TSTP Solution File: CAT018-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT018-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 17:29:49 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 54
% Syntax : Number of formulae : 125 ( 41 unt; 7 typ; 0 def)
% Number of atoms : 356 ( 99 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 416 ( 189 ~; 181 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 4 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 201 ( 181 !; 0 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
tff(there_exists_type,type,
there_exists: $i > $o ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(codomain_type,type,
codomain: $i > $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( compose(codomain(X),X) = X )
<=> ( compose(codomain(X),X) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( compose(codomain(X),X) = X )
<=> ! [X: $i] : ( compose(codomain(X),X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( compose(codomain(X),X) = X )
<=> ! [X: $i] : ( compose(codomain(X),X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( compose(codomain(X),X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',compose_codomain) ).
tff(5,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( compose(codomain(X),X) = X )
| ( compose(codomain(b),b) = b ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
compose(codomain(b),b) = b,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
compose(compose(codomain(b),b),c) = compose(b,c),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',associativity_of_compose) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( compose(codomain(b),compose(b,c)) = compose(compose(codomain(b),b),c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
compose(codomain(b),compose(b,c)) = compose(compose(codomain(b),b),c),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
compose(codomain(b),compose(b,c)) = compose(b,c),
inference(transitivity,[status(thm)],[19,10]) ).
tff(21,plain,
( there_exists(compose(codomain(b),compose(b,c)))
<=> there_exists(compose(b,c)) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( there_exists(compose(b,c))
<=> there_exists(compose(codomain(b),compose(b,c))) ),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( there_exists(compose(b,c))
<=> there_exists(compose(b,c)) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
there_exists(compose(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_bc_exists) ).
tff(25,plain,
there_exists(compose(b,c)),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
there_exists(compose(codomain(b),compose(b,c))),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
( there_exists(compose(a,b))
<=> there_exists(compose(a,b)) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_ab_exists) ).
tff(29,plain,
there_exists(compose(a,b)),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
<=> ( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_codomain_composition1) ).
tff(34,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(a,b))
| ( domain(a) = codomain(b) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(a,b))
| ( domain(a) = codomain(b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(a,b))
| ( domain(a) = codomain(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(a,b))
| ( domain(a) = codomain(b) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
domain(a) = codomain(b),
inference(unit_resolution,[status(thm)],[39,36,29]) ).
tff(41,plain,
codomain(b) = domain(a),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( there_exists(compose(codomain(b),b))
<=> there_exists(b) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(43,plain,
( there_exists(b)
<=> there_exists(compose(codomain(b),b)) ),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
^ [Y: $i,X: $i] :
refl(
( ( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) )
<=> ( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( ~ there_exists(compose(X,Y))
| there_exists(codomain(X)) )
<=> ( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| there_exists(codomain(X)) )
<=> ! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| there_exists(codomain(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',composition_implies_codomain) ).
tff(50,plain,
! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(codomain(b))
| ~ there_exists(compose(b,c)) )
<=> ( ~ ! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(codomain(b))
| ~ there_exists(compose(b,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(codomain(b))
| ~ there_exists(compose(b,c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(codomain(b))
| ~ there_exists(compose(b,c)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
there_exists(codomain(b)),
inference(unit_resolution,[status(thm)],[56,53,25]) ).
tff(58,plain,
^ [X: $i] :
refl(
( ( there_exists(X)
| ~ there_exists(codomain(X)) )
<=> ( there_exists(X)
| ~ there_exists(codomain(X)) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [X: $i] :
rewrite(
( ( ~ there_exists(codomain(X))
| there_exists(X) )
<=> ( there_exists(X)
| ~ there_exists(codomain(X)) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X: $i] :
( ~ there_exists(codomain(X))
| there_exists(X) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [X: $i] :
( ~ there_exists(codomain(X))
| there_exists(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',codomain_has_elements) ).
tff(64,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
| there_exists(b)
| ~ there_exists(codomain(b)) )
<=> ( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
| there_exists(b)
| ~ there_exists(codomain(b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
| there_exists(b)
| ~ there_exists(codomain(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
| there_exists(b)
| ~ there_exists(codomain(b)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
there_exists(b),
inference(unit_resolution,[status(thm)],[70,67,57]) ).
tff(72,plain,
there_exists(compose(codomain(b),b)),
inference(modus_ponens,[status(thm)],[71,43]) ).
tff(73,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(b),b))
| ( domain(codomain(b)) = codomain(b) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(b),b))
| ( domain(codomain(b)) = codomain(b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(b),b))
| ( domain(codomain(b)) = codomain(b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(b),b))
| ( domain(codomain(b)) = codomain(b) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( ~ there_exists(compose(codomain(b),b))
| ( domain(codomain(b)) = codomain(b) ) ),
inference(unit_resolution,[status(thm)],[75,36]) ).
tff(77,plain,
domain(codomain(b)) = codomain(b),
inference(unit_resolution,[status(thm)],[76,72]) ).
tff(78,plain,
domain(codomain(b)) = domain(a),
inference(transitivity,[status(thm)],[77,41]) ).
tff(79,plain,
( ( domain(codomain(b)) = codomain(compose(b,c)) )
<=> ( domain(a) = codomain(compose(b,c)) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( domain(a) = codomain(compose(b,c)) )
<=> ( domain(codomain(b)) = codomain(compose(b,c)) ) ),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ( domain(a) != codomain(compose(b,c)) )
<=> ( domain(codomain(b)) != codomain(compose(b,c)) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
^ [Y: $i,X: $i] :
refl(
( ( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
<=> ( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) )
<=> ( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) )
<=> ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',composition_implies_domain) ).
tff(88,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,b)) )
<=> ( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,b)) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
there_exists(domain(a)),
inference(unit_resolution,[status(thm)],[94,91,29]) ).
tff(96,plain,
( ~ there_exists(compose(a,compose(b,c)))
<=> ~ there_exists(compose(a,compose(b,c))) ),
inference(rewrite,[status(thm)],]) ).
tff(97,axiom,
~ there_exists(compose(a,compose(b,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_bc_exists) ).
tff(98,plain,
~ there_exists(compose(a,compose(b,c))),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) )
<=> ( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( ~ there_exists(domain(X))
| ( domain(X) != codomain(Y) )
| there_exists(compose(X,Y)) )
<=> ( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| ( domain(X) != codomain(Y) )
| there_exists(compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| ( domain(X) != codomain(Y) )
| there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_codomain_composition2) ).
tff(105,plain,
! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) )
| ~ there_exists(domain(a))
| there_exists(compose(a,compose(b,c)))
| ( domain(a) != codomain(compose(b,c)) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) )
| ~ there_exists(domain(a))
| there_exists(compose(a,compose(b,c)))
| ( domain(a) != codomain(compose(b,c)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) )
| ~ there_exists(domain(a))
| there_exists(compose(a,compose(b,c)))
| ( domain(a) != codomain(compose(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ( domain(X) != codomain(Y) ) )
| ~ there_exists(domain(a))
| there_exists(compose(a,compose(b,c)))
| ( domain(a) != codomain(compose(b,c)) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
domain(a) != codomain(compose(b,c)),
inference(unit_resolution,[status(thm)],[111,108,98,95]) ).
tff(113,plain,
domain(codomain(b)) != codomain(compose(b,c)),
inference(modus_ponens,[status(thm)],[112,81]) ).
tff(114,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(b),compose(b,c)))
| ( domain(codomain(b)) = codomain(compose(b,c)) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(b),compose(b,c)))
| ( domain(codomain(b)) = codomain(compose(b,c)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(b),compose(b,c)))
| ( domain(codomain(b)) = codomain(compose(b,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(b),compose(b,c)))
| ( domain(codomain(b)) = codomain(compose(b,c)) ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
( ~ there_exists(compose(codomain(b),compose(b,c)))
| ( domain(codomain(b)) = codomain(compose(b,c)) ) ),
inference(unit_resolution,[status(thm)],[116,36]) ).
tff(118,plain,
$false,
inference(unit_resolution,[status(thm)],[117,113,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : CAT018-3 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 06:27:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------