TSTP Solution File: PUZ136^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : PUZ136^1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.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 13:13:33 EDT 2023
% Result : Theorem 0.19s 0.54s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ136^1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n002.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 22:26:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 %----Proving TH0
% 0.19/0.54 %------------------------------------------------------------------------------
% 0.19/0.54 % File : PUZ136^1 : TPTP v8.1.2. Released v5.2.0.
% 0.19/0.54 % Domain : Puzzles
% 0.19/0.54 % Problem : Under two assumptions there are at least two individuals.
% 0.19/0.54 % Version : Especial.
% 0.19/0.54 % English :
% 0.19/0.54
% 0.19/0.54 % Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% 0.19/0.54 % Source : [Bro11]
% 0.19/0.54 % Names :
% 0.19/0.54
% 0.19/0.54 % Status : Theorem
% 0.19/0.54 % Rating : 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.2.0
% 0.19/0.54 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 0 def)
% 0.19/0.54 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.19/0.54 % Maximal formula atoms : 1 ( 0 avg)
% 0.19/0.54 % Number of connectives : 9 ( 2 ~; 0 |; 1 &; 6 @)
% 0.19/0.54 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.54 % Maximal formula depth : 7 ( 5 avg)
% 0.19/0.54 % Number of types : 2 ( 0 usr)
% 0.19/0.54 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.19/0.54 % Number of symbols : 5 ( 5 usr; 4 con; 0-2 aty)
% 0.19/0.54 % Number of variables : 3 ( 0 ^; 0 !; 3 ?; 3 :)
% 0.19/0.54 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.54
% 0.19/0.54 % Comments : The conclusion is given using a higher order quantifier.
% 0.19/0.54 % Satallax tends to find solutions by instantiating for P twice.
% 0.19/0.54 % A solution instantiating it once is to take P x := (x = horus),
% 0.19/0.54 % X := horus. Instantiating Y three times gives you that everyone
% 0.19/0.54 % is the same as horus, so the two axioms conflict. This problem
% 0.19/0.54 % is a simplification of CSR138^1.
% 0.19/0.54 %------------------------------------------------------------------------------
% 0.19/0.54 thf(parent,type,
% 0.19/0.54 parent: $i > $i > $o ).
% 0.19/0.54
% 0.19/0.54 thf(kronus,type,
% 0.19/0.54 kronus: $i ).
% 0.19/0.54
% 0.19/0.54 thf(zeus,type,
% 0.19/0.54 zeus: $i ).
% 0.19/0.54
% 0.19/0.54 thf(ax1,axiom,
% 0.19/0.54 parent @ kronus @ zeus ).
% 0.19/0.54
% 0.19/0.54 thf(sutekh,type,
% 0.19/0.54 sutekh: $i ).
% 0.19/0.54
% 0.19/0.54 thf(horus,type,
% 0.19/0.54 horus: $i ).
% 0.19/0.54
% 0.19/0.54 thf(ax2,axiom,
% 0.19/0.54 ~ ( parent @ sutekh @ horus ) ).
% 0.19/0.54
% 0.19/0.54 thf(hotwo,conjecture,
% 0.19/0.54 ? [P: $i > $o,X: $i,Y: $i] :
% 0.19/0.54 ( ( P @ X )
% 0.19/0.54 & ~ ( P @ Y ) ) ).
% 0.19/0.54
% 0.19/0.54 %------------------------------------------------------------------------------
% 0.19/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.nmqKQYX6Iy/cvc5---1.0.5_18593.p...
% 0.19/0.54 (declare-sort $$unsorted 0)
% 0.19/0.54 (declare-fun tptp.parent ($$unsorted $$unsorted) Bool)
% 0.19/0.54 (declare-fun tptp.kronus () $$unsorted)
% 0.19/0.54 (declare-fun tptp.zeus () $$unsorted)
% 0.19/0.54 (assert (@ (@ tptp.parent tptp.kronus) tptp.zeus))
% 0.19/0.54 (declare-fun tptp.sutekh () $$unsorted)
% 0.19/0.54 (declare-fun tptp.horus () $$unsorted)
% 0.19/0.54 (assert (not (@ (@ tptp.parent tptp.sutekh) tptp.horus)))
% 0.19/0.54 (assert (not (exists ((P (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ P X) (not (@ P Y))))))
% 0.19/0.54 (set-info :filename cvc5---1.0.5_18593)
% 0.19/0.54 (check-sat-assuming ( true ))
% 0.19/0.54 ------- get file name : TPTP file name is PUZ136^1
% 0.19/0.54 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18593.smt2...
% 0.19/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.19/0.54 % SZS status Theorem for PUZ136^1
% 0.19/0.54 % SZS output start Proof for PUZ136^1
% 0.19/0.54 (
% 0.19/0.54 (let ((_let_1 (not (exists ((P (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ P X) (not (@ P Y))))))) (let ((_let_2 (not (@ (@ tptp.parent tptp.sutekh) tptp.horus)))) (let ((_let_3 (@ (@ tptp.parent tptp.kronus) tptp.zeus))) (let ((_let_4 (forall ((BOUND_VARIABLE_617 |u_(-> $$unsorted Bool)|) (X $$unsorted) (Y $$unsorted)) (or (not (ho_4 BOUND_VARIABLE_617 X)) (ho_4 BOUND_VARIABLE_617 Y))))) (let ((_let_5 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_6 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 tptp.sutekh))) (let ((_let_7 (not _let_6))) (let ((_let_8 (or _let_7 _let_5))) (let ((_let_9 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((P (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (or (not (@ P X)) (@ P Y))) _let_4))))))) (let ((_let_10 (not _let_8))) (let ((_let_11 (ho_3 k_2 tptp.kronus))) (let ((_let_12 (ho_4 _let_11 tptp.sutekh))) (let ((_let_13 (= tptp.zeus tptp.sutekh))) (let ((_let_14 (not _let_13))) (let ((_let_15 (and _let_14 _let_12))) (let ((_let_16 (= _let_15 _let_6))) (let ((_let_17 (forall ((ii $$unsorted)) (= (and (not (= tptp.zeus ii)) (ho_4 (ho_3 k_2 tptp.kronus) ii)) (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 ii))))) (let ((_let_18 (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_4 v ii) (and (not (= tptp.zeus ii)) (ho_4 (ho_3 k_2 tptp.kronus) ii)))))))) (let ((_let_19 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_22 (forall ((u |u_(-> $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_23 (forall ((x |u_(-> $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_24 (ho_4 _let_11 tptp.zeus))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 _let_24)))))) (let ((_let_26 (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_25 (PREPROCESS :args ((and _let_23 _let_22 _let_21 _let_19)))) :args ((and _let_24 _let_23 _let_22 _let_21 _let_19))))) (let ((_let_27 (_let_19))) (let ((_let_28 (or))) (let ((_let_29 (_let_17))) (let ((_let_30 (_let_20))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_30)) :args _let_30) (REWRITE :args ((=> _let_20 (not (not (forall ((ii $$unsorted)) (= (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 ii) (and (not (= tptp.zeus ii)) (ho_4 (ho_3 k_2 tptp.kronus) ii))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_18))) (REFL :args _let_29) :args _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_27) :args (_let_11 false tptp.zeus QUANTIFIERS_INST_ENUM)) :args _let_27))) (AND_ELIM _let_26 :args (4)) :args (_let_20 false _let_19)) :args (_let_17 true _let_18)))) (let ((_let_32 (ASSUME :args _let_29))) (let ((_let_33 (not _let_24))) (let ((_let_34 (or _let_33 _let_12))) (let ((_let_35 (_let_4))) (let ((_let_36 (AND_ELIM _let_26 :args (0)))) (let ((_let_37 (ho_4 (ho_3 k_2 tptp.sutekh) tptp.horus))) (let ((_let_38 (= tptp.zeus tptp.horus))) (let ((_let_39 (= tptp.kronus tptp.zeus))) (let ((_let_40 (not _let_37))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_40)))))) (let ((_let_42 (ho_4 _let_11 tptp.horus))) (let ((_let_43 (not _let_38))) (let ((_let_44 (and _let_43 _let_42))) (let ((_let_45 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 tptp.horus))) (let ((_let_46 (= _let_44 _let_45))) (let ((_let_47 (not _let_44))) (let ((_let_48 ((ho_4 _let_11 ii)))) (let ((_let_49 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 tptp.zeus))) (let ((_let_50 (not _let_45))) (let ((_let_51 (or _let_50 _let_49))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_49 _let_50 (not _let_51)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.zeus QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_29))) _let_31 :args ((not _let_49) false _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 tptp.horus tptp.zeus QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_35)) _let_9 :args (_let_51 false _let_4)) :args (_let_50 true _let_49 false _let_51)))) (let ((_let_53 (or _let_33 _let_42))) (let ((_let_54 (not _let_42))) (let ((_let_55 (_let_44))) (let ((_let_56 (ho_4 _let_11 tptp.kronus))) (let ((_let_57 (not _let_39))) (let ((_let_58 (and _let_57 _let_56))) (let ((_let_59 (or _let_33 _let_56))) (let ((_let_60 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 tptp.kronus))) (let ((_let_61 (= _let_60 _let_58))) (let ((_let_62 (not _let_58))) (let ((_let_63 (not _let_60))) (let ((_let_64 (or _let_63 _let_5))) (let ((_let_65 (not _let_5))) (let ((_let_66 (or _let_65 _let_45))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_45 _let_65 (not _let_66)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 tptp.horus QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_35)) _let_9 :args (_let_66 false _let_4)) :args (_let_65 true _let_45 false _let_66)))) (let ((_let_68 (not _let_56))) (let ((_let_69 (_let_58))) (let ((_let_70 (ASSUME :args (_let_38)))) (let ((_let_71 (ASSUME :args (_let_39)))) (let ((_let_72 (ASSUME :args (_let_13)))) (let ((_let_73 (not _let_12))) (let ((_let_74 (_let_15))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 tptp.sutekh SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_8)) :args ((or _let_5 _let_7 _let_10))) _let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_16)) :args ((or _let_6 (not _let_15) (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_74) (CONG (REFL :args _let_74) (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) (REFL :args (_let_73)) :args _let_28)) :args ((or _let_13 _let_15 _let_73))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_25 _let_71 _let_72 _let_70 _let_41) :args (_let_24 _let_40 _let_13 _let_38 _let_39)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_41)) (CONG (CONG (REFL :args (k_2)) (TRANS (SYMM _let_72) (SYMM _let_71)) :args (APPLY_UF ho_3)) (SYMM _let_70) :args (APPLY_UF ho_4)) (TRUE_INTRO _let_25))) :args (_let_24 _let_39 _let_13 _let_38 _let_40)) :args ((not (and _let_24 _let_40 _let_13 _let_38 _let_39)) SB_LITERAL))) (CONG (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_37))) (REFL :args (_let_14)) (REFL :args (_let_43)) (REFL :args (_let_57)) :args _let_28)) :args ((or _let_37 _let_33 _let_43 _let_14 _let_57))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_69) (CONG (REFL :args _let_69) (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_39))) (REFL :args (_let_68)) :args _let_28)) :args ((or _let_39 _let_58 _let_68))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_61)) :args ((or _let_60 _let_62 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_5 _let_63 (not _let_64)))) _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 tptp.kronus SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_35)) _let_9 :args (_let_64 false _let_4)) :args (_let_63 true _let_5 false _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.kronus QUANTIFIERS_INST_ENUM)) :args _let_29))) _let_31 :args (_let_61 false _let_17)) :args (_let_62 true _let_60 false _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_33 _let_56 (not _let_59)))) _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (_let_11 tptp.zeus tptp.kronus QUANTIFIERS_INST_ENUM)) :args _let_35)) _let_9 :args (_let_59 false _let_4)) :args (_let_56 false _let_24 false _let_59)) :args (_let_39 true _let_58 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_55) (CONG (REFL :args _let_55) (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_38))) (REFL :args (_let_54)) :args _let_28)) :args ((or _let_54 _let_38 _let_44))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_33 _let_42 (not _let_53)))) _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (_let_11 tptp.zeus tptp.horus QUANTIFIERS_INST_ENUM)) :args _let_35)) _let_9 :args (_let_53 false _let_4)) :args (_let_42 false _let_24 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_46)) :args ((or _let_45 _let_47 (not _let_46)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.horus QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_29)) _let_31 :args (_let_46 false _let_17)) :args (_let_47 true _let_45 false _let_46)) :args (_let_38 false _let_42 true _let_44)) _let_41 _let_36 :args (_let_14 false _let_39 false _let_38 true _let_37 false _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_12 (not _let_34)))) _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_9 :args (_let_11 tptp.zeus tptp.sutekh QUANTIFIERS_INST_ENUM)) :args _let_35)) _let_9 :args (_let_34 false _let_4)) :args (_let_12 false _let_24 false _let_34)) :args (_let_15 true _let_13 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.sutekh QUANTIFIERS_INST_ENUM)) :args _let_29)) _let_31 :args (_let_16 false _let_17)) :args (_let_6 false _let_15 false _let_16)) :args (_let_10 true _let_5 false _let_6)) _let_9 :args (false true _let_8 false _let_4)) :args (_let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.55 )
% 0.19/0.55 % SZS output end Proof for PUZ136^1
% 0.19/0.55 % cvc5---1.0.5 exiting
% 0.19/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------