TSTP Solution File: CAT010-10 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 17:29:43 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 45
% Syntax : Number of formulae : 108 ( 71 unt; 9 typ; 0 def)
% Number of atoms : 147 ( 136 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 52 ( 14 ~; 10 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 13 ( 6 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 178 ( 158 !; 0 ?; 178 :)
% Comments :
%------------------------------------------------------------------------------
tff(codomain_type,type,
codomain: $i > $i ).
tff(a_type,type,
a: $i ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(ifeq2_type,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(there_exists_type,type,
there_exists: $i > $i ).
tff(true_type,type,
true: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) )
<=> ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) )
<=> ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) )
<=> ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) )
<=> ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) )
<=> ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
tff(7,plain,
! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) )
| ( ifeq2(there_exists(compose(codomain(a),a)),there_exists(compose(a,b)),domain(codomain(a)),codomain(a)) = codomain(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
ifeq2(there_exists(compose(codomain(a),a)),there_exists(compose(a,b)),domain(codomain(a)),codomain(a)) = codomain(a),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X: $i] :
refl(
( ( ifeq(there_exists(domain(X)),there_exists(compose(a,b)),there_exists(X),there_exists(compose(a,b))) = there_exists(compose(a,b)) )
<=> ( ifeq(there_exists(domain(X)),there_exists(compose(a,b)),there_exists(X),there_exists(compose(a,b))) = there_exists(compose(a,b)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] : ( ifeq(there_exists(domain(X)),there_exists(compose(a,b)),there_exists(X),there_exists(compose(a,b))) = there_exists(compose(a,b)) )
<=> ! [X: $i] : ( ifeq(there_exists(domain(X)),there_exists(compose(a,b)),there_exists(X),there_exists(compose(a,b))) = there_exists(compose(a,b)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [X: $i] :
rewrite(
( ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true )
<=> ( ifeq(there_exists(domain(X)),there_exists(compose(a,b)),there_exists(X),there_exists(compose(a,b))) = there_exists(compose(a,b)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true )
<=> ! [X: $i] : ( ifeq(there_exists(domain(X)),there_exists(compose(a,b)),there_exists(X),there_exists(compose(a,b))) = there_exists(compose(a,b)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true )
<=> ! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
tff(19,plain,
! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i] : ( ifeq(there_exists(domain(X)),there_exists(compose(a,b)),there_exists(X),there_exists(compose(a,b))) = there_exists(compose(a,b)) ),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
! [X: $i] : ( ifeq(there_exists(domain(X)),there_exists(compose(a,b)),there_exists(X),there_exists(compose(a,b))) = there_exists(compose(a,b)) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X: $i] : ( ifeq(there_exists(domain(X)),there_exists(compose(a,b)),there_exists(X),there_exists(compose(a,b))) = there_exists(compose(a,b)) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ~ ! [X: $i] : ( ifeq(there_exists(domain(X)),there_exists(compose(a,b)),there_exists(X),there_exists(compose(a,b))) = there_exists(compose(a,b)) )
| ( ifeq(there_exists(domain(a)),there_exists(compose(a,b)),there_exists(a),there_exists(compose(a,b))) = there_exists(compose(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
ifeq(there_exists(domain(a)),there_exists(compose(a,b)),there_exists(a),there_exists(compose(a,b))) = there_exists(compose(a,b)),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(there_exists(compose(a,b)),there_exists(compose(a,b)),there_exists(domain(a)),there_exists(compose(a,b))) = there_exists(domain(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
ifeq(there_exists(compose(a,b)),there_exists(compose(a,b)),there_exists(domain(a)),there_exists(compose(a,b))) = there_exists(domain(a)),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
^ [Y: $i,X: $i] :
refl(
( ( ifeq(there_exists(compose(X,Y)),there_exists(compose(a,b)),there_exists(domain(X)),there_exists(compose(a,b))) = there_exists(compose(a,b)) )
<=> ( ifeq(there_exists(compose(X,Y)),there_exists(compose(a,b)),there_exists(domain(X)),there_exists(compose(a,b))) = there_exists(compose(a,b)) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),there_exists(compose(a,b)),there_exists(domain(X)),there_exists(compose(a,b))) = there_exists(compose(a,b)) )
<=> ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),there_exists(compose(a,b)),there_exists(domain(X)),there_exists(compose(a,b))) = there_exists(compose(a,b)) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true )
<=> ( ifeq(there_exists(compose(X,Y)),there_exists(compose(a,b)),there_exists(domain(X)),there_exists(compose(a,b))) = there_exists(compose(a,b)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true )
<=> ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),there_exists(compose(a,b)),there_exists(domain(X)),there_exists(compose(a,b))) = there_exists(compose(a,b)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true )
<=> ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
tff(40,plain,
! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),there_exists(compose(a,b)),there_exists(domain(X)),there_exists(compose(a,b))) = there_exists(compose(a,b)) ),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),there_exists(compose(a,b)),there_exists(domain(X)),there_exists(compose(a,b))) = there_exists(compose(a,b)) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),there_exists(compose(a,b)),there_exists(domain(X)),there_exists(compose(a,b))) = there_exists(compose(a,b)) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),there_exists(compose(a,b)),there_exists(domain(X)),there_exists(compose(a,b))) = there_exists(compose(a,b)) )
| ( ifeq(there_exists(compose(a,b)),there_exists(compose(a,b)),there_exists(domain(a)),there_exists(compose(a,b))) = there_exists(compose(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
ifeq(there_exists(compose(a,b)),there_exists(compose(a,b)),there_exists(domain(a)),there_exists(compose(a,b))) = there_exists(compose(a,b)),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
there_exists(compose(a,b)) = ifeq(there_exists(compose(a,b)),there_exists(compose(a,b)),there_exists(domain(a)),there_exists(compose(a,b))),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
there_exists(compose(a,b)) = there_exists(domain(a)),
inference(transitivity,[status(thm)],[46,33]) ).
tff(48,plain,
ifeq(there_exists(compose(a,b)),there_exists(compose(a,b)),there_exists(a),there_exists(compose(a,b))) = ifeq(there_exists(domain(a)),there_exists(compose(a,b)),there_exists(a),there_exists(compose(a,b))),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(there_exists(compose(a,b)),there_exists(compose(a,b)),there_exists(a),there_exists(compose(a,b))) = there_exists(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
ifeq(there_exists(compose(a,b)),there_exists(compose(a,b)),there_exists(a),there_exists(compose(a,b))) = there_exists(a),
inference(unit_resolution,[status(thm)],[49,31]) ).
tff(51,plain,
there_exists(a) = ifeq(there_exists(compose(a,b)),there_exists(compose(a,b)),there_exists(a),there_exists(compose(a,b))),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
^ [X: $i] :
refl(
( ( compose(codomain(X),X) = X )
<=> ( compose(codomain(X),X) = X ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [X: $i] : ( compose(codomain(X),X) = X )
<=> ! [X: $i] : ( compose(codomain(X),X) = X ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [X: $i] : ( compose(codomain(X),X) = X )
<=> ! [X: $i] : ( compose(codomain(X),X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
! [X: $i] : ( compose(codomain(X),X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
tff(56,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [X: $i] : ( compose(codomain(X),X) = X )
| ( compose(codomain(a),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
compose(codomain(a),a) = a,
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
there_exists(compose(codomain(a),a)) = there_exists(a),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
there_exists(compose(codomain(a),a)) = there_exists(compose(a,b)),
inference(transitivity,[status(thm)],[61,51,48,24]) ).
tff(63,plain,
ifeq2(there_exists(compose(codomain(a),a)),there_exists(compose(a,b)),domain(codomain(a)),codomain(a)) = ifeq2(there_exists(compose(a,b)),there_exists(compose(a,b)),domain(codomain(a)),codomain(a)),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
ifeq2(there_exists(compose(a,b)),there_exists(compose(a,b)),domain(codomain(a)),codomain(a)) = ifeq2(there_exists(compose(codomain(a),a)),there_exists(compose(a,b)),domain(codomain(a)),codomain(a)),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq2(A,A,B,C) = B )
<=> ( ifeq2(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
tff(69,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(there_exists(compose(a,b)),there_exists(compose(a,b)),domain(codomain(a)),codomain(a)) = domain(codomain(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
ifeq2(there_exists(compose(a,b)),there_exists(compose(a,b)),domain(codomain(a)),codomain(a)) = domain(codomain(a)),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
domain(codomain(a)) = ifeq2(there_exists(compose(a,b)),there_exists(compose(a,b)),domain(codomain(a)),codomain(a)),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(there_exists(compose(a,b)),there_exists(compose(a,b)),domain(codomain(a)),codomain(compose(a,b))) = domain(codomain(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
ifeq2(there_exists(compose(a,b)),there_exists(compose(a,b)),domain(codomain(a)),codomain(compose(a,b))) = domain(codomain(a)),
inference(unit_resolution,[status(thm)],[75,71]) ).
tff(77,plain,
compose(compose(codomain(a),a),b) = compose(a,b),
inference(monotonicity,[status(thm)],[60]) ).
tff(78,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(79,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)],[78]) ).
tff(80,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(81,axiom,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
tff(82,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( compose(codomain(a),compose(a,b)) = compose(compose(codomain(a),a),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
compose(codomain(a),compose(a,b)) = compose(compose(codomain(a),a),b),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
compose(codomain(a),compose(a,b)) = compose(a,b),
inference(transitivity,[status(thm)],[86,77]) ).
tff(88,plain,
there_exists(compose(codomain(a),compose(a,b))) = there_exists(compose(a,b)),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
there_exists(compose(a,b)) = there_exists(compose(codomain(a),compose(a,b))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
ifeq2(there_exists(compose(a,b)),there_exists(compose(a,b)),domain(codomain(a)),codomain(compose(a,b))) = ifeq2(there_exists(compose(codomain(a),compose(a,b))),there_exists(compose(a,b)),domain(codomain(a)),codomain(compose(a,b))),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
ifeq2(there_exists(compose(codomain(a),compose(a,b))),there_exists(compose(a,b)),domain(codomain(a)),codomain(compose(a,b))) = ifeq2(there_exists(compose(a,b)),there_exists(compose(a,b)),domain(codomain(a)),codomain(compose(a,b))),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),there_exists(compose(a,b)),domain(X),codomain(Y)) = codomain(Y) )
| ( ifeq2(there_exists(compose(codomain(a),compose(a,b))),there_exists(compose(a,b)),domain(codomain(a)),codomain(compose(a,b))) = codomain(compose(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
ifeq2(there_exists(compose(codomain(a),compose(a,b))),there_exists(compose(a,b)),domain(codomain(a)),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(unit_resolution,[status(thm)],[92,10]) ).
tff(94,plain,
codomain(compose(a,b)) = ifeq2(there_exists(compose(codomain(a),compose(a,b))),there_exists(compose(a,b)),domain(codomain(a)),codomain(compose(a,b))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
codomain(compose(a,b)) = codomain(a),
inference(transitivity,[status(thm)],[94,91,76,74,64,12]) ).
tff(96,plain,
( ( codomain(compose(a,b)) != codomain(a) )
<=> ( codomain(compose(a,b)) != codomain(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,axiom,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
tff(98,plain,
codomain(compose(a,b)) != codomain(a),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
$false,
inference(unit_resolution,[status(thm)],[98,95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : CAT010-10 : TPTP v8.1.0. Released v7.3.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 06:32:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------