TSTP Solution File: SEV061^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV061^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 19:21:27 EDT 2023
% Result : Theorem 0.21s 0.55s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SEV061^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n031.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 02:26:05 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.21/0.51 %----Proving TH0
% 0.21/0.55 %------------------------------------------------------------------------------
% 0.21/0.55 % File : SEV061^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.55 % Domain : Set Theory (Relations)
% 0.21/0.55 % Problem : TPS problem THM176
% 0.21/0.55 % Version : Especial.
% 0.21/0.55 % English :
% 0.21/0.55
% 0.21/0.55 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.55 % Source : [Bro09]
% 0.21/0.55 % Names : tps_0331 [Bro09]
% 0.21/0.55 % : THM176 [TPS]
% 0.21/0.55
% 0.21/0.55 % Status : Theorem
% 0.21/0.55 % Rating : 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 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
% 0.21/0.55 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.21/0.55 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.21/0.55 % Maximal formula atoms : 4 ( 4 avg)
% 0.21/0.55 % Number of connectives : 16 ( 1 ~; 1 |; 3 &; 8 @)
% 0.21/0.55 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.21/0.55 % Maximal formula depth : 12 ( 12 avg)
% 0.21/0.55 % Number of types : 3 ( 2 usr)
% 0.21/0.55 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.21/0.55 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.21/0.55 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.21/0.55 % SPC : TH0_THM_EQU_NAR
% 0.21/0.55
% 0.21/0.55 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.55 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.55 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.55 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.55 % : Polymorphic definitions expanded.
% 0.21/0.55 %------------------------------------------------------------------------------
% 0.21/0.55 thf(b_type,type,
% 0.21/0.55 b: $tType ).
% 0.21/0.55
% 0.21/0.55 thf(a_type,type,
% 0.21/0.55 a: $tType ).
% 0.21/0.55
% 0.21/0.55 thf(cTHM176_pme,conjecture,
% 0.21/0.55 ! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
% 0.21/0.55 ( ! [Xx_2: b,Xy_47: a] :
% 0.21/0.55 ( ( Xk @ Xx_2 @ Xy_47 )
% 0.21/0.55 => ( ( Xs @ Xx_2 @ Xy_47 )
% 0.21/0.55 | ( ( Xx_2 = Xx )
% 0.21/0.55 & ( Xy_47 = Xy ) ) ) )
% 0.21/0.55 => ! [Xx_3: b,Xy_48: a] :
% 0.21/0.55 ( ( ( Xk @ Xx_3 @ Xy_48 )
% 0.21/0.55 & ~ ( ( Xx_3 = Xx )
% 0.21/0.55 & ( Xy_48 = Xy ) ) )
% 0.21/0.55 => ( Xs @ Xx_3 @ Xy_48 ) ) ) ).
% 0.21/0.55
% 0.21/0.55 %------------------------------------------------------------------------------
% 0.21/0.55 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.hCFqR7a8Wm/cvc5---1.0.5_21623.p...
% 0.21/0.55 (declare-sort $$unsorted 0)
% 0.21/0.55 (declare-sort tptp.b 0)
% 0.21/0.55 (declare-sort tptp.a 0)
% 0.21/0.55 (assert (not (forall ((Xx tptp.b) (Xy tptp.a) (Xs (-> tptp.b tptp.a Bool)) (Xk (-> tptp.b tptp.a Bool))) (=> (forall ((Xx_2 tptp.b) (Xy_47 tptp.a)) (=> (@ (@ Xk Xx_2) Xy_47) (or (@ (@ Xs Xx_2) Xy_47) (and (= Xx_2 Xx) (= Xy_47 Xy))))) (forall ((Xx_3 tptp.b) (Xy_48 tptp.a)) (=> (and (@ (@ Xk Xx_3) Xy_48) (not (and (= Xx_3 Xx) (= Xy_48 Xy)))) (@ (@ Xs Xx_3) Xy_48)))))))
% 0.21/0.55 (set-info :filename cvc5---1.0.5_21623)
% 0.21/0.55 (check-sat-assuming ( true ))
% 0.21/0.55 ------- get file name : TPTP file name is SEV061^5
% 0.21/0.55 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21623.smt2...
% 0.21/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.55 % SZS status Theorem for SEV061^5
% 0.21/0.55 % SZS output start Proof for SEV061^5
% 0.21/0.55 (
% 0.21/0.55 (let ((_let_1 (not (forall ((Xx tptp.b) (Xy tptp.a) (Xs (-> tptp.b tptp.a Bool)) (Xk (-> tptp.b tptp.a Bool))) (=> (forall ((Xx_2 tptp.b) (Xy_47 tptp.a)) (=> (@ (@ Xk Xx_2) Xy_47) (or (@ (@ Xs Xx_2) Xy_47) (and (= Xx_2 Xx) (= Xy_47 Xy))))) (forall ((Xx_3 tptp.b) (Xy_48 tptp.a)) (=> (and (@ (@ Xk Xx_3) Xy_48) (not (and (= Xx_3 Xx) (= Xy_48 Xy)))) (@ (@ Xs Xx_3) Xy_48)))))))) (let ((_let_2 (forall ((Xx_2 tptp.b) (Xy_47 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx_2) Xy_47)) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Xx_2) Xy_47) (and (= Xx_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (= Xy_47 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_3 (and (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_4 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_6 (not _let_5))) (let ((_let_7 (or _let_6 _let_4 _let_3))) (let ((_let_8 (not _let_2))) (let ((_let_9 (or _let_8 _let_6 _let_3 _let_4))) (let ((_let_10 (forall ((Xx tptp.b) (Xy tptp.a) (BOUND_VARIABLE_658 |u_(-> tptp.b tptp.a Bool)|) (BOUND_VARIABLE_666 |u_(-> tptp.b tptp.a Bool)|) (BOUND_VARIABLE_640 tptp.a) (BOUND_VARIABLE_638 tptp.b)) (or (not (forall ((Xx_2 tptp.b) (Xy_47 tptp.a)) (or (not (ho_3 (ho_2 BOUND_VARIABLE_666 Xx_2) Xy_47)) (ho_3 (ho_2 BOUND_VARIABLE_658 Xx_2) Xy_47) (and (= Xx Xx_2) (= Xy Xy_47))))) (not (ho_3 (ho_2 BOUND_VARIABLE_666 BOUND_VARIABLE_638) BOUND_VARIABLE_640)) (and (= Xx BOUND_VARIABLE_638) (= Xy BOUND_VARIABLE_640)) (ho_3 (ho_2 BOUND_VARIABLE_658 BOUND_VARIABLE_638) BOUND_VARIABLE_640))))) (let ((_let_11 (not _let_9))) (let ((_let_12 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_13 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_14 (forall ((u |u_(-> tptp.b tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.a Bool)|)) (not (forall ((ii tptp.b)) (= (ho_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_15 (forall ((x |u_(-> tptp.b tptp.a Bool)|) (y |u_(-> tptp.b tptp.a Bool)|)) (or (not (forall ((z tptp.b)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_16 (not _let_10))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xx tptp.b) (Xy tptp.a) (Xs (-> tptp.b tptp.a Bool)) (Xk (-> tptp.b tptp.a Bool)) (BOUND_VARIABLE_640 tptp.a) (BOUND_VARIABLE_638 tptp.b)) (or (not (forall ((Xx_2 tptp.b) (Xy_47 tptp.a)) (or (not (@ (@ Xk Xx_2) Xy_47)) (@ (@ Xs Xx_2) Xy_47) (and (= Xx Xx_2) (= Xy Xy_47))))) (not (@ (@ Xk BOUND_VARIABLE_638) BOUND_VARIABLE_640)) (and (= Xx BOUND_VARIABLE_638) (= Xy BOUND_VARIABLE_640)) (@ (@ Xs BOUND_VARIABLE_638) BOUND_VARIABLE_640)))) _let_16))))))) (let ((_let_18 (or))) (let ((_let_19 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_17) :args (_let_16)) (REWRITE :args ((=> _let_16 (not (or (not (forall ((Xx_2 tptp.b) (Xy_47 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx_2) Xy_47)) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Xx_2) Xy_47) (and (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx_2) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xy_47))))) _let_6 _let_3 _let_4))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_10))) (REFL :args (_let_11)) :args _let_18)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_17 (PREPROCESS :args ((and _let_15 _let_14 _let_13 _let_12)))) :args ((and _let_16 _let_15 _let_14 _let_13 _let_12))) :args (0)) :args (_let_11 true _let_10)))) (let ((_let_20 (REFL :args (_let_9)))) (let ((_let_21 (not _let_7))) (let ((_let_22 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_22) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_22))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_7)) :args ((or _let_6 _let_3 _let_4 _let_21))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_9 1)) (CONG _let_20 (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) :args _let_18)) :args ((or _let_5 _let_9))) _let_19 :args (_let_5 true _let_9)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_9 2)) _let_19 :args ((not _let_3) true _let_9)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_9 3)) _let_19 :args ((not _let_4) true _let_9)) :args (_let_21 false _let_5 true _let_3 true _let_4)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_9 0)) (CONG _let_20 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_2))) :args _let_18)) :args ((or _let_2 _let_9))) _let_19 :args (_let_2 true _let_9)) :args (false true _let_7 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))
% 0.21/0.55 )
% 0.21/0.55 % SZS output end Proof for SEV061^5
% 0.21/0.55 % cvc5---1.0.5 exiting
% 0.21/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------