TSTP Solution File: ALG286^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ALG286^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 : Wed Aug 30 16:09:11 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 : ALG286^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.17/0.35 % Computer : n016.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon Aug 28 06:08:29 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 % File : ALG286^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.52 % Domain : General Algebra (Domain theory)
% 0.21/0.52 % Problem : TPS problem from PAIRING-UNPAIRING-ALG-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_0979 [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, 0.00 v6.1.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 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 : 9 ( 0 unt; 8 typ; 0 def)
% 0.21/0.52 % Number of atoms : 8 ( 8 equ; 0 cnn)
% 0.21/0.52 % Maximal formula atoms : 8 ( 8 avg)
% 0.21/0.52 % Number of connectives : 23 ( 2 ~; 0 |; 4 &; 14 @)
% 0.21/0.52 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.52 % Maximal formula depth : 9 ( 9 avg)
% 0.21/0.52 % Number of types : 1 ( 1 usr)
% 0.21/0.52 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.21/0.52 % Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% 0.21/0.52 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 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(cZ,type,
% 0.21/0.52 cZ: a ).
% 0.21/0.52
% 0.21/0.52 thf(u,type,
% 0.21/0.52 u: a ).
% 0.21/0.52
% 0.21/0.52 thf(y,type,
% 0.21/0.52 y: a ).
% 0.21/0.52
% 0.21/0.52 thf(x,type,
% 0.21/0.52 x: a ).
% 0.21/0.52
% 0.21/0.52 thf(cP,type,
% 0.21/0.52 cP: a > a > a ).
% 0.21/0.52
% 0.21/0.52 thf(cR,type,
% 0.21/0.52 cR: a > a ).
% 0.21/0.52
% 0.21/0.52 thf(cL,type,
% 0.21/0.52 cL: a > a ).
% 0.21/0.52
% 0.21/0.52 thf(cPU_PAIR_NOT_ZERO_pme,conjecture,
% 0.21/0.52 ( ( ( ( cL @ cZ )
% 0.21/0.52 = cZ )
% 0.21/0.52 & ( ( cR @ cZ )
% 0.21/0.52 = cZ )
% 0.21/0.52 & ! [Xx0: a,Xy0: a] :
% 0.21/0.52 ( ( cL @ ( cP @ Xx0 @ Xy0 ) )
% 0.21/0.52 = Xx0 )
% 0.21/0.52 & ! [Xx0: a,Xy0: a] :
% 0.21/0.52 ( ( cR @ ( cP @ Xx0 @ Xy0 ) )
% 0.21/0.52 = Xy0 )
% 0.21/0.52 & ! [Xt: a] :
% 0.21/0.52 ( ( Xt != cZ )
% 0.21/0.52 <=> ( Xt
% 0.21/0.52 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
% 0.21/0.52 => ( ( u
% 0.21/0.52 = ( cP @ x @ y ) )
% 0.21/0.52 => ( u != cZ ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.1teSJkUyvh/cvc5---1.0.5_31068.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.cZ () tptp.a)
% 0.21/0.52 (declare-fun tptp.u () tptp.a)
% 0.21/0.52 (declare-fun tptp.y () tptp.a)
% 0.21/0.52 (declare-fun tptp.x () tptp.a)
% 0.21/0.52 (declare-fun tptp.cP (tptp.a tptp.a) tptp.a)
% 0.21/0.52 (declare-fun tptp.cR (tptp.a) tptp.a)
% 0.21/0.52 (declare-fun tptp.cL (tptp.a) tptp.a)
% 0.21/0.52 (assert (not (=> (and (= (@ tptp.cL tptp.cZ) tptp.cZ) (= (@ tptp.cR tptp.cZ) tptp.cZ) (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (= (@ tptp.cL (@ (@ tptp.cP Xx0) Xy0)) Xx0)) (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (= (@ tptp.cR (@ (@ tptp.cP Xx0) Xy0)) Xy0)) (forall ((Xt tptp.a)) (= (not (= Xt tptp.cZ)) (= Xt (@ (@ tptp.cP (@ tptp.cL Xt)) (@ tptp.cR Xt)))))) (=> (= tptp.u (@ (@ tptp.cP tptp.x) tptp.y)) (not (= tptp.u tptp.cZ))))))
% 0.21/0.52 (set-info :filename cvc5---1.0.5_31068)
% 0.21/0.52 (check-sat-assuming ( true ))
% 0.21/0.52 ------- get file name : TPTP file name is ALG286^5
% 0.21/0.52 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31068.smt2...
% 0.21/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.52 % SZS status Theorem for ALG286^5
% 0.21/0.52 % SZS output start Proof for ALG286^5
% 0.21/0.52 (
% 0.21/0.52 (let ((_let_1 (@ (@ tptp.cP tptp.x) tptp.y))) (let ((_let_2 (= tptp.u _let_1))) (let ((_let_3 (@ tptp.cR tptp.cZ))) (let ((_let_4 (@ tptp.cL tptp.cZ))) (let ((_let_5 (not (=> (and (= _let_4 tptp.cZ) (= _let_3 tptp.cZ) (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (= (@ tptp.cL (@ (@ tptp.cP Xx0) Xy0)) Xx0)) (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (= (@ tptp.cR (@ (@ tptp.cP Xx0) Xy0)) Xy0)) (forall ((Xt tptp.a)) (= (not (= Xt tptp.cZ)) (= Xt (@ (@ tptp.cP (@ tptp.cL Xt)) (@ tptp.cR Xt)))))) (=> _let_2 (not (= tptp.u tptp.cZ))))))) (let ((_let_6 (forall ((Xt tptp.a)) (= (not (= Xt (ho_4 (ho_3 k_2 tptp.x) tptp.y))) (= Xt (ho_4 (ho_3 k_2 (ho_4 k_6 Xt)) (ho_4 k_5 Xt))))))) (let ((_let_7 (ho_4 (ho_3 k_2 tptp.x) tptp.y))) (let ((_let_8 (ho_4 k_5 _let_7))) (let ((_let_9 (ho_4 k_6 _let_7))) (let ((_let_10 (= _let_7 (ho_4 (ho_3 k_2 _let_9) _let_8)))) (let ((_let_11 (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_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_12 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_13 (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_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_14 (forall ((x |u_(-> tptp.a tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_15 (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (= Xy0 (ho_4 k_5 (ho_4 (ho_3 k_2 Xx0) Xy0)))))) (let ((_let_16 (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (= Xx0 (ho_4 k_6 (ho_4 (ho_3 k_2 Xx0) Xy0)))))) (let ((_let_17 (= _let_7 _let_8))) (let ((_let_18 (= _let_7 _let_9))) (let ((_let_19 (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (= Xy0 (@ tptp.cR (@ (@ tptp.cP Xx0) Xy0)))))) (let ((_let_20 (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (= Xx0 (@ tptp.cL (@ (@ tptp.cP Xx0) Xy0)))))) (let ((_let_21 (= tptp.cZ tptp.u))) (let ((_let_22 (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_23 (ASSUME :args (_let_5)))) (let ((_let_24 (NOT_IMPLIES_ELIM2 (EQ_RESOLVE _let_23 _let_22)))) (let ((_let_25 (NOT_IMPLIES_ELIM1 _let_24))) (let ((_let_26 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE _let_23 (TRANS _let_22 (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (NOT_NOT_ELIM (NOT_IMPLIES_ELIM2 _let_24)) (MACRO_SR_EQ_INTRO _let_25 :args (_let_21 SB_DEFAULT SBA_FIXPOINT))) _let_25) :args ((not (=> (and (= tptp.cZ _let_4) (= tptp.cZ _let_3) _let_20 _let_19 (forall ((Xt tptp.a)) (= (= Xt (@ (@ tptp.cP (@ tptp.cL Xt)) (@ tptp.cR Xt))) (not (= tptp.cZ Xt))))) (=> _let_2 (not _let_21)))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and (= _let_1 (@ tptp.cL _let_1)) (= _let_1 (@ tptp.cR _let_1)) _let_20 _let_19 (forall ((Xt tptp.a)) (= (= Xt (@ (@ tptp.cP (@ tptp.cL Xt)) (@ tptp.cR Xt))) (not (= Xt (@ (@ tptp.cP tptp.x) tptp.y)))))) (and _let_18 _let_17 _let_16 _let_15 _let_6)))))) (PREPROCESS :args ((and _let_14 _let_13 _let_12 _let_11)))) :args ((and _let_18 _let_17 _let_16 _let_15 _let_6 _let_14 _let_13 _let_12 _let_11))))) (let ((_let_27 (= tptp.y _let_8))) (let ((_let_28 (= tptp.x _let_9))) (let ((_let_29 (_let_15))) (let ((_let_30 (tptp.x tptp.y QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_31 (_let_16))) (let ((_let_32 (and _let_28 _let_27))) (let ((_let_33 (_let_28 _let_27))) (let ((_let_34 (ASSUME :args (_let_27)))) (let ((_let_35 (ASSUME :args (_let_28)))) (let ((_let_36 (_let_6))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_36) :args (_let_7 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_36))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_32)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_35 _let_34) (SCOPE (CONG (CONG (REFL :args (k_2)) (SYMM (SYMM _let_35)) :args (APPLY_UF ho_3)) (SYMM (SYMM _let_34)) :args (APPLY_UF ho_4)) :args _let_33)) :args _let_33)) :args (true _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_31) :args _let_30) :args _let_31)) (AND_ELIM _let_26 :args (2)) :args (_let_28 false _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_29) :args _let_30) :args _let_29)) (AND_ELIM _let_26 :args (3)) :args (_let_27 false _let_15)) :args (_let_10 false _let_28 false _let_27)) (AND_ELIM _let_26 :args (4)) :args (false false _let_10 false _let_6)) :args (_let_5 true)))))))))))))))))))))))))))))))))))))))
% 0.21/0.53 )
% 0.21/0.53 % SZS output end Proof for ALG286^5
% 0.21/0.53 % cvc5---1.0.5 exiting
% 0.21/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------