%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW587_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 00:21:37 EDT 2023

% Result   : Theorem 25.10s 25.45s
% Output   : Proof 25.10s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem    : SWW587_2 : TPTP v8.1.2. Released v6.1.0.
% 0.12/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n011.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   : Sun Aug 27 22:15:40 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_ARI
% 25.10/25.45  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.eO8P363On4/cvc5---1.0.5_10184.p...
% 25.10/25.45  ------- get file name : TPTP file name is SWW587_2
% 25.10/25.45  ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10184.smt2...
% 25.10/25.45  --- Run --finite-model-find --decision=internal at 15...
% 25.10/25.45  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 25.10/25.45  % SZS status Theorem for SWW587_2
% 25.10/25.45  % SZS output start Proof for SWW587_2
% 25.10/25.45  (
% 25.10/25.45  (let ((_let_1 (not (forall ((Src tptp.vertex1) (Dst tptp.vertex1) (D tptp.map_vertex_int)) (let ((_let_1 (tptp.t2tb tptp.v1))) (=> (and (tptp.mem tptp.vertex (tptp.t2tb2 Src) _let_1) (tptp.mem tptp.vertex (tptp.t2tb2 Dst) _let_1)) (forall ((Q tptp.set_vertex) (D1 tptp.map_vertex_int) (Visited tptp.set_vertex)) (let ((_let_1 (tptp.t2tb2 Src))) (=> (and (forall ((X tptp.vertex1)) (not (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb Visited)))) (= Q (tptp.tb2t (tptp.add tptp.vertex _let_1 (tptp.empty tptp.vertex)))) (= D1 (tptp.tb2t1 (tptp.set1 tptp.int tptp.vertex (tptp.t2tb1 D) _let_1 (tptp.t2tb3 0))))) (forall ((Q1 tptp.set_vertex) (D2 tptp.map_vertex_int) (Visited1 tptp.set_vertex)) (let ((_let_1 (tptp.t2tb tptp.v1))) (=> (and (tptp.inv_src1 Src Visited1 Q1) (= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D2) (tptp.t2tb2 Src))) 0) (tptp.subset tptp.vertex (tptp.t2tb Visited1) _let_1) (tptp.subset tptp.vertex (tptp.t2tb Q1) _let_1) (forall ((V tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 V))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q1)) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Visited1)) false)))) (forall ((V tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 V))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Visited1)) (tptp.shortest_path1 Src V (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D2) _let_1)))))) (forall ((V tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 V))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q1)) (tptp.path1 Src V (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D2) _let_1)))))) (forall ((X tptp.vertex1)) (=> (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb Visited1)) (forall ((Y tptp.vertex1)) (let ((_let_1 (tptp.t2tb1 D2))) (let ((_let_2 (tptp.t2tb2 Y))) (=> (tptp.mem tptp.vertex _let_2 (tptp.t2tb (tptp.g_succ1 X))) (and (or (tptp.mem tptp.vertex _let_2 (tptp.t2tb Visited1)) (tptp.mem tptp.vertex _let_2 (tptp.t2tb Q1))) (<= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_1 _let_2)) (+ (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_1 (tptp.t2tb2 X))) (tptp.weight1 X Y)))))))))) (forall ((M tptp.vertex1)) (=> (and (tptp.mem tptp.vertex (tptp.t2tb2 M) (tptp.t2tb Q1)) (forall ((X tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 X))) (let ((_let_2 (tptp.t2tb1 D2))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q1)) (<= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_2 (tptp.t2tb2 M))) (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_2 _let_1)))))))) (forall ((X tptp.vertex1) (Dx Int)) (=> (tptp.path1 Src X Dx) (=> (< Dx (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D2) (tptp.t2tb2 M)))) (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb Visited1)))))))) (forall ((O tptp.bool1)) (let ((_let_1 (= O tptp.true1))) (=> (= _let_1 (forall ((X tptp.vertex1)) (not (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb Q1))))) (=> (not _let_1) (=> (not (forall ((X tptp.vertex1)) (not (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb Q1))))) (forall ((Q2 tptp.set_vertex) (U tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 U))) (let ((_let_2 (tptp.t2tb Q1))) (=> (and (tptp.mem tptp.vertex _let_1 _let_2) (forall ((X tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 X))) (let ((_let_2 (tptp.t2tb1 D2))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q1)) (<= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_2 (tptp.t2tb2 U))) (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_2 _let_1))))))) (= Q2 (tptp.tb2t (tptp.remove tptp.vertex _let_1 _let_2)))) (=> (and (tptp.path1 Src U (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D2) _let_1))) (forall ((Dqt Int)) (=> (tptp.path1 Src U Dqt) (<= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D2) (tptp.t2tb2 U))) Dqt)))) (forall ((Visited2 tptp.set_vertex)) (=> (= Visited2 (tptp.tb2t (tptp.add tptp.vertex (tptp.t2tb2 U) (tptp.t2tb Visited1)))) (forall ((Su tptp.set_vertex) (Q3 tptp.set_vertex) (D3 tptp.map_vertex_int)) (let ((_let_1 (tptp.t2tb tptp.v1))) (=> (and (forall ((X tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 X))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Su)) (tptp.mem tptp.vertex _let_1 (tptp.t2tb (tptp.g_succ1 U)))))) (tptp.inv_src1 Src Visited2 Q3) (= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D3) (tptp.t2tb2 Src))) 0) (tptp.subset tptp.vertex (tptp.t2tb Visited2) _let_1) (tptp.subset tptp.vertex (tptp.t2tb Q3) _let_1) (forall ((V tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 V))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q3)) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Visited2)) false)))) (forall ((V tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 V))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Visited2)) (tptp.shortest_path1 Src V (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D3) _let_1)))))) (forall ((V tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 V))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q3)) (tptp.path1 Src V (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D3) _let_1)))))) (forall ((X tptp.vertex1)) (=> (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb Visited2)) (forall ((Y tptp.vertex1)) (let ((_let_1 (tptp.t2tb1 D3))) (let ((_let_2 (tptp.t2tb2 Y))) (let ((_let_3 (= X U))) (=> (tptp.mem tptp.vertex _let_2 (tptp.t2tb (tptp.g_succ1 X))) (=> (or (not _let_3) (and _let_3 (not (tptp.mem tptp.vertex _let_2 (tptp.t2tb Su))))) (and (or (tptp.mem tptp.vertex _let_2 (tptp.t2tb Visited2)) (tptp.mem tptp.vertex _let_2 (tptp.t2tb Q3))) (<= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_1 _let_2)) (+ (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_1 (tptp.t2tb2 X))) (tptp.weight1 X Y))))))))))))) (forall ((Result tptp.bool1)) (let ((_let_1 (= Result tptp.true1))) (=> (= _let_1 (not (forall ((X tptp.vertex1)) (not (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb Su)))))) (=> _let_1 (=> (not (forall ((X tptp.vertex1)) (not (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb Su))))) (forall ((Su1 tptp.set_vertex) (V tptp.vertex1)) (let ((_let_1 (tptp.t2tb Su))) (let ((_let_2 (tptp.t2tb2 V))) (=> (and (tptp.mem tptp.vertex _let_2 _let_1) (= Su1 (tptp.tb2t (tptp.remove tptp.vertex _let_2 _let_1)))) (forall ((Q4 tptp.set_vertex) (D4 tptp.map_vertex_int)) (let ((_let_1 (tptp.weight1 U V))) (let ((_let_2 (tptp.t2tb2 U))) (let ((_let_3 (tptp.t2tb1 D4))) (let ((_let_4 (+ (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_3 _let_2)) _let_1))) (let ((_let_5 (tptp.t2tb2 V))) (let ((_let_6 (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_3 _let_5)))) (let ((_let_7 (tptp.t2tb1 D3))) (let ((_let_8 (+ (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_7 _let_2)) _let_1))) (let ((_let_9 (= D4 (tptp.tb2t1 (tptp.set1 tptp.int tptp.vertex _let_7 _let_5 (tptp.t2tb3 _let_8)))))) (let ((_let_10 (tptp.t2tb Q3))) (let ((_let_11 (tptp.mem tptp.vertex _let_5 (tptp.t2tb Visited2)))) (let ((_let_12 (= Q4 Q3))) (let ((_let_13 (tptp.mem tptp.vertex _let_5 (tptp.t2tb Q4)))) (let ((_let_14 (= D4 D3))) (=> (or (and _let_11 _let_12 _let_14) (and _let_13 (<= _let_6 _let_4) _let_12 _let_14) (and _let_13 (< _let_8 (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_7 _let_5))) _let_12 _let_9) (and (not _let_11) (not (tptp.mem tptp.vertex _let_5 _let_10)) (= Q4 (tptp.tb2t (tptp.add tptp.vertex _let_5 _let_10))) _let_9)) (=> (or (< _let_6 _let_4) (= _let_6 _let_4)) (forall ((X tptp.vertex1)) (=> (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb Visited2)) (forall ((Y tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 Y))) (let ((_let_2 (= X U))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb (tptp.g_succ1 X))) (=> (or (not _let_2) (and _let_2 (not (tptp.mem tptp.vertex _let_1 (tptp.t2tb Su1))))) (or (tptp.mem tptp.vertex _let_1 (tptp.t2tb Visited2)) (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (let ((_let_2 (forall ((X tptp.vertex1)) (tptp.sort1 tptp.vertex (tptp.t2tb2 X))))) (let ((_let_3 (forall ((J tptp.uni)) (=> (tptp.sort1 (tptp.set tptp.vertex) J) (= (tptp.t2tb (tptp.tb2t J)) J))))) (let ((_let_4 (forall ((X tptp.set_vertex)) (tptp.sort1 (tptp.set tptp.vertex) (tptp.t2tb X))))) (let ((_let_5 (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))))))) (let ((_let_6 (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)))))) (let ((_let_7 (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)))))))) (let ((_let_8 (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.set A) (tptp.remove A X X1))))) (let ((_let_9 (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))))))))) (let ((_let_10 (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort1 (tptp.set A) (tptp.add A X X1))))) (let ((_let_11 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_12 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_13 (tptp.mem tptp.vertex _let_12 _let_11))) (let ((_let_14 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_15 (= _let_14 _let_12))) (let ((_let_16 (not _let_15))) (let ((_let_17 (and _let_16 _let_13))) (let ((_let_18 (tptp.remove tptp.vertex _let_14 _let_11))) (let ((_let_19 (tptp.mem tptp.vertex _let_12 _let_18))) (let ((_let_20 (= _let_19 _let_17))) (let ((_let_21 (tptp.sort1 tptp.vertex _let_14))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.sort1 tptp.vertex _let_12))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_20))) (let ((_let_26 (forall ((A tptp.ty) (X tptp.uni) (Y tptp.uni) (S tptp.uni)) (or (not (tptp.sort1 A X)) (not (tptp.sort1 A Y)) (= (tptp.mem A X (tptp.remove A Y S)) (and (not (= X Y)) (tptp.mem A X S))))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_2))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 ((tptp.t2tb2 X)))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_28)) _let_29 :args (_let_23 false _let_2)))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_28)) _let_29 :args (_let_21 false _let_2)))) (let ((_let_33 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_34 (tptp.mem tptp.vertex _let_12 _let_33))) (let ((_let_35 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_36 (tptp.add tptp.vertex _let_14 _let_35))) (let ((_let_37 (tptp.tb2t _let_36))) (let ((_let_38 (= _let_36 (tptp.t2tb _let_37)))) (let ((_let_39 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_37))) (let ((_let_40 (tptp.mem tptp.vertex _let_14 _let_36))) (let ((_let_41 (= tptp.true1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_42 (= (not (forall ((X tptp.vertex1)) (not (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))) _let_41))) (let ((_let_43 (tptp.t2tb SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_44 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_45 (tptp.add tptp.vertex _let_44 _let_43))) (let ((_let_46 (tptp.tb2t _let_45))) (let ((_let_47 (tptp.t2tb _let_46))) (let ((_let_48 (tptp.mem tptp.vertex _let_12 _let_47))) (let ((_let_49 (tptp.t2tb (tptp.tb2t _let_18)))) (let ((_let_50 (tptp.mem tptp.vertex _let_12 _let_49))) (let ((_let_51 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_50))) (let ((_let_54 (and _let_51 _let_53))) (let ((_let_55 (tptp.mem tptp.vertex _let_12 (tptp.t2tb (tptp.g_succ1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))))) (let ((_let_56 (not _let_55))) (let ((_let_57 (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_58 (tptp.mem tptp.vertex _let_57 _let_47))) (let ((_let_59 (not _let_58))) (let ((_let_60 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_61 (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_60 _let_14)))) (let ((_let_62 (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_60 _let_44)))) (let ((_let_63 (tptp.weight1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_64 (+ _let_63 _let_62 (* (- 1) _let_61)))) (let ((_let_65 (and (not (>= _let_64 1)) (not (= _let_63 (+ (* (- 1) _let_62) _let_61)))))) (let ((_let_66 (tptp.t2tb1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_67 (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_66 _let_44)))) (let ((_let_68 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 (tptp.tb2t1 (tptp.set1 tptp.int tptp.vertex _let_66 _let_14 (tptp.t2tb3 (+ _let_63 _let_67)))))))) (let ((_let_69 (not _let_39))) (let ((_let_70 (tptp.mem tptp.vertex _let_14 _let_47))) (let ((_let_71 (or _let_70 (tptp.mem tptp.vertex _let_14 _let_35) _let_69 _let_68))) (let ((_let_72 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_73 (not _let_72))) (let ((_let_74 (>= (+ _let_63 _let_67 (* (- 1) (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_66 _let_14)))) 0))) (let ((_let_75 (tptp.mem tptp.vertex _let_14 _let_33))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_76 _let_74 _let_73 _let_68))) (let ((_let_78 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))) (let ((_let_79 (not (>= _let_64 0)))) (let ((_let_80 (or _let_76 _let_79 _let_73 _let_78))) (let ((_let_81 (not _let_70))) (let ((_let_82 (or _let_81 _let_73 _let_78))) (let ((_let_83 (and _let_82 _let_80 _let_77 _let_71))) (let ((_let_84 (tptp.mem tptp.vertex _let_14 _let_11))) (let ((_let_85 (not _let_84))) (let ((_let_86 (not (tptp.mem tptp.vertex (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) _let_11)))) (let ((_let_87 (not (tptp.mem tptp.vertex (tptp.t2tb2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) _let_11)))) (let 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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)) _let_10 _let_9 _let_8 _let_7 _let_6 (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))) _let_5 (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 ((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_4 (forall ((I tptp.set_vertex)) (= (tptp.tb2t (tptp.t2tb I)) I)) _let_3 (forall ((X tptp.vertex1)) (tptp.subset tptp.vertex (tptp.t2tb (tptp.g_succ1 X)) (tptp.t2tb tptp.v1))) (forall ((X tptp.vertex1) (Y tptp.vertex1)) (<= 0 (tptp.weight1 X Y))) (forall ((X tptp.map_vertex_int)) (tptp.sort1 (tptp.map tptp.vertex tptp.int) (tptp.t2tb1 X))) (forall ((I tptp.map_vertex_int)) (= (tptp.tb2t1 (tptp.t2tb1 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb1 (tptp.tb2t1 J)) J)) _let_2 (forall ((I tptp.vertex1)) (= (tptp.tb2t2 (tptp.t2tb2 I)) I)) (forall ((J tptp.uni)) (=> (tptp.sort1 tptp.vertex J) (= (tptp.t2tb2 (tptp.tb2t2 J)) J))) (forall ((X Int)) (tptp.sort1 tptp.int (tptp.t2tb3 X))) (forall ((I Int)) (= (tptp.tb2t3 (tptp.t2tb3 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb3 (tptp.tb2t3 J)) J)) (forall ((M tptp.vertex1) (Q tptp.set_vertex) (D tptp.map_vertex_int)) (= (tptp.min1 M Q D) (and (tptp.mem tptp.vertex (tptp.t2tb2 M) (tptp.t2tb Q)) (forall ((X tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 X))) (let ((_let_2 (tptp.t2tb1 D))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q)) (<= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_2 (tptp.t2tb2 M))) (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_2 _let_1)))))))))) (forall ((X tptp.vertex1)) (tptp.path1 X X 0)) (forall ((X tptp.vertex1) (Y tptp.vertex1) (Z tptp.vertex1) (D Int)) (=> (tptp.path1 X Y D) (=> (tptp.mem tptp.vertex (tptp.t2tb2 Z) (tptp.t2tb (tptp.g_succ1 Y))) (tptp.path1 X Z (+ D (tptp.weight1 Y Z)))))) (forall ((Z tptp.vertex1) (Z1 tptp.vertex1) (Z2 Int)) (=> (tptp.path1 Z Z1 Z2) (or (exists ((X tptp.vertex1)) (and (= Z X) (= Z1 X) (= Z2 0))) (exists ((X tptp.vertex1) (Y tptp.vertex1) (Z3 tptp.vertex1) (D Int)) (and (tptp.path1 X Y D) (tptp.mem tptp.vertex (tptp.t2tb2 Z3) (tptp.t2tb (tptp.g_succ1 Y))) (= Z X) (= Z1 Z3) (= Z2 (+ D (tptp.weight1 Y Z3)))))))) (forall ((X tptp.vertex1) (Y tptp.vertex1) (D Int)) (=> (tptp.path1 X Y D) (<= 0 D))) (forall ((X tptp.vertex1) (Y tptp.vertex1) (D Int)) (= (tptp.shortest_path1 X Y D) (and (tptp.path1 X Y D) (forall ((Dqt Int)) (=> (tptp.path1 X Y Dqt) (<= D Dqt)))))) (forall ((Src tptp.vertex1) (V tptp.vertex1) (D Int)) (=> (tptp.path1 Src V D) (or (and (= V Src) (= D 0)) (exists ((Vqt tptp.vertex1)) (and (tptp.path1 Src Vqt (- D (tptp.weight1 Vqt V))) (tptp.mem tptp.vertex (tptp.t2tb2 V) (tptp.t2tb (tptp.g_succ1 Vqt)))))))) (forall ((Src tptp.vertex1) (V tptp.vertex1) (D Int)) (=> (tptp.path1 Src V D) (exists ((Dqt Int)) (and (tptp.shortest_path1 Src V Dqt) (<= Dqt D))))) (forall ((Src tptp.vertex1) (V tptp.vertex1) (D Int)) (=> (tptp.path1 Src V D) (=> (not (tptp.shortest_path1 Src V D)) (or (and (= V Src) (< 0 D)) (exists ((Vqt tptp.vertex1) (Dqt Int)) (and (tptp.shortest_path1 Src Vqt Dqt) (tptp.mem tptp.vertex (tptp.t2tb2 V) (tptp.t2tb (tptp.g_succ1 Vqt))) (< (+ Dqt (tptp.weight1 Vqt V)) D))))))) (forall ((S tptp.set_vertex)) (=> (forall ((V tptp.vertex1)) (=> (tptp.mem tptp.vertex (tptp.t2tb2 V) (tptp.t2tb S)) (forall ((W tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 W))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb (tptp.g_succ1 V))) (tptp.mem tptp.vertex _let_1 (tptp.t2tb S))))))) (forall ((Src tptp.vertex1)) (=> (tptp.mem tptp.vertex (tptp.t2tb2 Src) (tptp.t2tb S)) (forall ((Dst tptp.vertex1) (D Int)) (=> (tptp.path1 Src Dst D) (tptp.mem tptp.vertex (tptp.t2tb2 Dst) (tptp.t2tb S)))))))) (forall ((Src tptp.vertex1) (S tptp.set_vertex) (Q tptp.set_vertex)) (let ((_let_1 (tptp.t2tb2 Src))) (= (tptp.inv_src1 Src S Q) (or (tptp.mem tptp.vertex _let_1 (tptp.t2tb S)) (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q)))))) (forall ((Src tptp.vertex1) (S tptp.set_vertex) (Q tptp.set_vertex) (D tptp.map_vertex_int)) (let ((_let_1 (tptp.t2tb tptp.v1))) (= (tptp.inv1 Src S Q D) (and (tptp.inv_src1 Src S Q) (= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D) (tptp.t2tb2 Src))) 0) (tptp.subset tptp.vertex (tptp.t2tb S) _let_1) (tptp.subset tptp.vertex (tptp.t2tb Q) _let_1) (forall ((V tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 V))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q)) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb S)) false)))) (forall ((V tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 V))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb S)) (tptp.shortest_path1 Src V (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D) _let_1)))))) (forall ((V tptp.vertex1)) (let ((_let_1 (tptp.t2tb2 V))) (=> (tptp.mem tptp.vertex _let_1 (tptp.t2tb Q)) (tptp.path1 Src V (tptp.tb2t3 (tptp.get tptp.int tptp.vertex (tptp.t2tb1 D) _let_1)))))))))) (forall ((Src tptp.vertex1) (S tptp.set_vertex) (Q tptp.set_vertex) (D tptp.map_vertex_int)) (= (tptp.inv_succ1 Src S Q D) (forall ((X tptp.vertex1)) (=> (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb S)) (forall ((Y tptp.vertex1)) (let ((_let_1 (tptp.t2tb1 D))) (let ((_let_2 (tptp.t2tb2 Y))) (=> (tptp.mem tptp.vertex _let_2 (tptp.t2tb (tptp.g_succ1 X))) (and (or (tptp.mem tptp.vertex _let_2 (tptp.t2tb S)) (tptp.mem tptp.vertex _let_2 (tptp.t2tb Q))) (<= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_1 _let_2)) (+ (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_1 (tptp.t2tb2 X))) (tptp.weight1 X Y)))))))))))) (forall ((Src tptp.vertex1) (S tptp.set_vertex) (Q tptp.set_vertex) (D tptp.map_vertex_int) (U tptp.vertex1) (Su tptp.set_vertex)) (= (tptp.inv_succ21 Src S Q D U Su) (forall ((X tptp.vertex1)) (=> (tptp.mem tptp.vertex (tptp.t2tb2 X) (tptp.t2tb S)) (forall ((Y tptp.vertex1)) (let ((_let_1 (tptp.t2tb1 D))) (let ((_let_2 (tptp.t2tb2 Y))) (let ((_let_3 (= X U))) (=> (tptp.mem tptp.vertex _let_2 (tptp.t2tb (tptp.g_succ1 X))) (=> (or (not _let_3) (and _let_3 (not (tptp.mem tptp.vertex _let_2 (tptp.t2tb Su))))) (and (or (tptp.mem tptp.vertex _let_2 (tptp.t2tb S)) (tptp.mem tptp.vertex _let_2 (tptp.t2tb Q))) (<= (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_1 _let_2)) (+ (tptp.tb2t3 (tptp.get tptp.int tptp.vertex _let_1 (tptp.t2tb2 X))) (tptp.weight1 X Y)))))))))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.10/25.46  )
% 25.10/25.46  % SZS output end Proof for SWW587_2
% 25.10/25.46  % cvc5---1.0.5 exiting
% 25.10/25.46  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------