TSTP Solution File: GRA029^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRA029^2 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 : Thu Aug 31 00:00:38 EDT 2023
% Result : Unknown 65.64s 65.95s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA029^2 : TPTP v8.1.2. Released v3.6.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 03:22:56 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : GRA029^2 : TPTP v8.1.2. Released v3.6.0.
% 0.21/0.50 % Domain : Graph Theory
% 0.21/0.50 % Problem : R(4,4) > 16
% 0.21/0.50 % Version : Especial.
% 0.21/0.50 % English :
% 0.21/0.50
% 0.21/0.50 % Refs : [Rad06] Radziszowski (2006), Small Ramsey Numbers
% 0.21/0.50 % : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.50 % Source : [Bro08]
% 0.21/0.50 % Names :
% 0.21/0.50
% 0.21/0.50 % Status : Theorem
% 0.21/0.50 % Rating : 1.00 v3.7.0
% 0.21/0.50 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.21/0.50 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 0 ( 0 avg)
% 0.21/0.50 % Number of connectives : 113 ( 24 ~; 10 |; 24 &; 52 @)
% 0.21/0.50 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 25 ( 25 avg)
% 0.21/0.50 % Number of types : 1 ( 0 usr)
% 0.21/0.50 % Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.21/0.50 % Number of variables : 17 ( 0 ^; 16 !; 1 ?; 17 :)
% 0.21/0.50 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.50
% 0.21/0.50 % Comments : If a type alpha has exactly n elements, then we can prove
% 0.21/0.50 % R(k,l) > n by finding a graph (symmetric binary relation) on type
% 0.21/0.50 % alpha with no k-cliques and no l-independent sets. Likewise, we
% 0.21/0.50 % can prove R(k,l) <= n by proving every graph (symmetric binary
% 0.21/0.50 % relation) on alpha must have a k-clique or l-independent set.
% 0.21/0.50 % There is one type with 4 elements: o > o. There are two types
% 0.21/0.50 % with 16 elements: o > o > o and (o > o) > o. There are two types
% 0.21/0.50 % with 256 elements: o > o > o > o and o > (o > o) > o. This means
% 0.21/0.50 % we always have two formulations of R(k,l) >/<= 16 and two
% 0.21/0.50 % formulations of R(k,l) >/<= 256.
% 0.21/0.50 % :
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(ramsey_l_4_4_16a,conjecture,
% 0.21/0.50 ? [G: ( ( $o > $o ) > $o ) > ( ( $o > $o ) > $o ) > $o] :
% 0.21/0.50 ( ! [Xx: ( $o > $o ) > $o,Xy: ( $o > $o ) > $o] :
% 0.21/0.50 ( ( G @ Xx @ Xy )
% 0.21/0.50 => ( G @ Xy @ Xx ) )
% 0.21/0.50 & ! [Xx0: ( $o > $o ) > $o,Xx1: ( $o > $o ) > $o,Xx2: ( $o > $o ) > $o,Xx3: ( $o > $o ) > $o,Xp0: ( ( $o > $o ) > $o ) > $o,Xp1: ( ( $o > $o ) > $o ) > $o,Xp2: ( ( $o > $o ) > $o ) > $o] :
% 0.21/0.50 ( ( ( Xp0 @ Xx0 )
% 0.21/0.50 & ~ ( Xp0 @ Xx1 )
% 0.21/0.50 & ~ ( Xp0 @ Xx2 )
% 0.21/0.50 & ~ ( Xp0 @ Xx3 )
% 0.21/0.50 & ~ ( Xp1 @ Xx0 )
% 0.21/0.50 & ( Xp1 @ Xx1 )
% 0.21/0.50 & ~ ( Xp1 @ Xx2 )
% 0.21/0.50 & ~ ( Xp1 @ Xx3 )
% 0.21/0.50 & ~ ( Xp2 @ Xx0 )
% 0.21/0.50 & ~ ( Xp2 @ Xx1 )
% 0.21/0.50 & ( Xp2 @ Xx2 )
% 0.21/0.50 & ~ ( Xp2 @ Xx3 ) )
% 0.21/0.50 => ( ~ ( G @ Xx1 @ Xx0 )
% 0.21/0.50 | ~ ( G @ Xx2 @ Xx0 )
% 0.21/0.50 | ~ ( G @ Xx2 @ Xx1 )
% 0.21/0.50 | ~ ( G @ Xx3 @ Xx0 )
% 0.21/0.50 | ~ ( G @ Xx3 @ Xx1 )
% 0.21/0.50 | ~ ( G @ Xx3 @ Xx2 ) ) )
% 0.21/0.50 & ! [Xx0: ( $o > $o ) > $o,Xx1: ( $o > $o ) > $o,Xx2: ( $o > $o ) > $o,Xx3: ( $o > $o ) > $o,Xp0: ( ( $o > $o ) > $o ) > $o,Xp1: ( ( $o > $o ) > $o ) > $o,Xp2: ( ( $o > $o ) > $o ) > $o] :
% 0.21/0.50 ( ( ( Xp0 @ Xx0 )
% 0.21/0.50 & ~ ( Xp0 @ Xx1 )
% 0.21/0.50 & ~ ( Xp0 @ Xx2 )
% 0.21/0.50 & ~ ( Xp0 @ Xx3 )
% 0.21/0.50 & ~ ( Xp1 @ Xx0 )
% 0.21/0.50 & ( Xp1 @ Xx1 )
% 0.21/0.50 & ~ ( Xp1 @ Xx2 )
% 0.21/0.50 & ~ ( Xp1 @ Xx3 )
% 0.21/0.50 & ~ ( Xp2 @ Xx0 )
% 0.21/0.50 & ~ ( Xp2 @ Xx1 )
% 0.21/0.50 & ( Xp2 @ Xx2 )
% 0.21/0.50 & ~ ( Xp2 @ Xx3 ) )
% 0.21/0.50 => ( ( G @ Xx1 @ Xx0 )
% 0.21/0.50 | ( G @ Xx2 @ Xx0 )
% 0.21/0.50 | ( G @ Xx2 @ Xx1 )
% 0.21/0.50 | ( G @ Xx3 @ Xx0 )
% 0.21/0.50 | ( G @ Xx3 @ Xx1 )
% 0.21/0.50 | ( G @ Xx3 @ Xx2 ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.OAX3OBSh3z/cvc5---1.0.5_21488.p...
% 0.21/0.50 (declare-sort $$unsorted 0)
% 0.21/0.50 (assert (not (exists ((G (-> (-> (-> Bool Bool) Bool) (-> (-> Bool Bool) Bool) Bool))) (and (forall ((Xx (-> (-> Bool Bool) Bool)) (Xy (-> (-> Bool Bool) Bool))) (=> (@ (@ G Xx) Xy) (@ (@ G Xy) Xx))) (forall ((Xx0 (-> (-> Bool Bool) Bool)) (Xx1 (-> (-> Bool Bool) Bool)) (Xx2 (-> (-> Bool Bool) Bool)) (Xx3 (-> (-> Bool Bool) Bool)) (Xp0 (-> (-> (-> Bool Bool) Bool) Bool)) (Xp1 (-> (-> (-> Bool Bool) Bool) Bool)) (Xp2 (-> (-> (-> Bool Bool) Bool) Bool))) (let ((_let_1 (@ G Xx3))) (let ((_let_2 (@ G Xx2))) (=> (and (@ Xp0 Xx0) (not (@ Xp0 Xx1)) (not (@ Xp0 Xx2)) (not (@ Xp0 Xx3)) (not (@ Xp1 Xx0)) (@ Xp1 Xx1) (not (@ Xp1 Xx2)) (not (@ Xp1 Xx3)) (not (@ Xp2 Xx0)) (not (@ Xp2 Xx1)) (@ Xp2 Xx2) (not (@ Xp2 Xx3))) (or (not (@ (@ G Xx1) Xx0)) (not (@ _let_2 Xx0)) (not (@ _let_2 Xx1)) (not (@ _let_1 Xx0)) (not (@ _let_1 Xx1)) (not (@ _let_1 Xx2))))))) (forall ((Xx0 (-> (-> Bool Bool) Bool)) (Xx1 (-> (-> Bool Bool) Bool)) (Xx2 (-> (-> Bool Bool) Bool)) (Xx3 (-> (-> Bool Bool) Bool)) (Xp0 (-> (-> (-> Bool Bool) Bool) Bool)) (Xp1 (-> (-> (-> Bool Bool) Bool) Bool)) (Xp2 (-> (-> (-> Bool Bool) Bool) Bool))) (let ((_let_1 (@ G Xx3))) (let ((_let_2 (@ G Xx2))) (=> (and (@ Xp0 Xx0) (not (@ Xp0 Xx1)) (not (@ Xp0 Xx2)) (not (@ Xp0 Xx3)) (not (@ Xp1 Xx0)) (@ Xp1 Xx1) (not (@ Xp1 Xx2)) (not (@ Xp1 Xx3)) (not (@ Xp2 Xx0)) (not (@ Xp2 Xx1)) (@ Xp2 Xx2) (not (@ Xp2 Xx3))) (or (@ (@ G Xx1) Xx0) (@ _let_2 Xx0) (@ _let_2 Xx1) (@ _let_1 Xx0) (@ _let_1 Xx1) (@ _let_1 Xx2))))))))))
% 65.64/65.94 (set-info :filename cvc5---1.0.5_21488)
% 65.64/65.94 (check-sat-assuming ( true ))
% 65.64/65.94 ------- get file name : TPTP file name is GRA029^2
% 65.64/65.94 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21488.smt2...
% 65.64/65.94 --- Run --ho-elim --full-saturate-quant at 10...
% 65.64/65.94 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 65.64/65.94 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 65.64/65.94 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 65.64/65.94 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 65.64/65.94 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 65.64/65.94 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 65.64/65.94 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 65.64/65.94 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 65.64/65.94 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 65.64/65.94 % cvc5---1.0.5 exiting
% 65.64/65.95 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------