TSTP Solution File: SWV447^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV447^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 21:51:33 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
% 0.07/0.12 % Problem : SWV447^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.13 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n018.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
% 0.14/0.35 % DateTime : Tue Aug 29 03:43:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 %----Proving TH0
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 % File : SWV447^1 : TPTP v8.1.2. Released v3.7.0.
% 0.21/0.52 % Domain : Software Verification
% 0.21/0.52 % Problem : Nipkow's simple map-cons problem
% 0.21/0.52 % Version : Especial.
% 0.21/0.52 % English :
% 0.21/0.52
% 0.21/0.52 % Refs :
% 0.21/0.52 % Source : [TPTP]
% 0.21/0.52 % Names :
% 0.21/0.52
% 0.21/0.52 % Status : Theorem
% 0.21/0.52 % Rating : 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.21/0.52 % Syntax : Number of formulae : 6 ( 3 unt; 3 typ; 0 def)
% 0.21/0.52 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.21/0.52 % Maximal formula atoms : 1 ( 1 avg)
% 0.21/0.52 % Number of connectives : 17 ( 0 ~; 0 |; 0 &; 17 @)
% 0.21/0.52 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.21/0.52 % Maximal formula depth : 4 ( 3 avg)
% 0.21/0.52 % Number of types : 1 ( 0 usr)
% 0.21/0.52 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.21/0.52 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.21/0.52 % Number of variables : 6 ( 1 ^; 5 !; 0 ?; 6 :)
% 0.21/0.52 % SPC : TH0_THM_EQU_NAR
% 0.21/0.52
% 0.21/0.52 % Comments :
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 thf(nil_type,type,
% 0.21/0.52 nil: $i ).
% 0.21/0.52
% 0.21/0.52 thf(cons_type,type,
% 0.21/0.52 cons: $i > $i > $i ).
% 0.21/0.52
% 0.21/0.52 thf(map_type,type,
% 0.21/0.52 map: ( $i > $i ) > $i > $i ).
% 0.21/0.52
% 0.21/0.52 thf(ax1,axiom,
% 0.21/0.52 ! [F: $i > $i] :
% 0.21/0.52 ( ( map @ F @ nil )
% 0.21/0.52 = nil ) ).
% 0.21/0.52
% 0.21/0.52 thf(ax2,axiom,
% 0.21/0.52 ! [F: $i > $i,X: $i,Y: $i] :
% 0.21/0.52 ( ( map @ F @ ( cons @ X @ Y ) )
% 0.21/0.52 = ( cons @ ( F @ X ) @ ( map @ F @ Y ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(test,conjecture,
% 0.21/0.52 ! [A: $i] :
% 0.21/0.52 ( ( map
% 0.21/0.52 @ ^ [X: $i] : X
% 0.21/0.52 @ ( cons @ A @ nil ) )
% 0.21/0.52 = ( cons @ A @ nil ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.EeoBDHzMzD/cvc5---1.0.5_15953.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (declare-fun tptp.nil () $$unsorted)
% 0.21/0.52 (declare-fun tptp.cons ($$unsorted $$unsorted) $$unsorted)
% 0.21/0.52 (declare-fun tptp.map ((-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.21/0.52 (assert (forall ((F (-> $$unsorted $$unsorted))) (= (@ (@ tptp.map F) tptp.nil) tptp.nil)))
% 0.21/0.52 (assert (forall ((F (-> $$unsorted $$unsorted)) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (@ tptp.map F))) (= (@ _let_1 (@ (@ tptp.cons X) Y)) (@ (@ tptp.cons (@ F X)) (@ _let_1 Y))))))
% 0.21/0.52 (assert (not (forall ((A $$unsorted)) (let ((_let_1 (@ (@ tptp.cons A) tptp.nil))) (= (@ (@ tptp.map (lambda ((X $$unsorted)) X)) _let_1) _let_1)))))
% 0.21/0.52 (set-info :filename cvc5---1.0.5_15953)
% 0.21/0.52 (check-sat-assuming ( true ))
% 0.21/0.52 ------- get file name : TPTP file name is SWV447^1
% 0.21/0.52 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15953.smt2...
% 0.21/0.52 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.52 % SZS status Theorem for SWV447^1
% 0.21/0.52 % SZS output start Proof for SWV447^1
% 0.21/0.52 (
% 0.21/0.52 (let ((_let_1 (not (forall ((A $$unsorted)) (let ((_let_1 (@ (@ tptp.cons A) tptp.nil))) (= (@ (@ tptp.map (lambda ((X $$unsorted)) X)) _let_1) _let_1)))))) (let ((_let_2 (forall ((F (-> $$unsorted $$unsorted)) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (@ tptp.map F))) (= (@ _let_1 (@ (@ tptp.cons X) Y)) (@ (@ tptp.cons (@ F X)) (@ _let_1 Y))))))) (let ((_let_3 (forall ((F (-> $$unsorted $$unsorted))) (= (@ (@ tptp.map F) tptp.nil) tptp.nil)))) (let ((_let_4 (ho_4 (ho_8 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) tptp.nil))) (let ((_let_5 (ho_6 k_5 k_3))) (let ((_let_6 (ho_4 _let_5 _let_4))) (let ((_let_7 (= _let_4 _let_6))) (let ((_let_8 (ho_4 _let_5 tptp.nil))) (let ((_let_9 (= tptp.nil _let_8))) (let ((_let_10 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_11 (= _let_6 (ho_4 (ho_8 k_7 _let_10) _let_8)))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_10))) (let ((_let_13 (forall ((A $$unsorted)) (let ((_let_1 (ho_4 (ho_8 k_7 A) tptp.nil))) (= _let_1 (ho_4 (ho_6 k_5 k_3) _let_1)))))) (let ((_let_14 (not _let_7))) (let ((_let_15 (not _let_13))) (let ((_let_16 (not (forall ((A $$unsorted)) (let ((_let_1 (@ (@ tptp.cons A) tptp.nil))) (= _let_1 (@ (@ tptp.map ll_2) _let_1))))))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((A $$unsorted)) (let ((_let_1 (@ (@ tptp.cons A) tptp.nil))) (= _let_1 (@ (@ tptp.map (lambda ((X $$unsorted)) X)) _let_1))))) _let_16))) (PREPROCESS :args ((= _let_16 _let_15))))))) (let ((_let_18 (forall ((BOUND_VARIABLE_640 |u_(-> $$unsorted $$unsorted)|)) (= tptp.nil (ho_4 (ho_6 k_5 BOUND_VARIABLE_640) tptp.nil))))) (let ((_let_19 (forall ((u |u_(-> $$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_20 (forall ((x |u_(-> $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_21 (forall ((u |u_(-> _u_(-> $$unsorted $$unsorted)_ $$unsorted $$unsorted)|) (e |u_(-> $$unsorted $$unsorted)|) (i |u_(-> $$unsorted $$unsorted)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted $$unsorted)_ $$unsorted $$unsorted)|)) (not (forall ((ii |u_(-> $$unsorted $$unsorted)|)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_22 (forall ((x |u_(-> _u_(-> $$unsorted $$unsorted)_ $$unsorted $$unsorted)|) (y |u_(-> _u_(-> $$unsorted $$unsorted)_ $$unsorted $$unsorted)|)) (or (not (forall ((z |u_(-> $$unsorted $$unsorted)|)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_23 (forall ((u |u_(-> $$unsorted $$unsorted $$unsorted)|) (e |u_(-> $$unsorted $$unsorted)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted $$unsorted)|)) (not (forall ((ii $$unsorted)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_24 (forall ((x |u_(-> $$unsorted $$unsorted $$unsorted)|) (y |u_(-> $$unsorted $$unsorted $$unsorted)|)) (or (not (forall ((z $$unsorted)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_25 (forall ((BOUND_VARIABLE_624 $$unsorted)) (= BOUND_VARIABLE_624 (ho_4 k_3 BOUND_VARIABLE_624))))) (let ((_let_26 (forall ((BOUND_VARIABLE_624 $$unsorted)) (= BOUND_VARIABLE_624 (ll_2 BOUND_VARIABLE_624))))) (let ((_let_27 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (PREPROCESS :args (_let_26))) (PREPROCESS :args ((= (and (forall ((F (-> $$unsorted $$unsorted))) (= tptp.nil (@ (@ tptp.map F) tptp.nil))) _let_26) (and _let_18 _let_25))))) (PREPROCESS :args ((and _let_24 _let_23 _let_22 _let_21 _let_20 _let_19)))) :args ((and _let_18 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19))))) (let ((_let_28 (_let_18))) (let ((_let_29 (forall ((BOUND_VARIABLE_652 |u_(-> $$unsorted $$unsorted)|) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (ho_6 k_5 BOUND_VARIABLE_652))) (= (ho_4 (ho_8 k_7 (ho_4 BOUND_VARIABLE_652 X)) (ho_4 _let_1 Y)) (ho_4 _let_1 (ho_4 (ho_8 k_7 X) Y))))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_2)) (PREPROCESS :args ((= _let_2 _let_29)))))) (let ((_let_31 (_let_25))) (let ((_let_32 (and _let_9 _let_11 _let_12))) (let ((_let_33 (ASSUME :args (_let_11)))) (let ((_let_34 (ASSUME :args (_let_9)))) (let ((_let_35 (ASSUME :args (_let_12)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_32)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_33 _let_35 _let_34) (SCOPE (TRANS (CONG (CONG (REFL :args (k_7)) (SYMM (SYMM _let_35)) :args (APPLY_UF ho_8)) (SYMM (SYMM _let_34)) :args (APPLY_UF ho_4)) (SYMM _let_33)) :args (_let_11 _let_12 _let_9))) :args (_let_9 _let_11 _let_12))) :args (true _let_32)) :args ((or _let_7 (not _let_9) (not _let_11) (not _let_12)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_31) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_PROP)) :args _let_31)) (AND_ELIM _let_27 :args (1)) :args (_let_12 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil QUANTIFIERS_INST_E_MATCHING ((ho_4 (ho_6 k_5 BOUND_VARIABLE_652) (ho_4 (ho_8 k_7 X) Y))))) :args (_let_29)))) _let_30 :args (_let_11 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_28) :args (k_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 k_5 BOUND_VARIABLE_640)))) :args _let_28)) (AND_ELIM _let_27 :args (0)) :args (_let_9 false _let_18)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_17) :args (_let_15))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_13))) (REFL :args (_let_14)) :args (or))) _let_17 :args (_let_14 true _let_13)) :args (false false _let_12 false _let_11 false _let_9 true _let_7)) :args (_let_3 _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))
% 0.21/0.52 )
% 0.21/0.52 % SZS output end Proof for SWV447^1
% 0.21/0.52 % cvc5---1.0.5 exiting
% 0.21/0.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------