TSTP Solution File: SEV208^5 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV208^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 19:21:52 EDT 2023
% Result : Theorem 0.21s 0.56s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV208^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.36 % Computer : n015.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 24 02:30:05 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : SEV208^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.50 % Domain : Set Theory (Sets of sets)
% 0.21/0.50 % Problem : TPS problem from S-THMS
% 0.21/0.50 % Version : Especial.
% 0.21/0.50 % English :
% 0.21/0.50
% 0.21/0.50 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.50 % Source : [Bro09]
% 0.21/0.50 % Names : tps_1209 [Bro09]
% 0.21/0.50
% 0.21/0.50 % Status : Theorem
% 0.21/0.50 % Rating : 0.23 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v4.0.0
% 0.21/0.50 % Syntax : Number of formulae : 8 ( 0 unt; 7 typ; 0 def)
% 0.21/0.50 % Number of atoms : 24 ( 21 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 24 ( 24 avg)
% 0.21/0.50 % Number of connectives : 95 ( 0 ~; 6 |; 22 &; 60 @)
% 0.21/0.50 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 25 ( 25 avg)
% 0.21/0.50 % Number of types : 2 ( 1 usr)
% 0.21/0.50 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 8 ( 6 usr; 6 con; 0-2 aty)
% 0.21/0.50 % Number of variables : 30 ( 0 ^; 12 !; 18 ?; 30 :)
% 0.21/0.50 % SPC : TH0_THM_EQU_NAR
% 0.21/0.50
% 0.21/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(a_type,type,
% 0.21/0.50 a: $tType ).
% 0.21/0.50
% 0.21/0.50 thf(z,type,
% 0.21/0.50 z: a ).
% 0.21/0.50
% 0.21/0.50 thf(y,type,
% 0.21/0.50 y: a ).
% 0.21/0.50
% 0.21/0.50 thf(cP,type,
% 0.21/0.50 cP: a > a > a ).
% 0.21/0.50
% 0.21/0.50 thf(w,type,
% 0.21/0.50 w: a ).
% 0.21/0.50
% 0.21/0.50 thf(x,type,
% 0.21/0.50 x: a ).
% 0.21/0.50
% 0.21/0.50 thf(c0,type,
% 0.21/0.50 c0: a ).
% 0.21/0.50
% 0.21/0.50 thf(cS_INCL_LEM1_pme,conjecture,
% 0.21/0.50 ( ( ! [R: a > a > a > $o] :
% 0.21/0.50 ( ( $true
% 0.21/0.50 & ! [Xa: a,Xb: a,Xc: a] :
% 0.21/0.50 ( ( ( ( Xa = c0 )
% 0.21/0.50 & ( Xb = Xc ) )
% 0.21/0.50 | ( ( Xb = c0 )
% 0.21/0.50 & ( Xa = Xc ) )
% 0.21/0.50 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 0.21/0.50 ( ( Xa
% 0.21/0.50 = ( cP @ Xx1 @ Xx2 ) )
% 0.21/0.50 & ( Xb
% 0.21/0.50 = ( cP @ Xy1 @ Xy2 ) )
% 0.21/0.50 & ( Xc
% 0.21/0.50 = ( cP @ Xz1 @ Xz2 ) )
% 0.21/0.50 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.21/0.50 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.21/0.50 => ( R @ Xa @ Xb @ Xc ) ) )
% 0.21/0.50 => ( R @ x @ y @ y ) )
% 0.21/0.50 & ! [R: a > a > a > $o] :
% 0.21/0.50 ( ( $true
% 0.21/0.50 & ! [Xa: a,Xb: a,Xc: a] :
% 0.21/0.50 ( ( ( ( Xa = c0 )
% 0.21/0.50 & ( Xb = Xc ) )
% 0.21/0.50 | ( ( Xb = c0 )
% 0.21/0.50 & ( Xa = Xc ) )
% 0.21/0.50 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 0.21/0.50 ( ( Xa
% 0.21/0.50 = ( cP @ Xx1 @ Xx2 ) )
% 0.21/0.50 & ( Xb
% 0.21/0.50 = ( cP @ Xy1 @ Xy2 ) )
% 0.21/0.50 & ( Xc
% 0.21/0.50 = ( cP @ Xz1 @ Xz2 ) )
% 0.21/0.50 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.21/0.50 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.21/0.50 => ( R @ Xa @ Xb @ Xc ) ) )
% 0.21/0.50 => ( R @ w @ z @ z ) ) )
% 0.21/0.50 => ! [R: a > a > a > $o] :
% 0.21/0.50 ( ( $true
% 0.21/0.50 & ! [Xa: a,Xb: a,Xc: a] :
% 0.21/0.50 ( ( ( ( Xa = c0 )
% 0.21/0.50 & ( Xb = Xc ) )
% 0.21/0.50 | ( ( Xb = c0 )
% 0.21/0.50 & ( Xa = Xc ) )
% 0.21/0.50 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 0.21/0.50 ( ( Xa
% 0.21/0.50 = ( cP @ Xx1 @ Xx2 ) )
% 0.21/0.50 & ( Xb
% 0.21/0.50 = ( cP @ Xy1 @ Xy2 ) )
% 0.21/0.50 & ( Xc
% 0.21/0.50 = ( cP @ Xz1 @ Xz2 ) )
% 0.21/0.50 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.21/0.50 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.21/0.50 => ( R @ Xa @ Xb @ Xc ) ) )
% 0.21/0.50 => ( R @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.a1hm9Vh0DH/cvc5---1.0.5_28620.p...
% 0.21/0.56 (declare-sort $$unsorted 0)
% 0.21/0.56 (declare-sort tptp.a 0)
% 0.21/0.56 (declare-fun tptp.z () tptp.a)
% 0.21/0.56 (declare-fun tptp.y () tptp.a)
% 0.21/0.56 (declare-fun tptp.cP (tptp.a tptp.a) tptp.a)
% 0.21/0.56 (declare-fun tptp.w () tptp.a)
% 0.21/0.56 (declare-fun tptp.x () tptp.a)
% 0.21/0.56 (declare-fun tptp.c0 () tptp.a)
% 0.21/0.56 (assert (not (=> (and (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (=> (and true (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a)) (=> (or (and (= Xa tptp.c0) (= Xb Xc)) (and (= Xb tptp.c0) (= Xa Xc)) (exists ((Xx1 tptp.a) (Xx2 tptp.a) (Xy1 tptp.a) (Xy2 tptp.a) (Xz1 tptp.a) (Xz2 tptp.a)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R tptp.x) tptp.y) tptp.y))) (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (=> (and true (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a)) (=> (or (and (= Xa tptp.c0) (= Xb Xc)) (and (= Xb tptp.c0) (= Xa Xc)) (exists ((Xx1 tptp.a) (Xx2 tptp.a) (Xy1 tptp.a) (Xy2 tptp.a) (Xz1 tptp.a) (Xz2 tptp.a)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R tptp.w) tptp.z) tptp.z)))) (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (let ((_let_1 (@ (@ tptp.cP tptp.y) tptp.z))) (=> (and true (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a)) (=> (or (and (= Xa tptp.c0) (= Xb Xc)) (and (= Xb tptp.c0) (= Xa Xc)) (exists ((Xx1 tptp.a) (Xx2 tptp.a) (Xy1 tptp.a) (Xy2 tptp.a) (Xz1 tptp.a) (Xz2 tptp.a)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R (@ (@ tptp.cP tptp.x) tptp.w)) _let_1) _let_1)))))))
% 0.21/0.56 (set-info :filename cvc5---1.0.5_28620)
% 0.21/0.56 (check-sat-assuming ( true ))
% 0.21/0.56 ------- get file name : TPTP file name is SEV208^5
% 0.21/0.56 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_28620.smt2...
% 0.21/0.56 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.56 % SZS status Theorem for SEV208^5
% 0.21/0.56 % SZS output start Proof for SEV208^5
% 0.21/0.56 (
% 0.21/0.56 (let ((_let_1 (not (=> (and (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (=> (and true (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a)) (=> (or (and (= Xa tptp.c0) (= Xb Xc)) (and (= Xb tptp.c0) (= Xa Xc)) (exists ((Xx1 tptp.a) (Xx2 tptp.a) (Xy1 tptp.a) (Xy2 tptp.a) (Xz1 tptp.a) (Xz2 tptp.a)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R tptp.x) tptp.y) tptp.y))) (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (=> (and true (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a)) (=> (or (and (= Xa tptp.c0) (= Xb Xc)) (and (= Xb tptp.c0) (= Xa Xc)) (exists ((Xx1 tptp.a) (Xx2 tptp.a) (Xy1 tptp.a) (Xy2 tptp.a) (Xz1 tptp.a) (Xz2 tptp.a)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R tptp.w) tptp.z) tptp.z)))) (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (let ((_let_1 (@ (@ tptp.cP tptp.y) tptp.z))) (=> (and true (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a)) (=> (or (and (= Xa tptp.c0) (= Xb Xc)) (and (= Xb tptp.c0) (= Xa Xc)) (exists ((Xx1 tptp.a) (Xx2 tptp.a) (Xy1 tptp.a) (Xy2 tptp.a) (Xz1 tptp.a) (Xz2 tptp.a)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R (@ (@ tptp.cP tptp.x) tptp.w)) _let_1) _let_1)))))))) (let ((_let_2 (ho_4 (ho_3 k_2 tptp.y) tptp.z))) (let ((_let_3 (ho_4 (ho_3 k_2 tptp.x) tptp.w))) (let ((_let_4 (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_3) _let_2) _let_2))) (let ((_let_5 (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.w) tptp.z) tptp.z))) (let ((_let_6 (not _let_5))) (let ((_let_7 (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.x) tptp.y) tptp.y))) (let ((_let_8 (not _let_7))) (let ((_let_9 (or _let_8 _let_6))) (let ((_let_10 (and (not (= tptp.c0 _let_3)) (or (not (= tptp.c0 _let_2)) (not (= _let_2 _let_3))) _let_9))) (let ((_let_11 (or _let_10 _let_4))) (let ((_let_12 (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_921 tptp.a) (BOUND_VARIABLE_919 tptp.a) (BOUND_VARIABLE_917 tptp.a) (BOUND_VARIABLE_915 tptp.a) (BOUND_VARIABLE_913 tptp.a) (BOUND_VARIABLE_911 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (ho_4 (ho_3 k_2 BOUND_VARIABLE_911) BOUND_VARIABLE_913))) (not (= Xb (ho_4 (ho_3 k_2 BOUND_VARIABLE_915) BOUND_VARIABLE_917))) (not (= Xc (ho_4 (ho_3 k_2 BOUND_VARIABLE_919) BOUND_VARIABLE_921))) (not (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 BOUND_VARIABLE_911) BOUND_VARIABLE_915) BOUND_VARIABLE_919)) (not (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 BOUND_VARIABLE_913) BOUND_VARIABLE_917) BOUND_VARIABLE_921)))) (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xa) Xb) Xc))))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_4))) (let ((_let_15 (forall ((BOUND_VARIABLE_972 |u_(-> tptp.a tptp.a tptp.a Bool)|)) (let ((_let_1 (ho_4 (ho_3 k_2 tptp.y) tptp.z))) (or (not (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_921 tptp.a) (BOUND_VARIABLE_919 tptp.a) (BOUND_VARIABLE_917 tptp.a) (BOUND_VARIABLE_915 tptp.a) (BOUND_VARIABLE_913 tptp.a) (BOUND_VARIABLE_911 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (ho_4 (ho_3 k_2 BOUND_VARIABLE_911) BOUND_VARIABLE_913))) (not (= Xb (ho_4 (ho_3 k_2 BOUND_VARIABLE_915) BOUND_VARIABLE_917))) (not (= Xc (ho_4 (ho_3 k_2 BOUND_VARIABLE_919) BOUND_VARIABLE_921))) (not (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_972 BOUND_VARIABLE_911) BOUND_VARIABLE_915) BOUND_VARIABLE_919)) (not (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_972 BOUND_VARIABLE_913) BOUND_VARIABLE_917) BOUND_VARIABLE_921)))) (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_972 Xa) Xb) Xc)))) (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_972 (ho_4 (ho_3 k_2 tptp.x) tptp.w)) _let_1) _let_1)))))) (let ((_let_16 (not _let_14))) (let ((_let_17 (0))) (let ((_let_18 (forall ((u |u_(-> tptp.a tptp.a)|) (e tptp.a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_19 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_20 (forall ((u |u_(-> tptp.a tptp.a tptp.a)|) (e |u_(-> tptp.a tptp.a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_21 (forall ((x |u_(-> tptp.a tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_22 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_23 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_7 x z) (ho_7 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_6 v ii) (ite (= i ii) e (ho_6 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_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_26 (forall ((u |u_(-> tptp.a tptp.a tptp.a Bool)|) (e |u_(-> tptp.a tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_27 (forall ((x |u_(-> tptp.a tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_28 (forall ((BOUND_VARIABLE_1015 |u_(-> tptp.a tptp.a tptp.a Bool)|)) (or (not (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_848 tptp.a) (BOUND_VARIABLE_846 tptp.a) (BOUND_VARIABLE_844 tptp.a) (BOUND_VARIABLE_842 tptp.a) (BOUND_VARIABLE_840 tptp.a) (BOUND_VARIABLE_838 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (ho_4 (ho_3 k_2 BOUND_VARIABLE_838) BOUND_VARIABLE_840))) (not (= Xb (ho_4 (ho_3 k_2 BOUND_VARIABLE_842) BOUND_VARIABLE_844))) (not (= Xc (ho_4 (ho_3 k_2 BOUND_VARIABLE_846) BOUND_VARIABLE_848))) (not (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_1015 BOUND_VARIABLE_838) BOUND_VARIABLE_842) BOUND_VARIABLE_846)) (not (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_1015 BOUND_VARIABLE_840) BOUND_VARIABLE_844) BOUND_VARIABLE_848)))) (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_1015 Xa) Xb) Xc)))) (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_1015 tptp.w) tptp.z) tptp.z))))) (let ((_let_29 (forall ((BOUND_VARIABLE_1050 |u_(-> tptp.a tptp.a tptp.a Bool)|)) (or (not (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_776 tptp.a) (BOUND_VARIABLE_774 tptp.a) (BOUND_VARIABLE_772 tptp.a) (BOUND_VARIABLE_770 tptp.a) (BOUND_VARIABLE_768 tptp.a) (BOUND_VARIABLE_766 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (ho_4 (ho_3 k_2 BOUND_VARIABLE_766) BOUND_VARIABLE_768))) (not (= Xb (ho_4 (ho_3 k_2 BOUND_VARIABLE_770) BOUND_VARIABLE_772))) (not (= Xc (ho_4 (ho_3 k_2 BOUND_VARIABLE_774) BOUND_VARIABLE_776))) (not (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_1050 BOUND_VARIABLE_766) BOUND_VARIABLE_770) BOUND_VARIABLE_774)) (not (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_1050 BOUND_VARIABLE_768) BOUND_VARIABLE_772) BOUND_VARIABLE_776)))) (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_1050 Xa) Xb) Xc)))) (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_1050 tptp.x) tptp.y) tptp.y))))) (let ((_let_30 (not (=> (and _let_29 _let_28) _let_15)))) (let ((_let_31 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> (and (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (or (not (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_776 tptp.a) (BOUND_VARIABLE_774 tptp.a) (BOUND_VARIABLE_772 tptp.a) (BOUND_VARIABLE_770 tptp.a) (BOUND_VARIABLE_768 tptp.a) (BOUND_VARIABLE_766 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_766) BOUND_VARIABLE_768))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_770) BOUND_VARIABLE_772))) (not (= Xc (@ (@ tptp.cP BOUND_VARIABLE_774) BOUND_VARIABLE_776))) (not (@ (@ (@ R BOUND_VARIABLE_766) BOUND_VARIABLE_770) BOUND_VARIABLE_774)) (not (@ (@ (@ R BOUND_VARIABLE_768) BOUND_VARIABLE_772) BOUND_VARIABLE_776)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R tptp.x) tptp.y) tptp.y))) (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (or (not (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_848 tptp.a) (BOUND_VARIABLE_846 tptp.a) (BOUND_VARIABLE_844 tptp.a) (BOUND_VARIABLE_842 tptp.a) (BOUND_VARIABLE_840 tptp.a) (BOUND_VARIABLE_838 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_838) BOUND_VARIABLE_840))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_842) BOUND_VARIABLE_844))) (not (= Xc (@ (@ tptp.cP BOUND_VARIABLE_846) BOUND_VARIABLE_848))) (not (@ (@ (@ R BOUND_VARIABLE_838) BOUND_VARIABLE_842) BOUND_VARIABLE_846)) (not (@ (@ (@ R BOUND_VARIABLE_840) BOUND_VARIABLE_844) BOUND_VARIABLE_848)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R tptp.w) tptp.z) tptp.z)))) (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (let ((_let_1 (@ (@ tptp.cP tptp.y) tptp.z))) (or (not (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_921 tptp.a) (BOUND_VARIABLE_919 tptp.a) (BOUND_VARIABLE_917 tptp.a) (BOUND_VARIABLE_915 tptp.a) (BOUND_VARIABLE_913 tptp.a) (BOUND_VARIABLE_911 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_911) BOUND_VARIABLE_913))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_915) BOUND_VARIABLE_917))) (not (= Xc (@ (@ tptp.cP BOUND_VARIABLE_919) BOUND_VARIABLE_921))) (not (@ (@ (@ R BOUND_VARIABLE_911) BOUND_VARIABLE_915) BOUND_VARIABLE_919)) (not (@ (@ (@ R BOUND_VARIABLE_913) BOUND_VARIABLE_917) BOUND_VARIABLE_921)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R (@ (@ tptp.cP tptp.x) tptp.w)) _let_1) _let_1)))))) _let_30))))) (PREPROCESS :args ((and _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18)))) :args ((and _let_30 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18))) :args _let_17))) (let ((_let_32 (or))) (let ((_let_33 (not _let_15))) (let ((_let_34 (_let_33))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_34)) :args _let_34)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_15))) (REFL :args (_let_16)) :args _let_32)) (NOT_IMPLIES_ELIM2 _let_31) :args (_let_16 true _let_15)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 0)) (CONG (REFL :args (_let_14)) (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_32)) :args ((or _let_12 _let_14))) _let_35 :args (_let_12 true _let_14)))) (let ((_let_37 (_let_12))) (let ((_let_38 (not _let_10))) (let ((_let_39 (not _let_9))) (let ((_let_40 (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_848 tptp.a) (BOUND_VARIABLE_846 tptp.a) (BOUND_VARIABLE_844 tptp.a) (BOUND_VARIABLE_842 tptp.a) (BOUND_VARIABLE_840 tptp.a) (BOUND_VARIABLE_838 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (ho_4 (ho_3 k_2 BOUND_VARIABLE_838) BOUND_VARIABLE_840))) (not (= Xb (ho_4 (ho_3 k_2 BOUND_VARIABLE_842) BOUND_VARIABLE_844))) (not (= Xc (ho_4 (ho_3 k_2 BOUND_VARIABLE_846) BOUND_VARIABLE_848))) (not (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 BOUND_VARIABLE_838) BOUND_VARIABLE_842) BOUND_VARIABLE_846)) (not (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 BOUND_VARIABLE_840) BOUND_VARIABLE_844) BOUND_VARIABLE_848)))) (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xa) Xb) Xc))))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_5))) (let ((_let_43 (NOT_IMPLIES_ELIM1 _let_31))) (let ((_let_44 (_let_28))) (let ((_let_45 (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_776 tptp.a) (BOUND_VARIABLE_774 tptp.a) (BOUND_VARIABLE_772 tptp.a) (BOUND_VARIABLE_770 tptp.a) (BOUND_VARIABLE_768 tptp.a) (BOUND_VARIABLE_766 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (ho_4 (ho_3 k_2 BOUND_VARIABLE_766) BOUND_VARIABLE_768))) (not (= Xb (ho_4 (ho_3 k_2 BOUND_VARIABLE_770) BOUND_VARIABLE_772))) (not (= Xc (ho_4 (ho_3 k_2 BOUND_VARIABLE_774) BOUND_VARIABLE_776))) (not (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 BOUND_VARIABLE_766) BOUND_VARIABLE_770) BOUND_VARIABLE_774)) (not (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 BOUND_VARIABLE_768) BOUND_VARIABLE_772) BOUND_VARIABLE_776)))) (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xa) Xb) Xc))))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_7))) (let ((_let_48 (_let_29))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_11)) :args ((or _let_4 _let_10 (not _let_11)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_10 2)) :args ((or _let_9 _let_38))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_9)) :args ((or _let_8 _let_6 _let_39))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_7 (not _let_47)))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_12 (= Xa Xa) (= Xb Xb) (= Xc Xc) (= BOUND_VARIABLE_911 BOUND_VARIABLE_766) (= BOUND_VARIABLE_915 BOUND_VARIABLE_770) (= BOUND_VARIABLE_919 BOUND_VARIABLE_774) (= BOUND_VARIABLE_913 BOUND_VARIABLE_768) (= BOUND_VARIABLE_917 BOUND_VARIABLE_772) (= BOUND_VARIABLE_921 BOUND_VARIABLE_776)))) _let_36 :args (_let_45 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_48) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_5 BOUND_VARIABLE_1050 tptp.x)))) :args _let_48)) (AND_ELIM _let_43 :args _let_17) :args (_let_47 false _let_29)) :args (_let_7 false _let_45 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_5 (not _let_42)))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_12 (= Xa Xa) (= Xb Xb) (= Xc Xc) (= BOUND_VARIABLE_911 BOUND_VARIABLE_838) (= BOUND_VARIABLE_915 BOUND_VARIABLE_842) (= BOUND_VARIABLE_919 BOUND_VARIABLE_846) (= BOUND_VARIABLE_913 BOUND_VARIABLE_840) (= BOUND_VARIABLE_917 BOUND_VARIABLE_844) (= BOUND_VARIABLE_921 BOUND_VARIABLE_848)))) _let_36 :args (_let_40 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_5 BOUND_VARIABLE_1015 tptp.w)))) :args _let_44)) (AND_ELIM _let_43 :args (1)) :args (_let_42 false _let_28)) :args (_let_5 false _let_40 false _let_42)) :args (_let_39 false _let_7 false _let_5)) :args (_let_38 true _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_37) :args (_let_3 _let_2 _let_2 tptp.z tptp.y tptp.z tptp.y tptp.w tptp.x QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_37))) _let_36 :args (_let_11 false _let_12)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_14 1)) _let_35 :args ((not _let_4) true _let_14)) :args (false true _let_10 false _let_11 true _let_4)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.57 )
% 0.21/0.57 % SZS output end Proof for SEV208^5
% 0.21/0.57 % cvc5---1.0.5 exiting
% 0.21/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------