TSTP Solution File: SEV097^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV097^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 19:21:32 EDT 2023
% Result : Theorem 0.21s 0.57s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV097^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 02:38:32 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.57 %------------------------------------------------------------------------------
% 0.21/0.57 % File : SEV097^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.57 % Domain : Set Theory (Relations)
% 0.21/0.57 % Problem : TPS problem from RELN-THMS
% 0.21/0.57 % Version : Especial.
% 0.21/0.57 % English :
% 0.21/0.57
% 0.21/0.57 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.57 % Source : [Bro09]
% 0.21/0.57 % Names : tps_1073 [Bro09]
% 0.21/0.57
% 0.21/0.57 % Status : Theorem
% 0.21/0.57 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.21/0.57 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.21/0.57 % Number of atoms : 14 ( 0 equ; 0 cnn)
% 0.21/0.57 % Maximal formula atoms : 14 ( 14 avg)
% 0.21/0.57 % Number of connectives : 42 ( 1 ~; 1 |; 7 &; 28 @)
% 0.21/0.57 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.21/0.57 % Maximal formula depth : 12 ( 12 avg)
% 0.21/0.57 % Number of types : 3 ( 2 usr)
% 0.21/0.57 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.21/0.57 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.21/0.57 % Number of variables : 15 ( 0 ^; 13 !; 2 ?; 15 :)
% 0.21/0.57 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.57
% 0.21/0.57 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.57 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.57 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.57 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.57 %------------------------------------------------------------------------------
% 0.21/0.57 thf(a_type,type,
% 0.21/0.57 a: $tType ).
% 0.21/0.57
% 0.21/0.57 thf(b_type,type,
% 0.21/0.57 b: $tType ).
% 0.21/0.57
% 0.21/0.57 thf(z,type,
% 0.21/0.57 z: a ).
% 0.21/0.57
% 0.21/0.57 thf(cR,type,
% 0.21/0.57 cR: a > a > $o ).
% 0.21/0.57
% 0.21/0.57 thf(f,type,
% 0.21/0.57 f: a > b > $o ).
% 0.21/0.57
% 0.21/0.57 thf(cS,type,
% 0.21/0.57 cS: b > b > $o ).
% 0.21/0.57
% 0.21/0.57 thf(cTHM552C_pme,conjecture,
% 0.21/0.57 ( ( ! [Xu: a,Xv: a,Xw: a] :
% 0.21/0.57 ( ( ( cR @ Xu @ Xv )
% 0.21/0.57 & ( cR @ Xw @ Xv ) )
% 0.21/0.57 => ( cR @ Xu @ Xw ) )
% 0.21/0.57 & ! [Xx: a] : ( cR @ Xx @ Xx ) )
% 0.21/0.57 => ( ( ! [Xx: a] :
% 0.21/0.57 ? [Xy: b] : ( f @ Xx @ Xy )
% 0.21/0.57 & ! [Xx: a,Xy1: b,Xy2: b] :
% 0.21/0.57 ( ( ( f @ Xx @ Xy1 )
% 0.21/0.57 & ( f @ Xx @ Xy2 ) )
% 0.21/0.57 => ( cS @ Xy1 @ Xy2 ) )
% 0.21/0.57 & ! [Xx1: a,Xx2: a,Xy: b] :
% 0.21/0.57 ( ( ( f @ Xx1 @ Xy )
% 0.21/0.57 & ( f @ Xx2 @ Xy ) )
% 0.21/0.57 => ( cR @ Xx1 @ Xx2 ) ) )
% 0.21/0.57 => ! [Xx: a] :
% 0.21/0.57 ? [Xy: b] :
% 0.21/0.57 ! [Xw: a] :
% 0.21/0.57 ( ( f @ Xx @ Xy )
% 0.21/0.57 | ( ~ ( f @ Xw @ Xy )
% 0.21/0.57 & ( cR @ Xx @ z ) ) ) ) ) ).
% 0.21/0.57
% 0.21/0.57 %------------------------------------------------------------------------------
% 0.21/0.57 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.IPn0CLAbci/cvc5---1.0.5_24321.p...
% 0.21/0.57 (declare-sort $$unsorted 0)
% 0.21/0.57 (declare-sort tptp.a 0)
% 0.21/0.57 (declare-sort tptp.b 0)
% 0.21/0.57 (declare-fun tptp.z () tptp.a)
% 0.21/0.57 (declare-fun tptp.cR (tptp.a tptp.a) Bool)
% 0.21/0.57 (declare-fun tptp.f (tptp.a tptp.b) Bool)
% 0.21/0.57 (declare-fun tptp.cS (tptp.b tptp.b) Bool)
% 0.21/0.57 (assert (not (=> (and (forall ((Xu tptp.a) (Xv tptp.a) (Xw tptp.a)) (let ((_let_1 (@ tptp.cR Xu))) (=> (and (@ _let_1 Xv) (@ (@ tptp.cR Xw) Xv)) (@ _let_1 Xw)))) (forall ((Xx tptp.a)) (@ (@ tptp.cR Xx) Xx))) (=> (and (forall ((Xx tptp.a)) (exists ((Xy tptp.b)) (@ (@ tptp.f Xx) Xy))) (forall ((Xx tptp.a) (Xy1 tptp.b) (Xy2 tptp.b)) (let ((_let_1 (@ tptp.f Xx))) (=> (and (@ _let_1 Xy1) (@ _let_1 Xy2)) (@ (@ tptp.cS Xy1) Xy2)))) (forall ((Xx1 tptp.a) (Xx2 tptp.a) (Xy tptp.b)) (=> (and (@ (@ tptp.f Xx1) Xy) (@ (@ tptp.f Xx2) Xy)) (@ (@ tptp.cR Xx1) Xx2)))) (forall ((Xx tptp.a)) (exists ((Xy tptp.b)) (forall ((Xw tptp.a)) (or (@ (@ tptp.f Xx) Xy) (and (not (@ (@ tptp.f Xw) Xy)) (@ (@ tptp.cR Xx) tptp.z))))))))))
% 0.21/0.57 (set-info :filename cvc5---1.0.5_24321)
% 0.21/0.57 (check-sat-assuming ( true ))
% 0.21/0.57 ------- get file name : TPTP file name is SEV097^5
% 0.21/0.57 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24321.smt2...
% 0.21/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.57 % SZS status Theorem for SEV097^5
% 0.21/0.57 % SZS output start Proof for SEV097^5
% 0.21/0.57 (
% 0.21/0.57 (let ((_let_1 (forall ((Xx tptp.a)) (@ (@ tptp.cR Xx) Xx)))) (let ((_let_2 (not (=> (and (forall ((Xu tptp.a) (Xv tptp.a) (Xw tptp.a)) (let ((_let_1 (@ tptp.cR Xu))) (=> (and (@ _let_1 Xv) (@ (@ tptp.cR Xw) Xv)) (@ _let_1 Xw)))) _let_1) (=> (and (forall ((Xx tptp.a)) (exists ((Xy tptp.b)) (@ (@ tptp.f Xx) Xy))) (forall ((Xx tptp.a) (Xy1 tptp.b) (Xy2 tptp.b)) (let ((_let_1 (@ tptp.f Xx))) (=> (and (@ _let_1 Xy1) (@ _let_1 Xy2)) (@ (@ tptp.cS Xy1) Xy2)))) (forall ((Xx1 tptp.a) (Xx2 tptp.a) (Xy tptp.b)) (=> (and (@ (@ tptp.f Xx1) Xy) (@ (@ tptp.f Xx2) Xy)) (@ (@ tptp.cR Xx1) Xx2)))) (forall ((Xx tptp.a)) (exists ((Xy tptp.b)) (forall ((Xw tptp.a)) (or (@ (@ tptp.f Xx) Xy) (and (not (@ (@ tptp.f Xw) Xy)) (@ (@ tptp.cR Xx) tptp.z))))))))))) (let ((_let_3 (forall ((Xx tptp.a)) (not (forall ((Xy tptp.b)) (not (ho_4 (ho_3 k_2 Xx) Xy))))))) (let ((_let_4 (forall ((Xy tptp.b)) (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) Xy))))) (let ((_let_5 (0))) (let ((_let_6 (forall ((u |u_(-> tptp.b Bool)|) (e Bool) (i tptp.b)) (not (forall ((v |u_(-> tptp.b Bool)|)) (not (forall ((ii tptp.b)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_7 (forall ((x |u_(-> tptp.b Bool)|) (y |u_(-> tptp.b Bool)|)) (or (not (forall ((z tptp.b)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_8 (forall ((u |u_(-> tptp.a tptp.b Bool)|) (e |u_(-> tptp.b Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.b Bool)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_9 (forall ((x |u_(-> tptp.a tptp.b Bool)|) (y |u_(-> tptp.a tptp.b Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_10 (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_11 (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_12 (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_13 (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_14 (forall ((u |u_(-> tptp.b tptp.b Bool)|) (e |u_(-> tptp.b Bool)|) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.b Bool)|)) (not (forall ((ii tptp.b)) (= (ho_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_15 (forall ((x |u_(-> tptp.b tptp.b Bool)|) (y |u_(-> tptp.b tptp.b Bool)|)) (or (not (forall ((z tptp.b)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_16 (forall ((Xx tptp.a)) (or (not (forall ((BOUND_VARIABLE_705 tptp.b)) (not (ho_4 (ho_3 k_2 Xx) BOUND_VARIABLE_705)))) (and (ho_7 (ho_6 k_5 Xx) tptp.z) (not (forall ((BOUND_VARIABLE_711 tptp.b)) (not (forall ((BOUND_VARIABLE_683 tptp.a)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_683) BOUND_VARIABLE_711))))))))))) (let ((_let_17 (not (=> (and (forall ((Xu tptp.a) (Xv tptp.a) (Xw tptp.a)) (let ((_let_1 (ho_6 k_5 Xu))) (or (not (ho_7 _let_1 Xv)) (not (ho_7 (ho_6 k_5 Xw) Xv)) (ho_7 _let_1 Xw)))) (forall ((Xx tptp.a)) (ho_7 (ho_6 k_5 Xx) Xx))) (=> (and _let_3 (forall ((Xx tptp.a) (Xy1 tptp.b) (Xy2 tptp.b)) (let ((_let_1 (ho_3 k_2 Xx))) (or (not (ho_4 _let_1 Xy1)) (not (ho_4 _let_1 Xy2)) (ho_4 (ho_9 k_8 Xy1) Xy2)))) (forall ((Xx1 tptp.a) (Xx2 tptp.a) (Xy tptp.b)) (or (not (ho_4 (ho_3 k_2 Xx1) Xy)) (not (ho_4 (ho_3 k_2 Xx2) Xy)) (ho_7 (ho_6 k_5 Xx1) Xx2)))) _let_16))))) (let ((_let_18 (NOT_IMPLIES_ELIM2 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> (and (forall ((Xu tptp.a) (Xv tptp.a) (Xw tptp.a)) (let ((_let_1 (@ tptp.cR Xu))) (or (not (@ _let_1 Xv)) (not (@ (@ tptp.cR Xw) Xv)) (@ _let_1 Xw)))) _let_1) (=> (and (forall ((Xx tptp.a)) (not (forall ((Xy tptp.b)) (not (@ (@ tptp.f Xx) Xy))))) (forall ((Xx tptp.a) (Xy1 tptp.b) (Xy2 tptp.b)) (let ((_let_1 (@ tptp.f Xx))) (or (not (@ _let_1 Xy1)) (not (@ _let_1 Xy2)) (@ (@ tptp.cS Xy1) Xy2)))) (forall ((Xx1 tptp.a) (Xx2 tptp.a) (Xy tptp.b)) (or (not (@ (@ tptp.f Xx1) Xy)) (not (@ (@ tptp.f Xx2) Xy)) (@ (@ tptp.cR Xx1) Xx2)))) (forall ((Xx tptp.a)) (or (not (forall ((BOUND_VARIABLE_705 tptp.b)) (not (@ (@ tptp.f Xx) BOUND_VARIABLE_705)))) (and (@ (@ tptp.cR Xx) tptp.z) (not (forall ((BOUND_VARIABLE_711 tptp.b)) (not (forall ((BOUND_VARIABLE_683 tptp.a)) (not (@ (@ tptp.f BOUND_VARIABLE_683) BOUND_VARIABLE_711)))))))))))) _let_17))))) (PREPROCESS :args ((and _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6)))) :args ((and _let_17 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6))) :args _let_5)))) (let ((_let_19 (forall ((BOUND_VARIABLE_705 tptp.b)) (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) BOUND_VARIABLE_705))))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 (and (ho_7 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) tptp.z) (not (forall ((BOUND_VARIABLE_711 tptp.b)) (not (forall ((BOUND_VARIABLE_683 tptp.a)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_683) BOUND_VARIABLE_711)))))))))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or))) (let ((_let_24 (not _let_16))) (let ((_let_25 (_let_24))) (let ((_let_26 (_let_3))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_26) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_ENUM)) :args _let_26)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_19 (= BOUND_VARIABLE_705 Xy)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_21 0)) (CONG (REFL :args (_let_21)) (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_23)) :args ((or _let_19 _let_21))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_25)) :args _let_25)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_16))) (REFL :args (_let_22)) :args _let_23)) (NOT_IMPLIES_ELIM2 _let_18) :args (_let_22 true _let_16)) :args (_let_19 true _let_21)) :args (_let_4 false _let_19)) (AND_ELIM (NOT_IMPLIES_ELIM1 _let_18) :args _let_5) :args (false false _let_4 false _let_3)) :args (_let_2 true)))))))))))))))))))))))))))))
% 0.21/0.58 )
% 0.21/0.58 % SZS output end Proof for SEV097^5
% 0.21/0.58 % cvc5---1.0.5 exiting
% 0.21/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------