TSTP Solution File: SWW634_2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW634_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 00:21:46 EDT 2023
% Result : Theorem 15.48s 15.78s
% Output : Proof 15.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW634_2 : TPTP v8.1.2. Released v6.1.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n023.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 : Sun Aug 27 19:37:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.50 %----Proving TF0_ARI
% 15.48/15.78 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ueOamZaBhN/cvc5---1.0.5_20154.p...
% 15.48/15.78 ------- get file name : TPTP file name is SWW634_2
% 15.48/15.78 ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_20154.smt2...
% 15.48/15.78 --- Run --finite-model-find --decision=internal at 15...
% 15.48/15.78 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 15.48/15.78 % SZS status Theorem for SWW634_2
% 15.48/15.78 % SZS output start Proof for SWW634_2
% 15.48/15.78 (
% 15.48/15.78 (let ((_let_1 (not (forall ((Q Int) (S Int) (Sol tptp.map_int_lpmap_int_intrp) (K Int) (Col tptp.map_int_int)) (=> (and (<= 0 Q) (= Q tptp.n1) (= S 0) (= K 0)) (=> (and (<= 0 K) (= (+ K (tptp.cardinal1 tptp.int (tptp.t2tb (tptp.below1 Q)))) tptp.n1) (<= 0 S) (forall ((I Int)) (= (tptp.mem tptp.int (tptp.t2tb1 I) (tptp.t2tb (tptp.below1 Q))) (and (<= 0 I) (< I tptp.n1) (forall ((J Int)) (=> (and (<= 0 J) (< J K)) (not (= (tptp.tb2t1 (tptp.get tptp.int tptp.int (tptp.t2tb2 Col) (tptp.t2tb1 J))) I))))))) (forall ((I Int)) (=> (<= 0 I) (= (not (tptp.mem tptp.int (tptp.t2tb1 I) (tptp.empty tptp.int))) (forall ((J Int)) (=> (and (<= 0 J) (< J K)) (not (= (tptp.tb2t1 (tptp.get tptp.int tptp.int (tptp.t2tb2 Col) (tptp.t2tb1 J))) (- (+ I J) K)))))))) (forall ((I Int)) (=> (<= 0 I) (= (not (tptp.mem tptp.int (tptp.t2tb1 I) (tptp.empty tptp.int))) (forall ((J Int)) (=> (and (<= 0 J) (< J K)) (not (= (tptp.tb2t1 (tptp.get tptp.int tptp.int (tptp.t2tb2 Col) (tptp.t2tb1 J))) (- (+ I K) J)))))))) (tptp.partial_solution1 K Col)) (forall ((S1 Int) (Sol1 tptp.map_int_lpmap_int_intrp) (K1 Int) (Col1 tptp.map_int_int)) (let ((_let_1 (- S1 S))) (=> (and (<= 0 _let_1) (= K1 K) (tptp.sorted1 Sol1 S S1) (forall ((T tptp.map_int_int)) (= (and (tptp.partial_solution1 tptp.n1 T) (tptp.eq_prefix1 tptp.int (tptp.t2tb2 Col1) (tptp.t2tb2 T) K1)) (exists ((I Int)) (and (<= S I) (< I S1) (tptp.eq_prefix1 tptp.int (tptp.t2tb2 T) (tptp.get (tptp.map tptp.int tptp.int) tptp.int (tptp.t2tb3 Sol1) (tptp.t2tb1 I)) tptp.n1))))) (tptp.eq_prefix1 tptp.int (tptp.t2tb2 Col) (tptp.t2tb2 Col1) K1) (tptp.eq_prefix1 (tptp.map tptp.int tptp.int) (tptp.t2tb3 Sol) (tptp.t2tb3 Sol1) S)) (and (= _let_1 S1) (tptp.sorted1 Sol1 0 S1) (forall ((T tptp.map_int_int)) (= (tptp.partial_solution1 tptp.n1 T) (exists ((I Int)) (and (<= 0 I) (< I (- S1 S)) (tptp.eq_prefix1 tptp.int (tptp.t2tb2 T) (tptp.get (tptp.map tptp.int tptp.int) tptp.int (tptp.t2tb3 Sol1) (tptp.t2tb1 I)) tptp.n1))))))))))))))) (let ((_let_2 (forall ((A tptp.ty) (T tptp.uni) (U tptp.uni) (I Int)) (= (tptp.eq_prefix1 A T U I) (forall ((K Int)) (let ((_let_1 (tptp.t2tb1 K))) (=> (and (<= 0 K) (< K I)) (= (tptp.get A tptp.int T _let_1) (tptp.get A tptp.int U _let_1))))))))) (let ((_let_3 (forall ((A tptp.ty) (T tptp.uni) (U tptp.uni) (I Int)) (= (tptp.eq_prefix1 A T U I) (forall ((K Int)) (let ((_let_1 (tptp.t2tb1 K))) (or (not (>= K 0)) (not (>= (+ I (* (- 1) K)) 1)) (= (tptp.get A tptp.int T _let_1) (tptp.get A tptp.int U _let_1))))))))) (let ((_let_4 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_5 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_6 (tptp.eq_prefix1 tptp.int _let_5 _let_4 0))) (let ((_let_7 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_8 (tptp.partial_solution1 tptp.n1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_9 (and _let_8 _let_6))) (let ((_let_10 (not _let_6))) (let ((_let_11 (forall ((I Int)) (or (not (>= I 0)) (>= (+ I (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) 0) (not (tptp.eq_prefix1 tptp.int (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) (tptp.get (tptp.map tptp.int tptp.int) tptp.int (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.t2tb1 I)) tptp.n1)))))) (let ((_let_12 (not _let_11))) (let ((_let_13 (= _let_9 _let_12))) (let ((_let_14 (not _let_9))) (let ((_let_15 (forall ((T tptp.map_int_int)) (= (and (tptp.partial_solution1 tptp.n1 T) (tptp.eq_prefix1 tptp.int (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.t2tb2 T) 0)) (not (forall ((I Int)) (or (not (>= I 0)) (>= (+ I (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) 0) (not (tptp.eq_prefix1 tptp.int (tptp.t2tb2 T) (tptp.get (tptp.map tptp.int tptp.int) tptp.int (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.t2tb1 I)) tptp.n1))))))))) (let ((_let_16 (forall ((I Int)) (or (not (>= I 0)) (>= (+ I (* (- 1) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) 0) (not (tptp.eq_prefix1 tptp.int (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) (tptp.get (tptp.map tptp.int tptp.int) tptp.int (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.t2tb1 I)) tptp.n1)))))) (let ((_let_17 (not _let_16))) (let ((_let_18 (= _let_8 _let_17))) (let ((_let_19 (tptp.sorted1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (and _let_19 _let_18))) (let ((_let_21 (not _let_15))) (let ((_let_22 (not _let_19))) (let ((_let_23 (or (not (tptp.partial_solution1 0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 0)) _let_22 _let_21 (not (tptp.eq_prefix1 tptp.int (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_5 0)) (not (tptp.eq_prefix1 (tptp.map tptp.int tptp.int) (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) (tptp.t2tb3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) 0)) _let_20))) (let ((_let_24 (forall ((Col tptp.map_int_int) (BOUND_VARIABLE_2609 Int) (BOUND_VARIABLE_2611 tptp.map_int_lpmap_int_intrp) (BOUND_VARIABLE_2613 tptp.map_int_int) (Sol tptp.map_int_lpmap_int_intrp) (BOUND_VARIABLE_2615 tptp.map_int_int)) (let ((_let_1 (tptp.sorted1 BOUND_VARIABLE_2611 0 BOUND_VARIABLE_2609))) (or (not (tptp.partial_solution1 0 Col)) (not (>= BOUND_VARIABLE_2609 0)) (not _let_1) (not (forall ((T tptp.map_int_int)) (= (and (tptp.partial_solution1 tptp.n1 T) (tptp.eq_prefix1 tptp.int (tptp.t2tb2 BOUND_VARIABLE_2613) (tptp.t2tb2 T) 0)) (not (forall ((I Int)) (or (not (>= I 0)) (>= (+ I (* (- 1) BOUND_VARIABLE_2609)) 0) (not (tptp.eq_prefix1 tptp.int (tptp.t2tb2 T) (tptp.get (tptp.map tptp.int tptp.int) tptp.int (tptp.t2tb3 BOUND_VARIABLE_2611) (tptp.t2tb1 I)) tptp.n1)))))))) (not (tptp.eq_prefix1 tptp.int (tptp.t2tb2 Col) (tptp.t2tb2 BOUND_VARIABLE_2613) 0)) (not (tptp.eq_prefix1 (tptp.map tptp.int tptp.int) (tptp.t2tb3 Sol) (tptp.t2tb3 BOUND_VARIABLE_2611) 0)) (and _let_1 (= (tptp.partial_solution1 tptp.n1 BOUND_VARIABLE_2615) (not (forall ((I Int)) (or (not (>= I 0)) (>= (+ I (* (- 1) BOUND_VARIABLE_2609)) 0) (not (tptp.eq_prefix1 tptp.int (tptp.t2tb2 BOUND_VARIABLE_2615) (tptp.get (tptp.map tptp.int tptp.int) tptp.int (tptp.t2tb3 BOUND_VARIABLE_2611) (tptp.t2tb1 I)) tptp.n1)))))))))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (or))) (let ((_let_27 (not _let_24))) (let ((_let_28 (_let_27))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_28)) :args _let_28)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_24))) (REFL :args (_let_25)) :args _let_26)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (5)) :args (_let_25 true _let_24)))) (let ((_let_30 (REFL :args (_let_23)))) (let ((_let_31 (_let_15))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_31) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.partial_solution1 tptp.n1 T)))) :args _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 3)) (CONG _let_30 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_15))) :args _let_26)) :args ((or _let_15 _let_23))) _let_29 :args (_let_15 true _let_23)) :args (_let_13 false _let_15)))) (let ((_let_33 (not _let_18))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_20)) :args ((or _let_22 _let_20 _let_33))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 2)) (CONG _let_30 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_19))) :args _let_26)) :args ((or _let_19 _let_23))) _let_29 :args (_let_19 true _let_23)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 6)) _let_29 :args ((not _let_20) true _let_23)) :args (_let_33 false _let_19 true _let_20)))) (let ((_let_35 (not _let_8))) (let ((_let_36 (_let_18))) (let ((_let_37 (ALPHA_EQUIV :args (_let_16 (= I I))))) (let ((_let_38 (not _let_13))) (let ((_let_39 (_let_9))) (let ((_let_40 (_let_13))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args _let_40) (CONG (REFL :args (_let_38)) (REFL :args _let_39) (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_26)) :args ((or _let_9 _let_11 _let_38))) _let_32 (REORDERING (CNF_AND_POS :args (_let_9 0)) :args ((or _let_8 _let_14))) (EQUIV_ELIM2 _let_37) (REORDERING (EQ_RESOLVE (CNF_EQUIV_NEG2 :args _let_36) (CONG (REFL :args _let_36) (REFL :args (_let_35)) (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_26)) :args ((or _let_16 _let_18 _let_35))) _let_34 :args (_let_16 false _let_13 true _let_9 true _let_11 true _let_8 true _let_18)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_7 :args (tptp.int _let_5 _let_4 0 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.eq_prefix1 A T U I)))) :args (_let_3)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args _let_39) :args ((or _let_35 _let_9 _let_10))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_36) :args ((or _let_8 _let_17 _let_18))) _let_41 _let_34 :args (_let_8 false _let_16 true _let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_40) :args ((or _let_12 _let_14 _let_38))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 _let_37) _let_41 :args (_let_11 false _let_16)) _let_32 :args (_let_14 false _let_11 false _let_13)) :args (_let_10 false _let_8 true _let_9)) _let_7 :args (false true _let_6 false _let_3)) :args ((forall ((A tptp.ty)) (tptp.sort1 A (tptp.witness1 A))) (forall ((A tptp.ty) (X tptp.bool1) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 A (tptp.match_bool1 A X X1 X2))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z) (= (tptp.match_bool1 A tptp.true1 Z Z1) Z))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort1 A Z1) (= (tptp.match_bool1 A tptp.false1 Z Z1) Z1))) (not (= tptp.true1 tptp.false1)) (forall ((U tptp.bool1)) (or (= U tptp.true1) (= U tptp.false1))) (forall ((U tptp.tuple02)) (= U tptp.tuple03)) (forall ((X Int) (Y Int) (Z Int)) (=> (<= X Y) (=> (<= 0 Z) (<= (* X Z) (* Y Z))))) (forall ((A tptp.ty) (S1 tptp.uni) (S2 tptp.uni)) (let ((_let_1 (tptp.infix_eqeq A S1 S2))) (and (=> _let_1 (forall ((X tptp.uni)) (= (tptp.mem A X S1) (tptp.mem A X S2)))) (=> (forall ((X tptp.uni)) (=> (tptp.sort1 A X) (= (tptp.mem A X S1) (tptp.mem A X S2)))) _let_1)))) (forall ((A tptp.ty) (S1 tptp.uni) (S2 tptp.uni)) (let ((_let_1 (tptp.set A))) (=> (tptp.sort1 _let_1 S1) (=> (tptp.sort1 _let_1 S2) (=> (tptp.infix_eqeq A S1 S2) (= S1 S2)))))) (forall ((A tptp.ty) (S1 tptp.uni) (S2 tptp.uni)) (let ((_let_1 (tptp.subset A S1 S2))) (and (=> _let_1 (forall ((X tptp.uni)) (=> (tptp.mem A X S1) (tptp.mem A X S2)))) (=> (forall ((X tptp.uni)) (=> (tptp.sort1 A X) (=> (tptp.mem A X S1) (tptp.mem A X S2)))) _let_1)))) (forall ((A tptp.ty) (S tptp.uni)) (tptp.subset A S S)) (forall ((A tptp.ty) (S1 tptp.uni) (S2 tptp.uni) (S3 tptp.uni)) (=> (tptp.subset A S1 S2) (=> (tptp.subset A S2 S3) (tptp.subset A S1 S3)))) (forall ((A tptp.ty)) (tptp.sort1 (tptp.set A) (tptp.empty A))) (forall ((A tptp.ty) (S tptp.uni)) (let ((_let_1 (tptp.is_empty A S))) (and (=> _let_1 (forall ((X tptp.uni)) (not (tptp.mem A X S)))) (=> (forall ((X tptp.uni)) (=> (tptp.sort1 A X) (not (tptp.mem A X S)))) _let_1)))) (forall ((A tptp.ty)) (tptp.is_empty A (tptp.empty A))) (forall ((A tptp.ty) (X tptp.uni)) (= (tptp.mem A X (tptp.empty A)) false)) (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.set A) (tptp.add A X X1))) (forall ((A tptp.ty) (X tptp.uni) (Y tptp.uni)) (=> (tptp.sort1 A X) (=> (tptp.sort1 A Y) (forall ((S tptp.uni)) (= (tptp.mem A X (tptp.add A Y S)) (or (= X Y) (tptp.mem A X S))))))) (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.set A) (tptp.remove A X X1))) (forall ((A tptp.ty) (X tptp.uni) (Y tptp.uni) (S tptp.uni)) (=> (tptp.sort1 A X) (=> (tptp.sort1 A Y) (= (tptp.mem A X (tptp.remove A Y S)) (and (not (= X Y)) (tptp.mem A X S)))))) (forall ((A tptp.ty) (X tptp.uni) (S tptp.uni)) (=> (tptp.sort1 (tptp.set A) S) (=> (tptp.mem A X S) (= (tptp.add A X (tptp.remove A X S)) S)))) (forall ((A tptp.ty) (X tptp.uni) (S tptp.uni)) (= (tptp.remove A X (tptp.add A X S)) (tptp.remove A X S))) (forall ((A tptp.ty) (X tptp.uni) (S tptp.uni)) (tptp.subset A (tptp.remove A X S) S)) (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.set A) (tptp.union A X X1))) (forall ((A tptp.ty) (S1 tptp.uni) (S2 tptp.uni) (X tptp.uni)) (= (tptp.mem A X (tptp.union A S1 S2)) (or (tptp.mem A X S1) (tptp.mem A X S2)))) (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.set A) (tptp.inter A X X1))) (forall ((A tptp.ty) (S1 tptp.uni) (S2 tptp.uni) (X tptp.uni)) (= (tptp.mem A X (tptp.inter A S1 S2)) (and (tptp.mem A X S1) (tptp.mem A X S2)))) (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.set A) (tptp.diff A X X1))) (forall ((A tptp.ty) (S1 tptp.uni) (S2 tptp.uni) (X tptp.uni)) (= (tptp.mem A X (tptp.diff A S1 S2)) (and (tptp.mem A X S1) (not (tptp.mem A X S2))))) (forall ((A tptp.ty) (S1 tptp.uni) (S2 tptp.uni)) (tptp.subset A (tptp.diff A S1 S2) S1)) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 A (tptp.choose A X))) (forall ((A tptp.ty) (S tptp.uni)) (=> (not (tptp.is_empty A S)) (tptp.mem A (tptp.choose A S) S))) (forall ((A tptp.ty) (S tptp.uni)) (<= 0 (tptp.cardinal1 A S))) (forall ((A tptp.ty) (S tptp.uni)) (= (= (tptp.cardinal1 A S) 0) (tptp.is_empty A S))) (forall ((A tptp.ty) (X tptp.uni) (S tptp.uni)) (=> (not (tptp.mem A X S)) (= (tptp.cardinal1 A (tptp.add A X S)) (+ 1 (tptp.cardinal1 A S))))) (forall ((A tptp.ty) (X tptp.uni) (S tptp.uni)) (=> (tptp.mem A X S) (= (tptp.cardinal1 A S) (+ 1 (tptp.cardinal1 A (tptp.remove A X S)))))) (forall ((A tptp.ty) (S1 tptp.uni) (S2 tptp.uni)) (=> (tptp.subset A S1 S2) (<= (tptp.cardinal1 A S1) (tptp.cardinal1 A S2)))) (forall ((A tptp.ty) (S tptp.uni)) (=> (= (tptp.cardinal1 A S) 1) (forall ((X tptp.uni)) (=> (tptp.sort1 A X) (=> (tptp.mem A X S) (= X (tptp.choose A S))))))) (forall ((X tptp.set_int)) (tptp.sort1 (tptp.set tptp.int) (tptp.t2tb X))) (forall ((I tptp.set_int)) (= (tptp.tb2t (tptp.t2tb I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb (tptp.tb2t J)) J)) (forall ((X Int)) (tptp.sort1 tptp.int (tptp.t2tb1 X))) (forall ((I Int)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb1 (tptp.tb2t1 J)) J)) (forall ((S tptp.set_int)) (let ((_let_1 (tptp.t2tb S))) (=> (not (tptp.is_empty tptp.int _let_1)) (tptp.mem tptp.int (tptp.t2tb1 (tptp.min_elt1 S)) _let_1)))) (forall ((S tptp.set_int)) (=> (not (tptp.is_empty tptp.int (tptp.t2tb S))) (forall ((X Int)) (=> (tptp.mem tptp.int (tptp.t2tb1 X) (tptp.t2tb S)) (<= (tptp.min_elt1 S) X))))) (forall ((S tptp.set_int)) (let ((_let_1 (tptp.t2tb S))) (=> (not (tptp.is_empty tptp.int _let_1)) (tptp.mem tptp.int (tptp.t2tb1 (tptp.max_elt1 S)) _let_1)))) (forall ((S tptp.set_int)) (=> (not (tptp.is_empty tptp.int (tptp.t2tb S))) (forall ((X Int)) (=> (tptp.mem tptp.int (tptp.t2tb1 X) (tptp.t2tb S)) (<= X (tptp.max_elt1 S)))))) (forall ((X Int) (N Int)) (= (tptp.mem tptp.int (tptp.t2tb1 X) (tptp.t2tb (tptp.below1 N))) (and (<= 0 X) (< X N)))) (forall ((N Int)) (let ((_let_1 (tptp.cardinal1 tptp.int (tptp.t2tb (tptp.below1 N))))) (let ((_let_2 (<= 0 N))) (and (=> _let_2 (= _let_1 N)) (=> (not _let_2) (= _let_1 0)))))) (forall ((S tptp.set_int) (I Int)) (= (tptp.mem tptp.int (tptp.t2tb1 I) (tptp.t2tb (tptp.succ1 S))) (and (<= 1 I) (tptp.mem tptp.int (tptp.t2tb1 (- I 1)) (tptp.t2tb S))))) (forall ((S tptp.set_int) (I Int)) (= (tptp.mem tptp.int (tptp.t2tb1 I) (tptp.t2tb (tptp.pred1 S))) (and (<= 0 I) (tptp.mem tptp.int (tptp.t2tb1 (+ I 1)) (tptp.t2tb S))))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.ref A) (tptp.mk_ref A X))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort1 A (tptp.contents A X))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort1 A U) (= (tptp.contents A (tptp.mk_ref A U)) U))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort1 (tptp.ref A) U) (= U (tptp.mk_ref A (tptp.contents A U))))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 B (tptp.get B A X X1))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort1 (tptp.map A B) (tptp.set1 B A X X1 X2))) (forall ((A tptp.ty) (B tptp.ty) (M tptp.uni) (A1 tptp.uni) (A2 tptp.uni) (B1 tptp.uni)) (=> (tptp.sort1 B B1) (=> (= A1 A2) (= (tptp.get B A (tptp.set1 B A M A1 B1) A2) B1)))) (forall ((A tptp.ty) (B tptp.ty) (M tptp.uni) (A1 tptp.uni) (A2 tptp.uni)) (=> (tptp.sort1 A A1) (=> (tptp.sort1 A A2) (forall ((B1 tptp.uni)) (=> (not (= A1 A2)) (= (tptp.get B A (tptp.set1 B A M A1 B1) A2) (tptp.get B A M A2))))))) (forall ((A tptp.ty) (B tptp.ty) (X tptp.uni)) (tptp.sort1 (tptp.map A B) (tptp.const B A X))) (forall ((A tptp.ty) (B tptp.ty) (B1 tptp.uni) (A1 tptp.uni)) (=> (tptp.sort1 B B1) (= (tptp.get B A (tptp.const B A B1) A1) B1))) _let_2 (forall ((X tptp.map_int_int)) (tptp.sort1 (tptp.map tptp.int tptp.int) (tptp.t2tb2 X))) (forall ((I tptp.map_int_int)) (= (tptp.tb2t2 (tptp.t2tb2 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb2 (tptp.tb2t2 J)) J)) (forall ((K Int) (S tptp.map_int_int)) (= (tptp.partial_solution1 K S) (forall ((I Int)) (let ((_let_1 (tptp.tb2t1 (tptp.get tptp.int tptp.int (tptp.t2tb2 S) (tptp.t2tb1 I))))) (=> (and (<= 0 I) (< I K)) (and (<= 0 _let_1) (< _let_1 tptp.n1) (forall ((J Int)) (let ((_let_1 (tptp.t2tb2 S))) (let ((_let_2 (tptp.tb2t1 (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb1 J))))) (let ((_let_3 (tptp.tb2t1 (tptp.get tptp.int tptp.int _let_1 (tptp.t2tb1 I))))) (let ((_let_4 (- _let_3 _let_2))) (=> (and (<= 0 J) (< J I)) (and (not (= _let_3 _let_2)) (not (= _let_4 (- I J))) (not (= _let_4 (- J I)))))))))))))))) (forall ((U tptp.map_int_int) (T tptp.map_int_int) (K Int)) (=> (tptp.partial_solution1 K T) (=> (tptp.eq_prefix1 tptp.int (tptp.t2tb2 T) (tptp.t2tb2 U) K) (tptp.partial_solution1 K U)))) (forall ((S1 tptp.map_int_int) (S2 tptp.map_int_int)) (= (tptp.lt_sol1 S1 S2) (exists ((I Int)) (let ((_let_1 (tptp.t2tb1 I))) (let ((_let_2 (tptp.t2tb2 S2))) (let ((_let_3 (tptp.t2tb2 S1))) (and (<= 0 I) (< I tptp.n1) (tptp.eq_prefix1 tptp.int _let_3 _let_2 I) (< (tptp.tb2t1 (tptp.get tptp.int tptp.int _let_3 _let_1)) (tptp.tb2t1 (tptp.get tptp.int tptp.int _let_2 _let_1)))))))))) (forall ((X tptp.map_int_lpmap_int_intrp)) (tptp.sort1 (tptp.map tptp.int (tptp.map tptp.int tptp.int)) (tptp.t2tb3 X))) (forall ((I tptp.map_int_lpmap_int_intrp)) (= (tptp.tb2t3 (tptp.t2tb3 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb3 (tptp.tb2t3 J)) J)) (forall ((S tptp.map_int_lpmap_int_intrp) (A Int) (B Int)) (= (tptp.sorted1 S A B) (forall ((I Int) (J Int)) (let ((_let_1 (tptp.t2tb3 S))) (let ((_let_2 (tptp.map tptp.int tptp.int))) (=> (and (<= A I) (< I J) (< J B)) (tptp.lt_sol1 (tptp.tb2t2 (tptp.get _let_2 tptp.int _let_1 (tptp.t2tb1 I))) (tptp.tb2t2 (tptp.get _let_2 tptp.int _let_1 (tptp.t2tb1 J)))))))))) (forall ((S tptp.map_int_lpmap_int_intrp) (A Int) (B Int)) (=> (tptp.sorted1 S A B) (forall ((I Int) (J Int)) (let ((_let_1 (tptp.t2tb3 S))) (let ((_let_2 (tptp.map tptp.int tptp.int))) (=> (and (<= A I) (< I J) (< J B)) (not (tptp.eq_prefix1 tptp.int (tptp.get _let_2 tptp.int _let_1 (tptp.t2tb1 I)) (tptp.get _let_2 tptp.int _let_1 (tptp.t2tb1 J)) tptp.n1)))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))
% 15.61/15.79 )
% 15.61/15.79 % SZS output end Proof for SWW634_2
% 15.61/15.79 % cvc5---1.0.5 exiting
% 15.61/15.79 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------