TSTP Solution File: SYO357^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SYO357^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 : Fri Sep 1 04:15:13 EDT 2023
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO357^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.16/0.35 % Computer : n019.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri Aug 25 23:19:43 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 % File : SYO357^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.53 % Domain : Syntactic
% 0.21/0.53 % Problem : TPS problem E2LEIBEQ2
% 0.21/0.53 % Version : Especial.
% 0.21/0.53 % English : Example from [Ben99] about alternative defns of equality.
% 0.21/0.53
% 0.21/0.53 % Refs : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
% 0.21/0.53 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.53 % Source : [Bro09]
% 0.21/0.53 % Names : tps_0221 [Bro09]
% 0.21/0.53 % : E2LEIBEQ2 [TPS]
% 0.21/0.53
% 0.21/0.53 % Status : Theorem
% 0.21/0.53 % Rating : 0.18 v8.1.0, 0.08 v7.5.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.21/0.53 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.21/0.53 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.21/0.53 % Maximal formula atoms : 4 ( 4 avg)
% 0.21/0.53 % Number of connectives : 13 ( 2 ~; 2 |; 2 &; 4 @)
% 0.21/0.53 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.21/0.53 % Maximal formula depth : 7 ( 7 avg)
% 0.21/0.53 % Number of types : 2 ( 1 usr)
% 0.21/0.53 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.21/0.53 % Number of symbols : 4 ( 4 usr; 4 con; 0-0 aty)
% 0.21/0.53 % Number of variables : 2 ( 0 ^; 2 !; 0 ?; 2 :)
% 0.21/0.53 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.53
% 0.21/0.53 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.53 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.53 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.53 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.53 % : Polymorphic definitions expanded.
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 thf(a_type,type,
% 0.21/0.53 atype: $tType ).
% 0.21/0.53
% 0.21/0.53 thf(a,type,
% 0.21/0.53 a: $o ).
% 0.21/0.53
% 0.21/0.53 thf(v,type,
% 0.21/0.53 v: atype ).
% 0.21/0.53
% 0.21/0.53 thf(u,type,
% 0.21/0.53 u: atype ).
% 0.21/0.53
% 0.21/0.53 thf(b,type,
% 0.21/0.53 b: $o ).
% 0.21/0.53
% 0.21/0.53 thf(cE2LEIBEQ2_pme,conjecture,
% 0.21/0.53 ( ! [P: atype > $o] :
% 0.21/0.53 ( ( ( a
% 0.21/0.53 | ~ a )
% 0.21/0.53 & ( P @ u ) )
% 0.21/0.53 => ( ( b
% 0.21/0.53 | ~ b )
% 0.21/0.53 & ( P @ v ) ) )
% 0.21/0.53 => ! [Xq: atype > $o] :
% 0.21/0.53 ( ( Xq @ u )
% 0.21/0.53 => ( Xq @ v ) ) ) ).
% 0.21/0.53
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.lSsIePOb24/cvc5---1.0.5_29406.p...
% 0.21/0.53 (declare-sort $$unsorted 0)
% 0.21/0.53 (declare-sort tptp.atype 0)
% 0.21/0.53 (declare-fun tptp.a () Bool)
% 0.21/0.53 (declare-fun tptp.v () tptp.atype)
% 0.21/0.53 (declare-fun tptp.u () tptp.atype)
% 0.21/0.53 (declare-fun tptp.b () Bool)
% 0.21/0.53 (assert (not (=> (forall ((P (-> tptp.atype Bool))) (=> (and (or tptp.a (not tptp.a)) (@ P tptp.u)) (and (or tptp.b (not tptp.b)) (@ P tptp.v)))) (forall ((Xq (-> tptp.atype Bool))) (=> (@ Xq tptp.u) (@ Xq tptp.v))))))
% 0.21/0.53 (set-info :filename cvc5---1.0.5_29406)
% 0.21/0.53 (check-sat-assuming ( true ))
% 0.21/0.53 ------- get file name : TPTP file name is SYO357^5
% 0.21/0.53 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_29406.smt2...
% 0.21/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.53 % SZS status Theorem for SYO357^5
% 0.21/0.53 % SZS output start Proof for SYO357^5
% 0.21/0.53 (
% 0.21/0.53 (let ((_let_1 (not (=> (forall ((P (-> tptp.atype Bool))) (=> (and (or tptp.a (not tptp.a)) (@ P tptp.u)) (and (or tptp.b (not tptp.b)) (@ P tptp.v)))) (forall ((Xq (-> tptp.atype Bool))) (=> (@ Xq tptp.u) (@ Xq tptp.v))))))) (let ((_let_2 (forall ((BOUND_VARIABLE_620 |u_(-> tptp.atype Bool)|)) (or (not (ho_2 BOUND_VARIABLE_620 tptp.u)) (ho_2 BOUND_VARIABLE_620 tptp.v))))) (let ((_let_3 (forall ((BOUND_VARIABLE_629 |u_(-> tptp.atype Bool)|)) (or (not (ho_2 BOUND_VARIABLE_629 tptp.u)) (ho_2 BOUND_VARIABLE_629 tptp.v))))) (let ((_let_4 (forall ((u |u_(-> tptp.atype Bool)|) (e Bool) (i tptp.atype)) (not (forall ((v |u_(-> tptp.atype Bool)|)) (not (forall ((ii tptp.atype)) (= (ho_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_5 (forall ((x |u_(-> tptp.atype Bool)|) (y |u_(-> tptp.atype Bool)|)) (or (not (forall ((z tptp.atype)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_6 (not (=> _let_3 _let_2)))) (let ((_let_7 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> (forall ((P (-> tptp.atype Bool))) (or (not (@ P tptp.u)) (@ P tptp.v))) (forall ((Xq (-> tptp.atype Bool))) (or (not (@ Xq tptp.u)) (@ Xq tptp.v))))) _let_6))))) (PREPROCESS :args ((and _let_5 _let_4)))) :args ((and _let_6 _let_5 _let_4))) :args (0)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_IMPLIES_ELIM2 _let_7) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (SYMM (ALPHA_EQUIV :args (_let_3 (= BOUND_VARIABLE_629 BOUND_VARIABLE_620))))) (NOT_IMPLIES_ELIM1 _let_7) :args (_let_2 false _let_3)) :args (false false _let_2)) :args (_let_1 true))))))))))
% 0.21/0.53 )
% 0.21/0.53 % SZS output end Proof for SYO357^5
% 0.21/0.53 % cvc5---1.0.5 exiting
% 0.21/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------