TSTP Solution File: CAT038^2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : CAT038^2 : TPTP v8.1.2. Released v4.1.0.
% 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 : Wed Aug 30 18:14:49 EDT 2023
% Result : Theorem 0.18s 0.61s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : CAT038^2 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.12 % Command : do_cvc5 %s %d
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 00:34:03 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.46 %----Proving TH0
% 0.18/0.61 %------------------------------------------------------------------------------
% 0.18/0.61 % File : CAT038^2 : TPTP v8.1.2. Released v4.1.0.
% 0.18/0.61 % Domain : Syntactic
% 0.18/0.61 % Problem : For any X,Y:i, there is a function swapping X and Y
% 0.18/0.61 % Version : Especial.
% 0.18/0.61 % English :
% 0.18/0.61
% 0.18/0.61 % Refs : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.18/0.61 % Source : [Bro09]
% 0.18/0.61 % Names : swapi [Bro09]
% 0.18/0.61
% 0.18/0.61 % Status : Theorem
% 0.18/0.61 % Rating : 0.77 v8.1.0, 0.82 v7.5.0, 0.86 v7.4.0, 0.89 v7.3.0, 1.00 v4.1.0
% 0.18/0.61 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.18/0.61 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.18/0.61 % Maximal formula atoms : 2 ( 2 avg)
% 0.18/0.61 % Number of connectives : 3 ( 0 ~; 0 |; 1 &; 2 @)
% 0.18/0.61 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.61 % Maximal formula depth : 5 ( 5 avg)
% 0.18/0.61 % Number of types : 1 ( 0 usr)
% 0.18/0.61 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.18/0.61 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.18/0.61 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.18/0.61 % SPC : TH0_THM_EQU_NAR
% 0.18/0.61
% 0.18/0.61 % Comments : This is a theorem because the default semantics is Henkin with
% 0.18/0.61 % choice.
% 0.18/0.61 %------------------------------------------------------------------------------
% 0.18/0.61 thf(ifi,conjecture,
% 0.18/0.61 ! [X: $i,Y: $i] :
% 0.18/0.61 ? [F: $i > $i] :
% 0.18/0.61 ( ( ( F @ X )
% 0.18/0.61 = Y )
% 0.18/0.61 & ( ( F @ Y )
% 0.18/0.61 = X ) ) ).
% 0.18/0.61
% 0.18/0.61 %------------------------------------------------------------------------------
% 0.18/0.61 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.1h2notsswW/cvc5---1.0.5_29358.p...
% 0.18/0.61 (declare-sort $$unsorted 0)
% 0.18/0.61 (assert (not (forall ((X $$unsorted) (Y $$unsorted)) (exists ((F (-> $$unsorted $$unsorted))) (and (= (@ F X) Y) (= (@ F Y) X))))))
% 0.18/0.61 (set-info :filename cvc5---1.0.5_29358)
% 0.18/0.61 (check-sat-assuming ( true ))
% 0.18/0.61 ------- get file name : TPTP file name is CAT038^2
% 0.18/0.61 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29358.smt2...
% 0.18/0.61 --- Run --ho-elim --full-saturate-quant at 10...
% 0.18/0.61 % SZS status Theorem for CAT038^2
% 0.18/0.61 % SZS output start Proof for CAT038^2
% 0.18/0.61 (
% 0.18/0.61 (let ((_let_1 (not (forall ((X $$unsorted) (Y $$unsorted)) (exists ((F (-> $$unsorted $$unsorted))) (and (= (@ F X) Y) (= (@ F Y) X))))))) (let ((_let_2 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_104 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_3 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_2))) (let ((_let_4 (= _let_2 termITE_115))) (let ((_let_5 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_6 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 termITE_115))) (let ((_let_7 (not _let_3))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_104 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_7))) (let ((_let_11 (forall ((BOUND_VARIABLE_602 |u_(-> $$unsorted $$unsorted)|)) (or (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (ho_2 BOUND_VARIABLE_602 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (ho_2 BOUND_VARIABLE_602 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted)) (not (forall ((BOUND_VARIABLE_602 |u_(-> $$unsorted $$unsorted)|)) (or (not (= Y (ho_2 BOUND_VARIABLE_602 X))) (not (= X (ho_2 BOUND_VARIABLE_602 Y))))))))) (let ((_let_13 (forall ((u |u_(-> $$unsorted $$unsorted)|) (e $$unsorted) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_14 (forall ((x |u_(-> $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_15 (not _let_12))) (let ((_let_16 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((X $$unsorted) (Y $$unsorted)) (not (forall ((F (-> $$unsorted $$unsorted))) (or (not (= Y (@ F X))) (not (= X (@ F Y)))))))) _let_15))))))) (let ((_let_17 (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_16 (PREPROCESS :args ((and _let_14 _let_13)))) :args ((and _let_15 _let_14 _let_13))))) (let ((_let_18 (or))) (let ((_let_19 (_let_11))) (let ((_let_20 (forall ((ii $$unsorted)) (= (ite (= ii SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 ii)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_104 ii))))) (let ((_let_21 (forall ((v |u_(-> $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_2 v ii) (ite (= ii SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 ii)))))))) (let ((_let_22 (not _let_21))) (let ((_let_23 (AND_ELIM _let_17 :args (2)))) (let ((_let_24 (_let_13))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (_let_20))) (let ((_let_27 (REFL :args _let_26))) (let ((_let_28 (_let_22))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_28)) :args _let_28) (REWRITE :args ((=> _let_22 (not (not (forall ((ii $$unsorted)) (= (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_104 ii) (ite (= ii SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 ii))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) _let_27 :args _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_ENUM)) :args _let_24))) _let_23 :args (_let_22 false _let_13)) :args (_let_20 true _let_21)))) (let ((_let_30 (ASSUME :args _let_26))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_9 _let_7 (not _let_10)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 ii)))) :args _let_26))) _let_29 :args (_let_8 false _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_19) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_104 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_19)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_16) :args (_let_15)) (REWRITE :args ((=> _let_15 (not (not _let_11))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_12))) (REFL :args _let_19) :args _let_18)) (AND_ELIM _let_17 :args (0)) :args (_let_11 true _let_12)) :args (_let_10 false _let_11)) :args (_let_7 false _let_8 false _let_10)))) (let ((_let_32 (=))) (let ((_let_33 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_34 (ite _let_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_33))) (let ((_let_35 (MACRO_SR_PRED_INTRO :args ((= _let_34 termITE_115))))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_104 ii)))) :args _let_26)) (CONG _let_27 (CONG (REFL :args (_let_2)) _let_35 :args _let_32) :args (=>)))) _let_29 :args (_let_4 false _let_20)))) (let ((_let_37 (= _let_33 termITE_115))) (let ((_let_38 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_33))) (let ((_let_39 (not _let_37))) (let ((_let_40 (forall ((ii $$unsorted)) (= (ite (= ii SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (ho_2 |e__u_(-> $$unsorted $$unsorted)__7| ii)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 ii))))) (let ((_let_41 (forall ((v |u_(-> $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_2 v ii) (ite (= ii SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (ho_2 |e__u_(-> $$unsorted $$unsorted)__7| ii)))))))) (let ((_let_42 (not _let_41))) (let ((_let_43 (_let_40))) (let ((_let_44 (_let_42))) (let ((_let_45 (REFL :args ((not _let_4))))) (let ((_let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_3))))) (let ((_let_47 (and _let_38 _let_7 _let_4))) (let ((_let_48 (ASSUME :args (_let_7)))) (let ((_let_49 (FALSE_INTRO _let_48))) (let ((_let_50 (ASSUME :args (_let_4)))) (let ((_let_51 (SYMM _let_50))) (let ((_let_52 (ASSUME :args (_let_38)))) (let ((_let_53 ((ite _let_5 (= termITE_115 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (= termITE_115 _let_33))))) (let ((_let_54 (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (REMOVE_TERM_FORMULA_AXIOM :args (_let_34)) _let_35 :args _let_53) (REWRITE :args _let_53)))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (ITE_ELIM2 _let_54) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_47)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_48 _let_52 _let_50) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_52) _let_51 :args _let_32) _let_49)) :args (_let_7 _let_38 _let_4))) :args (_let_38 _let_7 _let_4))) :args (true _let_47)) (CONG (REFL :args ((not _let_38))) _let_46 _let_45 (REFL :args (_let_39)) :args _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_43) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_2 |e__u_(-> $$unsorted $$unsorted)__7| ii)))) :args _let_43))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_44)) :args _let_44) (REWRITE :args ((=> _let_42 (not (not (forall ((ii $$unsorted)) (= (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 ii) (ite (= ii SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (ho_2 |e__u_(-> $$unsorted $$unsorted)__7| ii))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) (REFL :args _let_43) :args _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (|e__u_(-> $$unsorted $$unsorted)__7| SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_ENUM)) :args _let_24))) _let_23 :args (_let_42 false _let_13)) :args (_let_40 true _let_41)) :args (_let_38 false _let_40)) _let_31 _let_36 :args (_let_39 false _let_38 true _let_3 false _let_4)) :args (_let_5 true _let_37)))) (let ((_let_56 (and _let_5 _let_7 _let_4))) (let ((_let_57 (ASSUME :args (_let_5)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_56)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_48 _let_57 _let_50) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_57) _let_51 :args _let_32) _let_49)) :args (_let_7 _let_5 _let_4))) :args (_let_5 _let_7 _let_4))) :args (true _let_56)) (CONG (REFL :args ((not _let_5))) _let_46 _let_45 (REFL :args ((not _let_6))) :args _let_18)) (MACRO_RESOLUTION_TRUST (ITE_ELIM1 _let_54) _let_55 :args (_let_6 false _let_5)) _let_55 _let_36 _let_31 :args (false false _let_6 false _let_5 false _let_4 true _let_3)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.18/0.62 )
% 0.18/0.62 % SZS output end Proof for CAT038^2
% 0.18/0.62 % cvc5---1.0.5 exiting
% 0.18/0.62 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------