TSTP Solution File: SEV160^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV160^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 19:21:43 EDT 2023
% Result : Theorem 0.21s 0.54s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEV160^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n010.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 03:35:06 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.54 %------------------------------------------------------------------------------
% 0.21/0.54 % File : SEV160^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.54 % Domain : Set Theory
% 0.21/0.54 % Problem : TPS problem THM186
% 0.21/0.54 % Version : Especial.
% 0.21/0.54 % English : Basic theorem about pairing.
% 0.21/0.54
% 0.21/0.54 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.54 % Source : [Bro09]
% 0.21/0.54 % Names : tps_0061 [Bro09]
% 0.21/0.54 % : THM186 [TPS]
% 0.21/0.54
% 0.21/0.54 % Status : Theorem
% 0.21/0.54 % 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
% 0.21/0.54 % Syntax : Number of formulae : 4 ( 1 unt; 3 typ; 0 def)
% 0.21/0.54 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.21/0.54 % Maximal formula atoms : 1 ( 1 avg)
% 0.21/0.54 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 4 @)
% 0.21/0.54 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.21/0.54 % Maximal formula depth : 1 ( 1 avg)
% 0.21/0.54 % Number of types : 1 ( 1 usr)
% 0.21/0.54 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.21/0.54 % Number of symbols : 3 ( 2 usr; 2 con; 0-2 aty)
% 0.21/0.54 % Number of variables : 2 ( 2 ^; 0 !; 0 ?; 2 :)
% 0.21/0.54 % SPC : TH0_THM_EQU_NAR
% 0.21/0.54
% 0.21/0.54 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.54 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.54 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.54 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.54 % : Polymorphic definitions expanded.
% 0.21/0.54 %------------------------------------------------------------------------------
% 0.21/0.54 thf(a_type,type,
% 0.21/0.54 a: $tType ).
% 0.21/0.54
% 0.21/0.54 thf(y,type,
% 0.21/0.54 y: a ).
% 0.21/0.54
% 0.21/0.54 thf(x,type,
% 0.21/0.54 x: a ).
% 0.21/0.54
% 0.21/0.54 thf(cTHM186_pme,conjecture,
% 0.21/0.54 ( ( ^ [Xg: a > a > a] : ( Xg @ x @ y ) )
% 0.21/0.54 = ( ^ [Xg: a > a > a] : ( Xg @ x @ y ) ) ) ).
% 0.21/0.54
% 0.21/0.54 %------------------------------------------------------------------------------
% 0.21/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.OwLasqpGuY/cvc5---1.0.5_22680.p...
% 0.21/0.54 (declare-sort $$unsorted 0)
% 0.21/0.54 (declare-sort tptp.a 0)
% 0.21/0.54 (declare-fun tptp.y () tptp.a)
% 0.21/0.54 (declare-fun tptp.x () tptp.a)
% 0.21/0.54 (assert (not (= (lambda ((Xg (-> tptp.a tptp.a tptp.a))) (@ (@ Xg tptp.x) tptp.y)) (lambda ((Xg (-> tptp.a tptp.a tptp.a))) (@ (@ Xg tptp.x) tptp.y)))))
% 0.21/0.54 (set-info :filename cvc5---1.0.5_22680)
% 0.21/0.54 (check-sat-assuming ( true ))
% 0.21/0.54 ------- get file name : TPTP file name is SEV160^5
% 0.21/0.54 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22680.smt2...
% 0.21/0.54 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.54 % SZS status Theorem for SEV160^5
% 0.21/0.54 % SZS output start Proof for SEV160^5
% 0.21/0.54 (
% 0.21/0.54 (let ((_let_1 (not (= (lambda ((Xg (-> tptp.a tptp.a tptp.a))) (@ (@ Xg tptp.x) tptp.y)) (lambda ((Xg (-> tptp.a tptp.a tptp.a))) (@ (@ Xg tptp.x) tptp.y)))))) (let ((_let_2 (ho_6 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_3 (ho_6 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_4 (= _let_3 _let_2))) (let ((_let_5 (ho_7 (ho_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 tptp.x) tptp.y))) (let ((_let_6 (= _let_3 _let_5))) (let ((_let_7 (= _let_2 _let_5))) (let ((_let_8 (forall ((z |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_6 k_8 z) (ho_6 k_5 z))))) (let ((_let_9 (not _let_4))) (let ((_let_10 (= k_5 k_8))) (let ((_let_11 (not _let_8))) (let ((_let_12 (or _let_11 _let_10))) (let ((_let_13 (forall ((x |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a)|) (y |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_14 (forall ((u |u_(-> tptp.a tptp.a tptp.a)|) (e |u_(-> tptp.a tptp.a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_15 (forall ((x |u_(-> tptp.a tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_16 (forall ((u |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a)|) (e tptp.a) (i |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a tptp.a)_ tptp.a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_17 (forall ((u |u_(-> tptp.a tptp.a)|) (e tptp.a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_18 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_19 (forall ((BOUND_VARIABLE_621 |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_6 k_5 BOUND_VARIABLE_621) (ho_7 (ho_4 BOUND_VARIABLE_621 tptp.x) tptp.y))))) (let ((_let_20 (forall ((BOUND_VARIABLE_639 |u_(-> tptp.a tptp.a tptp.a)|)) (= (ho_6 k_8 BOUND_VARIABLE_639) (ho_7 (ho_4 BOUND_VARIABLE_639 tptp.x) tptp.y))))) (let ((_let_21 (not _let_10))) (let ((_let_22 (forall ((BOUND_VARIABLE_604 (-> tptp.a tptp.a tptp.a))) (= (@ (@ BOUND_VARIABLE_604 tptp.x) tptp.y) (ll_3 BOUND_VARIABLE_604))))) (let ((_let_23 (forall ((BOUND_VARIABLE_597 (-> tptp.a tptp.a tptp.a))) (= (@ (@ BOUND_VARIABLE_597 tptp.x) tptp.y) (ll_2 BOUND_VARIABLE_597))))) (let ((_let_24 (not (= ll_2 ll_3)))) (let ((_let_25 (and _let_24 _let_23 _let_22))) (let ((_let_26 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 _let_24)))) (PREPROCESS :args ((and _let_23 _let_22)))) :args (_let_25)) (PREPROCESS :args ((= _let_25 (and _let_21 _let_20 _let_19))))) (PREPROCESS :args ((and _let_18 _let_17 _let_13 _let_16 _let_15 _let_14)))) :args ((and _let_21 _let_20 _let_19 _let_18 _let_17 _let_13 _let_16 _let_15 _let_14))))) (let ((_let_27 (_let_13))) (let ((_let_28 (or))) (let ((_let_29 (_let_9))) (let ((_let_30 (_let_11))) (let ((_let_31 (_let_20))) (let ((_let_32 (_let_19))) (let ((_let_33 (ASSUME :args (_let_7)))) (let ((_let_34 (ASSUME :args (_let_6)))) (let ((_let_35 (ASSUME :args _let_29))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_34 _let_33 _let_35) :args (_let_9 _let_6 _let_7)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_35)) (TRUE_INTRO (TRANS (SYMM (SYMM _let_34)) (SYMM _let_33))))) :args (_let_6 _let_7 _let_9)) :args ((not (and _let_9 _let_6 _let_7)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_4))) (REFL :args ((not _let_6))) (REFL :args ((not _let_7))) :args _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_5 BOUND_VARIABLE_621)))) :args _let_32)) (AND_ELIM _let_26 :args (2)) :args (_let_7 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_31) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_8 BOUND_VARIABLE_639)))) :args _let_31)) (AND_ELIM _let_26 :args (1)) :args (_let_6 false _let_20)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_30)) :args _let_30)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_8))) (REFL :args _let_29) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_10 _let_11 (not _let_12)))) (AND_ELIM _let_26 :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_27) :args (k_8 k_5 QUANTIFIERS_INST_ENUM)) :args _let_27))) (AND_ELIM _let_26 :args (5)) :args (_let_12 false _let_13)) :args (_let_11 true _let_10 false _let_12)) :args (_let_9 true _let_8)) :args (false false _let_7 false _let_6 true _let_4)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))
% 0.21/0.55 )
% 0.21/0.55 % SZS output end Proof for SEV160^5
% 0.21/0.55 % cvc5---1.0.5 exiting
% 0.21/0.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------