TSTP Solution File: SYO103^5 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SYO103^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 04:14:24 EDT 2023
% Result : Theorem 0.22s 0.58s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO103^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 00:38:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.51 %----Proving TH0
% 0.22/0.58 %------------------------------------------------------------------------------
% 0.22/0.58 % File : SYO103^5 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.58 % Domain : Syntactic
% 0.22/0.58 % Problem : TPS problem THM147
% 0.22/0.58 % Version : Especial.
% 0.22/0.58 % English : Theorem 211 on page 120 of [Chu56].
% 0.22/0.58
% 0.22/0.58 % Refs : [Chu56] Church (1956), Introduction to Mathematical Logic I
% 0.22/0.58 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.58 % Source : [Bro09]
% 0.22/0.58 % Names : tps_0367 [Bro09]
% 0.22/0.58 % : THM147 [TPS]
% 0.22/0.58
% 0.22/0.58 % Status : Theorem
% 0.22/0.58 % Rating : 0.09 v8.1.0, 0.17 v7.5.0, 0.08 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 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.22/0.58 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.22/0.58 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.22/0.58 % Maximal formula atoms : 7 ( 7 avg)
% 0.22/0.58 % Number of connectives : 45 ( 4 ~; 2 |; 4 &; 35 @)
% 0.22/0.58 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.22/0.58 % Maximal formula depth : 14 ( 14 avg)
% 0.22/0.58 % Number of types : 2 ( 0 usr)
% 0.22/0.58 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.22/0.58 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.22/0.58 % Number of variables : 10 ( 0 ^; 9 !; 1 ?; 10 :)
% 0.22/0.58 % SPC : TH0_THM_NEQ_NAR
% 0.22/0.58
% 0.22/0.58 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.58 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.58 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.58 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.58 %------------------------------------------------------------------------------
% 0.22/0.58 thf(imp,type,
% 0.22/0.58 imp: $i > $i > $i ).
% 0.22/0.58
% 0.22/0.58 thf(cT,type,
% 0.22/0.58 cT: $i > $o ).
% 0.22/0.58
% 0.22/0.58 thf(nt,type,
% 0.22/0.58 nt: $i > $i ).
% 0.22/0.58
% 0.22/0.58 thf(cTHM147,conjecture,
% 0.22/0.58 ~ ( ! [Xp: $i,Xq: $i] :
% 0.22/0.58 ( ~ ( cT @ ( imp @ Xp @ Xq ) )
% 0.22/0.58 | ~ ( cT @ Xp )
% 0.22/0.58 | ( cT @ Xq ) )
% 0.22/0.58 & ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ Xp @ ( imp @ Xq @ Xp ) ) )
% 0.22/0.58 & ! [Xp: $i,Xq: $i,Xr: $i] : ( cT @ ( imp @ ( imp @ Xp @ ( imp @ Xq @ Xr ) ) @ ( imp @ ( imp @ Xp @ Xq ) @ ( imp @ Xp @ Xr ) ) ) )
% 0.22/0.58 & ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ ( imp @ ( nt @ Xp ) @ ( nt @ Xq ) ) @ ( imp @ Xq @ Xp ) ) )
% 0.22/0.58 & ? [Xa: $i] :
% 0.22/0.58 ~ ( cT @ ( imp @ Xa @ Xa ) ) ) ).
% 0.22/0.58
% 0.22/0.58 %------------------------------------------------------------------------------
% 0.22/0.58 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ShDbZVsKFc/cvc5---1.0.5_18386.p...
% 0.22/0.58 (declare-sort $$unsorted 0)
% 0.22/0.58 (declare-fun tptp.imp ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.cT ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.nt ($$unsorted) $$unsorted)
% 0.22/0.58 (assert (not (not (and (forall ((Xp $$unsorted) (Xq $$unsorted)) (or (not (@ tptp.cT (@ (@ tptp.imp Xp) Xq))) (not (@ tptp.cT Xp)) (@ tptp.cT Xq))) (forall ((Xp $$unsorted) (Xq $$unsorted)) (@ tptp.cT (@ (@ tptp.imp Xp) (@ (@ tptp.imp Xq) Xp)))) (forall ((Xp $$unsorted) (Xq $$unsorted) (Xr $$unsorted)) (let ((_let_1 (@ tptp.imp Xp))) (@ tptp.cT (@ (@ tptp.imp (@ _let_1 (@ (@ tptp.imp Xq) Xr))) (@ (@ tptp.imp (@ _let_1 Xq)) (@ _let_1 Xr)))))) (forall ((Xp $$unsorted) (Xq $$unsorted)) (@ tptp.cT (@ (@ tptp.imp (@ (@ tptp.imp (@ tptp.nt Xp)) (@ tptp.nt Xq))) (@ (@ tptp.imp Xq) Xp)))) (exists ((Xa $$unsorted)) (not (@ tptp.cT (@ (@ tptp.imp Xa) Xa))))))))
% 0.22/0.58 (set-info :filename cvc5---1.0.5_18386)
% 0.22/0.58 (check-sat-assuming ( true ))
% 0.22/0.58 ------- get file name : TPTP file name is SYO103^5
% 0.22/0.58 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_18386.smt2...
% 0.22/0.58 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.58 % SZS status Theorem for SYO103^5
% 0.22/0.58 % SZS output start Proof for SYO103^5
% 0.22/0.58 (
% 0.22/0.58 (let ((_let_1 (forall ((Xp $$unsorted) (Xq $$unsorted)) (@ tptp.cT (@ (@ tptp.imp (@ (@ tptp.imp (@ tptp.nt Xp)) (@ tptp.nt Xq))) (@ (@ tptp.imp Xq) Xp)))))) (let ((_let_2 (forall ((Xp $$unsorted) (Xq $$unsorted) (Xr $$unsorted)) (let ((_let_1 (@ tptp.imp Xp))) (@ tptp.cT (@ (@ tptp.imp (@ _let_1 (@ (@ tptp.imp Xq) Xr))) (@ (@ tptp.imp (@ _let_1 Xq)) (@ _let_1 Xr)))))))) (let ((_let_3 (forall ((Xp $$unsorted) (Xq $$unsorted)) (@ tptp.cT (@ (@ tptp.imp Xp) (@ (@ tptp.imp Xq) Xp)))))) (let ((_let_4 (forall ((Xp $$unsorted) (Xq $$unsorted)) (or (not (@ tptp.cT (@ (@ tptp.imp Xp) Xq))) (not (@ tptp.cT Xp)) (@ tptp.cT Xq))))) (let ((_let_5 (not (not (and _let_4 _let_3 _let_2 _let_1 (exists ((Xa $$unsorted)) (not (@ tptp.cT (@ (@ tptp.imp Xa) Xa))))))))) (let ((_let_6 (forall ((Xp $$unsorted) (Xq $$unsorted)) (or (not (ho_6 k_5 (ho_4 (ho_3 k_2 Xp) Xq))) (not (ho_6 k_5 Xp)) (ho_6 k_5 Xq))))) (let ((_let_7 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_8 (ho_4 _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_9 (ho_4 _let_7 _let_8))) (let ((_let_10 (ho_4 (ho_3 k_2 _let_9) _let_8))) (let ((_let_11 (ho_6 k_5 _let_10))) (let ((_let_12 (ho_4 _let_7 (ho_4 (ho_3 k_2 _let_8) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_13 (ho_6 k_5 _let_12))) (let ((_let_14 (not _let_13))) (let ((_let_15 (ho_6 k_5 (ho_4 (ho_3 k_2 _let_12) _let_10)))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_14 _let_11))) (let ((_let_18 (forall ((u |u_(-> $$unsorted $$unsorted)|) (e $$unsorted) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_19 (forall ((x |u_(-> $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_20 (forall ((u |u_(-> $$unsorted $$unsorted $$unsorted)|) (e |u_(-> $$unsorted $$unsorted)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_21 (forall ((x |u_(-> $$unsorted $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_22 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_23 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_24 (forall ((Xa $$unsorted)) (ho_6 k_5 (ho_4 (ho_3 k_2 Xa) Xa))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (forall ((Xp $$unsorted) (Xq $$unsorted)) (ho_6 k_5 (ho_4 (ho_3 k_2 (ho_4 (ho_3 k_2 (ho_4 k_7 Xp)) (ho_4 k_7 Xq))) (ho_4 (ho_3 k_2 Xq) Xp)))))) (let ((_let_27 (forall ((Xp $$unsorted) (Xq $$unsorted) (Xr $$unsorted)) (let ((_let_1 (ho_3 k_2 Xp))) (ho_6 k_5 (ho_4 (ho_3 k_2 (ho_4 _let_1 (ho_4 (ho_3 k_2 Xq) Xr))) (ho_4 (ho_3 k_2 (ho_4 _let_1 Xq)) (ho_4 _let_1 Xr)))))))) (let ((_let_28 (forall ((Xp $$unsorted) (Xq $$unsorted)) (ho_6 k_5 (ho_4 (ho_3 k_2 Xp) (ho_4 (ho_3 k_2 Xq) Xp)))))) (let ((_let_29 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (and _let_4 _let_3 _let_2 _let_1 (not (forall ((Xa $$unsorted)) (@ tptp.cT (@ (@ tptp.imp Xa) Xa))))) (and _let_6 _let_28 _let_27 _let_26 _let_25)))))) (PREPROCESS :args ((and _let_23 _let_22 _let_21 _let_20 _let_19 _let_18)))) :args ((and _let_6 _let_28 _let_27 _let_26 _let_25 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18))))) (let ((_let_30 (AND_ELIM _let_29 :args (0)))) (let ((_let_31 (not _let_17))) (let ((_let_32 (_let_27))) (let ((_let_33 (ho_6 k_5 _let_8))) (let ((_let_34 (ho_6 k_5 _let_9))) (let ((_let_35 (not _let_34))) (let ((_let_36 (not _let_11))) (let ((_let_37 (or _let_36 _let_35 _let_33))) (let ((_let_38 (_let_6))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (AND_ELIM _let_29 :args (1)))) (let ((_let_41 (_let_28))) (let ((_let_42 (ho_3 k_2 Xq))) (let ((_let_43 (ASSUME :args _let_41))) (let ((_let_44 (not _let_33))) (let ((_let_45 (_let_25))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_12 _let_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_14 _let_11 _let_16 _let_31))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_8 QUANTIFIERS_INST_E_MATCHING ((ho_3 k_2 Xp) _let_42))) :args _let_41)) _let_40 :args (_let_13 false _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_33 _let_35 _let_36 (not _let_37)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_45)) :args _let_45)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) (REFL :args (_let_44)) :args (or))) (AND_ELIM _let_29 :args (4)) :args (_let_44 true _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING ((ho_4 _let_42 Xp)))) :args _let_41)) _let_40 :args (_let_34 false _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_9 _let_8 QUANTIFIERS_INST_E_MATCHING ((ho_4 (ho_3 k_2 Xp) Xq)))) :args _let_38)) _let_30 :args (_let_37 false _let_6)) :args (_let_36 true _let_33 false _let_34 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING ((ho_3 k_2 (ho_4 (ho_3 k_2 Xp) (ho_4 (ho_3 k_2 Xq) Xr)))))) :args _let_32)) (AND_ELIM _let_29 :args (2)) :args (_let_15 false _let_27)) :args (_let_31 false _let_13 true _let_11 false _let_15)) _let_30 :args (false true _let_17 false _let_6)) :args (_let_5 true))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.58 )
% 0.22/0.58 % SZS output end Proof for SYO103^5
% 0.22/0.58 % cvc5---1.0.5 exiting
% 0.22/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------