TSTP Solution File: PUZ107^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : PUZ107^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 13:13:23 EDT 2023
% Result : Theorem 0.21s 0.52s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : PUZ107^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n022.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 : Sat Aug 26 22:39:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : PUZ107^5 : TPTP v8.1.2. Bugfixed v6.2.0.
% 0.21/0.50 % Domain : Puzzles
% 0.21/0.50 % Problem : TPS problem from CHECKERBOARD-THMS
% 0.21/0.50 % Version : Especial.
% 0.21/0.50 % English :
% 0.21/0.50
% 0.21/0.50 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.50 % Source : [Bro09]
% 0.21/0.50 % Names : tps_0672 [Bro09]
% 0.21/0.50
% 0.21/0.50 % Status : Theorem
% 0.21/0.50 % Rating : 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0
% 0.21/0.50 % Syntax : Number of formulae : 10 ( 4 unt; 5 typ; 4 def)
% 0.21/0.50 % Number of atoms : 18 ( 10 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 3 ( 3 avg)
% 0.21/0.50 % Number of connectives : 37 ( 2 ~; 0 |; 8 &; 25 @)
% 0.21/0.50 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 5 ( 2 avg)
% 0.21/0.50 % Number of types : 2 ( 0 usr)
% 0.21/0.50 % Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 6 ( 5 usr; 1 con; 0-4 aty)
% 0.21/0.50 % Number of variables : 22 ( 9 ^; 8 !; 5 ?; 22 :)
% 0.21/0.50 % SPC : TH0_THM_EQU_NAR
% 0.21/0.50
% 0.21/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.50 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.21/0.50 % : v6.2.0 - Reordered definitions.
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(c1_type,type,
% 0.21/0.50 c1: $i ).
% 0.21/0.50
% 0.21/0.50 thf(cCKB_FIN_type,type,
% 0.21/0.50 cCKB_FIN: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(cCKB_INF_type,type,
% 0.21/0.50 cCKB_INF: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(cCKB_INJ_type,type,
% 0.21/0.50 cCKB_INJ: ( $i > $i > $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(cCKB_XPL_type,type,
% 0.21/0.50 cCKB_XPL: ( $i > $i > $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(cCKB_INJ_def,definition,
% 0.21/0.50 ( cCKB_INJ
% 0.21/0.50 = ( ^ [Xh: $i > $i > $i > $i > $o] :
% 0.21/0.50 ! [Xx1: $i,Xy1: $i,Xx2: $i,Xy2: $i,Xu: $i,Xv: $i] :
% 0.21/0.50 ( ( ( Xh @ Xx1 @ Xy1 @ Xu @ Xv )
% 0.21/0.50 & ( Xh @ Xx2 @ Xy2 @ Xu @ Xv ) )
% 0.21/0.50 => ( ( Xx1 = Xx2 )
% 0.21/0.50 & ( Xy1 = Xy2 ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(cCKB_XPL_def,definition,
% 0.21/0.50 ( cCKB_XPL
% 0.21/0.50 = ( ^ [Xh: $i > $i > $i > $i > $o,Xk: $i > $i > $o,Xm: $i,Xn: $i] :
% 0.21/0.50 ( ( Xk @ Xm @ Xn )
% 0.21/0.50 & ! [Xx: $i,Xy: $i] :
% 0.21/0.50 ( ( Xk @ Xx @ Xy )
% 0.21/0.50 => ? [Xu: $i,Xv: $i] :
% 0.21/0.50 ( ( Xh @ Xx @ Xy @ Xu @ Xv )
% 0.21/0.50 & ( Xk @ Xu @ Xv )
% 0.21/0.50 & ~ ( ( Xu = Xm )
% 0.21/0.50 & ( Xv = Xn ) ) ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(cCKB_INF_def,definition,
% 0.21/0.50 ( cCKB_INF
% 0.21/0.50 = ( ^ [Xk: $i > $i > $o] :
% 0.21/0.50 ? [Xh: $i > $i > $i > $i > $o,Xm: $i,Xn: $i] :
% 0.21/0.50 ( ( cCKB_INJ @ Xh )
% 0.21/0.50 & ( cCKB_XPL @ Xh @ Xk @ Xm @ Xn ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(cCKB_FIN_def,definition,
% 0.21/0.50 ( cCKB_FIN
% 0.21/0.50 = ( ^ [Xk: $i > $i > $o] :
% 0.21/0.50 ~ ( cCKB_INF @ Xk ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(cL3000,conjecture,
% 0.21/0.50 ( cCKB_FIN
% 0.21/0.50 @ ^ [Xu: $i,Xv: $i] :
% 0.21/0.50 ( ( Xu = c1 )
% 0.21/0.50 & ( Xv = c1 ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.5pnIrRCBSt/cvc5---1.0.5_32069.p...
% 0.21/0.50 (declare-sort $$unsorted 0)
% 0.21/0.50 (declare-fun tptp.c1 () $$unsorted)
% 0.21/0.50 (declare-fun tptp.cCKB_FIN ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.50 (declare-fun tptp.cCKB_INF ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.50 (declare-fun tptp.cCKB_INJ ((-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.50 (declare-fun tptp.cCKB_XPL ((-> $$unsorted $$unsorted $$unsorted $$unsorted Bool) (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.21/0.50 (assert (= tptp.cCKB_INJ (lambda ((Xh (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool))) (forall ((Xx1 $$unsorted) (Xy1 $$unsorted) (Xx2 $$unsorted) (Xy2 $$unsorted) (Xu $$unsorted) (Xv $$unsorted)) (=> (and (@ (@ (@ (@ Xh Xx1) Xy1) Xu) Xv) (@ (@ (@ (@ Xh Xx2) Xy2) Xu) Xv)) (and (= Xx1 Xx2) (= Xy1 Xy2)))))))
% 0.21/0.52 (assert (= tptp.cCKB_XPL (lambda ((Xh (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) (Xk (-> $$unsorted $$unsorted Bool)) (Xm $$unsorted) (Xn $$unsorted)) (and (@ (@ Xk Xm) Xn) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ Xk Xx) Xy) (exists ((Xu $$unsorted) (Xv $$unsorted)) (and (@ (@ (@ (@ Xh Xx) Xy) Xu) Xv) (@ (@ Xk Xu) Xv) (not (and (= Xu Xm) (= Xv Xn)))))))))))
% 0.21/0.52 (assert (= tptp.cCKB_INF (lambda ((Xk (-> $$unsorted $$unsorted Bool))) (exists ((Xh (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) (Xm $$unsorted) (Xn $$unsorted)) (and (@ tptp.cCKB_INJ Xh) (@ (@ (@ (@ tptp.cCKB_XPL Xh) Xk) Xm) Xn))))))
% 0.21/0.52 (assert (= tptp.cCKB_FIN (lambda ((Xk (-> $$unsorted $$unsorted Bool))) (not (@ tptp.cCKB_INF Xk)))))
% 0.21/0.52 (assert (not (@ tptp.cCKB_FIN (lambda ((Xu $$unsorted) (Xv $$unsorted)) (and (= Xu tptp.c1) (= Xv tptp.c1))))))
% 0.21/0.52 (set-info :filename cvc5---1.0.5_32069)
% 0.21/0.52 (check-sat-assuming ( true ))
% 0.21/0.52 ------- get file name : TPTP file name is PUZ107^5
% 0.21/0.52 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32069.smt2...
% 0.21/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.52 % SZS status Theorem for PUZ107^5
% 0.21/0.52 % SZS output start Proof for PUZ107^5
% 0.21/0.52 (
% 0.21/0.52 (let ((_let_1 (not (@ tptp.cCKB_FIN (lambda ((Xu $$unsorted) (Xv $$unsorted)) (and (= Xu tptp.c1) (= Xv tptp.c1))))))) (let ((_let_2 (= tptp.cCKB_FIN (lambda ((Xk (-> $$unsorted $$unsorted Bool))) (not (@ tptp.cCKB_INF Xk)))))) (let ((_let_3 (= tptp.cCKB_INF (lambda ((Xk (-> $$unsorted $$unsorted Bool))) (exists ((Xh (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) (Xm $$unsorted) (Xn $$unsorted)) (and (@ tptp.cCKB_INJ Xh) (@ (@ (@ (@ tptp.cCKB_XPL Xh) Xk) Xm) Xn))))))) (let ((_let_4 (= tptp.cCKB_XPL (lambda ((Xh (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) (Xk (-> $$unsorted $$unsorted Bool)) (Xm $$unsorted) (Xn $$unsorted)) (and (@ (@ Xk Xm) Xn) (forall ((Xx $$unsorted) (Xy $$unsorted)) (=> (@ (@ Xk Xx) Xy) (exists ((Xu $$unsorted) (Xv $$unsorted)) (and (@ (@ (@ (@ Xh Xx) Xy) Xu) Xv) (@ (@ Xk Xu) Xv) (not (and (= Xu Xm) (= Xv Xn)))))))))))) (let ((_let_5 (= tptp.cCKB_INJ (lambda ((Xh (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool))) (forall ((Xx1 $$unsorted) (Xy1 $$unsorted) (Xx2 $$unsorted) (Xy2 $$unsorted) (Xu $$unsorted) (Xv $$unsorted)) (=> (and (@ (@ (@ (@ Xh Xx1) Xy1) Xu) Xv) (@ (@ (@ (@ Xh Xx2) Xy2) Xu) Xv)) (and (= Xx1 Xx2) (= Xy1 Xy2)))))))) (let ((_let_6 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_7 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_8 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_7 _let_6) :args ((= tptp.cCKB_INF (lambda ((Xk (-> $$unsorted $$unsorted Bool))) (not (forall ((Xh (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) (Xm $$unsorted) (Xn $$unsorted)) (or (not (@ tptp.cCKB_INJ Xh)) (not (@ (@ (@ (@ tptp.cCKB_XPL Xh) Xk) Xm) Xn))))))) SB_DEFAULT SBA_FIXPOINT))))) (SCOPE (SCOPE (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_8 _let_7 _let_6) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) _let_8 _let_7 _let_6) :args ((not (@ tptp.cCKB_FIN (lambda ((Xu $$unsorted) (Xv $$unsorted)) (and (= tptp.c1 Xu) (= tptp.c1 Xv))))) SB_DEFAULT SBA_FIXPOINT))) :args (_let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))
% 0.21/0.52 )
% 0.21/0.52 % SZS output end Proof for PUZ107^5
% 0.21/0.52 % cvc5---1.0.5 exiting
% 0.21/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------