TSTP Solution File: SEV232^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV232^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEV232^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 03:24:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 % File : SEV232^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.53 % Domain : Set Theory (Sets of sets)
% 0.20/0.53 % Problem : TPS problem X6007
% 0.20/0.53 % Version : Especial.
% 0.20/0.53 % English :
% 0.20/0.53
% 0.20/0.53 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.53 % Source : [Bro09]
% 0.20/0.53 % Names : tps_0359 [Bro09]
% 0.20/0.53 % : X6007 [TPS]
% 0.20/0.53
% 0.20/0.53 % Status : Theorem
% 0.20/0.53 % Rating : 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.20/0.53 % Syntax : Number of formulae : 3 ( 1 unt; 2 typ; 0 def)
% 0.20/0.53 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.20/0.53 % Maximal formula atoms : 1 ( 5 avg)
% 0.20/0.53 % Number of connectives : 16 ( 0 ~; 0 |; 2 &; 10 @)
% 0.20/0.53 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.53 % Maximal formula depth : 1 ( 1 avg)
% 0.20/0.53 % Number of types : 2 ( 0 usr)
% 0.20/0.53 % Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% 0.20/0.53 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.20/0.53 % Number of variables : 6 ( 2 ^; 4 !; 0 ?; 6 :)
% 0.20/0.53 % SPC : TH0_THM_EQU_NAR
% 0.20/0.53
% 0.20/0.53 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.53 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.53 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.53 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.53 % : Polymorphic definitions expanded.
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 thf(cS,type,
% 0.20/0.53 cS: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
% 0.20/0.53
% 0.20/0.53 thf(c0,type,
% 0.20/0.53 c0: ( $i > $o ) > $o ).
% 0.20/0.53
% 0.20/0.53 thf(cX6007_pme,conjecture,
% 0.20/0.53 ( ( ^ [N: ( $i > $o ) > $o] :
% 0.20/0.53 ! [P: ( ( $i > $o ) > $o ) > $o] :
% 0.20/0.53 ( ( ( P @ c0 )
% 0.20/0.53 & ! [X: ( $i > $o ) > $o] :
% 0.20/0.53 ( ( P @ X )
% 0.20/0.53 => ( P @ ( cS @ X ) ) ) )
% 0.20/0.53 => ( P @ N ) ) )
% 0.20/0.53 = ( ^ [Xx: ( $i > $o ) > $o] :
% 0.20/0.53 ! [S0: ( ( $i > $o ) > $o ) > $o] :
% 0.20/0.53 ( ( ( S0 @ c0 )
% 0.20/0.53 & ! [X: ( $i > $o ) > $o] :
% 0.20/0.53 ( ( S0 @ X )
% 0.20/0.53 => ( S0 @ ( cS @ X ) ) ) )
% 0.20/0.53 => ( S0 @ Xx ) ) ) ) ).
% 0.20/0.53
% 0.20/0.53 %------------------------------------------------------------------------------
% 0.20/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Vh5vyQZPK6/cvc5---1.0.5_8811.p...
% 0.20/0.53 (declare-sort $$unsorted 0)
% 0.20/0.53 (declare-fun tptp.cS ((-> (-> $$unsorted Bool) Bool) (-> $$unsorted Bool)) Bool)
% 0.20/0.53 (declare-fun tptp.c0 ((-> $$unsorted Bool)) Bool)
% 0.20/0.53 (assert (not (= (lambda ((N (-> (-> $$unsorted Bool) Bool))) (forall ((P (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ P tptp.c0) (forall ((X (-> (-> $$unsorted Bool) Bool))) (=> (@ P X) (@ P (@ tptp.cS X))))) (@ P N)))) (lambda ((Xx (-> (-> $$unsorted Bool) Bool))) (forall ((S0 (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ S0 tptp.c0) (forall ((X (-> (-> $$unsorted Bool) Bool))) (=> (@ S0 X) (@ S0 (@ tptp.cS X))))) (@ S0 Xx)))))))
% 0.20/0.53 (set-info :filename cvc5---1.0.5_8811)
% 0.20/0.53 (check-sat-assuming ( true ))
% 0.20/0.53 ------- get file name : TPTP file name is SEV232^5
% 0.20/0.53 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8811.smt2...
% 0.20/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.53 % SZS status Theorem for SEV232^5
% 0.20/0.53 % SZS output start Proof for SEV232^5
% 0.20/0.53 (
% 0.20/0.53 (let ((_let_1 (not (= (lambda ((N (-> (-> $$unsorted Bool) Bool))) (forall ((P (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ P tptp.c0) (forall ((X (-> (-> $$unsorted Bool) Bool))) (=> (@ P X) (@ P (@ tptp.cS X))))) (@ P N)))) (lambda ((Xx (-> (-> $$unsorted Bool) Bool))) (forall ((S0 (-> (-> (-> $$unsorted Bool) Bool) Bool))) (=> (and (@ S0 tptp.c0) (forall ((X (-> (-> $$unsorted Bool) Bool))) (=> (@ S0 X) (@ S0 (@ tptp.cS X))))) (@ S0 Xx)))))))) (let ((_let_2 (forall ((BOUND_VARIABLE_715 |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ Bool)|)) (or (not (ho_6 BOUND_VARIABLE_715 k_9)) (not (forall ((BOUND_VARIABLE_717 |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (or (not (ho_6 BOUND_VARIABLE_715 BOUND_VARIABLE_717)) (ho_6 BOUND_VARIABLE_715 (ho_8 k_7 BOUND_VARIABLE_717))))) (ho_6 BOUND_VARIABLE_715 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))))) (let ((_let_3 (forall ((BOUND_VARIABLE_687 |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ Bool)|)) (or (not (ho_6 BOUND_VARIABLE_687 k_9)) (not (forall ((BOUND_VARIABLE_689 |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (or (not (ho_6 BOUND_VARIABLE_687 BOUND_VARIABLE_689)) (ho_6 BOUND_VARIABLE_687 (ho_8 k_7 BOUND_VARIABLE_689))))) (ho_6 BOUND_VARIABLE_687 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))))) (let ((_let_4 (ho_6 k_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))) (let ((_let_5 (= _let_4 _let_2))) (let ((_let_6 (not _let_2))) (let ((_let_7 (forall ((BOUND_VARIABLE_712 |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_6 k_10 BOUND_VARIABLE_712) (forall ((BOUND_VARIABLE_715 |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ Bool)|)) (or (not (ho_6 BOUND_VARIABLE_715 k_9)) (not (forall ((BOUND_VARIABLE_717 |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (or (not (ho_6 BOUND_VARIABLE_715 BOUND_VARIABLE_717)) (ho_6 BOUND_VARIABLE_715 (ho_8 k_7 BOUND_VARIABLE_717))))) (ho_6 BOUND_VARIABLE_715 BOUND_VARIABLE_712))))))) (let ((_let_8 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (e Bool) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_9 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (y |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_10 (forall ((u |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ Bool)|) (e Bool) (i |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_11 (forall ((x |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_12 (forall ((u |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ _u_(-> $$unsorted Bool)_ Bool)|) (e |u_(-> _u_(-> $$unsorted Bool)_ Bool)|) (i |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ _u_(-> $$unsorted Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_13 (forall ((x |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ _u_(-> $$unsorted Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ _u_(-> $$unsorted Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_14 (forall ((BOUND_VARIABLE_678 |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_6 k_5 BOUND_VARIABLE_678) (forall ((BOUND_VARIABLE_687 |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ Bool)_ Bool)|)) (or (not (ho_6 BOUND_VARIABLE_687 k_9)) (not (forall ((BOUND_VARIABLE_689 |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (or (not (ho_6 BOUND_VARIABLE_687 BOUND_VARIABLE_689)) (ho_6 BOUND_VARIABLE_687 (ho_8 k_7 BOUND_VARIABLE_689))))) (ho_6 BOUND_VARIABLE_687 BOUND_VARIABLE_678))))))) (let ((_let_15 (= k_5 k_10))) (let ((_let_16 (not _let_15))) (let ((_let_17 (forall ((BOUND_VARIABLE_658 (-> (-> $$unsorted Bool) Bool))) (= (forall ((P (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ P tptp.c0)) (not (forall ((X (-> (-> $$unsorted Bool) Bool))) (or (not (@ P X)) (@ P (@ tptp.cS X))))) (@ P BOUND_VARIABLE_658))) (ll_3 BOUND_VARIABLE_658))))) (let ((_let_18 (forall ((BOUND_VARIABLE_650 (-> (-> $$unsorted Bool) Bool))) (= (forall ((S0 (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ S0 tptp.c0)) (not (forall ((X (-> (-> $$unsorted Bool) Bool))) (or (not (@ S0 X)) (@ S0 (@ tptp.cS X))))) (@ S0 BOUND_VARIABLE_650))) (ll_2 BOUND_VARIABLE_650))))) (let ((_let_19 (not (= ll_2 ll_3)))) (let ((_let_20 (and _let_19 _let_18 _let_17))) (let ((_let_21 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (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 (= (lambda ((N (-> (-> $$unsorted Bool) Bool))) (forall ((P (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ P tptp.c0)) (not (forall ((X (-> (-> $$unsorted Bool) Bool))) (or (not (@ P X)) (@ P (@ tptp.cS X))))) (@ P N)))) (lambda ((Xx (-> (-> $$unsorted Bool) Bool))) (forall ((S0 (-> (-> (-> $$unsorted Bool) Bool) Bool))) (or (not (@ S0 tptp.c0)) (not (forall ((X (-> (-> $$unsorted Bool) Bool))) (or (not (@ S0 X)) (@ S0 (@ tptp.cS X))))) (@ S0 Xx)))))) _let_19))))) (PREPROCESS :args ((and _let_18 _let_17)))) :args (_let_20)) (PREPROCESS :args ((= _let_20 (and _let_16 _let_7 _let_14))))) (PREPROCESS :args ((and _let_13 _let_12 _let_11 _let_10 _let_9 _let_8)))) :args ((and _let_16 _let_7 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8))))) (let ((_let_22 (_let_7))) (let ((_let_23 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_22) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_10 BOUND_VARIABLE_712)))) :args _let_22)) (AND_ELIM _let_21 :args (1)) :args (_let_5 false _let_7)))) (let ((_let_24 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))) (let ((_let_25 (= _let_4 _let_24))) (let ((_let_26 (= _let_24 _let_3))) (let ((_let_27 (not _let_4))) (let ((_let_28 (forall ((z |u_(-> _u_(-> $$unsorted Bool)_ Bool)|)) (= (ho_6 k_10 z) (ho_6 k_5 z))))) (let ((_let_29 (not _let_25))) (let ((_let_30 (not _let_28))) (let ((_let_31 (or _let_30 _let_15))) (let ((_let_32 (_let_11))) (let ((_let_33 (_let_30))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_33)) :args _let_33)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_28))) (REFL :args (_let_29)) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_15 _let_30 (not _let_31)))) (AND_ELIM _let_21 :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (k_10 k_5 QUANTIFIERS_INST_ENUM)) :args _let_32))) (AND_ELIM _let_21 :args (5)) :args (_let_31 false _let_11)) :args (_let_30 true _let_15 false _let_31)) :args (_let_29 true _let_28)))) (let ((_let_35 (_let_25))) (let ((_let_36 (not _let_5))) (let ((_let_37 (_let_5))) (let ((_let_38 (_let_14))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_38) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_5 BOUND_VARIABLE_678)))) :args _let_38)) (AND_ELIM _let_21 :args (2)) :args (_let_26 false _let_14)))) (let ((_let_40 (not _let_26))) (let ((_let_41 (_let_26))) (let ((_let_42 (ALPHA_EQUIV :args (_let_2 (= BOUND_VARIABLE_715 BOUND_VARIABLE_687) (= BOUND_VARIABLE_717 BOUND_VARIABLE_689))))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 _let_42) :args ((or _let_3 _let_6))) (REORDERING (CNF_EQUIV_POS2 :args _let_41) :args ((or _let_24 (not _let_3) _let_40))) _let_39 (REORDERING (CNF_EQUIV_POS1 :args _let_37) :args ((or _let_27 _let_2 _let_36))) _let_23 (CNF_EQUIV_NEG2 :args _let_35) _let_34 :args (_let_27 true _let_3 false _let_26 false _let_2 false _let_5 true _let_24 true _let_25)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_42) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_41) :args ((or (not _let_24) _let_3 _let_40))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_35) :args ((or _let_4 _let_24 _let_25))) _let_43 _let_34 :args (_let_24 true _let_4 true _let_25)) _let_39 :args (_let_3 false _let_24 false _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_37) :args ((or _let_4 _let_6 _let_36))) _let_43 _let_23 :args (_let_6 true _let_4 false _let_5)) :args (false false _let_3 true _let_2)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.53 )
% 0.20/0.53 % SZS output end Proof for SEV232^5
% 0.20/0.53 % cvc5---1.0.5 exiting
% 0.20/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------