%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT004-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:00:19 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 65
% Syntax : Number of formulae : 182 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 927 ( 904 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1361 ( 650 ~; 625 |; 0 &)
% ( 86 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 34 ( 34 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 349 ( 327 !; 0 ?; 349 :)
% Comments :
%------------------------------------------------------------------------------
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(h_type,type,
h: $i ).
tff(b_type,type,
b: $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(a_type,type,
a: $i ).
tff(g_type,type,
g: $i ).
tff(codomain_type,type,
codomain: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( codomain(domain(X)) = domain(X) )
<=> ( codomain(domain(X)) = domain(X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( codomain(domain(X)) = domain(X) )
<=> ! [X: $i] : ( codomain(domain(X)) = domain(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( codomain(domain(X)) = domain(X) )
<=> ! [X: $i] : ( codomain(domain(X)) = domain(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_of_domain_is_domain) ).
tff(5,plain,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( codomain(domain(X)) = domain(X) )
| ( codomain(domain(b)) = domain(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
codomain(domain(b)) = domain(b),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( codomain(compose(a,b)) = domain(h) )
<=> ( codomain(compose(a,b)) = domain(h) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
codomain(compose(a,b)) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_h) ).
tff(12,plain,
codomain(compose(a,b)) = domain(h),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( ( codomain(a) = domain(b) )
<=> ( codomain(a) = domain(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
tff(15,plain,
codomain(a) = domain(b),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,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(17,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)],[16]) ).
tff(18,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(19,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(20,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( codomain(compose(X,Y)) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,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(24,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(25,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)],[24,23]) ).
tff(26,plain,
codomain(compose(a,b)) = codomain(b),
inference(unit_resolution,[status(thm)],[25,22,15]) ).
tff(27,plain,
codomain(b) = codomain(compose(a,b)),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
codomain(b) = domain(h),
inference(transitivity,[status(thm)],[27,12]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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(32,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(33,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)],[32]) ).
tff(34,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(35,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)],[34,33]) ).
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) ) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
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) ) ),
inference(skolemize,[status(sab)],[36]) ).
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) ) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
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(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(40,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(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(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)],[40]) ).
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) ) )
| ( 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)],[41,39]) ).
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) ) )
| ( 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(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) ) )
| ( 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)],[43,42]) ).
tff(45,plain,
compose(domain(b),compose(b,h)) = compose(compose(domain(b),b),h),
inference(unit_resolution,[status(thm)],[44,38,28,9]) ).
tff(46,plain,
compose(compose(domain(b),b),h) = compose(domain(b),compose(b,h)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
compose(a,compose(compose(domain(b),b),h)) = compose(a,compose(domain(b),compose(b,h))),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
compose(a,compose(domain(b),compose(b,h))) = compose(a,compose(compose(domain(b),b),h)),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
^ [X: $i] :
refl(( ( compose(domain(X),X) = X )
<=> ( compose(domain(X),X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] : ( compose(domain(X),X) = X )
<=> ! [X: $i] : ( compose(domain(X),X) = X ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X: $i] : ( compose(domain(X),X) = X )
<=> ! [X: $i] : ( compose(domain(X),X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [X: $i] : ( compose(domain(X),X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',domain_composition) ).
tff(53,plain,
! [X: $i] : ( compose(domain(X),X) = X ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X: $i] : ( compose(domain(X),X) = X ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i] : ( compose(domain(X),X) = X ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [X: $i] : ( compose(domain(X),X) = X )
| ( compose(domain(b),b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
compose(domain(b),b) = b,
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
b = compose(domain(b),b),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
compose(b,h) = compose(compose(domain(b),b),h),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
compose(compose(domain(b),b),h) = compose(b,h),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
compose(domain(b),compose(b,h)) = compose(b,h),
inference(transitivity,[status(thm)],[45,60]) ).
tff(62,plain,
compose(a,compose(domain(b),compose(b,h))) = compose(a,compose(b,h)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
compose(a,compose(b,h)) = compose(a,compose(domain(b),compose(b,h))),
inference(symmetry,[status(thm)],[62]) ).
tff(64,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(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,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(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ( ( codomain(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) )
| ( codomain(b) != domain(h) ) )
<=> ( ( codomain(b) != domain(h) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,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) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) ) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,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) )
| ( codomain(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) ) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,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(69,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(a) != domain(b) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ( codomain(b) != domain(h) )
| ( compose(a,compose(b,h)) = compose(compose(a,b),h) ) ),
inference(unit_resolution,[status(thm)],[69,38,15]) ).
tff(71,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
inference(unit_resolution,[status(thm)],[70,28]) ).
tff(72,plain,
compose(compose(a,b),h) = compose(a,compose(b,h)),
inference(symmetry,[status(thm)],[71]) ).
tff(73,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(74,axiom,
compose(compose(a,b),h) = compose(compose(a,b),g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_h_equals_ab_g) ).
tff(75,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
compose(compose(a,b),g) = compose(compose(a,b),h),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ( codomain(compose(a,b)) = domain(g) )
<=> ( codomain(compose(a,b)) = domain(g) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
codomain(compose(a,b)) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_g) ).
tff(79,plain,
codomain(compose(a,b)) = domain(g),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
domain(g) = codomain(compose(a,b)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
domain(g) = domain(h),
inference(transitivity,[status(thm)],[80,12]) ).
tff(82,plain,
( ( codomain(b) = domain(g) )
<=> ( codomain(b) = domain(h) ) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ( codomain(b) = domain(h) )
<=> ( codomain(b) = domain(g) ) ),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
codomain(b) = domain(g),
inference(modus_ponens,[status(thm)],[28,83]) ).
tff(85,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(86,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(87,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)],[86]) ).
tff(88,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)],[87,85]) ).
tff(89,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(90,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)],[89,88]) ).
tff(91,plain,
( ( codomain(b) != domain(g) )
| ( compose(a,compose(b,g)) = compose(compose(a,b),g) ) ),
inference(unit_resolution,[status(thm)],[90,38,15]) ).
tff(92,plain,
compose(a,compose(b,g)) = compose(compose(a,b),g),
inference(unit_resolution,[status(thm)],[91,84]) ).
tff(93,plain,
compose(b,g) = compose(compose(domain(b),b),g),
inference(monotonicity,[status(thm)],[58]) ).
tff(94,plain,
compose(compose(domain(b),b),g) = compose(b,g),
inference(symmetry,[status(thm)],[93]) ).
tff(95,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(96,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(97,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)],[96]) ).
tff(98,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)],[97,95]) ).
tff(99,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(100,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)],[99,98]) ).
tff(101,plain,
compose(domain(b),compose(b,g)) = compose(compose(domain(b),b),g),
inference(unit_resolution,[status(thm)],[100,38,84,9]) ).
tff(102,plain,
compose(domain(b),compose(b,g)) = compose(b,g),
inference(transitivity,[status(thm)],[101,94]) ).
tff(103,plain,
compose(a,compose(domain(b),compose(b,g))) = compose(a,compose(b,g)),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
compose(compose(domain(b),b),g) = compose(domain(b),compose(b,g)),
inference(symmetry,[status(thm)],[101]) ).
tff(105,plain,
compose(a,compose(compose(domain(b),b),g)) = compose(a,compose(domain(b),compose(b,g))),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
compose(a,compose(compose(domain(b),b),g)) = compose(a,compose(compose(domain(b),b),h)),
inference(transitivity,[status(thm)],[105,103,92,76,72,63,48]) ).
tff(107,plain,
( ( compose(b,g) = compose(b,h) )
<=> ( compose(b,h) = compose(b,g) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(108,plain,
( ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
<=> ( compose(b,g) = compose(b,h) ) ),
inference(monotonicity,[status(thm)],[94,60]) ).
tff(109,plain,
( ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
<=> ( compose(b,h) = compose(b,g) ) ),
inference(transitivity,[status(thm)],[108,107]) ).
tff(110,plain,
( ( compose(b,h) = compose(b,g) )
<=> ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) ) ),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
( ( compose(b,h) != compose(b,g) )
<=> ( compose(compose(domain(b),b),g) != compose(compose(domain(b),b),h) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( h != g )
<=> ( h != g ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,axiom,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
tff(114,plain,
h != g,
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
^ [Z: $i,X: $i] :
refl(( ( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
<=> ( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
<=> ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
<=> ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
<=> ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(119,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] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(120,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,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ) ),
inference(transitivity,[status(thm)],[119,118]) ).
tff(121,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(122,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)],[121]) ).
tff(123,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,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ) ),
inference(transitivity,[status(thm)],[122,120]) ).
tff(124,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(125,plain,
! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ),
inference(modus_ponens,[status(thm)],[125,117]) ).
tff(127,plain,
! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) ),
inference(modus_ponens,[status(thm)],[127,116]) ).
tff(129,plain,
( ( ~ ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
| ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) )
<=> ( ~ ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
| ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
( ( ( codomain(b) != domain(h) )
| ( h = g )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) )
<=> ( ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,plain,
( ( ~ ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
| ( codomain(b) != domain(h) )
| ( h = g )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) )
<=> ( ~ ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
| ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) ) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ( ~ ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
| ( codomain(b) != domain(h) )
| ( h = g )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) )
<=> ( ~ ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
| ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) ) ),
inference(transitivity,[status(thm)],[131,129]) ).
tff(133,plain,
( ~ ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
| ( codomain(b) != domain(h) )
| ( h = g )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
( ~ ! [Z: $i,X: $i] :
( ( codomain(b) != domain(X) )
| ( X = Z )
| ( codomain(b) != domain(Z) )
| ( compose(b,X) != compose(b,Z) ) )
| ( h = g )
| ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( ( codomain(b) != domain(h) )
| ( codomain(b) != domain(g) )
| ( compose(b,h) != compose(b,g) ) ),
inference(unit_resolution,[status(thm)],[134,128,114]) ).
tff(136,plain,
compose(b,h) != compose(b,g),
inference(unit_resolution,[status(thm)],[135,84,28]) ).
tff(137,plain,
compose(compose(domain(b),b),g) != compose(compose(domain(b),b),h),
inference(modus_ponens,[status(thm)],[136,111]) ).
tff(138,plain,
domain(compose(compose(domain(b),b),g)) = domain(compose(b,g)),
inference(monotonicity,[status(thm)],[94]) ).
tff(139,plain,
domain(compose(b,g)) = domain(compose(compose(domain(b),b),g)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,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(141,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)],[140]) ).
tff(142,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(143,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(144,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ),
inference(skolemize,[status(sab)],[144]) ).
tff(146,plain,
! [Y: $i,X: $i] :
( ( codomain(X) != domain(Y) )
| ( domain(compose(X,Y)) = domain(X) ) ),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,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(148,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(149,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)],[148,147]) ).
tff(150,plain,
domain(compose(b,g)) = domain(b),
inference(unit_resolution,[status(thm)],[149,146,84]) ).
tff(151,plain,
domain(b) = domain(compose(b,g)),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
codomain(a) = domain(compose(compose(domain(b),b),g)),
inference(transitivity,[status(thm)],[15,151,139]) ).
tff(153,plain,
domain(compose(compose(domain(b),b),h)) = domain(compose(b,h)),
inference(monotonicity,[status(thm)],[60]) ).
tff(154,plain,
domain(compose(b,h)) = domain(compose(compose(domain(b),b),h)),
inference(symmetry,[status(thm)],[153]) ).
tff(155,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(156,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(157,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)],[156,155]) ).
tff(158,plain,
domain(compose(b,h)) = domain(b),
inference(unit_resolution,[status(thm)],[157,146,28]) ).
tff(159,plain,
domain(b) = domain(compose(b,h)),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
codomain(a) = domain(compose(compose(domain(b),b),h)),
inference(transitivity,[status(thm)],[15,159,154]) ).
tff(161,plain,
^ [Z: $i,X: $i] :
refl(( ( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
<=> ( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ) )),
inference(bind,[status(th)],[]) ).
tff(162,plain,
( ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
<=> ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,plain,
( ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
<=> ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
<=> ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(165,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] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(166,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,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ) ),
inference(transitivity,[status(thm)],[165,164]) ).
tff(167,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(168,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)],[167]) ).
tff(169,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,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ) ),
inference(transitivity,[status(thm)],[168,166]) ).
tff(170,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(171,plain,
! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ),
inference(modus_ponens,[status(thm)],[171,163]) ).
tff(173,plain,
! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ),
inference(skolemize,[status(sab)],[172]) ).
tff(174,plain,
! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) ),
inference(modus_ponens,[status(thm)],[173,162]) ).
tff(175,plain,
( ( ~ ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
| ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) )
<=> ( ~ ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
| ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,plain,
( ( ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) )
<=> ( ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,plain,
( ( ~ ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
| ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) )
<=> ( ~ ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
| ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) ) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ( ~ ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
| ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) )
<=> ( ~ ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
| ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) ) ),
inference(transitivity,[status(thm)],[177,175]) ).
tff(179,plain,
( ~ ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
| ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
( ~ ! [Z: $i,X: $i] :
( ( codomain(a) != domain(X) )
| ( X = Z )
| ( codomain(a) != domain(Z) )
| ( compose(a,X) != compose(a,Z) ) )
| ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
( ( codomain(a) != domain(compose(compose(domain(b),b),g)) )
| ( codomain(a) != domain(compose(compose(domain(b),b),h)) )
| ( compose(compose(domain(b),b),g) = compose(compose(domain(b),b),h) )
| ( compose(a,compose(compose(domain(b),b),g)) != compose(a,compose(compose(domain(b),b),h)) ) ),
inference(unit_resolution,[status(thm)],[180,174]) ).
tff(182,plain,
$false,
inference(unit_resolution,[status(thm)],[181,160,152,137,106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : CAT004-2 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 11:49:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% See solution above
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------