TSTP Solution File: PUZ110^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : PUZ110^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 13:13:25 EDT 2023
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ110^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n015.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 : Sat Aug 26 22:15:23 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 % File : PUZ110^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.21/0.53 % Domain : Puzzles
% 0.21/0.53 % Problem : TPS problem from CHECKERBOARD-THMS
% 0.21/0.53 % Version : Especial.
% 0.21/0.53 % English :
% 0.21/0.53
% 0.21/0.53 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.53 % Source : [Bro09]
% 0.21/0.53 % Names : tps_0681 [Bro09]
% 0.21/0.53
% 0.21/0.53 % Status : Theorem
% 0.21/0.53 % Rating : 0.23 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, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.21/0.53 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.21/0.53 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.21/0.53 % Maximal formula atoms : 2 ( 2 avg)
% 0.21/0.53 % Number of connectives : 25 ( 0 ~; 0 |; 2 &; 20 @)
% 0.21/0.53 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.21/0.53 % Maximal formula depth : 8 ( 5 avg)
% 0.21/0.53 % Number of types : 2 ( 0 usr)
% 0.21/0.53 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.21/0.53 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.21/0.53 % Number of variables : 7 ( 2 ^; 5 !; 0 ?; 7 :)
% 0.21/0.53 % SPC : TH0_THM_EQU_NAR
% 0.21/0.53
% 0.21/0.53 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.53 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.53 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.53 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.53 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 thf(c1_type,type,
% 0.21/0.53 c1: $i ).
% 0.21/0.53
% 0.21/0.53 thf(s_type,type,
% 0.21/0.53 s: $i > $i ).
% 0.21/0.53
% 0.21/0.53 thf(cCKB6_BLACK_type,type,
% 0.21/0.53 cCKB6_BLACK: $i > $i > $o ).
% 0.21/0.53
% 0.21/0.53 thf(cCKB6_BLACK_def,definition,
% 0.21/0.53 ( cCKB6_BLACK
% 0.21/0.53 = ( ^ [Xu: $i,Xv: $i] :
% 0.21/0.53 ! [Xw: $i > $i > $o] :
% 0.21/0.53 ( ( ( Xw @ c1 @ c1 )
% 0.21/0.53 & ! [Xj: $i,Xk: $i] :
% 0.21/0.53 ( ( Xw @ Xj @ Xk )
% 0.21/0.53 => ( ( Xw @ ( s @ ( s @ Xj ) ) @ Xk )
% 0.21/0.53 & ( Xw @ ( s @ Xj ) @ ( s @ Xk ) ) ) ) )
% 0.21/0.53 => ( Xw @ Xu @ Xv ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 thf(cCKB6_L8000,conjecture,
% 0.21/0.53 ! [Xj: $i,Xk: $i] :
% 0.21/0.53 ( ( cCKB6_BLACK @ Xj @ Xk )
% 0.21/0.53 => ( cCKB6_BLACK @ ( s @ ( s @ Xj ) ) @ Xk ) ) ).
% 0.21/0.53
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.PHkC5VD31b/cvc5---1.0.5_3407.p...
% 0.21/0.53 (declare-sort $$unsorted 0)
% 0.21/0.53 (declare-fun tptp.c1 () $$unsorted)
% 0.21/0.53 (declare-fun tptp.s ($$unsorted) $$unsorted)
% 0.21/0.53 (declare-fun tptp.cCKB6_BLACK ($$unsorted $$unsorted) Bool)
% 0.21/0.53 (assert (= tptp.cCKB6_BLACK (lambda ((Xu $$unsorted) (Xv $$unsorted)) (forall ((Xw (-> $$unsorted $$unsorted Bool))) (=> (and (@ (@ Xw tptp.c1) tptp.c1) (forall ((Xj $$unsorted) (Xk $$unsorted)) (let ((_let_1 (@ tptp.s Xj))) (=> (@ (@ Xw Xj) Xk) (and (@ (@ Xw (@ tptp.s _let_1)) Xk) (@ (@ Xw _let_1) (@ tptp.s Xk))))))) (@ (@ Xw Xu) Xv))))))
% 0.21/0.53 (assert (not (forall ((Xj $$unsorted) (Xk $$unsorted)) (=> (@ (@ tptp.cCKB6_BLACK Xj) Xk) (@ (@ tptp.cCKB6_BLACK (@ tptp.s (@ tptp.s Xj))) Xk)))))
% 0.21/0.53 (set-info :filename cvc5---1.0.5_3407)
% 0.21/0.53 (check-sat-assuming ( true ))
% 0.21/0.53 ------- get file name : TPTP file name is PUZ110^5
% 0.21/0.53 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_3407.smt2...
% 0.21/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.53 % SZS status Theorem for PUZ110^5
% 0.21/0.53 % SZS output start Proof for PUZ110^5
% 0.21/0.53 (
% 0.21/0.53 (let ((_let_1 (not (forall ((Xj $$unsorted) (Xk $$unsorted)) (=> (@ (@ tptp.cCKB6_BLACK Xj) Xk) (@ (@ tptp.cCKB6_BLACK (@ tptp.s (@ tptp.s Xj))) Xk)))))) (let ((_let_2 (= tptp.cCKB6_BLACK (lambda ((Xu $$unsorted) (Xv $$unsorted)) (forall ((Xw (-> $$unsorted $$unsorted Bool))) (=> (and (@ (@ Xw tptp.c1) tptp.c1) (forall ((Xj $$unsorted) (Xk $$unsorted)) (let ((_let_1 (@ tptp.s Xj))) (=> (@ (@ Xw Xj) Xk) (and (@ (@ Xw (@ tptp.s _let_1)) Xk) (@ (@ Xw _let_1) (@ tptp.s Xk))))))) (@ (@ Xw Xu) Xv))))))) (let ((_let_3 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_4 (ho_5 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (ho_3 k_2 _let_3)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_5 (and _let_4 (ho_5 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_3) (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_6 (ho_5 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_7 (not _let_6))) (let ((_let_8 (or _let_7 _let_5))) (let ((_let_9 (forall ((Xj $$unsorted) (Xk $$unsorted)) (let ((_let_1 (ho_3 k_2 Xj))) (or (not (ho_5 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xj) Xk)) (and (ho_5 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (ho_3 k_2 _let_1)) Xk) (ho_5 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_1) (ho_3 k_2 Xk)))))))) (let ((_let_10 (not _let_9))) (let ((_let_11 (ho_5 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.c1) tptp.c1))) (let ((_let_12 (not _let_11))) (let ((_let_13 (forall ((BOUND_VARIABLE_730 |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (ho_5 (ho_4 BOUND_VARIABLE_730 tptp.c1) tptp.c1)) (not (forall ((Xj $$unsorted) (Xk $$unsorted)) (let ((_let_1 (ho_3 k_2 Xj))) (or (not (ho_5 (ho_4 BOUND_VARIABLE_730 Xj) Xk)) (and (ho_5 (ho_4 BOUND_VARIABLE_730 (ho_3 k_2 _let_1)) Xk) (ho_5 (ho_4 BOUND_VARIABLE_730 _let_1) (ho_3 k_2 Xk))))))) (ho_5 (ho_4 BOUND_VARIABLE_730 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_10 _let_4))) (let ((_let_16 (forall ((Xj $$unsorted) (Xk $$unsorted) (BOUND_VARIABLE_705 |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((BOUND_VARIABLE_730 |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (ho_5 (ho_4 BOUND_VARIABLE_730 tptp.c1) tptp.c1)) (not (forall ((Xj $$unsorted) (Xk $$unsorted)) (let ((_let_1 (ho_3 k_2 Xj))) (or (not (ho_5 (ho_4 BOUND_VARIABLE_730 Xj) Xk)) (and (ho_5 (ho_4 BOUND_VARIABLE_730 (ho_3 k_2 _let_1)) Xk) (ho_5 (ho_4 BOUND_VARIABLE_730 _let_1) (ho_3 k_2 Xk))))))) (ho_5 (ho_4 BOUND_VARIABLE_730 Xj) Xk)))) (not (ho_5 (ho_4 BOUND_VARIABLE_705 tptp.c1) tptp.c1)) (not (forall ((Xj $$unsorted) (Xk $$unsorted)) (let ((_let_1 (ho_3 k_2 Xj))) (or (not (ho_5 (ho_4 BOUND_VARIABLE_705 Xj) Xk)) (and (ho_5 (ho_4 BOUND_VARIABLE_705 (ho_3 k_2 _let_1)) Xk) (ho_5 (ho_4 BOUND_VARIABLE_705 _let_1) (ho_3 k_2 Xk))))))) (ho_5 (ho_4 BOUND_VARIABLE_705 (ho_3 k_2 (ho_3 k_2 Xj))) Xk))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (not _let_16))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args ((not (forall ((Xj $$unsorted) (Xk $$unsorted)) (or (not (@ (@ tptp.cCKB6_BLACK Xj) Xk)) (@ (@ tptp.cCKB6_BLACK (@ tptp.s (@ tptp.s Xj))) Xk)))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xj $$unsorted) (Xk $$unsorted) (BOUND_VARIABLE_671 (-> $$unsorted $$unsorted Bool))) (or (not (forall ((Xw (-> $$unsorted $$unsorted Bool))) (or (not (@ (@ Xw tptp.c1) tptp.c1)) (not (forall ((Xj $$unsorted) (Xk $$unsorted)) (let ((_let_1 (@ tptp.s Xj))) (or (not (@ (@ Xw Xj) Xk)) (and (@ (@ Xw (@ tptp.s _let_1)) Xk) (@ (@ Xw _let_1) (@ tptp.s Xk))))))) (@ (@ Xw Xj) Xk)))) (not (@ (@ BOUND_VARIABLE_671 tptp.c1) tptp.c1)) (not (forall ((Xj $$unsorted) (Xk $$unsorted)) (let ((_let_1 (@ tptp.s Xj))) (or (not (@ (@ BOUND_VARIABLE_671 Xj) Xk)) (and (@ (@ BOUND_VARIABLE_671 (@ tptp.s _let_1)) Xk) (@ (@ BOUND_VARIABLE_671 _let_1) (@ tptp.s Xk))))))) (@ (@ BOUND_VARIABLE_671 (@ tptp.s (@ tptp.s Xj))) Xk)))) _let_18))))))) (let ((_let_20 (or))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_19) :args (_let_18))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_16))) (REFL :args (_let_17)) :args _let_20)) _let_19 :args (_let_17 true _let_16)))) (let ((_let_22 (REFL :args (_let_15)))) (let ((_let_23 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 2)) (CONG _let_22 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_20)) :args ((or _let_9 _let_15))) _let_21 :args (_let_9 true _let_15)))) (let ((_let_24 (_let_9))) (let ((_let_25 (not _let_5))) (let ((_let_26 (or _let_12 _let_10 _let_6))) (let ((_let_27 (_let_13))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_8)) :args ((or _let_7 _let_5 (not _let_8)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_12 _let_10 _let_6 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 1)) (CONG _let_22 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_20)) :args ((or _let_11 _let_15))) _let_21 :args (_let_11 true _let_15)) _let_23 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_27) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_4 BOUND_VARIABLE_730 tptp.c1)))) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 0)) (CONG _let_22 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_20)) :args ((or _let_13 _let_15))) _let_21 :args (_let_13 true _let_15)) :args (_let_26 false _let_13)) :args (_let_6 false _let_11 false _let_9 false _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_5 0)) :args ((or _let_4 _let_25))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_15 3)) _let_21 :args ((not _let_4) true _let_15)) :args (_let_25 true _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_24) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING ((ho_5 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (ho_3 k_2 (ho_3 k_2 Xj))) Xk)))) :args _let_24)) _let_23 :args (_let_8 false _let_9)) :args (false false _let_6 true _let_5 false _let_8)) :args (_let_2 _let_1 true))))))))))))))))))))))))))))))
% 0.21/0.54 )
% 0.21/0.54 % SZS output end Proof for PUZ110^5
% 0.21/0.54 % cvc5---1.0.5 exiting
% 0.21/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------