TSTP Solution File: SEV231^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV231^5 : 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 19:21:56 EDT 2023
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV231^5 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % 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 02:05:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 %----Proving TH0
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 % File : SEV231^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.52 % Domain : Set Theory (Sets of sets)
% 0.20/0.52 % Problem : TPS problem X5201
% 0.20/0.52 % Version : Especial.
% 0.20/0.52 % English :
% 0.20/0.52
% 0.20/0.52 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.52 % Source : [Bro09]
% 0.20/0.52 % Names : tps_0343 [Bro09]
% 0.20/0.52 % : X5201 [TPS]
% 0.20/0.52
% 0.20/0.52 % Status : Theorem
% 0.20/0.52 % Rating : 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 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
% 0.20/0.52 % Syntax : Number of formulae : 4 ( 1 unt; 3 typ; 0 def)
% 0.20/0.52 % Number of atoms : 7 ( 3 equ; 0 cnn)
% 0.20/0.52 % Maximal formula atoms : 1 ( 7 avg)
% 0.20/0.52 % Number of connectives : 6 ( 0 ~; 1 |; 1 &; 3 @)
% 0.20/0.52 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.52 % Maximal formula depth : 1 ( 1 avg)
% 0.20/0.52 % Number of types : 2 ( 1 usr)
% 0.20/0.52 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.52 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.20/0.52 % Number of variables : 3 ( 2 ^; 1 !; 0 ?; 3 :)
% 0.20/0.52 % SPC : TH0_THM_EQU_NAR
% 0.20/0.52
% 0.20/0.52 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.52 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.52 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.52 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.52 % : Polymorphic definitions expanded.
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 thf(a_type,type,
% 0.20/0.52 a: $tType ).
% 0.20/0.52
% 0.20/0.52 thf(y,type,
% 0.20/0.52 y: a > $o ).
% 0.20/0.52
% 0.20/0.52 thf(x,type,
% 0.20/0.52 x: a > $o ).
% 0.20/0.52
% 0.20/0.52 thf(cX5201_pme,conjecture,
% 0.20/0.52 ( ( ^ [Xx0: a] :
% 0.20/0.52 ( ( x @ Xx0 )
% 0.20/0.52 & ( y @ Xx0 ) ) )
% 0.20/0.52 = ( ^ [Xx0: a] :
% 0.20/0.52 ! [S: a > $o] :
% 0.20/0.52 ( ( ( S = x )
% 0.20/0.52 | ( S = y ) )
% 0.20/0.52 => ( S @ Xx0 ) ) ) ) ).
% 0.20/0.52
% 0.20/0.52 %------------------------------------------------------------------------------
% 0.20/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.mJetLyP0rB/cvc5---1.0.5_26863.p...
% 0.20/0.52 (declare-sort $$unsorted 0)
% 0.20/0.52 (declare-sort tptp.a 0)
% 0.20/0.52 (declare-fun tptp.y (tptp.a) Bool)
% 0.20/0.52 (declare-fun tptp.x (tptp.a) Bool)
% 0.20/0.52 (assert (not (= (lambda ((Xx0 tptp.a)) (and (@ tptp.x Xx0) (@ tptp.y Xx0))) (lambda ((Xx0 tptp.a)) (forall ((S (-> tptp.a Bool))) (=> (or (= S tptp.x) (= S tptp.y)) (@ S Xx0)))))))
% 0.20/0.52 (set-info :filename cvc5---1.0.5_26863)
% 0.20/0.52 (check-sat-assuming ( true ))
% 0.20/0.52 ------- get file name : TPTP file name is SEV231^5
% 0.20/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26863.smt2...
% 0.20/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.52 % SZS status Theorem for SEV231^5
% 0.20/0.52 % SZS output start Proof for SEV231^5
% 0.20/0.52 (
% 0.20/0.52 (let ((_let_1 (lambda ((Xx0 tptp.a)) (and (@ tptp.x Xx0) (@ tptp.y Xx0))))) (let ((_let_2 (not (= _let_1 (lambda ((Xx0 tptp.a)) (forall ((S (-> tptp.a Bool))) (=> (or (= S tptp.x) (= S tptp.y)) (@ S Xx0)))))))) (let ((_let_3 (and (ho_5 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19) (ho_5 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)))) (let ((_let_4 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_5 (= _let_4 _let_3))) (let ((_let_6 (forall ((BOUND_VARIABLE_657 tptp.a)) (= (ho_5 k_4 BOUND_VARIABLE_657) (and (ho_5 k_7 BOUND_VARIABLE_657) (ho_5 k_6 BOUND_VARIABLE_657)))))) (let ((_let_7 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_8 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_9 (forall ((BOUND_VARIABLE_649 tptp.a)) (= (ho_5 k_8 BOUND_VARIABLE_649) (and (ho_5 k_7 BOUND_VARIABLE_649) (ho_5 k_6 BOUND_VARIABLE_649)))))) (let ((_let_10 (= k_4 k_8))) (let ((_let_11 (not _let_10))) (let ((_let_12 (forall ((BOUND_VARIABLE_657 tptp.a)) (= (and (@ tptp.x BOUND_VARIABLE_657) (@ tptp.y BOUND_VARIABLE_657)) (ll_3 BOUND_VARIABLE_657))))) (let ((_let_13 (forall ((BOUND_VARIABLE_649 tptp.a)) (= (and (@ tptp.x BOUND_VARIABLE_649) (@ tptp.y BOUND_VARIABLE_649)) (ll_2 BOUND_VARIABLE_649))))) (let ((_let_14 (not (= ll_2 ll_3)))) (let ((_let_15 (and _let_14 _let_13 _let_12))) (let ((_let_16 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (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 (= _let_1 (lambda ((Xx0 tptp.a)) (and (@ tptp.x Xx0) (@ tptp.y Xx0))))) _let_14))))) (PREPROCESS :args ((and _let_13 _let_12)))) :args (_let_15)) (PREPROCESS :args ((= _let_15 (and _let_11 _let_9 _let_6))))) (PREPROCESS :args ((and _let_8 _let_7)))) :args ((and _let_11 _let_9 _let_6 _let_8 _let_7))))) (let ((_let_17 (_let_6))) (let ((_let_18 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_17) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_5 k_4 BOUND_VARIABLE_657)))) :args _let_17)) (AND_ELIM _let_16 :args (2)) :args (_let_5 false _let_6)))) (let ((_let_19 (ho_5 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_20 (= _let_19 _let_4))) (let ((_let_21 (forall ((z tptp.a)) (= (ho_5 k_8 z) (ho_5 k_4 z))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (not _let_21))) (let ((_let_24 (or _let_23 _let_10))) (let ((_let_25 (_let_8))) (let ((_let_26 (_let_23))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_26)) :args _let_26)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_21))) (REFL :args (_let_22)) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_10 _let_23 (not _let_24)))) (AND_ELIM _let_16 :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_25) :args (k_8 k_4 QUANTIFIERS_INST_ENUM)) :args _let_25))) (AND_ELIM _let_16 :args (3)) :args (_let_24 false _let_8)) :args (_let_23 true _let_10 false _let_24)) :args (_let_22 true _let_21)))) (let ((_let_28 (= _let_19 _let_3))) (let ((_let_29 (not _let_19))) (let ((_let_30 (_let_20))) (let ((_let_31 (_let_9))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_31) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_5 k_8 BOUND_VARIABLE_649)))) :args _let_31)) (AND_ELIM _let_16 :args (1)) :args (_let_28 false _let_9)))) (let ((_let_33 (not _let_28))) (let ((_let_34 (_let_28))) (let ((_let_35 (not _let_5))) (let ((_let_36 (not _let_3))) (let ((_let_37 (_let_5))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_37) :args ((or _let_4 _let_36 _let_35))) _let_18 (REORDERING (CNF_EQUIV_POS1 :args _let_34) :args ((or _let_29 _let_3 _let_33))) _let_32 (CNF_EQUIV_NEG2 :args _let_30) _let_27 :args (_let_29 false _let_5 false _let_3 false _let_28 true _let_4 true _let_20)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_37) :args ((or (not _let_4) _let_3 _let_35))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_34) :args ((or _let_19 _let_36 _let_33))) _let_38 _let_32 :args (_let_36 true _let_19 false _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_30) :args ((or _let_19 _let_4 _let_20))) _let_38 _let_27 :args (_let_4 true _let_19 true _let_20)) _let_18 :args (false true _let_3 false _let_4 false _let_5)) :args (_let_2 true)))))))))))))))))))))))))))))))))))))))))
% 0.20/0.52 )
% 0.20/0.52 % SZS output end Proof for SEV231^5
% 0.20/0.52 % cvc5---1.0.5 exiting
% 0.20/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------