TSTP Solution File: SEV175^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV175^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 0.21s 0.52s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV175^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n011.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
% 0.14/0.35 % DateTime : Thu Aug 24 03:36:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 %----Proving TH0
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 % File : SEV175^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.52 % Domain : Set Theory (Sets of sets)
% 0.21/0.52 % Problem : TPS problem THM144A
% 0.21/0.52 % Version : Especial.
% 0.21/0.52 % English : A lemma for the Injective Cantor Theorem X5309.
% 0.21/0.52
% 0.21/0.52 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.52 % Source : [Bro09]
% 0.21/0.52 % Names : tps_0230 [Bro09]
% 0.21/0.52 % : THM144A [TPS]
% 0.21/0.52
% 0.21/0.52 % Status : Theorem
% 0.21/0.52 % Rating : 0.23 v8.1.0, 0.18 v7.5.0, 0.14 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 v5.3.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v4.0.0
% 0.21/0.52 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.21/0.52 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.21/0.52 % Maximal formula atoms : 1 ( 2 avg)
% 0.21/0.52 % Number of connectives : 11 ( 2 ~; 0 |; 2 &; 7 @)
% 0.21/0.52 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.21/0.52 % Maximal formula depth : 7 ( 7 avg)
% 0.21/0.52 % Number of types : 2 ( 0 usr)
% 0.21/0.52 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.21/0.52 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.21/0.52 % Number of variables : 4 ( 1 ^; 1 !; 2 ?; 4 :)
% 0.21/0.52 % SPC : TH0_THM_EQU_NAR
% 0.21/0.52
% 0.21/0.52 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.52 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.52 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.52 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.52 % : Polymorphic definitions expanded.
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 thf(cTHM144A_pme,conjecture,
% 0.21/0.52 ! [Xh: ( $i > $o ) > $i] :
% 0.21/0.52 ? [Xt: $i > $o] :
% 0.21/0.52 ( ~ ( Xt @ ( Xh @ Xt ) )
% 0.21/0.52 & ( ( Xh
% 0.21/0.52 @ ^ [Xz: $i] :
% 0.21/0.52 ? [Xt0: $i > $o] :
% 0.21/0.52 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 0.21/0.52 & ( Xz
% 0.21/0.52 = ( Xh @ Xt0 ) ) ) )
% 0.21/0.52 = ( Xh @ Xt ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.uj8GA39Hjj/cvc5---1.0.5_10314.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (assert (not (forall ((Xh (-> (-> $$unsorted Bool) $$unsorted))) (exists ((Xt (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt))) (and (not (@ Xt _let_1)) (= (@ Xh (lambda ((Xz $$unsorted)) (exists ((Xt0 (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt0))) (and (not (@ Xt0 _let_1)) (= Xz _let_1)))))) _let_1)))))))
% 0.21/0.52 (set-info :filename cvc5---1.0.5_10314)
% 0.21/0.52 (check-sat-assuming ( true ))
% 0.21/0.52 ------- get file name : TPTP file name is SEV175^5
% 0.21/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10314.smt2...
% 0.21/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.52 % SZS status Theorem for SEV175^5
% 0.21/0.52 % SZS output start Proof for SEV175^5
% 0.21/0.52 (
% 0.21/0.52 (let ((_let_1 (not (forall ((Xh (-> (-> $$unsorted Bool) $$unsorted))) (exists ((Xt (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt))) (and (not (@ Xt _let_1)) (= (@ Xh (lambda ((Xz $$unsorted)) (exists ((Xt0 (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt0))) (and (not (@ Xt0 _let_1)) (= Xz _let_1)))))) _let_1)))))))) (let ((_let_2 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_3 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_2))) (let ((_let_4 (ho_6 _let_2 _let_3))) (let ((_let_5 (forall ((BOUND_VARIABLE_676 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 BOUND_VARIABLE_676))) (or (ho_6 BOUND_VARIABLE_676 _let_1) (not (= (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) _let_1))))))) (let ((_let_6 (not _let_5))) (let ((_let_7 (= _let_4 _let_6))) (let ((_let_8 (forall ((BOUND_VARIABLE_691 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 BOUND_VARIABLE_691))) (or (ho_6 BOUND_VARIABLE_691 _let_1) (not (= _let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))))) (let ((_let_9 (forall ((BOUND_VARIABLE_688 |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (not (forall ((BOUND_VARIABLE_691 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 BOUND_VARIABLE_688 BOUND_VARIABLE_691))) (or (ho_6 BOUND_VARIABLE_691 _let_1) (not (= (ho_3 BOUND_VARIABLE_688 (ho_5 k_4 BOUND_VARIABLE_688)) _let_1))))))))) (let ((_let_10 (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_11 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_12 (forall ((u |u_(-> _u_(-> $$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_13 (forall ((x |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (y |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|)) (or (not (forall ((z |u_(-> $$unsorted Bool)|)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_14 (forall ((u |u_(-> _u_(-> _u_(-> $$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_15 (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_16 (forall ((BOUND_VARIABLE_664 |u_(-> _u_(-> $$unsorted Bool)_ $$unsorted)|) (BOUND_VARIABLE_644 $$unsorted)) (= (ho_6 (ho_5 k_4 BOUND_VARIABLE_664) BOUND_VARIABLE_644) (not (forall ((BOUND_VARIABLE_676 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 BOUND_VARIABLE_664 BOUND_VARIABLE_676))) (or (ho_6 BOUND_VARIABLE_676 _let_1) (not (= BOUND_VARIABLE_644 _let_1)))))))))) (let ((_let_17 (not _let_9))) (let ((_let_18 (forall ((BOUND_VARIABLE_643 (-> (-> $$unsorted Bool) $$unsorted)) (BOUND_VARIABLE_644 $$unsorted)) (= (not (forall ((Xt0 (-> $$unsorted Bool))) (let ((_let_1 (@ BOUND_VARIABLE_643 Xt0))) (or (@ Xt0 _let_1) (not (= BOUND_VARIABLE_644 _let_1)))))) (ll_2 BOUND_VARIABLE_643 BOUND_VARIABLE_644))))) (let ((_let_19 (not (forall ((Xh (-> (-> $$unsorted Bool) $$unsorted))) (not (forall ((Xt (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt))) (or (@ Xt _let_1) (not (= _let_1 (@ Xh (@ ll_2 Xh)))))))))))) (let ((_let_20 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xh (-> (-> $$unsorted Bool) $$unsorted))) (not (forall ((Xt (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt))) (or (@ Xt _let_1) (not (= _let_1 (@ Xh (lambda ((Xz $$unsorted)) (not (forall ((Xt0 (-> $$unsorted Bool))) (let ((_let_1 (@ Xh Xt0))) (or (@ Xt0 _let_1) (not (= Xz _let_1)))))))))))))))) _let_19))))) (PREPROCESS :args (_let_18))) (PREPROCESS :args ((= (and _let_19 _let_18) (and _let_17 _let_16))))) (PREPROCESS :args ((and _let_15 _let_14 _let_13 _let_12 _let_11 _let_10)))) :args ((and _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10))))) (let ((_let_21 (_let_8))) (let ((_let_22 (_let_17))) (let ((_let_23 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_22)) :args _let_22) (REWRITE :args ((=> _let_17 (not (not (forall ((BOUND_VARIABLE_691 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 BOUND_VARIABLE_691))) (or (ho_6 BOUND_VARIABLE_691 _let_1) (not (= (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) _let_1)))))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_9))) (REFL :args _let_21) :args (or))) (AND_ELIM _let_20 :args (0)) :args (_let_8 true _let_9)))) (let ((_let_24 (_let_16))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_7)) :args ((or (not _let_4) _let_6 (not _let_7)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_24) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_3 QUANTIFIERS_INST_E_MATCHING ((ho_6 (ho_5 k_4 BOUND_VARIABLE_664) BOUND_VARIABLE_644)))) :args _let_24)) (AND_ELIM _let_20 :args (1)) :args (_let_7 false _let_16)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_8 (= BOUND_VARIABLE_691 BOUND_VARIABLE_676))) (MACRO_SR_PRED_INTRO :args ((= (forall ((BOUND_VARIABLE_676 |u_(-> $$unsorted Bool)|)) (let ((_let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 BOUND_VARIABLE_676))) (or (ho_6 BOUND_VARIABLE_676 _let_1) (not (= _let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))) _let_5) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) _let_23 :args (_let_5 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_21) :args (_let_2 QUANTIFIERS_INST_ENUM)) :args _let_21))) _let_23 :args (_let_4 false _let_8)) :args (false false _let_7 false _let_5 false _let_4)) :args (_let_1 true)))))))))))))))))))))))))))
% 0.21/0.53 )
% 0.21/0.53 % SZS output end Proof for SEV175^5
% 0.21/0.53 % cvc5---1.0.5 exiting
% 0.21/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------