X: $i] : ( compose(domain(X),X) = X ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X: $i] : ( compose(domain(X),X) = X )
<=> ! [X: $i] : ( compose(domain(X),X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
! [X: $i] : ( compose(domain(X),X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',domain_composition) ).
tff(54,plain,
! [X: $i] : ( compose(domain(X),X) = X ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X: $i] : ( compose(domain(X),X) = X ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [X: $i] : ( compose(domain(X),X) = X ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [X: $i] : ( compose(domain(X),X) = X )
| ( compose(domain(b),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
compose(domain(b),b) = b,
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
b = compose(domain(b),b),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
compose(b,h) = compose(compose(domain(b),b),h),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
compose(compose(domain(b),b),h) = compose(b,h),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
^ [X: $i] :
refl(
( ( codomain(domain(X)) = domain(X) )
<=> ( codomain(domain(X)) = domain(X) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [X: $i] : ( codomain(domain(X)) = domain(X) )
<=> ! [X: $i] : ( codomain(domain(X)) = domain(X) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [X: $i] : ( codomain(domain(X)) = domain(X) )
<=> ! [X: $i] : ( codomain(domain(X)) = domain(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,axiom,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_of_domain_is_domain) ).
tff(66,plain,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ~ ! [X: $i] : ( codomain(domain(X)) = domain(X) )
| ( codomain(domain(b)) = domain(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
codomain(domain(b)) = domain(b),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,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) )
| ( codomain(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,h)) = compose(compose(domain(b),b),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) )
| ( codomain(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,h)) = compose(compose(domain(b),b),h) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ( codomain(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,h)) = compose(compose(domain(b),b),h) )
| ( codomain(b) != domain(h) ) )
<=> ( ( codomain(b) != domain(h) )
| ( codomain(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,h)) = compose(compose(domain(b),b),h) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,h)) = compose(compose(domain(b),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) )
| ( codomain(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,h)) = compose(compose(domain(b),b),h) ) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,h)) = compose(compose(domain(b),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) )
| ( codomain(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,h)) = compose(compose(domain(b),b),h) ) ) ),
inference(transitivity,[status(thm)],[73,71]) ).
tff(75,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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,h)) = compose(compose(domain(b),b),h) )
| ( codomain(b) != domain(h) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,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) )
| ( codomain(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,h)) = compose(compose(domain(b),b),h) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
compose(domain(b),compose(b,h)) = compose(compose(domain(b),b),h),
inference(unit_resolution,[status(thm)],[76,44,70,34]) ).
tff(78,plain,
compose(domain(b),compose(b,h)) = compose(b,h),
inference(transitivity,[status(thm)],[77,61]) ).
tff(79,plain,
compose(a,compose(domain(b),compose(b,h))) = compose(a,compose(b,h)),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
compose(compose(domain(b),b),h) = compose(domain(b),compose(b,h)),
inference(symmetry,[status(thm)],[77]) ).
tff(81,plain,
compose(a,compose(compose(domain(b),b),h)) = compose(a,compose(domain(b),compose(b,h))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
compose(a,compose(compose(domain(b),b),h)) = compose(compose(a,b),g),
inference(transitivity,[status(thm)],[81,79,49,3]) ).
tff(83,plain,
domain(compose(compose(domain(b),b),h)) = domain(compose(b,h)),
inference(monotonicity,[status(thm)],[61]) ).
tff(84,plain,
domain(compose(b,h)) = domain(compose(compose(domain(b),b),h)),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
^ [Y: $i,X: $i] :
refl(
( ( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
<=> ( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
<=> ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
<=> ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_domain1) ).
tff(89,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
| ( codomain(b) != domain(h) )
| ( domain(compose(b,h)) = domain(b) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
| ( codomain(b) != domain(h) )
| ( domain(compose(b,h)) = domain(b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
| ( codomain(b) != domain(h) )
| ( domain(compose(b,h)) = domain(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
| ( codomain(b) != domain(h) )
| ( domain(compose(b,h)) = domain(b) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
domain(compose(b,h)) = domain(b),
inference(unit_resolution,[status(thm)],[94,91,34]) ).
tff(96,plain,
domain(b) = domain(compose(b,h)),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
domain(b) = domain(compose(compose(domain(b),b),h)),
inference(transitivity,[status(thm)],[96,84]) ).
tff(98,plain,
( ( codomain(b) = domain(g) )
<=> ( codomain(b) = codomain(compose(a,b)) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(99,plain,
( ( codomain(b) = domain(g) )
<=> ( codomain(compose(a,b)) = codomain(b) ) ),
inference(transitivity,[status(thm)],[98,4]) ).
tff(100,plain,
( ( codomain(compose(a,b)) = codomain(b) )
<=> ( codomain(b) = domain(g) ) ),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
codomain(b) = domain(g),
inference(modus_ponens,[status(thm)],[33,100]) ).
tff(102,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(a) != domain(b) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) )
| ( codomain(b) != domain(g) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,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(104,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(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( ( compose(a,compose(b,g)) = compose(compose(a,b),g) )
| ( codomain(b) != domain(g) ) ),
inference(unit_resolution,[status(thm)],[104,44,22]) ).
tff(106,plain,
compose(a,compose(b,g)) = compose(compose(a,b),g),
inference(unit_resolution,[status(thm)],[105,101]) ).
tff(107,plain,
compose(b,g) = compose(compose(domain(b),b),g),
inference(monotonicity,[status(thm)],[59]) ).
tff(108,plain,
compose(compose(domain(b),b),g) = compose(b,g),
inference(symmetry,[status(thm)],[107]) ).
tff(109,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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,g)) = compose(compose(domain(b),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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,g)) = compose(compose(domain(b),b),g) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( ( codomain(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,g)) = compose(compose(domain(b),b),g) )
| ( codomain(b) != domain(g) ) )
<=> ( ( codomain(b) != domain(g) )
| ( codomain(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,g)) = compose(compose(domain(b),b),g) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,g)) = compose(compose(domain(b),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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,g)) = compose(compose(domain(b),b),g) ) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,g)) = compose(compose(domain(b),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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,g)) = compose(compose(domain(b),b),g) ) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,g)) = compose(compose(domain(b),b),g) )
| ( codomain(b) != domain(g) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,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(domain(b)) != domain(b) )
| ( compose(domain(b),compose(b,g)) = compose(compose(domain(b),b),g) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
compose(domain(b),compose(b,g)) = compose(compose(domain(b),b),g),
inference(unit_resolution,[status(thm)],[114,44,70,101]) ).
tff(116,plain,
compose(domain(b),compose(b,g)) = compose(b,g),
inference(transitivity,[status(thm)],[115,108]) ).
tff(117,plain,
compose(a,compose(domain(b),compose(b,g))) = compose(a,compose(b,g)),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
compose(compose(domain(b),b),g) = compose(domain(b),compose(b,g)),
inference(symmetry,[status(thm)],[115]) ).
tff(119,plain,
compose(a,compose(compose(domain(b),b),g)) = compose(a,compose(domain(b),compose(b,g))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
compose(a,compose(compose(domain(b),b),g)) = compose(compose(a,b),g),
inference(transitivity,[status(thm)],[119,117,106]) ).
tff(121,plain,
domain(compose(compose(domain(b),b),g)) = domain(compose(b,g)),
inference(monotonicity,[status(thm)],[108]) ).
tff(122,plain,
domain(compose(b,g)) = domain(compose(compose(domain(b),b),g)),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
| ( codomain(b) != domain(g) )
| ( domain(compose(b,g)) = domain(b) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
| ( codomain(b) != domain(g) )
| ( domain(compose(b,g)) = domain(b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
| ( codomain(b) != domain(g) )
| ( domain(compose(b,g)) = domain(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( ~ ! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) )
| ( codomain(b) != domain(g) )
| ( domain(compose(b,g)) = domain(b) ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
domain(compose(b,g)) = domain(b),
inference(unit_resolution,[status(thm)],[125,91,101]) ).
tff(127,plain,
domain(b) = domain(compose(b,g)),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
domain(b) = domain(compose(compose(domain(b),b),g)),
inference(transitivity,[status(thm)],[127,122]) ).
tff(129,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( codomain(a) != domain(Z) )
<=> ( domain(b) != domain(Z) ) )),
rewrite(
( ( codomain(a) != domain(X) )
<=> ( domain(b) != domain(X) ) )),
( ( ( X = Z )
| ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) )
<=> ( ( X = Z )
| ( compose(a,Z) != Y )
| ( domain(b) != domain(Z) )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) ) ) )),
rewrite(
( ( ( X = Z )
| ( compose(a,Z) != Y )
| ( domain(b) != domain(Z) )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) ) )
<=> ( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) ) )),
( ( ( X = Z )
| ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) )
<=> ( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) ) )),
inference(bind,[status(th)],]) ).
tff(130,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( codomain(a) != domain(X) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(Z) ) )
<=> ( ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) ) )),
( ( ( codomain(a) != domain(X) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,Z) != Y ) )
<=> ( ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) )
| ( compose(a,Z) != Y ) ) )),
rewrite(
( ( ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) )
| ( compose(a,Z) != Y ) )
<=> ( ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) ) )),
( ( ( codomain(a) != domain(X) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,Z) != Y ) )
<=> ( ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) ) )),
( ( ( codomain(a) != domain(X) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,Z) != Y )
| ( X = Z ) )
<=> ( ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) )
| ( X = Z ) ) )),
rewrite(
( ( ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) )
| ( X = Z ) )
<=> ( ( X = Z )
| ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) ) )),
( ( ( codomain(a) != domain(X) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,Z) != Y )
| ( X = Z ) )
<=> ( ( X = Z )
| ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(133,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,Z) != Y )
| ( X = Z ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,Z) != Y )
| ( X = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism1) ).
tff(135,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != Y )
| ( codomain(a) != domain(X) ) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) ),
inference(modus_ponens,[status(thm)],[136,130]) ).
tff(138,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) ),
inference(skolemize,[status(sab)],[137]) ).
tff(139,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) )
| ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) )
| ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
( ( ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) )
| ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) ) )
<=> ( ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) )
| ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) )
| ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) )
| ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) ) ) ),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) )
| ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) )
| ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) )
| ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) ) ) ),
inference(transitivity,[status(thm)],[141,139]) ).
tff(143,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) )
| ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) )
| ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(a,Z) != Y )
| ( compose(a,X) != Y )
| ( domain(b) != domain(X) )
| ( domain(b) != domain(Z) ) )
| ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
( ( domain(b) != domain(compose(compose(domain(b),b),h)) )
| ( domain(b) != domain(compose(compose(domain(b),b),g)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(compose(a,b),g) )
| ( compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g) )
| ( compose(a,compose(compose(domain(b),b),h)) != compose(compose(a,b),g) ) ),
inference(unit_resolution,[status(thm)],[144,138]) ).
tff(146,plain,
compose(compose(domain(b),b),h) = compose(compose(domain(b),b),g),
inference(unit_resolution,[status(thm)],[145,128,120,97,82]) ).
tff(147,plain,
compose(b,h) = compose(compose(domain(b),b),g),
inference(transitivity,[status(thm)],[60,146]) ).
tff(148,plain,
( ( h != g )
<=> ( h != g ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,axiom,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
tff(150,plain,
h != g,
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( codomain(b) != domain(X) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(Z) ) )
<=> ( ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) ) )),
( ( ( codomain(b) != domain(X) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,Z) != Y ) )
<=> ( ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) )
| ( compose(b,Z) != Y ) ) )),
rewrite(
( ( ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) )
| ( compose(b,Z) != Y ) )
<=> ( ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) ) )),
( ( ( codomain(b) != domain(X) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,Z) != Y ) )
<=> ( ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) ) )),
( ( ( codomain(b) != domain(X) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,Z) != Y )
| ( X = Z ) )
<=> ( ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) )
| ( X = Z ) ) )),
rewrite(
( ( ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) )
| ( X = Z ) )
<=> ( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) ) )),
( ( ( codomain(b) != domain(X) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,Z) != Y )
| ( X = Z ) )
<=> ( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(153,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,Z) != Y )
| ( X = Z ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,Z) != Y )
| ( X = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism2) ).
tff(155,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) ),
inference(skolemize,[status(sab)],[156]) ).
tff(158,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) )
| ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,g) != compose(compose(domain(b),b),g) )
| ( compose(b,h) != compose(compose(domain(b),b),g) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) )
| ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,g) != compose(compose(domain(b),b),g) )
| ( compose(b,h) != compose(compose(domain(b),b),g) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
( ( ( h = g )
| ( compose(b,g) != compose(compose(domain(b),b),g) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(compose(domain(b),b),g) )
| ( codomain(b) != domain(h) ) )
<=> ( ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,g) != compose(compose(domain(b),b),g) )
| ( compose(b,h) != compose(compose(domain(b),b),g) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) )
| ( h = g )
| ( compose(b,g) != compose(compose(domain(b),b),g) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(compose(domain(b),b),g) )
| ( codomain(b) != domain(h) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) )
| ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,g) != compose(compose(domain(b),b),g) )
| ( compose(b,h) != compose(compose(domain(b),b),g) ) ) ),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) )
| ( h = g )
| ( compose(b,g) != compose(compose(domain(b),b),g) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(compose(domain(b),b),g) )
| ( codomain(b) != domain(h) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) )
| ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,g) != compose(compose(domain(b),b),g) )
| ( compose(b,h) != compose(compose(domain(b),b),g) ) ) ),
inference(transitivity,[status(thm)],[160,158]) ).
tff(162,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) )
| ( h = g )
| ( compose(b,g) != compose(compose(domain(b),b),g) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(compose(domain(b),b),g) )
| ( codomain(b) != domain(h) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X = Z )
| ( compose(b,Z) != Y )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != Y )
| ( codomain(b) != domain(X) ) )
| ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,g) != compose(compose(domain(b),b),g) )
| ( compose(b,h) != compose(compose(domain(b),b),g) ) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
$false,
inference(unit_resolution,[status(thm)],[163,157,150,34,101,107,147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : CAT004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32 % Computer : n007.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue Aug 30 05:49:30 EDT 2022
% 0.16/0.32 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 1.13/1.03 % SZS status Unsatisfiable
% 1.13/1.03 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------