TSTP Solution File: CAT006-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 17:29:40 EDT 2022
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 49
% Syntax : Number of formulae : 102 ( 31 unt; 6 typ; 0 def)
% Number of atoms : 500 ( 37 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 710 ( 334 ~; 324 |; 0 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 272 ( 246 !; 0 ?; 272 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(h_type,type,
h: $i ).
tff(codomain_type,type,
codomain: $i > $i ).
tff(a_type,type,
a: $i ).
tff(defined_type,type,
defined: ( $i * $i ) > $o ).
tff(identity_map_type,type,
identity_map: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(
( defined(codomain(X),X)
<=> defined(codomain(X),X) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : defined(codomain(X),X)
<=> ! [X: $i] : defined(codomain(X),X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : defined(codomain(X),X)
<=> ! [X: $i] : defined(codomain(X),X) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : defined(codomain(X),X),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_codomain_of_x_to_x) ).
tff(5,plain,
! [X: $i] : defined(codomain(X),X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : defined(codomain(X),X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : defined(codomain(X),X),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : defined(codomain(X),X)
| defined(codomain(a),a) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
defined(codomain(a),a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( identity_map(h)
<=> identity_map(h) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
identity_map(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_is_the_identity_map) ).
tff(12,plain,
identity_map(h),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( defined(h,a)
<=> defined(h,a) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
defined(h,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ha_defined) ).
tff(15,plain,
defined(h,a),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
<=> ( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ defined(X,Y)
| ~ identity_map(X) )
<=> ( ~ defined(X,Y)
| ~ identity_map(X) ) )),
( ( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) )
<=> ( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) ) )),
rewrite(
( ( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) )
<=> ( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) )),
( ( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) )
<=> ( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).
tff(22,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(h,a)
| product(h,a,a)
| ~ identity_map(h) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(h,a)
| product(h,a,a)
| ~ identity_map(h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(h,a)
| product(h,a,a)
| ~ identity_map(h) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(h,a)
| product(h,a,a)
| ~ identity_map(h) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
product(h,a,a),
inference(unit_resolution,[status(thm)],[28,25,15,12]) ).
tff(30,plain,
^ [Z: $i,Y: $i,X: $i,Yz: $i] :
refl(
( ( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
<=> ( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
<=> ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
<=> ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [Z: $i,Y: $i,X: $i,Yz: $i] :
trans(
monotonicity(
rewrite(
( ( ~ product(Y,Z,Yz)
| ~ defined(X,Yz) )
<=> ( ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ) )),
( ( ~ product(Y,Z,Yz)
| ~ defined(X,Yz)
| defined(X,Y) )
<=> ( ~ defined(X,Yz)
| ~ product(Y,Z,Yz)
| defined(X,Y) ) )),
rewrite(
( ( ~ defined(X,Yz)
| ~ product(Y,Z,Yz)
| defined(X,Y) )
<=> ( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) ) )),
( ( ~ product(Y,Z,Yz)
| ~ defined(X,Yz)
| defined(X,Y) )
<=> ( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ product(Y,Z,Yz)
| ~ defined(X,Yz)
| defined(X,Y) )
<=> ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ product(Y,Z,Yz)
| ~ defined(X,Yz)
| defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
| ~ product(h,a,a)
| ~ defined(codomain(a),a)
| defined(codomain(a),h) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
| ~ product(h,a,a)
| ~ defined(codomain(a),a)
| defined(codomain(a),h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ defined(codomain(a),a)
| defined(codomain(a),h)
| ~ product(h,a,a) )
<=> ( ~ product(h,a,a)
| ~ defined(codomain(a),a)
| defined(codomain(a),h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
| ~ defined(codomain(a),a)
| defined(codomain(a),h)
| ~ product(h,a,a) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
| ~ product(h,a,a)
| ~ defined(codomain(a),a)
| defined(codomain(a),h) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
| ~ defined(codomain(a),a)
| defined(codomain(a),h)
| ~ product(h,a,a) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
| ~ product(h,a,a)
| ~ defined(codomain(a),a)
| defined(codomain(a),h) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
| ~ defined(codomain(a),a)
| defined(codomain(a),h)
| ~ product(h,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(X,Y)
| ~ product(Y,Z,Yz) )
| ~ product(h,a,a)
| ~ defined(codomain(a),a)
| defined(codomain(a),h) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
defined(codomain(a),h),
inference(unit_resolution,[status(thm)],[45,39,29,9]) ).
tff(47,plain,
^ [X: $i] :
refl(
( identity_map(codomain(X))
<=> identity_map(codomain(X)) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [X: $i] : identity_map(codomain(X))
<=> ! [X: $i] : identity_map(codomain(X)) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X: $i] : identity_map(codomain(X))
<=> ! [X: $i] : identity_map(codomain(X)) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
! [X: $i] : identity_map(codomain(X)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).
tff(51,plain,
! [X: $i] : identity_map(codomain(X)),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X: $i] : identity_map(codomain(X)),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X: $i] : identity_map(codomain(X)),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [X: $i] : identity_map(codomain(X))
| identity_map(codomain(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
identity_map(codomain(a)),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(codomain(a),h)
| product(codomain(a),h,h)
| ~ identity_map(codomain(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(codomain(a),h)
| product(codomain(a),h,h)
| ~ identity_map(codomain(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(codomain(a),h)
| product(codomain(a),h,h)
| ~ identity_map(codomain(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(codomain(a),h)
| product(codomain(a),h,h)
| ~ identity_map(codomain(a)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
product(codomain(a),h,h),
inference(unit_resolution,[status(thm)],[58,25,55,46]) ).
tff(60,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ defined(X,Y)
| ~ identity_map(Y) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y) ) )),
( ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) )),
rewrite(
( ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) )),
( ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2) ).
tff(66,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(h)
| ~ defined(codomain(a),h)
| product(codomain(a),h,codomain(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(h)
| ~ defined(codomain(a),h)
| product(codomain(a),h,codomain(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ~ defined(codomain(a),h)
| ~ identity_map(h)
| product(codomain(a),h,codomain(a)) )
<=> ( ~ identity_map(h)
| ~ defined(codomain(a),h)
| product(codomain(a),h,codomain(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ defined(codomain(a),h)
| ~ identity_map(h)
| product(codomain(a),h,codomain(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(h)
| ~ defined(codomain(a),h)
| product(codomain(a),h,codomain(a)) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ defined(codomain(a),h)
| ~ identity_map(h)
| product(codomain(a),h,codomain(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(h)
| ~ defined(codomain(a),h)
| product(codomain(a),h,codomain(a)) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ defined(codomain(a),h)
| ~ identity_map(h)
| product(codomain(a),h,codomain(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(h)
| ~ defined(codomain(a),h)
| product(codomain(a),h,codomain(a)) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
product(codomain(a),h,codomain(a)),
inference(unit_resolution,[status(thm)],[75,69,12,46]) ).
tff(77,plain,
( ( codomain(a) != h )
<=> ( codomain(a) != h ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
codomain(a) != h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_a_is_h) ).
tff(79,plain,
codomain(a) != h,
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(
( ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ) )),
inference(bind,[status(th)],]) ).
tff(81,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
tff(86,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
inference(modus_ponens,[status(thm)],[88,81]) ).
tff(90,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ( codomain(a) = h )
| ~ product(codomain(a),h,codomain(a))
| ~ product(codomain(a),h,h) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ( codomain(a) = h )
| ~ product(codomain(a),h,codomain(a))
| ~ product(codomain(a),h,h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( ~ product(codomain(a),h,codomain(a))
| ~ product(codomain(a),h,h)
| ( codomain(a) = h ) )
<=> ( ( codomain(a) = h )
| ~ product(codomain(a),h,codomain(a))
| ~ product(codomain(a),h,h) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(codomain(a),h,codomain(a))
| ~ product(codomain(a),h,h)
| ( codomain(a) = h ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ( codomain(a) = h )
| ~ product(codomain(a),h,codomain(a))
| ~ product(codomain(a),h,h) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(codomain(a),h,codomain(a))
| ~ product(codomain(a),h,h)
| ( codomain(a) = h ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ( codomain(a) = h )
| ~ product(codomain(a),h,codomain(a))
| ~ product(codomain(a),h,h) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(codomain(a),h,codomain(a))
| ~ product(codomain(a),h,h)
| ( codomain(a) = h ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ( codomain(a) = h )
| ~ product(codomain(a),h,codomain(a))
| ~ product(codomain(a),h,h) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
$false,
inference(unit_resolution,[status(thm)],[95,89,79,76,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n018.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 06:03:40 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------