TSTP Solution File: SEV059^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV059^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 19:21:27 EDT 2023
% Result : Theorem 0.22s 0.54s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV059^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.19/0.36 % Computer : n028.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Thu Aug 24 03:44:49 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 % File : SEV059^5 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.54 % Domain : Set Theory (Relations)
% 0.22/0.54 % Problem : TPS problem THM89A
% 0.22/0.54 % Version : Especial.
% 0.22/0.54 % English :
% 0.22/0.54
% 0.22/0.54 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.54 % Source : [Bro09]
% 0.22/0.54 % Names : tps_0326 [Bro09]
% 0.22/0.54 % : THM89 [TPS]
% 0.22/0.54 % : THM89A [TPS]
% 0.22/0.54
% 0.22/0.54 % Status : Theorem
% 0.22/0.54 % Rating : 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.22/0.54 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.22/0.54 % Number of atoms : 6 ( 1 equ; 0 cnn)
% 0.22/0.54 % Maximal formula atoms : 6 ( 6 avg)
% 0.22/0.54 % Number of connectives : 23 ( 0 ~; 0 |; 3 &; 18 @)
% 0.22/0.54 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.22/0.54 % Maximal formula depth : 10 ( 10 avg)
% 0.22/0.54 % Number of types : 3 ( 2 usr)
% 0.22/0.54 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.22/0.54 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.22/0.54 % Number of variables : 6 ( 1 ^; 5 !; 0 ?; 6 :)
% 0.22/0.54 % SPC : TH0_THM_EQU_NAR
% 0.22/0.54
% 0.22/0.54 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.54 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.54 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.54 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.54 % : Polymorphic definitions expanded.
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 thf(b_type,type,
% 0.22/0.54 b: $tType ).
% 0.22/0.54
% 0.22/0.54 thf(a_type,type,
% 0.22/0.54 a: $tType ).
% 0.22/0.54
% 0.22/0.54 thf(cG,type,
% 0.22/0.54 cG: b > b ).
% 0.22/0.54
% 0.22/0.54 thf(cA,type,
% 0.22/0.54 cA: b > a ).
% 0.22/0.54
% 0.22/0.54 thf(c_less_,type,
% 0.22/0.54 c_less_: a > a > $o ).
% 0.22/0.54
% 0.22/0.54 thf(cF,type,
% 0.22/0.54 cF: b > b ).
% 0.22/0.54
% 0.22/0.54 thf(cTHM89A_pme,conjecture,
% 0.22/0.54 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.22/0.54 ( ( ( c_less_ @ Xx @ Xy )
% 0.22/0.54 & ( c_less_ @ Xy @ Xz ) )
% 0.22/0.54 => ( c_less_ @ Xx @ Xz ) )
% 0.22/0.54 & ! [X: b] : ( c_less_ @ ( cA @ X ) @ ( cA @ ( cF @ X ) ) )
% 0.22/0.54 & ( cG
% 0.22/0.54 = ( ^ [Z: b] : ( cF @ ( cF @ Z ) ) ) ) )
% 0.22/0.54 => ! [Y: b] : ( c_less_ @ ( cA @ Y ) @ ( cA @ ( cG @ Y ) ) ) ) ).
% 0.22/0.54
% 0.22/0.54 %------------------------------------------------------------------------------
% 0.22/0.54 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.gAt9QyNlNd/cvc5---1.0.5_30470.p...
% 0.22/0.54 (declare-sort $$unsorted 0)
% 0.22/0.54 (declare-sort tptp.b 0)
% 0.22/0.54 (declare-sort tptp.a 0)
% 0.22/0.54 (declare-fun tptp.cG (tptp.b) tptp.b)
% 0.22/0.54 (declare-fun tptp.cA (tptp.b) tptp.a)
% 0.22/0.54 (declare-fun tptp.c_less_ (tptp.a tptp.a) Bool)
% 0.22/0.54 (declare-fun tptp.cF (tptp.b) tptp.b)
% 0.22/0.54 (assert (not (=> (and (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ tptp.c_less_ Xx))) (=> (and (@ _let_1 Xy) (@ (@ tptp.c_less_ Xy) Xz)) (@ _let_1 Xz)))) (forall ((X tptp.b)) (@ (@ tptp.c_less_ (@ tptp.cA X)) (@ tptp.cA (@ tptp.cF X)))) (= tptp.cG (lambda ((Z tptp.b)) (@ tptp.cF (@ tptp.cF Z))))) (forall ((Y tptp.b)) (@ (@ tptp.c_less_ (@ tptp.cA Y)) (@ tptp.cA (@ tptp.cG Y)))))))
% 0.22/0.54 (set-info :filename cvc5---1.0.5_30470)
% 0.22/0.54 (check-sat-assuming ( true ))
% 0.22/0.54 ------- get file name : TPTP file name is SEV059^5
% 0.22/0.54 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30470.smt2...
% 0.22/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.54 % SZS status Theorem for SEV059^5
% 0.22/0.54 % SZS output start Proof for SEV059^5
% 0.22/0.54 (
% 0.22/0.54 (let ((_let_1 (forall ((Y tptp.b)) (@ (@ tptp.c_less_ (@ tptp.cA Y)) (@ tptp.cA (@ tptp.cG Y)))))) (let ((_let_2 (= tptp.cG (lambda ((Z tptp.b)) (@ tptp.cF (@ tptp.cF Z)))))) (let ((_let_3 (forall ((X tptp.b)) (@ (@ tptp.c_less_ (@ tptp.cA X)) (@ tptp.cA (@ tptp.cF X)))))) (let ((_let_4 (not (=> (and (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ tptp.c_less_ Xx))) (=> (and (@ _let_1 Xy) (@ (@ tptp.c_less_ Xy) Xz)) (@ _let_1 Xz)))) _let_3 _let_2) _let_1)))) (let ((_let_5 (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_7 k_6 Xx))) (or (not (ho_8 _let_1 Xy)) (not (ho_8 (ho_7 k_6 Xy) Xz)) (ho_8 _let_1 Xz)))))) (let ((_let_6 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_7 (ho_5 k_4 (ho_3 k_2 _let_6)))) (let ((_let_8 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_9 (ho_7 k_6 _let_8))) (let ((_let_10 (ho_8 _let_9 _let_7))) (let ((_let_11 (ho_5 k_4 _let_6))) (let ((_let_12 (ho_8 (ho_7 k_6 _let_11) _let_7))) (let ((_let_13 (not _let_12))) (let ((_let_14 (ho_8 _let_9 _let_11))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13 _let_10))) (let ((_let_17 (0))) (let ((_let_18 (forall ((u |u_(-> tptp.b tptp.b)|) (e tptp.b) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.b)|)) (not (forall ((ii tptp.b)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_19 (forall ((x |u_(-> tptp.b tptp.b)|) (y |u_(-> tptp.b tptp.b)|)) (or (not (forall ((z tptp.b)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_20 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_21 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_22 (forall ((u |u_(-> tptp.b tptp.a)|) (e tptp.a) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.a)|)) (not (forall ((ii tptp.b)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_23 (forall ((x |u_(-> tptp.b tptp.a)|) (y |u_(-> tptp.b tptp.a)|)) (or (not (forall ((z tptp.b)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_24 (forall ((u |u_(-> tptp.a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_25 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_26 (forall ((Y tptp.b)) (ho_8 (ho_7 k_6 (ho_5 k_4 Y)) (ho_5 k_4 (ho_3 k_2 (ho_3 k_2 Y))))))) (let ((_let_27 (forall ((X tptp.b)) (ho_8 (ho_7 k_6 (ho_5 k_4 X)) (ho_5 k_4 (ho_3 k_2 X)))))) (let ((_let_28 (not (=> (and _let_5 _let_27) _let_26)))) (let ((_let_29 (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ tptp.c_less_ Xx))) (or (not (@ _let_1 Xy)) (not (@ (@ tptp.c_less_ Xy) Xz)) (@ _let_1 Xz)))))) (let ((_let_30 (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_31 (ASSUME :args (_let_4)))) (let ((_let_32 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE _let_31 (TRANS _let_30 (MACRO_SR_EQ_INTRO (AND_ELIM (NOT_IMPLIES_ELIM1 (EQ_RESOLVE _let_31 _let_30)) :args (2)) :args ((not (=> (and _let_29 _let_3 _let_2) _let_1)) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> (and _let_29 _let_3) (forall ((Y tptp.b)) (@ (@ tptp.c_less_ (@ tptp.cA Y)) (@ tptp.cA (@ tptp.cF (@ tptp.cF Y))))))) _let_28))))) (PREPROCESS :args ((and _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18)))) :args ((and _let_28 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18))) :args _let_17))) (let ((_let_33 (NOT_IMPLIES_ELIM1 _let_32))) (let ((_let_34 (not _let_16))) (let ((_let_35 (AND_ELIM _let_33 :args (1)))) (let ((_let_36 (_let_27))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (not _let_10))) (let ((_let_39 (not _let_26))) (let ((_let_40 (_let_39))) (let ((_let_41 (_let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_41) :args (_let_8 _let_11 _let_7 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_10 _let_15 _let_13 _let_34))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_40)) :args _let_40)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_26))) (REFL :args (_let_38)) :args (or))) (NOT_IMPLIES_ELIM2 _let_32) :args (_let_38 true _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((ho_7 k_6 (ho_5 k_4 X))))) :args _let_36)) _let_35 :args (_let_14 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_3 k_2 X)))) :args _let_36)) _let_35 :args (_let_12 false _let_27)) :args (_let_34 true _let_10 false _let_14 false _let_12)) (AND_ELIM _let_33 :args _let_17) :args (false true _let_16 false _let_5)) :args (_let_4 true))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.54 )
% 0.22/0.54 % SZS output end Proof for SEV059^5
% 0.22/0.54 % cvc5---1.0.5 exiting
% 0.22/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------