TSTP Solution File: SEV241^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV241^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 19:21:58 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
% 0.00/0.13 % Problem : SEV241^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 03:21:06 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 % File : SEV241^5 : 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 from SETS-OF-SETS-THMS
% 0.21/0.52 % Version : Especial.
% 0.21/0.52 % English :
% 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_0779 [Bro09]
% 0.21/0.52
% 0.21/0.52 % Status : Theorem
% 0.21/0.52 % 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.21/0.52 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.21/0.52 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.21/0.52 % Maximal formula atoms : 4 ( 6 avg)
% 0.21/0.52 % Number of connectives : 7 ( 0 ~; 1 |; 1 &; 3 @)
% 0.21/0.52 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.52 % Maximal formula depth : 6 ( 6 avg)
% 0.21/0.52 % Number of types : 2 ( 1 usr)
% 0.21/0.52 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.21/0.52 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.21/0.52 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 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 %------------------------------------------------------------------------------
% 0.21/0.52 thf(a_type,type,
% 0.21/0.52 a: $tType ).
% 0.21/0.52
% 0.21/0.52 thf(cW,type,
% 0.21/0.52 cW: a > $o ).
% 0.21/0.52
% 0.21/0.52 thf(cU,type,
% 0.21/0.52 cU: a > $o ).
% 0.21/0.52
% 0.21/0.52 thf(cX5201A_pme,conjecture,
% 0.21/0.52 ! [Xx: a] :
% 0.21/0.52 ( ( ( cU @ Xx )
% 0.21/0.52 & ( cW @ Xx ) )
% 0.21/0.52 => ! [S: a > $o] :
% 0.21/0.52 ( ( ( S = cU )
% 0.21/0.52 | ( S = cW ) )
% 0.21/0.52 => ( S @ Xx ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.jDZTZBDnOP/cvc5---1.0.5_12346.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (declare-sort tptp.a 0)
% 0.21/0.52 (declare-fun tptp.cW (tptp.a) Bool)
% 0.21/0.52 (declare-fun tptp.cU (tptp.a) Bool)
% 0.21/0.52 (assert (not (forall ((Xx tptp.a)) (=> (and (@ tptp.cU Xx) (@ tptp.cW Xx)) (forall ((S (-> tptp.a Bool))) (=> (or (= S tptp.cU) (= S tptp.cW)) (@ S Xx)))))))
% 0.21/0.52 (set-info :filename cvc5---1.0.5_12346)
% 0.21/0.52 (check-sat-assuming ( true ))
% 0.21/0.52 ------- get file name : TPTP file name is SEV241^5
% 0.21/0.52 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12346.smt2...
% 0.21/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.52 % SZS status Theorem for SEV241^5
% 0.21/0.52 % SZS output start Proof for SEV241^5
% 0.21/0.52 (
% 0.21/0.52 (let ((_let_1 (not (forall ((Xx tptp.a)) (=> (and (@ tptp.cU Xx) (@ tptp.cW Xx)) (forall ((S (-> tptp.a Bool))) (=> (or (= S tptp.cU) (= S tptp.cW)) (@ S Xx)))))))) (let ((_let_2 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_3 (ho_3 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_4 (and _let_3 _let_2))) (let ((_let_5 (not _let_2))) (let ((_let_6 (not _let_3))) (let ((_let_7 (or _let_6 _let_5 _let_4))) (let ((_let_8 (forall ((Xx tptp.a)) (let ((_let_1 (ho_3 k_2 Xx))) (let ((_let_2 (ho_3 k_4 Xx))) (or (not _let_2) (not _let_1) (and _let_2 _let_1))))))) (let ((_let_9 (not _let_7))) (let ((_let_10 (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_11 (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_12 (not _let_8))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xx tptp.a)) (let ((_let_1 (@ tptp.cW Xx))) (let ((_let_2 (@ tptp.cU Xx))) (or (not _let_2) (not _let_1) (and _let_2 _let_1)))))) _let_12))))))) (let ((_let_14 (or))) (let ((_let_15 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_13) :args (_let_12))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_8))) (REFL :args (_let_9)) :args _let_14)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_13 (PREPROCESS :args ((and _let_11 _let_10)))) :args ((and _let_12 _let_11 _let_10))) :args (0)) :args (_let_9 true _let_8)))) (let ((_let_16 (_let_7))) (let ((_let_17 (REFL :args _let_16))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_4)) :args _let_16) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_7 1)) (CONG _let_17 (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_2))) :args _let_14)) :args ((or _let_2 _let_7))) _let_15 :args (_let_2 true _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_7 0)) (CONG _let_17 (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_3))) :args _let_14)) :args ((or _let_3 _let_7))) _let_15 :args (_let_3 true _let_7)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_7 2)) _let_15 :args ((not _let_4) true _let_7)) :args (false false _let_2 false _let_3 true _let_4)) :args (_let_1 true))))))))))))))))))))
% 0.21/0.52 )
% 0.21/0.52 % SZS output end Proof for SEV241^5
% 0.21/0.52 % cvc5---1.0.5 exiting
% 0.21/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------