TSTP Solution File: SEV179^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV179^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 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 19:21:46 EDT 2023
% Result : Theorem 0.23s 0.57s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEV179^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.15/0.16 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n021.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 24 02:51:09 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.52 %----Proving TH0
% 0.23/0.57 %------------------------------------------------------------------------------
% 0.23/0.57 % File : SEV179^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.23/0.57 % Domain : Set Theory (Sets of sets)
% 0.23/0.57 % Problem : TPS problem from CANTOR-THMS
% 0.23/0.57 % Version : Especial.
% 0.23/0.57 % English :
% 0.23/0.57
% 0.23/0.57 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.23/0.57 % Source : [Bro09]
% 0.23/0.57 % Names : tps_0598 [Bro09]
% 0.23/0.57
% 0.23/0.57 % Status : Theorem
% 0.23/0.57 % Rating : 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 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, 0.40 v5.2.0
% 0.23/0.57 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.23/0.57 % Number of atoms : 5 ( 2 equ; 0 cnn)
% 0.23/0.57 % Maximal formula atoms : 2 ( 2 avg)
% 0.23/0.57 % Number of connectives : 9 ( 1 ~; 0 |; 1 &; 7 @)
% 0.23/0.57 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.23/0.57 % Maximal formula depth : 5 ( 3 avg)
% 0.23/0.57 % Number of types : 2 ( 0 usr)
% 0.23/0.57 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.23/0.57 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.23/0.57 % Number of variables : 4 ( 2 ^; 1 !; 1 ?; 4 :)
% 0.23/0.57 % SPC : TH0_THM_EQU_NAR
% 0.23/0.57
% 0.23/0.57 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.23/0.57 % project in the Department of Mathematical Sciences at Carnegie
% 0.23/0.57 % Mellon University. Distributed under the Creative Commons copyleft
% 0.23/0.57 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.23/0.57 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.23/0.57 %------------------------------------------------------------------------------
% 0.23/0.57 thf(cD_FOR_X5309_type,type,
% 0.23/0.57 cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
% 0.23/0.57
% 0.23/0.57 thf(cD_FOR_X5309_def,definition,
% 0.23/0.57 ( cD_FOR_X5309
% 0.23/0.57 = ( ^ [Xh: ( $i > $o ) > $i,Xz: $i] :
% 0.23/0.57 ? [Xt: $i > $o] :
% 0.23/0.57 ( ~ ( Xt @ ( Xh @ Xt ) )
% 0.23/0.57 & ( Xz
% 0.23/0.57 = ( Xh @ Xt ) ) ) ) ) ).
% 0.23/0.57
% 0.23/0.57 thf(cTHM144C_pme,conjecture,
% 0.23/0.57 ! [Xh: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ Xh @ ( Xh @ ( cD_FOR_X5309 @ Xh ) ) ) ).
% 0.23/0.57
% 0.23/0.57 %------------------------------------------------------------------------------
% 0.23/0.57 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.TfV0gYuMGr/cvc5---1.0.5_6987.p...
% 0.23/0.57 (declare-sort $$unsorted 0)
% 0.23/0.57 (declare-fun tptp.cD_FOR_X5309 ((-> (-> $$unsorted Bool) $$unsorted) $$unsorted) Bool)
% 0.23/0.57 (assert (= tptp.cD_FOR_X5309 (lambda ((Xh (-> (-> $$unsorted Bool) $$unsorted)) (Xz $$unsorted)) (exists ((Xt (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt))) (and (not (@ Xt _let_1)) (= Xz _let_1)))))))
% 0.23/0.57 (assert (not (forall ((Xh (-> (-> $$unsorted Bool) $$unsorted))) (let ((_let_1 (@ tptp.cD_FOR_X5309 Xh))) (@ _let_1 (@ Xh _let_1))))))
% 0.23/0.57 (set-info :filename cvc5---1.0.5_6987)
% 0.23/0.57 (check-sat-assuming ( true ))
% 0.23/0.57 ------- get file name : TPTP file name is SEV179^5
% 0.23/0.57 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_6987.smt2...
% 0.23/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.57 % SZS status Theorem for SEV179^5
% 0.23/0.57 % SZS output start Proof for SEV179^5
% 0.23/0.57 (
% 0.23/0.57 (let ((_let_1 (not (forall ((Xh (-> (-> $$unsorted Bool) $$unsorted))) (let ((_let_1 (@ tptp.cD_FOR_X5309 Xh))) (@ _let_1 (@ Xh _let_1))))))) (let ((_let_2 (= tptp.cD_FOR_X5309 (lambda ((Xh (-> (-> $$unsorted Bool) $$unsorted)) (Xz $$unsorted)) (exists ((Xt (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt))) (and (not (@ Xt _let_1)) (= Xz _let_1)))))))) (let ((_let_3 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_4 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_3))) (let ((_let_5 (ho_6 _let_3 _let_4))) (let ((_let_6 (forall ((BOUND_VARIABLE_708 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 BOUND_VARIABLE_708))) (or (ho_6 BOUND_VARIABLE_708 _let_1) (not (= (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) _let_1))))))) (let ((_let_7 (not _let_6))) (let ((_let_8 (= _let_5 _let_7))) (let ((_let_9 (forall ((BOUND_VARIABLE_726 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 BOUND_VARIABLE_726))) (or (ho_6 BOUND_VARIABLE_726 _let_1) (not (= _let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))))) (let ((_let_10 (forall ((BOUND_VARIABLE_723 |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (not (forall ((BOUND_VARIABLE_726 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 BOUND_VARIABLE_723 BOUND_VARIABLE_726))) (or (ho_6 BOUND_VARIABLE_726 _let_1) (not (= (ho_3 BOUND_VARIABLE_723 (ho_5 k_4 BOUND_VARIABLE_723)) _let_1))))))))) (let ((_let_11 (not _let_10))) (let ((_let_12 (not (forall ((Xh (-> (-> $$unsorted Bool) $$unsorted))) (not (forall ((Xt (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt))) (or (@ Xt _let_1) (not (= _let_1 (@ Xh (@ ll_2 Xh)))))))))))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xh (-> (-> $$unsorted Bool) $$unsorted))) (not (forall ((Xt (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt))) (or (@ Xt _let_1) (not (= _let_1 (@ Xh (lambda ((Xz $$unsorted)) (not (forall ((BOUND_VARIABLE_633 (-> $$unsorted Bool))) (let ((_let_1 (@ Xh BOUND_VARIABLE_633))) (or (@ BOUND_VARIABLE_633 _let_1) (not (= Xz _let_1)))))))))))))))) _let_12))) (PREPROCESS :args ((= _let_12 _let_11))))))) (let ((_let_14 (_let_9))) (let ((_let_15 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_13) :args (_let_11)) (REWRITE :args ((=> _let_11 (not (not (forall ((BOUND_VARIABLE_726 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 BOUND_VARIABLE_726))) (or (ho_6 BOUND_VARIABLE_726 _let_1) (not (= (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) _let_1)))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) (REFL :args _let_14) :args (or))) _let_13 :args (_let_9 true _let_10)))) (let ((_let_16 (forall ((BOUND_VARIABLE_696 |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (BOUND_VARIABLE_676 $$unsorted)) (= (ho_6 (ho_5 k_4 BOUND_VARIABLE_696) BOUND_VARIABLE_676) (not (forall ((BOUND_VARIABLE_708 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 BOUND_VARIABLE_696 BOUND_VARIABLE_708))) (or (ho_6 BOUND_VARIABLE_708 _let_1) (not (= BOUND_VARIABLE_676 _let_1)))))))))) (let ((_let_17 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_18 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_19 (forall ((u |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (e $$unsorted) (i |u_(-> $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (not (forall ((ii |u_(-> $$unsorted Bool)|)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_20 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (y |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_21 (forall ((u |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)_ $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_22 (forall ((x |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)_ $$unsorted Bool)|) (y |u_(-> _u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_23 (forall ((BOUND_VARIABLE_675 (-> (-> $$unsorted Bool) $$unsorted)) (BOUND_VARIABLE_676 $$unsorted)) (= (not (forall ((BOUND_VARIABLE_633 (-> $$unsorted Bool))) (let ((_let_1 (@ BOUND_VARIABLE_675 BOUND_VARIABLE_633))) (or (@ BOUND_VARIABLE_633 _let_1) (not (= BOUND_VARIABLE_676 _let_1)))))) (ll_2 BOUND_VARIABLE_675 BOUND_VARIABLE_676))))) (let ((_let_24 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (PREPROCESS_LEMMA :args (_let_23)) (PREPROCESS :args ((= _let_23 _let_16)))) (PREPROCESS :args ((and _let_22 _let_21 _let_20 _let_19 _let_18 _let_17)))) :args ((and _let_16 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17))) :args (0)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_8)) :args ((or (not _let_5) _let_7 (not _let_8)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_4 QUANTIFIERS_INST_E_MATCHING ((ho_6 (ho_5 k_4 BOUND_VARIABLE_696) BOUND_VARIABLE_676)))) :args (_let_16))) _let_24 :args (_let_8 false _let_16)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_9 (= BOUND_VARIABLE_726 BOUND_VARIABLE_708))) (MACRO_SR_PRED_INTRO :args ((= (forall ((BOUND_VARIABLE_708 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 BOUND_VARIABLE_708))) (or (ho_6 BOUND_VARIABLE_708 _let_1) (not (= _let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))) _let_6) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) _let_15 :args (_let_6 false _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_14) :args (_let_3 QUANTIFIERS_INST_ENUM)) :args _let_14))) _let_15 :args (_let_5 false _let_9)) :args (false false _let_8 false _let_6 false _let_5)) :args (_let_2 _let_1 true)))))))))))))))))))))))))))
% 0.23/0.58 )
% 0.23/0.58 % SZS output end Proof for SEV179^5
% 0.23/0.58 % cvc5---1.0.5 exiting
% 0.23/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------