TSTP Solution File: CAT011-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT011-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 17:29:44 EDT 2022
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 32
% Syntax : Number of formulae : 80 ( 32 unt; 5 typ; 0 def)
% Number of atoms : 174 ( 79 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 167 ( 73 ~; 66 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 5 ( 5 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 92 ( 84 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(codomain_type,type,
codomain: $i > $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(a_type,type,
a: $i ).
tff(there_exists_type,type,
there_exists: $i > $o ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(1,plain,
( ( domain(a) = domain(domain(a)) )
<=> ( domain(domain(a)) = domain(a) ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
^ [X: $i] :
refl(
( ( compose(X,domain(X)) = X )
<=> ( compose(X,domain(X)) = X ) )),
inference(bind,[status(th)],]) ).
tff(3,plain,
( ! [X: $i] : ( compose(X,domain(X)) = X )
<=> ! [X: $i] : ( compose(X,domain(X)) = X ) ),
inference(quant_intro,[status(thm)],[2]) ).
tff(4,plain,
( ! [X: $i] : ( compose(X,domain(X)) = X )
<=> ! [X: $i] : ( compose(X,domain(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
! [X: $i] : ( compose(X,domain(X)) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',compose_domain) ).
tff(6,plain,
! [X: $i] : ( compose(X,domain(X)) = X ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
! [X: $i] : ( compose(X,domain(X)) = X ),
inference(skolemize,[status(sab)],[6]) ).
tff(8,plain,
! [X: $i] : ( compose(X,domain(X)) = X ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
( ~ ! [X: $i] : ( compose(X,domain(X)) = X )
| ( compose(domain(a),domain(domain(a))) = domain(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(10,plain,
compose(domain(a),domain(domain(a))) = domain(a),
inference(unit_resolution,[status(thm)],[9,8]) ).
tff(11,plain,
( there_exists(compose(domain(a),domain(domain(a))))
<=> there_exists(domain(a)) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( there_exists(domain(a))
<=> there_exists(compose(domain(a),domain(domain(a)))) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( there_exists(domain(a))
<=> there_exists(domain(a)) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
there_exists(domain(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_domain_exists) ).
tff(15,plain,
there_exists(domain(a)),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
there_exists(compose(domain(a),domain(domain(a)))),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,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(18,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)],[17]) ).
tff(19,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(20,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(21,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(domain(a),domain(domain(a))))
| ( domain(domain(a)) = codomain(domain(domain(a))) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(domain(a),domain(domain(a))))
| ( domain(domain(a)) = codomain(domain(domain(a))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(domain(a),domain(domain(a))))
| ( domain(domain(a)) = codomain(domain(domain(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(domain(a),domain(domain(a))))
| ( domain(domain(a)) = codomain(domain(domain(a))) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
( ~ there_exists(compose(domain(a),domain(domain(a))))
| ( domain(domain(a)) = codomain(domain(domain(a))) ) ),
inference(unit_resolution,[status(thm)],[26,23]) ).
tff(28,plain,
domain(domain(a)) = codomain(domain(domain(a))),
inference(unit_resolution,[status(thm)],[27,16]) ).
tff(29,plain,
codomain(domain(domain(a))) = domain(domain(a)),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ( domain(a) = codomain(domain(domain(a))) )
<=> ( domain(a) = domain(domain(a)) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( domain(a) = codomain(domain(domain(a))) )
<=> ( domain(domain(a)) = domain(a) ) ),
inference(transitivity,[status(thm)],[30,1]) ).
tff(32,plain,
( ( domain(domain(a)) = domain(a) )
<=> ( domain(a) = codomain(domain(domain(a))) ) ),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ( domain(domain(a)) != domain(a) )
<=> ( domain(a) != codomain(domain(domain(a))) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( domain(domain(a)) != domain(a) )
<=> ( domain(domain(a)) != domain(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
domain(domain(a)) != domain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_is_idempotent) ).
tff(36,plain,
domain(domain(a)) != domain(a),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
domain(a) != codomain(domain(domain(a))),
inference(modus_ponens,[status(thm)],[36,33]) ).
tff(38,plain,
( ~ ! [X: $i] : ( compose(X,domain(X)) = X )
| ( compose(a,domain(a)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
compose(a,domain(a)) = a,
inference(unit_resolution,[status(thm)],[38,8]) ).
tff(40,plain,
compose(a,compose(domain(a),domain(domain(a)))) = compose(a,domain(a)),
inference(monotonicity,[status(thm)],[10]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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(45,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( compose(a,compose(domain(a),domain(domain(a)))) = compose(compose(a,domain(a)),domain(domain(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
compose(a,compose(domain(a),domain(domain(a)))) = compose(compose(a,domain(a)),domain(domain(a))),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
compose(compose(a,domain(a)),domain(domain(a))) = compose(a,compose(domain(a),domain(domain(a)))),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
a = compose(a,domain(a)),
inference(symmetry,[status(thm)],[39]) ).
tff(52,plain,
compose(a,domain(domain(a))) = compose(compose(a,domain(a)),domain(domain(a))),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
compose(a,domain(domain(a))) = a,
inference(transitivity,[status(thm)],[52,50,40,39]) ).
tff(54,plain,
( there_exists(compose(a,domain(domain(a))))
<=> there_exists(a) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( there_exists(a)
<=> there_exists(compose(a,domain(domain(a)))) ),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
^ [X: $i] :
refl(
( ( there_exists(X)
| ~ there_exists(domain(X)) )
<=> ( there_exists(X)
| ~ there_exists(domain(X)) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
^ [X: $i] :
rewrite(
( ( ~ there_exists(domain(X))
| there_exists(X) )
<=> ( there_exists(X)
| ~ there_exists(domain(X)) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [X: $i] :
( ~ there_exists(domain(X))
| there_exists(X) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [X: $i] :
( ~ there_exists(domain(X))
| there_exists(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_has_elements) ).
tff(62,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
| there_exists(a)
| ~ there_exists(domain(a)) )
<=> ( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
| there_exists(a)
| ~ there_exists(domain(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
| there_exists(a)
| ~ there_exists(domain(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
| there_exists(a)
| ~ there_exists(domain(a)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
there_exists(a),
inference(unit_resolution,[status(thm)],[68,65,15]) ).
tff(70,plain,
there_exists(compose(a,domain(domain(a)))),
inference(modus_ponens,[status(thm)],[69,55]) ).
tff(71,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(a,domain(domain(a))))
| ( domain(a) = codomain(domain(domain(a))) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(a,domain(domain(a))))
| ( domain(a) = codomain(domain(domain(a))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(a,domain(domain(a))))
| ( domain(a) = codomain(domain(domain(a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(a,domain(domain(a))))
| ( domain(a) = codomain(domain(domain(a))) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ there_exists(compose(a,domain(domain(a))))
| ( domain(a) = codomain(domain(domain(a))) ) ),
inference(unit_resolution,[status(thm)],[73,23]) ).
tff(75,plain,
$false,
inference(unit_resolution,[status(thm)],[74,70,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : CAT011-3 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n020.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 : Tue Aug 30 06:16:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------