TSTP Solution File: SEV122^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV122^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 19:21:36 EDT 2023
% Result : Theorem 35.58s 35.80s
% Output : Proof 35.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEV122^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n024.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 03:32:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 35.58/35.80 %------------------------------------------------------------------------------
% 35.58/35.80 % File : SEV122^5 : TPTP v8.1.2. Released v4.0.0.
% 35.58/35.80 % Domain : Set Theory (Relations)
% 35.58/35.80 % Problem : TPS problem THM530
% 35.58/35.80 % Version : Especial.
% 35.58/35.80 % English :
% 35.58/35.80
% 35.58/35.80 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 35.58/35.80 % Source : [Bro09]
% 35.58/35.80 % Names : tps_0494 [Bro09]
% 35.58/35.80 % : THM530 [TPS]
% 35.58/35.80
% 35.58/35.80 % Status : Theorem
% 35.58/35.80 % 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 v4.0.1, 0.33 v4.0.0
% 35.58/35.80 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 35.58/35.80 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 35.58/35.80 % Maximal formula atoms : 1 ( 1 avg)
% 35.58/35.80 % Number of connectives : 20 ( 0 ~; 0 |; 2 &; 14 @)
% 35.58/35.80 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 35.58/35.80 % Maximal formula depth : 3 ( 3 avg)
% 35.58/35.80 % Number of types : 2 ( 1 usr)
% 35.58/35.80 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 35.58/35.80 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 35.58/35.80 % Number of variables : 14 ( 4 ^; 8 !; 2 ?; 14 :)
% 35.58/35.80 % SPC : TH0_THM_EQU_NAR
% 35.58/35.80
% 35.58/35.80 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 35.58/35.80 % project in the Department of Mathematical Sciences at Carnegie
% 35.58/35.80 % Mellon University. Distributed under the Creative Commons copyleft
% 35.58/35.80 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 35.58/35.80 % : Polymorphic definitions expanded.
% 35.58/35.80 %------------------------------------------------------------------------------
% 35.58/35.80 thf(a_type,type,
% 35.58/35.80 a: $tType ).
% 35.58/35.80
% 35.58/35.80 thf(cTHM530_pme,conjecture,
% 35.58/35.80 ! [PROP: ( a > a > $o ) > $o,F: ( a > a > $o ) > $o] :
% 35.58/35.80 ( ( ^ [Xx: a,Xy: a] :
% 35.58/35.80 ! [Xp: a > a > $o] :
% 35.58/35.80 ( ( ! [Xx0: a,Xy0: a] :
% 35.58/35.80 ( ? [R: a > a > $o] : ( R @ Xx0 @ Xy0 )
% 35.58/35.80 => ( Xp @ Xx0 @ Xy0 ) )
% 35.58/35.80 & ( PROP @ Xp ) )
% 35.58/35.80 => ( Xp @ Xx @ Xy ) ) )
% 35.58/35.80 = ( ^ [Xx: a,Xy: a] :
% 35.58/35.80 ! [Xp: a > a > $o] :
% 35.58/35.80 ( ( ! [Xx0: a,Xy0: a] :
% 35.58/35.80 ( ? [R: a > a > $o] : ( R @ Xx0 @ Xy0 )
% 35.58/35.80 => ( Xp @ Xx0 @ Xy0 ) )
% 35.58/35.80 & ( PROP @ Xp ) )
% 35.58/35.80 => ( Xp @ Xx @ Xy ) ) ) ) ).
% 35.58/35.80
% 35.58/35.80 %------------------------------------------------------------------------------
% 35.58/35.80 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.3Izar933J0/cvc5---1.0.5_25055.p...
% 35.58/35.80 (declare-sort $$unsorted 0)
% 35.58/35.80 (declare-sort tptp.a 0)
% 35.58/35.80 (assert (not (forall ((PROP (-> (-> tptp.a tptp.a Bool) Bool)) (F (-> (-> tptp.a tptp.a Bool) Bool))) (= (lambda ((Xx tptp.a) (Xy tptp.a)) (forall ((Xp (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (exists ((R (-> tptp.a tptp.a Bool))) (@ (@ R Xx0) Xy0)) (@ (@ Xp Xx0) Xy0))) (@ PROP Xp)) (@ (@ Xp Xx) Xy)))) (lambda ((Xx tptp.a) (Xy tptp.a)) (forall ((Xp (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (exists ((R (-> tptp.a tptp.a Bool))) (@ (@ R Xx0) Xy0)) (@ (@ Xp Xx0) Xy0))) (@ PROP Xp)) (@ (@ Xp Xx) Xy))))))))
% 35.58/35.80 (set-info :filename cvc5---1.0.5_25055)
% 35.58/35.80 (check-sat-assuming ( true ))
% 35.58/35.80 ------- get file name : TPTP file name is SEV122^5
% 35.58/35.80 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25055.smt2...
% 35.58/35.80 --- Run --ho-elim --full-saturate-quant at 10...
% 35.58/35.80 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 35.58/35.80 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 35.58/35.80 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 35.58/35.80 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 35.58/35.80 % SZS status Theorem for SEV122^5
% 35.58/35.80 % SZS output start Proof for SEV122^5
% 35.58/35.80 (
% 35.58/35.80 (let ((_let_1 (not (forall ((PROP (-> (-> tptp.a tptp.a Bool) Bool)) (F (-> (-> tptp.a tptp.a Bool) Bool))) (= (lambda ((Xx tptp.a) (Xy tptp.a)) (forall ((Xp (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (exists ((R (-> tptp.a tptp.a Bool))) (@ (@ R Xx0) Xy0)) (@ (@ Xp Xx0) Xy0))) (@ PROP Xp)) (@ (@ Xp Xx) Xy)))) (lambda ((Xx tptp.a) (Xy tptp.a)) (forall ((Xp (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (exists ((R (-> tptp.a tptp.a Bool))) (@ (@ R Xx0) Xy0)) (@ (@ Xp Xx0) Xy0))) (@ PROP Xp)) (@ (@ Xp Xx) Xy))))))))) (let ((_let_2 (forall ((Xp (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_665 (-> tptp.a tptp.a Bool))) (or (not (@ (@ BOUND_VARIABLE_665 Xx0) Xy0)) (@ (@ Xp Xx0) Xy0)))) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xp)) (@ (@ Xp k_5) k_6))))) (let ((_let_3 (forall ((Xp (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_638 (-> tptp.a tptp.a Bool))) (or (not (@ (@ BOUND_VARIABLE_638 Xx0) Xy0)) (@ (@ Xp Xx0) Xy0)))) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xp)) (@ (@ Xp k_5) k_6))))) (let ((_let_4 (lambdaF_3 k_5 k_6))) (let ((_let_5 (= _let_4 _let_2))) (let ((_let_6 (not _let_2))) (let ((_let_7 (forall ((Xx tptp.a) (Xy tptp.a)) (= (forall ((Xp (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_665 (-> tptp.a tptp.a Bool))) (or (not (@ (@ BOUND_VARIABLE_665 Xx0) Xy0)) (@ (@ Xp Xx0) Xy0)))) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xp)) (@ (@ Xp Xx) Xy))) (lambdaF_3 Xx Xy))))) (let ((_let_8 ((forall ((Xx tptp.a) (Xy tptp.a)) (= (lambdaF_3 Xx Xy) (@ (@ (lambda ((Xx tptp.a) (Xy tptp.a)) (forall ((Xp (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_665 (-> tptp.a tptp.a Bool))) (or (not (@ (@ BOUND_VARIABLE_665 Xx0) Xy0)) (@ (@ Xp Xx0) Xy0)))) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xp)) (@ (@ Xp Xx) Xy)))) Xx) Xy)))))) (let ((_let_9 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_8) (REWRITE :args _let_8)))) (let ((_let_10 (k_5 k_6 QUANTIFIERS_INST_FMF_FMC_EXH))) (let ((_let_11 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_9 :args _let_10) :args (_let_7)))) _let_9 :args (_let_5 false _let_7)))) (let ((_let_12 (lambdaF_4 k_5 k_6))) (let ((_let_13 (= _let_4 _let_12))) (let ((_let_14 (= _let_12 _let_3))) (let ((_let_15 (not _let_4))) (let ((_let_16 (= lambdaF_3 lambdaF_4))) (let ((_let_17 (not _let_13))) (let ((_let_18 (forall ((PROP (-> (-> tptp.a tptp.a Bool) Bool))) (= (lambda ((Xx tptp.a) (Xy tptp.a)) (forall ((Xp (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_638 (-> tptp.a tptp.a Bool))) (or (not (@ (@ BOUND_VARIABLE_638 Xx0) Xy0)) (@ (@ Xp Xx0) Xy0)))) (not (@ PROP Xp)) (@ (@ Xp Xx) Xy)))) (lambda ((Xx tptp.a) (Xy tptp.a)) (forall ((Xp (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_665 (-> tptp.a tptp.a Bool))) (or (not (@ (@ BOUND_VARIABLE_665 Xx0) Xy0)) (@ (@ Xp Xx0) Xy0)))) (not (@ PROP Xp)) (@ (@ Xp Xx) Xy)))))))) (let ((_let_19 (not _let_16))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (not _let_18))) (let ((_let_22 (_let_21))) (let ((_let_23 (MACRO_RESOLUTION_TRUST (THEORY_LEMMA :args ((or _let_16 _let_17) THEORY_UF)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_20) :args _let_22) (CONG (REFL :args _let_22) (CONG (TRANS (CONG (MACRO_SR_PRED_INTRO :args ((= (lambda ((Xx tptp.a) (Xy tptp.a)) (forall ((Xp (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_638 (-> tptp.a tptp.a Bool))) (or (not (@ (@ BOUND_VARIABLE_638 Xx0) Xy0)) (@ (@ Xp Xx0) Xy0)))) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xp)) (@ (@ Xp Xx) Xy)))) lambdaF_4))) (MACRO_SR_PRED_INTRO :args ((= (lambda ((Xx tptp.a) (Xy tptp.a)) (forall ((Xp (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_665 (-> tptp.a tptp.a Bool))) (or (not (@ (@ BOUND_VARIABLE_665 Xx0) Xy0)) (@ (@ Xp Xx0) Xy0)))) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xp)) (@ (@ Xp Xx) Xy)))) lambdaF_3))) :args (=)) (REWRITE :args ((= lambdaF_4 lambdaF_3)))) :args (not)) :args (=>)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_18))) (REFL :args (_let_19)) :args (or))) _let_20 :args (_let_19 true _let_18)) :args (_let_17 true _let_16)))) (let ((_let_24 (_let_13))) (let ((_let_25 (not _let_5))) (let ((_let_26 (_let_5))) (let ((_let_27 (forall ((Xx tptp.a) (Xy tptp.a)) (= (forall ((Xp (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_638 (-> tptp.a tptp.a Bool))) (or (not (@ (@ BOUND_VARIABLE_638 Xx0) Xy0)) (@ (@ Xp Xx0) Xy0)))) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xp)) (@ (@ Xp Xx) Xy))) (lambdaF_4 Xx Xy))))) (let ((_let_28 ((forall ((Xx tptp.a) (Xy tptp.a)) (= (lambdaF_4 Xx Xy) (@ (@ (lambda ((Xx tptp.a) (Xy tptp.a)) (forall ((Xp (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (BOUND_VARIABLE_638 (-> tptp.a tptp.a Bool))) (or (not (@ (@ BOUND_VARIABLE_638 Xx0) Xy0)) (@ (@ Xp Xx0) Xy0)))) (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xp)) (@ (@ Xp Xx) Xy)))) Xx) Xy)))))) (let ((_let_29 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_28) (REWRITE :args _let_28)))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_29 :args _let_10) :args (_let_27)))) _let_29 :args (_let_14 false _let_27)))) (let ((_let_31 (not _let_14))) (let ((_let_32 (_let_14))) (let ((_let_33 (ALPHA_EQUIV :args (_let_2 (= Xx0 Xx0) (= Xy0 Xy0) (= Xp Xp) (= BOUND_VARIABLE_665 BOUND_VARIABLE_638))))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 _let_33) :args ((or _let_3 _let_6))) (REORDERING (CNF_EQUIV_POS2 :args _let_32) :args ((or _let_12 (not _let_3) _let_31))) _let_30 (REORDERING (CNF_EQUIV_POS1 :args _let_26) :args ((or _let_15 _let_2 _let_25))) _let_11 (CNF_EQUIV_NEG2 :args _let_24) _let_23 :args (_let_15 true _let_3 false _let_14 false _let_2 false _let_5 true _let_12 true _let_13)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_33) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_32) :args ((or (not _let_12) _let_3 _let_31))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_24) :args ((or _let_4 _let_12 _let_13))) _let_34 _let_23 :args (_let_12 true _let_4 true _let_13)) _let_30 :args (_let_3 false _let_12 false _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_26) :args ((or _let_4 _let_6 _let_25))) _let_34 _let_11 :args (_let_6 true _let_4 false _let_5)) :args (false false _let_3 true _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))
% 35.58/35.80 )
% 35.58/35.80 % SZS output end Proof for SEV122^5
% 35.58/35.80 % cvc5---1.0.5 exiting
% 35.58/35.81 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------