TSTP Solution File: SEV129^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV129^5 : TPTP v8.1.2. Released v4.0.0.
% 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 19:21:38 EDT 2023
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV129^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n009.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 : Thu Aug 24 03:02:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 %----Proving TH0
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 % File : SEV129^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.49 % Domain : Set Theory (Relations)
% 0.20/0.49 % Problem : TPS problem from SETS-OF-RELNS-THMS
% 0.20/0.49 % Version : Especial.
% 0.20/0.49 % English :
% 0.20/0.49
% 0.20/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.49 % Source : [Bro09]
% 0.20/0.49 % Names : tps_1139 [Bro09]
% 0.20/0.49
% 0.20/0.49 % Status : Theorem
% 0.20/0.49 % Rating : 0.46 v8.1.0, 0.55 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v4.0.0
% 0.20/0.49 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.20/0.49 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.20/0.49 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.49 % Number of connectives : 57 ( 0 ~; 0 |; 9 &; 38 @)
% 0.20/0.49 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.20/0.49 % Maximal formula depth : 16 ( 16 avg)
% 0.20/0.49 % Number of types : 2 ( 1 usr)
% 0.20/0.49 % Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% 0.20/0.49 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.20/0.49 % Number of variables : 26 ( 2 ^; 21 !; 3 ?; 26 :)
% 0.20/0.49 % SPC : TH0_THM_EQU_NAR
% 0.20/0.49
% 0.20/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 thf(a_type,type,
% 0.20/0.49 a: $tType ).
% 0.20/0.49
% 0.20/0.49 thf(cTHM253_A_pme,conjecture,
% 0.20/0.49 ! [S: ( a > a > $o ) > $o,Xx: a,Xy: a] :
% 0.20/0.49 ( ! [Xp1: a > a > $o] :
% 0.20/0.49 ( ( ! [Xx0: a,Xy0: a] :
% 0.20/0.49 ( ? [R: a > a > $o] :
% 0.20/0.49 ( ( S @ R )
% 0.20/0.49 & ( R @ Xx0 @ Xy0 ) )
% 0.20/0.49 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.20/0.49 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.20/0.49 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.20/0.49 & ( Xp1 @ Xy0 @ Xz ) )
% 0.20/0.49 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.20/0.49 => ( Xp1 @ Xx @ Xy ) )
% 0.20/0.49 => ! [Xp1: a > a > $o] :
% 0.20/0.49 ( ( ! [Xx0: a,Xy0: a] :
% 0.20/0.49 ( ? [R: a > a > $o] :
% 0.20/0.49 ( ? [Q: a > a > $o] :
% 0.20/0.49 ( ( S @ Q )
% 0.20/0.49 & ( R
% 0.20/0.49 = ( ^ [Xx1: a,Xy1: a] :
% 0.20/0.49 ! [Xp10: a > a > $o] :
% 0.20/0.49 ( ( ! [Xx2: a,Xy2: a] :
% 0.20/0.49 ( ( Q @ Xx2 @ Xy2 )
% 0.20/0.49 => ( Xp10 @ Xx2 @ Xy2 ) )
% 0.20/0.49 & ! [Xx2: a,Xy2: a,Xz: a] :
% 0.20/0.49 ( ( ( Xp10 @ Xx2 @ Xy2 )
% 0.20/0.49 & ( Xp10 @ Xy2 @ Xz ) )
% 0.20/0.49 => ( Xp10 @ Xx2 @ Xz ) ) )
% 0.20/0.49 => ( Xp10 @ Xx1 @ Xy1 ) ) ) ) )
% 0.20/0.49 & ( R @ Xx0 @ Xy0 ) )
% 0.20/0.49 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.20/0.49 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.20/0.49 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.20/0.49 & ( Xp1 @ Xy0 @ Xz ) )
% 0.20/0.49 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.20/0.49 => ( Xp1 @ Xx @ Xy ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.MWM4LQ3UJ6/cvc5---1.0.5_19483.p...
% 0.20/0.49 (declare-sort $$unsorted 0)
% 0.20/0.49 (declare-sort tptp.a 0)
% 0.20/0.49 (assert (not (forall ((S (-> (-> tptp.a tptp.a Bool) Bool)) (Xx tptp.a) (Xy tptp.a)) (=> (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (exists ((R (-> tptp.a tptp.a Bool))) (and (@ S R) (@ (@ R Xx0) Xy0))) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp1 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx) Xy))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (exists ((R (-> tptp.a tptp.a Bool))) (and (exists ((Q (-> tptp.a tptp.a Bool))) (and (@ S Q) (= R (lambda ((Xx1 tptp.a) (Xy1 tptp.a)) (forall ((Xp10 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx2 tptp.a) (Xy2 tptp.a)) (=> (@ (@ Q Xx2) Xy2) (@ (@ Xp10 Xx2) Xy2))) (forall ((Xx2 tptp.a) (Xy2 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx2))) (=> (and (@ _let_1 Xy2) (@ (@ Xp10 Xy2) Xz)) (@ _let_1 Xz))))) (@ (@ Xp10 Xx1) Xy1))))))) (@ (@ R Xx0) Xy0))) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp1 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx) Xy)))))))
% 0.20/0.53 (set-info :filename cvc5---1.0.5_19483)
% 0.20/0.53 (check-sat-assuming ( true ))
% 0.20/0.53 ------- get file name : TPTP file name is SEV129^5
% 0.20/0.53 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19483.smt2...
% 0.20/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Theorem for SEV129^5
% 0.20/0.53 % SZS output start Proof for SEV129^5
% 0.20/0.53 (
% 0.20/0.53 (let ((_let_1 (not (forall ((S (-> (-> tptp.a tptp.a Bool) Bool)) (Xx tptp.a) (Xy tptp.a)) (=> (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (exists ((R (-> tptp.a tptp.a Bool))) (and (@ S R) (@ (@ R Xx0) Xy0))) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp1 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx) Xy))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (exists ((R (-> tptp.a tptp.a Bool))) (and (exists ((Q (-> tptp.a tptp.a Bool))) (and (@ S Q) (= R (lambda ((Xx1 tptp.a) (Xy1 tptp.a)) (forall ((Xp10 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx2 tptp.a) (Xy2 tptp.a)) (=> (@ (@ Q Xx2) Xy2) (@ (@ Xp10 Xx2) Xy2))) (forall ((Xx2 tptp.a) (Xy2 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx2))) (=> (and (@ _let_1 Xy2) (@ (@ Xp10 Xy2) Xz)) (@ _let_1 Xz))))) (@ (@ Xp10 Xx1) Xy1))))))) (@ (@ R Xx0) Xy0))) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp1 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx) Xy)))))))) (let ((_let_2 (forall ((Xx2 tptp.a) (Xy2 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 Xx2) Xy2)) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 Xx2) Xy2))))) (let ((_let_3 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_4 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_5 (not _let_4))) (let ((_let_6 (or _let_5 _let_3))) (let ((_let_7 (not _let_2))) (let ((_let_8 (or _let_7 (not (forall ((Xx2 tptp.a) (Xy2 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 Xx2))) (or (not (ho_3 _let_1 Xy2)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 Xy2) Xz)) (ho_3 _let_1 Xz))))) _let_3))) (let ((_let_9 (forall ((BOUND_VARIABLE_907 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx2 tptp.a) (Xy2 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 Xx2) Xy2)) (ho_3 (ho_2 BOUND_VARIABLE_907 Xx2) Xy2)))) (not (forall ((Xx2 tptp.a) (Xy2 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_907 Xx2))) (or (not (ho_3 _let_1 Xy2)) (not (ho_3 (ho_2 BOUND_VARIABLE_907 Xy2) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_907 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (let ((_let_10 (not _let_8))) (let ((_let_11 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_12 (not _let_11))) (let ((_let_13 (not _let_9))) (let ((_let_14 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_15 (or _let_14 _let_13 _let_12))) (let ((_let_16 (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_899 |u_(-> tptp.a tptp.a Bool)|)) (or (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0) Xy0) (not (forall ((BOUND_VARIABLE_907 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx2 tptp.a) (Xy2 tptp.a)) (or (not (ho_3 (ho_2 BOUND_VARIABLE_899 Xx2) Xy2)) (ho_3 (ho_2 BOUND_VARIABLE_907 Xx2) Xy2)))) (not (forall ((Xx2 tptp.a) (Xy2 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_907 Xx2))) (or (not (ho_3 _let_1 Xy2)) (not (ho_3 (ho_2 BOUND_VARIABLE_907 Xy2) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_907 Xx0) Xy0)))) (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_899)))))) (let ((_let_17 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_18 (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xy0) Xz)) (ho_3 _let_1 Xz)))))) (let ((_let_19 (not _let_18))) (let ((_let_20 (not _let_16))) (let ((_let_21 (forall ((BOUND_VARIABLE_938 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_951 |u_(-> tptp.a tptp.a Bool)|)) (or (ho_3 (ho_2 BOUND_VARIABLE_938 Xx0) Xy0) (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_951)) (not (ho_3 (ho_2 BOUND_VARIABLE_951 Xx0) Xy0))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_938 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 BOUND_VARIABLE_938 Xy0) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_938 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_19 _let_17))) (let ((_let_24 (forall ((BOUND_VARIABLE_902 |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (Xx tptp.a) (Xy tptp.a) (BOUND_VARIABLE_881 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((BOUND_VARIABLE_938 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_951 |u_(-> tptp.a tptp.a Bool)|)) (or (ho_3 (ho_2 BOUND_VARIABLE_938 Xx0) Xy0) (not (ho_4 BOUND_VARIABLE_902 BOUND_VARIABLE_951)) (not (ho_3 (ho_2 BOUND_VARIABLE_951 Xx0) Xy0))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_938 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 BOUND_VARIABLE_938 Xy0) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_938 Xx) Xy)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_899 |u_(-> tptp.a tptp.a Bool)|)) (or (ho_3 (ho_2 BOUND_VARIABLE_881 Xx0) Xy0) (not (forall ((BOUND_VARIABLE_907 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx2 tptp.a) (Xy2 tptp.a)) (or (not (ho_3 (ho_2 BOUND_VARIABLE_899 Xx2) Xy2)) (ho_3 (ho_2 BOUND_VARIABLE_907 Xx2) Xy2)))) (not (forall ((Xx2 tptp.a) (Xy2 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_907 Xx2))) (or (not (ho_3 _let_1 Xy2)) (not (ho_3 (ho_2 BOUND_VARIABLE_907 Xy2) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_907 Xx0) Xy0)))) (not (ho_4 BOUND_VARIABLE_902 BOUND_VARIABLE_899))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_881 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 BOUND_VARIABLE_881 Xy0) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_881 Xx) Xy))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_27 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_28 (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_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_29 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_30 (forall ((u |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a Bool)|)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_31 (forall ((x |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a Bool)|)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_32 (not _let_24))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((S (-> (-> tptp.a tptp.a Bool) Bool)) (Xx tptp.a) (Xy tptp.a) (BOUND_VARIABLE_854 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xp1 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_699 (-> tptp.a tptp.a Bool))) (or (@ (@ Xp1 Xx0) Xy0) (not (@ S BOUND_VARIABLE_699)) (not (@ (@ BOUND_VARIABLE_699 Xx0) Xy0))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp1 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx) Xy)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_815 (-> tptp.a tptp.a Bool))) (or (@ (@ BOUND_VARIABLE_854 Xx0) Xy0) (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx2 tptp.a) (Xy2 tptp.a)) (or (not (@ (@ BOUND_VARIABLE_815 Xx2) Xy2)) (@ (@ Xp10 Xx2) Xy2)))) (not (forall ((Xx2 tptp.a) (Xy2 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx2))) (or (not (@ _let_1 Xy2)) (not (@ (@ Xp10 Xy2) Xz)) (@ _let_1 Xz))))) (@ (@ Xp10 Xx0) Xy0)))) (not (@ S BOUND_VARIABLE_815))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ BOUND_VARIABLE_854 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ BOUND_VARIABLE_854 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ BOUND_VARIABLE_854 Xx) Xy)))) _let_32))))))) (let ((_let_34 (or))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_33) :args (_let_32))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_24))) (REFL :args (_let_25)) :args _let_34)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_33 (PREPROCESS :args ((and _let_31 _let_30 _let_29 _let_28 _let_27 _let_26)))) :args ((and _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26))) :args (0)) :args (_let_25 true _let_24)))) (let ((_let_36 (REFL :args (_let_23)))) (let ((_let_37 (_let_16))) (let ((_let_38 (or _let_14 _let_12 _let_5))) (let ((_let_39 (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_951 |u_(-> tptp.a tptp.a Bool)|)) (or (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0) Xy0) (not (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_951)) (not (ho_3 (ho_2 BOUND_VARIABLE_951 Xx0) Xy0)))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xy0) Xz)) (ho_3 _let_1 Xz)))))) (let ((_let_42 (not _let_41))) (let ((_let_43 (not _let_39))) (let ((_let_44 (or _let_43 _let_42 _let_17))) (let ((_let_45 (_let_21))) (let ((_let_46 (_let_43))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_46)) :args _let_46)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_39))) (REFL :args (_let_40)) :args _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_17 _let_43 _let_42 (not _let_44)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 3)) _let_35 :args ((not _let_17) true _let_23)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_18 (= Xx0 Xx0) (= Xz Xz) (= Xy0 Xy0)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 2)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_34)) :args ((or _let_18 _let_23))) _let_35 :args (_let_18 true _let_23)) :args (_let_41 false _let_18)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_45) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_2 BOUND_VARIABLE_938 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_34)) :args ((or _let_21 _let_23))) _let_35 :args (_let_21 true _let_23)) :args (_let_44 false _let_21)) :args (_let_43 true _let_17 false _let_41 false _let_44)) :args (_let_40 true _let_39)))) (let ((_let_48 (REFL :args (_let_38)))) (let ((_let_49 (_let_13))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_49)) :args _let_49)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_9))) (REFL :args (_let_10)) :args _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_14 _let_12 _let_13 (not _let_15)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 0)) _let_47 :args ((not _let_14) true _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_34)) :args ((or _let_11 _let_38))) _let_47 :args (_let_11 true _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_37) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0) Xy0) true)) (not (= (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_899) false))))) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_16))) :args _let_34)) :args ((or _let_16 _let_23))) _let_35 :args (_let_16 true _let_23)) :args (_let_15 false _let_16)) :args (_let_13 true _let_14 false _let_11 false _let_15)) :args (_let_10 true _let_9)))) (let ((_let_51 (not _let_6))) (let ((_let_52 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_52) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_5 _let_3 _let_51))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 2)) (CONG _let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) :args _let_34)) :args ((or _let_4 _let_38))) _let_47 :args (_let_4 true _let_38)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_8 2)) _let_50 :args ((not _let_3) true _let_8)) :args (_let_51 false _let_4 true _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_8 0)) (CONG (REFL :args (_let_8)) (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_2))) :args _let_34)) :args ((or _let_2 _let_8))) _let_50 :args (_let_2 true _let_8)) :args (false true _let_6 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.54 )
% 0.20/0.54 % SZS output end Proof for SEV129^5
% 0.20/0.54 % cvc5---1.0.5 exiting
% 0.20/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------