TSTP Solution File: SEV137^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV137^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 19:21:40 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
% 0.00/0.12 % Problem : SEV137^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 03:51:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 % File : SEV137^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.53 % Domain : Set Theory (Relations)
% 0.21/0.53 % Problem : TPS problem THM204
% 0.21/0.53 % Version : Especial.
% 0.21/0.53 % English :
% 0.21/0.53
% 0.21/0.53 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.53 % Source : [Bro09]
% 0.21/0.53 % Names : tps_0472 [Bro09]
% 0.21/0.53 % : THM204 [TPS]
% 0.21/0.53
% 0.21/0.53 % Status : Theorem
% 0.21/0.53 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.21/0.53 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.21/0.53 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.21/0.53 % Maximal formula atoms : 0 ( 0 avg)
% 0.21/0.53 % Number of connectives : 32 ( 0 ~; 0 |; 4 &; 18 @)
% 0.21/0.53 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.21/0.53 % Maximal formula depth : 15 ( 15 avg)
% 0.21/0.53 % Number of types : 2 ( 1 usr)
% 0.21/0.53 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.21/0.53 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.21/0.53 % Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 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 a: $tType ).
% 0.21/0.53
% 0.21/0.53 thf(cTHM204_pme,conjecture,
% 0.21/0.53 ! [Xr: a > a > $o,Xx: a,Xy: a,Xz: a] :
% 0.21/0.53 ( ( ! [Xx0: a > $o] :
% 0.21/0.53 ( ! [Xy0: a,Xz0: a] :
% 0.21/0.53 ( ( ( Xr @ Xy0 @ Xz0 )
% 0.21/0.53 & ( Xx0 @ Xy0 ) )
% 0.21/0.53 => ( Xx0 @ Xz0 ) )
% 0.21/0.53 => ( ( Xx0 @ Xx )
% 0.21/0.53 => ( Xx0 @ Xy ) ) )
% 0.21/0.53 & ! [Xx0: a > $o] :
% 0.21/0.53 ( ! [Xy0: a,Xz0: a] :
% 0.21/0.53 ( ( ( Xr @ Xy0 @ Xz0 )
% 0.21/0.53 & ( Xx0 @ Xy0 ) )
% 0.21/0.53 => ( Xx0 @ Xz0 ) )
% 0.21/0.53 => ( ( Xx0 @ Xy )
% 0.21/0.53 => ( Xx0 @ Xz ) ) ) )
% 0.21/0.53 => ! [Xx0: a > $o] :
% 0.21/0.53 ( ! [Xy0: a,Xz0: a] :
% 0.21/0.53 ( ( ( Xr @ Xy0 @ Xz0 )
% 0.21/0.53 & ( Xx0 @ Xy0 ) )
% 0.21/0.53 => ( Xx0 @ Xz0 ) )
% 0.21/0.53 => ( ( Xx0 @ Xx )
% 0.21/0.53 => ( Xx0 @ Xz ) ) ) ) ).
% 0.21/0.53
% 0.21/0.53 %------------------------------------------------------------------------------
% 0.21/0.53 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.4LTBu49O3h/cvc5---1.0.5_22543.p...
% 0.21/0.53 (declare-sort $$unsorted 0)
% 0.21/0.53 (declare-sort tptp.a 0)
% 0.21/0.53 (assert (not (forall ((Xr (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (=> (and (forall ((Xx0 (-> tptp.a Bool))) (=> (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (=> (and (@ (@ Xr Xy0) Xz0) (@ Xx0 Xy0)) (@ Xx0 Xz0))) (=> (@ Xx0 Xx) (@ Xx0 Xy)))) (forall ((Xx0 (-> tptp.a Bool))) (=> (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (=> (and (@ (@ Xr Xy0) Xz0) (@ Xx0 Xy0)) (@ Xx0 Xz0))) (=> (@ Xx0 Xy) (@ Xx0 Xz))))) (forall ((Xx0 (-> tptp.a Bool))) (=> (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (=> (and (@ (@ Xr Xy0) Xz0) (@ Xx0 Xy0)) (@ Xx0 Xz0))) (=> (@ Xx0 Xx) (@ Xx0 Xz))))))))
% 0.21/0.53 (set-info :filename cvc5---1.0.5_22543)
% 0.21/0.53 (check-sat-assuming ( true ))
% 0.21/0.53 ------- get file name : TPTP file name is SEV137^5
% 0.21/0.53 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22543.smt2...
% 0.21/0.53 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.53 % SZS status Theorem for SEV137^5
% 0.21/0.53 % SZS output start Proof for SEV137^5
% 0.21/0.53 (
% 0.21/0.53 (let ((_let_1 (not (forall ((Xr (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (=> (and (forall ((Xx0 (-> tptp.a Bool))) (=> (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (=> (and (@ (@ Xr Xy0) Xz0) (@ Xx0 Xy0)) (@ Xx0 Xz0))) (=> (@ Xx0 Xx) (@ Xx0 Xy)))) (forall ((Xx0 (-> tptp.a Bool))) (=> (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (=> (and (@ (@ Xr Xy0) Xz0) (@ Xx0 Xy0)) (@ Xx0 Xz0))) (=> (@ Xx0 Xy) (@ Xx0 Xz))))) (forall ((Xx0 (-> tptp.a Bool))) (=> (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (=> (and (@ (@ Xr Xy0) Xz0) (@ Xx0 Xy0)) (@ Xx0 Xz0))) (=> (@ Xx0 Xx) (@ Xx0 Xz))))))))) (let ((_let_2 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_4 (not _let_3))) (let ((_let_5 (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xy0) Xz0)) (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xy0)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xz0))))) (let ((_let_6 (not _let_5))) (let ((_let_7 (or _let_6 _let_4 _let_2))) (let ((_let_8 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (not _let_8))) (let ((_let_10 (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xy0) Xz0)) (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xy0)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xz0))))) (let ((_let_11 (not _let_10))) (let ((_let_12 (forall ((BOUND_VARIABLE_722 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xy0) Xz0)) (not (ho_2 BOUND_VARIABLE_722 Xy0)) (ho_2 BOUND_VARIABLE_722 Xz0)))) (not (ho_2 BOUND_VARIABLE_722 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (ho_2 BOUND_VARIABLE_722 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_13 (not _let_12))) (let ((_let_14 (forall ((BOUND_VARIABLE_739 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xy0) Xz0)) (not (ho_2 BOUND_VARIABLE_739 Xy0)) (ho_2 BOUND_VARIABLE_739 Xz0)))) (not (ho_2 BOUND_VARIABLE_739 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (ho_2 BOUND_VARIABLE_739 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13 _let_11 _let_9 _let_2))) (let ((_let_17 (forall ((BOUND_VARIABLE_713 |u_(-> tptp.a tptp.a Bool)|) (Xx tptp.a) (Xy tptp.a) (Xz tptp.a) (BOUND_VARIABLE_703 |u_(-> tptp.a Bool)|)) (or (not (forall ((BOUND_VARIABLE_739 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (ho_2 (ho_3 BOUND_VARIABLE_713 Xy0) Xz0)) (not (ho_2 BOUND_VARIABLE_739 Xy0)) (ho_2 BOUND_VARIABLE_739 Xz0)))) (not (ho_2 BOUND_VARIABLE_739 Xx)) (ho_2 BOUND_VARIABLE_739 Xy)))) (not (forall ((BOUND_VARIABLE_722 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (ho_2 (ho_3 BOUND_VARIABLE_713 Xy0) Xz0)) (not (ho_2 BOUND_VARIABLE_722 Xy0)) (ho_2 BOUND_VARIABLE_722 Xz0)))) (not (ho_2 BOUND_VARIABLE_722 Xy)) (ho_2 BOUND_VARIABLE_722 Xz)))) (not (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (ho_2 (ho_3 BOUND_VARIABLE_713 Xy0) Xz0)) (not (ho_2 BOUND_VARIABLE_703 Xy0)) (ho_2 BOUND_VARIABLE_703 Xz0)))) (not (ho_2 BOUND_VARIABLE_703 Xx)) (ho_2 BOUND_VARIABLE_703 Xz))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_20 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_21 (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_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_22 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_23 (not _let_17))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xr (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a) (Xz tptp.a) (BOUND_VARIABLE_684 (-> tptp.a Bool))) (or (not (forall ((Xx0 (-> tptp.a Bool))) (or (not (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (@ (@ Xr Xy0) Xz0)) (not (@ Xx0 Xy0)) (@ Xx0 Xz0)))) (not (@ Xx0 Xx)) (@ Xx0 Xy)))) (not (forall ((Xx0 (-> tptp.a Bool))) (or (not (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (@ (@ Xr Xy0) Xz0)) (not (@ Xx0 Xy0)) (@ Xx0 Xz0)))) (not (@ Xx0 Xy)) (@ Xx0 Xz)))) (not (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (@ (@ Xr Xy0) Xz0)) (not (@ BOUND_VARIABLE_684 Xy0)) (@ BOUND_VARIABLE_684 Xz0)))) (not (@ BOUND_VARIABLE_684 Xx)) (@ BOUND_VARIABLE_684 Xz)))) _let_23))))))) (let ((_let_25 (or))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_24) :args (_let_23))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_17))) (REFL :args (_let_18)) :args _let_25)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_24 (PREPROCESS :args ((and _let_22 _let_21 _let_20 _let_19)))) :args ((and _let_23 _let_22 _let_21 _let_20 _let_19))) :args (0)) :args (_let_18 true _let_17)))) (let ((_let_27 (REFL :args (_let_16)))) (let ((_let_28 (_let_12))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 2)) (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_25)) :args ((or _let_10 _let_16))) _let_26 :args (_let_10 true _let_16)))) (let ((_let_30 (forall ((Xy0 tptp.a) (Xz0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xy0) Xz0)) (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xy0)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xz0))))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_9 _let_3))) (let ((_let_33 (_let_14))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_7)) :args ((or _let_2 _let_6 _let_4 (not _let_7)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_9 _let_31 _let_3 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 3)) (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_25)) :args ((or _let_8 _let_16))) _let_26 :args (_let_8 true _let_16)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_10 (= Xz0 Xz0) (= Xy0 Xy0)))) _let_29 :args (_let_30 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_33) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 BOUND_VARIABLE_739 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 0)) (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_25)) :args ((or _let_14 _let_16))) _let_26 :args (_let_14 true _let_16)) :args (_let_32 false _let_14)) :args (_let_3 false _let_8 false _let_30 false _let_32)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_10 (= Xz0 Xz0) (= Xy0 Xy0)))) _let_29 :args (_let_5 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_28) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 BOUND_VARIABLE_722 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) true))))) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 1)) (CONG _let_27 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_25)) :args ((or _let_12 _let_16))) _let_26 :args (_let_12 true _let_16)) :args (_let_7 false _let_12)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_16 4)) _let_26 :args ((not _let_2) true _let_16)) :args (false false _let_3 false _let_5 false _let_7 true _let_2)) :args (_let_1 true))))))))))))))))))))))))))))))))))))
% 0.21/0.53 )
% 0.21/0.53 % SZS output end Proof for SEV137^5
% 0.21/0.53 % cvc5---1.0.5 exiting
% 0.21/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------