TSTP Solution File: PUZ103^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : PUZ103^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : PUZ103^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.06/0.13 % Command : do_cvc5 %s %d
% 0.12/0.34 % Computer : n009.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 : Sat Aug 26 22:02:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.48 %----Proving TH0
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 % File : PUZ103^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.19/0.52 % Domain : Puzzles
% 0.19/0.52 % Problem : TPS problem from CHECKERBOARD-THMS
% 0.19/0.52 % Version : Especial.
% 0.19/0.52 % English :
% 0.19/0.52
% 0.19/0.52 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.52 % Source : [Bro09]
% 0.19/0.52 % Names : tps_0623 [Bro09]
% 0.19/0.52
% 0.19/0.52 % Status : Theorem
% 0.19/0.52 % Rating : 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.19/0.52 % Syntax : Number of formulae : 5 ( 1 unt; 3 typ; 1 def)
% 0.19/0.52 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.19/0.52 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.52 % Number of connectives : 12 ( 0 ~; 0 |; 1 &; 8 @)
% 0.19/0.52 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.52 % Maximal formula depth : 5 ( 3 avg)
% 0.19/0.52 % Number of types : 2 ( 0 usr)
% 0.19/0.52 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.52 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.52 % Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% 0.19/0.52 % SPC : TH0_THM_EQU_NAR
% 0.19/0.52
% 0.19/0.52 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.52 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.52 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.52 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.52 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 thf(c1_type,type,
% 0.19/0.52 c1: $i ).
% 0.19/0.52
% 0.19/0.52 thf(s_type,type,
% 0.19/0.52 s: $i > $i ).
% 0.19/0.52
% 0.19/0.52 thf(cCKB6_NUM_type,type,
% 0.19/0.52 cCKB6_NUM: $i > $o ).
% 0.19/0.52
% 0.19/0.52 thf(cCKB6_NUM_def,definition,
% 0.19/0.52 ( cCKB6_NUM
% 0.19/0.52 = ( ^ [Xx: $i] :
% 0.19/0.52 ! [Xp: $i > $o] :
% 0.19/0.52 ( ( ( Xp @ c1 )
% 0.19/0.52 & ! [Xw: $i] :
% 0.19/0.52 ( ( Xp @ Xw )
% 0.19/0.52 => ( Xp @ ( s @ Xw ) ) ) )
% 0.19/0.52 => ( Xp @ Xx ) ) ) ) ).
% 0.19/0.52
% 0.19/0.52 thf(cCKB6_L3000,conjecture,
% 0.19/0.52 ! [Xx: $i] :
% 0.19/0.52 ( ( cCKB6_NUM @ Xx )
% 0.19/0.52 => ( cCKB6_NUM @ ( s @ Xx ) ) ) ).
% 0.19/0.52
% 0.19/0.52 %------------------------------------------------------------------------------
% 0.19/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.xd51hglyXx/cvc5---1.0.5_20448.p...
% 0.19/0.52 (declare-sort $$unsorted 0)
% 0.19/0.52 (declare-fun tptp.c1 () $$unsorted)
% 0.19/0.52 (declare-fun tptp.s ($$unsorted) $$unsorted)
% 0.19/0.52 (declare-fun tptp.cCKB6_NUM ($$unsorted) Bool)
% 0.19/0.52 (assert (= tptp.cCKB6_NUM (lambda ((Xx $$unsorted)) (forall ((Xp (-> $$unsorted Bool))) (=> (and (@ Xp tptp.c1) (forall ((Xw $$unsorted)) (=> (@ Xp Xw) (@ Xp (@ tptp.s Xw))))) (@ Xp Xx))))))
% 0.19/0.52 (assert (not (forall ((Xx $$unsorted)) (=> (@ tptp.cCKB6_NUM Xx) (@ tptp.cCKB6_NUM (@ tptp.s Xx))))))
% 0.19/0.52 (set-info :filename cvc5---1.0.5_20448)
% 0.19/0.52 (check-sat-assuming ( true ))
% 0.19/0.52 ------- get file name : TPTP file name is PUZ103^5
% 0.19/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20448.smt2...
% 0.19/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.19/0.52 % SZS status Theorem for PUZ103^5
% 0.19/0.52 % SZS output start Proof for PUZ103^5
% 0.19/0.52 (
% 0.19/0.52 (let ((_let_1 (not (forall ((Xx $$unsorted)) (=> (@ tptp.cCKB6_NUM Xx) (@ tptp.cCKB6_NUM (@ tptp.s Xx))))))) (let ((_let_2 (= tptp.cCKB6_NUM (lambda ((Xx $$unsorted)) (forall ((Xp (-> $$unsorted Bool))) (=> (and (@ Xp tptp.c1) (forall ((Xw $$unsorted)) (=> (@ Xp Xw) (@ Xp (@ tptp.s Xw))))) (@ Xp Xx))))))) (let ((_let_3 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_4 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_5 (not _let_4))) (let ((_let_6 (or _let_5 _let_3))) (let ((_let_7 (forall ((Xw $$unsorted)) (or (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Xw)) (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (ho_3 k_2 Xw)))))) (let ((_let_8 (not _let_7))) (let ((_let_9 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.c1))) (let ((_let_10 (not _let_9))) (let ((_let_11 (forall ((BOUND_VARIABLE_678 |u_(-> $$unsorted Bool)|)) (or (not (ho_4 BOUND_VARIABLE_678 tptp.c1)) (not (forall ((Xw $$unsorted)) (or (not (ho_4 BOUND_VARIABLE_678 Xw)) (ho_4 BOUND_VARIABLE_678 (ho_3 k_2 Xw))))) (ho_4 BOUND_VARIABLE_678 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10 _let_8 _let_3))) (let ((_let_14 (forall ((Xx $$unsorted) (BOUND_VARIABLE_665 |u_(-> $$unsorted Bool)|)) (or (not (forall ((BOUND_VARIABLE_678 |u_(-> $$unsorted Bool)|)) (or (not (ho_4 BOUND_VARIABLE_678 tptp.c1)) (not (forall ((Xw $$unsorted)) (or (not (ho_4 BOUND_VARIABLE_678 Xw)) (ho_4 BOUND_VARIABLE_678 (ho_3 k_2 Xw))))) (ho_4 BOUND_VARIABLE_678 Xx)))) (not (ho_4 BOUND_VARIABLE_665 tptp.c1)) (not (forall ((Xw $$unsorted)) (or (not (ho_4 BOUND_VARIABLE_665 Xw)) (ho_4 BOUND_VARIABLE_665 (ho_3 k_2 Xw))))) (ho_4 BOUND_VARIABLE_665 (ho_3 k_2 Xx)))))) (let ((_let_15 (not _let_13))) (let ((_let_16 (not _let_14))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args ((not (forall ((Xx $$unsorted)) (or (not (@ tptp.cCKB6_NUM Xx)) (@ tptp.cCKB6_NUM (@ tptp.s Xx))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xx $$unsorted) (BOUND_VARIABLE_639 (-> $$unsorted Bool))) (or (not (forall ((Xp (-> $$unsorted Bool))) (or (not (@ Xp tptp.c1)) (not (forall ((Xw $$unsorted)) (or (not (@ Xp Xw)) (@ Xp (@ tptp.s Xw))))) (@ Xp Xx)))) (not (@ BOUND_VARIABLE_639 tptp.c1)) (not (forall ((Xw $$unsorted)) (or (not (@ BOUND_VARIABLE_639 Xw)) (@ BOUND_VARIABLE_639 (@ tptp.s Xw))))) (@ BOUND_VARIABLE_639 (@ tptp.s Xx))))) _let_16))))))) (let ((_let_18 (or))) (let ((_let_19 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_17) :args (_let_16))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_14))) (REFL :args (_let_15)) :args _let_18)) _let_17 :args (_let_15 true _let_14)))) (let ((_let_20 (REFL :args (_let_13)))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 2)) (CONG _let_20 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_18)) :args ((or _let_7 _let_13))) _let_19 :args (_let_7 true _let_13)))) (let ((_let_22 (_let_7))) (let ((_let_23 (or _let_10 _let_8 _let_4))) (let ((_let_24 (_let_11))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_3 _let_5 (not _let_6)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_10 _let_8 _let_4 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 1)) (CONG _let_20 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_18)) :args ((or _let_9 _let_13))) _let_19 :args (_let_9 true _let_13)) _let_21 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_24) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_4 BOUND_VARIABLE_678 tptp.c1) false))))) :args _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 0)) (CONG _let_20 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_18)) :args ((or _let_11 _let_13))) _let_19 :args (_let_11 true _let_13)) :args (_let_23 false _let_11)) :args (_let_4 false _let_9 false _let_7 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_22) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_3 k_2 Xw)))) :args _let_22)) _let_21 :args (_let_6 false _let_7)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_13 3)) _let_19 :args ((not _let_3) true _let_13)) :args (false false _let_4 false _let_6 true _let_3)) :args (_let_2 _let_1 true)))))))))))))))))))))))))))
% 0.19/0.52 )
% 0.19/0.52 % SZS output end Proof for PUZ103^5
% 0.19/0.52 % cvc5---1.0.5 exiting
% 0.19/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------