TSTP Solution File: SEV196^5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV196^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 19:21:50 EDT 2023
% Result : Theorem 4.35s 4.53s
% Output : Proof 4.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV196^5 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n003.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
% 0.14/0.36 % DateTime : Thu Aug 24 03:03:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TH0
% 4.35/4.53 %------------------------------------------------------------------------------
% 4.35/4.53 % File : SEV196^5 : TPTP v8.1.2. Released v4.0.0.
% 4.35/4.53 % Domain : Set Theory (Sets of sets)
% 4.35/4.53 % Problem : TPS problem from S-THMS
% 4.35/4.53 % Version : Especial.
% 4.35/4.53 % English :
% 4.35/4.53
% 4.35/4.53 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 4.35/4.53 % Source : [Bro09]
% 4.35/4.53 % Names : tps_1058 [Bro09]
% 4.35/4.53
% 4.35/4.53 % Status : Theorem
% 4.35/4.53 % Rating : 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 4.35/4.53 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 4.35/4.53 % Number of atoms : 8 ( 7 equ; 0 cnn)
% 4.35/4.53 % Maximal formula atoms : 8 ( 8 avg)
% 4.35/4.53 % Number of connectives : 35 ( 0 ~; 2 |; 7 &; 24 @)
% 4.35/4.53 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 4.35/4.53 % Maximal formula depth : 23 ( 23 avg)
% 4.35/4.53 % Number of types : 2 ( 1 usr)
% 4.35/4.53 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 4.35/4.53 % Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% 4.35/4.53 % Number of variables : 10 ( 0 ^; 4 !; 6 ?; 10 :)
% 4.35/4.53 % SPC : TH0_THM_EQU_NAR
% 4.35/4.53
% 4.35/4.53 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 4.35/4.53 % project in the Department of Mathematical Sciences at Carnegie
% 4.35/4.53 % Mellon University. Distributed under the Creative Commons copyleft
% 4.35/4.53 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 4.35/4.53 %------------------------------------------------------------------------------
% 4.35/4.53 thf(a_type,type,
% 4.35/4.53 a: $tType ).
% 4.35/4.53
% 4.35/4.53 thf(y,type,
% 4.35/4.53 y: a ).
% 4.35/4.53
% 4.35/4.53 thf(x,type,
% 4.35/4.53 x: a ).
% 4.35/4.53
% 4.35/4.53 thf(cP,type,
% 4.35/4.53 cP: a > a > a ).
% 4.35/4.53
% 4.35/4.53 thf(c0,type,
% 4.35/4.53 c0: a ).
% 4.35/4.53
% 4.35/4.53 thf(cS_JOIN_LEM2_pme,conjecture,
% 4.35/4.53 ! [R: a > a > a > $o] :
% 4.35/4.53 ( ( $true
% 4.35/4.53 & ! [Xa: a,Xb: a,Xc: a] :
% 4.35/4.53 ( ( ( ( Xa = c0 )
% 4.35/4.53 & ( Xb = Xc ) )
% 4.35/4.53 | ( ( Xb = c0 )
% 4.35/4.53 & ( Xa = Xc ) )
% 4.35/4.53 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 4.35/4.53 ( ( Xa
% 4.35/4.53 = ( cP @ Xx1 @ Xx2 ) )
% 4.35/4.53 & ( Xb
% 4.35/4.53 = ( cP @ Xy1 @ Xy2 ) )
% 4.35/4.53 & ( Xc
% 4.35/4.53 = ( cP @ Xz1 @ Xz2 ) )
% 4.35/4.53 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 4.35/4.53 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 4.35/4.53 => ( R @ Xa @ Xb @ Xc ) ) )
% 4.35/4.53 => ( R @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) ) ) ).
% 4.35/4.53
% 4.35/4.53 %------------------------------------------------------------------------------
% 4.35/4.53 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.soCm0gMZjz/cvc5---1.0.5_7607.p...
% 4.35/4.53 (declare-sort $$unsorted 0)
% 4.35/4.53 (declare-sort tptp.a 0)
% 4.35/4.53 (declare-fun tptp.y () tptp.a)
% 4.35/4.53 (declare-fun tptp.x () tptp.a)
% 4.35/4.53 (declare-fun tptp.cP (tptp.a tptp.a) tptp.a)
% 4.35/4.53 (declare-fun tptp.c0 () tptp.a)
% 4.35/4.53 (assert (not (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (let ((_let_1 (@ tptp.cP tptp.x))) (=> (and true (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a)) (=> (or (and (= Xa tptp.c0) (= Xb Xc)) (and (= Xb tptp.c0) (= Xa Xc)) (exists ((Xx1 tptp.a) (Xx2 tptp.a) (Xy1 tptp.a) (Xy2 tptp.a) (Xz1 tptp.a) (Xz2 tptp.a)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R (@ _let_1 tptp.c0)) (@ (@ tptp.cP tptp.c0) tptp.y)) (@ _let_1 tptp.y)))))))
% 4.35/4.53 (set-info :filename cvc5---1.0.5_7607)
% 4.35/4.53 (check-sat-assuming ( true ))
% 4.35/4.53 ------- get file name : TPTP file name is SEV196^5
% 4.35/4.53 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7607.smt2...
% 4.35/4.53 --- Run --ho-elim --full-saturate-quant at 10...
% 4.35/4.53 % SZS status Theorem for SEV196^5
% 4.35/4.53 % SZS output start Proof for SEV196^5
% 4.35/4.53 (
% 4.35/4.53 (let ((_let_1 (not (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (let ((_let_1 (@ tptp.cP tptp.x))) (=> (and true (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a)) (=> (or (and (= Xa tptp.c0) (= Xb Xc)) (and (= Xb tptp.c0) (= Xa Xc)) (exists ((Xx1 tptp.a) (Xx2 tptp.a) (Xy1 tptp.a) (Xy2 tptp.a) (Xz1 tptp.a) (Xz2 tptp.a)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R (@ _let_1 tptp.c0)) (@ (@ tptp.cP tptp.c0) tptp.y)) (@ _let_1 tptp.y)))))))) (let ((_let_2 (ho_3 k_2 tptp.x))) (let ((_let_3 (ho_4 _let_2 tptp.y))) (let ((_let_4 (ho_4 (ho_3 k_2 tptp.c0) tptp.y))) (let ((_let_5 (ho_4 _let_2 tptp.c0))) (let ((_let_6 (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_5) _let_4) _let_3))) (let ((_let_7 (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.c0) tptp.y) tptp.y))) (let ((_let_8 (not _let_7))) (let ((_let_9 (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.x) tptp.c0) tptp.x))) (let ((_let_10 (not _let_9))) (let ((_let_11 (or _let_10 _let_8))) (let ((_let_12 (and (or (not (= tptp.c0 _let_5)) (not (= _let_3 _let_4))) (or (not (= tptp.c0 _let_4)) (not (= _let_3 _let_5))) _let_11))) (let ((_let_13 (or _let_12 _let_6))) (let ((_let_14 (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_677 tptp.a) (BOUND_VARIABLE_675 tptp.a) (BOUND_VARIABLE_673 tptp.a) (BOUND_VARIABLE_671 tptp.a) (BOUND_VARIABLE_669 tptp.a) (BOUND_VARIABLE_667 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (ho_4 (ho_3 k_2 BOUND_VARIABLE_667) BOUND_VARIABLE_669))) (not (= Xb (ho_4 (ho_3 k_2 BOUND_VARIABLE_671) BOUND_VARIABLE_673))) (not (= Xc (ho_4 (ho_3 k_2 BOUND_VARIABLE_675) BOUND_VARIABLE_677))) (not (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 BOUND_VARIABLE_667) BOUND_VARIABLE_671) BOUND_VARIABLE_675)) (not (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 BOUND_VARIABLE_669) BOUND_VARIABLE_673) BOUND_VARIABLE_677)))) (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xa) Xb) Xc))))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_6))) (let ((_let_17 (forall ((BOUND_VARIABLE_723 |u_(-> tptp.a tptp.a tptp.a Bool)|)) (let ((_let_1 (ho_3 k_2 tptp.x))) (or (not (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_677 tptp.a) (BOUND_VARIABLE_675 tptp.a) (BOUND_VARIABLE_673 tptp.a) (BOUND_VARIABLE_671 tptp.a) (BOUND_VARIABLE_669 tptp.a) (BOUND_VARIABLE_667 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (ho_4 (ho_3 k_2 BOUND_VARIABLE_667) BOUND_VARIABLE_669))) (not (= Xb (ho_4 (ho_3 k_2 BOUND_VARIABLE_671) BOUND_VARIABLE_673))) (not (= Xc (ho_4 (ho_3 k_2 BOUND_VARIABLE_675) BOUND_VARIABLE_677))) (not (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_723 BOUND_VARIABLE_667) BOUND_VARIABLE_671) BOUND_VARIABLE_675)) (not (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_723 BOUND_VARIABLE_669) BOUND_VARIABLE_673) BOUND_VARIABLE_677)))) (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_723 Xa) Xb) Xc)))) (ho_7 (ho_6 (ho_5 BOUND_VARIABLE_723 (ho_4 _let_1 tptp.c0)) (ho_4 (ho_3 k_2 tptp.c0) tptp.y)) (ho_4 _let_1 tptp.y))))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (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_20 (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_21 (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_22 (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_23 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_24 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_25 (forall ((u |u_(-> tptp.a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_26 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_27 (forall ((u |u_(-> tptp.a tptp.a tptp.a Bool)|) (e |u_(-> tptp.a tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_28 (forall ((x |u_(-> tptp.a tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_29 (not _let_17))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((R (-> tptp.a tptp.a tptp.a Bool))) (let ((_let_1 (@ tptp.cP tptp.x))) (or (not (forall ((Xa tptp.a) (Xb tptp.a) (Xc tptp.a) (BOUND_VARIABLE_677 tptp.a) (BOUND_VARIABLE_675 tptp.a) (BOUND_VARIABLE_673 tptp.a) (BOUND_VARIABLE_671 tptp.a) (BOUND_VARIABLE_669 tptp.a) (BOUND_VARIABLE_667 tptp.a)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_667) BOUND_VARIABLE_669))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_671) BOUND_VARIABLE_673))) (not (= Xc (@ (@ tptp.cP BOUND_VARIABLE_675) BOUND_VARIABLE_677))) (not (@ (@ (@ R BOUND_VARIABLE_667) BOUND_VARIABLE_671) BOUND_VARIABLE_675)) (not (@ (@ (@ R BOUND_VARIABLE_669) BOUND_VARIABLE_673) BOUND_VARIABLE_677)))) (@ (@ (@ R Xa) Xb) Xc)))) (@ (@ (@ R (@ _let_1 tptp.c0)) (@ (@ tptp.cP tptp.c0) tptp.y)) (@ _let_1 tptp.y)))))) _let_29))))))) (let ((_let_31 (or))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_30) :args (_let_29))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_17))) (REFL :args (_let_18)) :args _let_31)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_30 (PREPROCESS :args ((and _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19)))) :args ((and _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19))) :args (0)) :args (_let_18 true _let_17)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 0)) (CONG (REFL :args (_let_16)) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_31)) :args ((or _let_14 _let_16))) _let_32 :args (_let_14 true _let_16)))) (let ((_let_34 (_let_14))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (not _let_12))) (let ((_let_37 (not _let_11))) (let ((_let_38 ((ho_4 (ho_3 k_2 BOUND_VARIABLE_667) BOUND_VARIABLE_669) (ho_4 (ho_3 k_2 BOUND_VARIABLE_671) BOUND_VARIABLE_673) (ho_4 (ho_3 k_2 BOUND_VARIABLE_675) BOUND_VARIABLE_677) (not (= (ho_7 (ho_6 (ho_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xa) Xb) Xc) true))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_13)) :args ((or _let_6 _let_12 (not _let_13)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_12 2)) :args ((or _let_11 _let_36))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_11)) :args ((or _let_8 _let_10 _let_37))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.c0 tptp.y tptp.y tptp.c0 tptp.x tptp.c0 tptp.x tptp.c0 tptp.x QUANTIFIERS_INST_E_MATCHING _let_38)) :args _let_34))) _let_33 :args (_let_7 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.x tptp.c0 tptp.x tptp.y tptp.c0 tptp.y tptp.c0 tptp.y tptp.c0 QUANTIFIERS_INST_E_MATCHING _let_38)) :args _let_34))) _let_33 :args (_let_9 false _let_14)) :args (_let_37 false _let_7 false _let_9)) :args (_let_36 true _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_5 _let_4 _let_3 tptp.y tptp.x tptp.y tptp.c0 tptp.c0 tptp.x QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_34))) _let_33 :args (_let_13 false _let_14)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_16 1)) _let_32 :args ((not _let_6) true _let_16)) :args (false true _let_12 false _let_13 true _let_6)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))
% 4.36/4.54 )
% 4.36/4.54 % SZS output end Proof for SEV196^5
% 4.36/4.54 % cvc5---1.0.5 exiting
% 4.36/4.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------