TSTP Solution File: SWW577_2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW577_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : Fri Sep 1 00:21:34 EDT 2023
% Result : Theorem 58.15s 58.36s
% Output : Proof 58.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.16 % Problem : SWW577_2 : TPTP v8.1.2. Released v6.1.0.
% 0.12/0.18 % Command : do_cvc5 %s %d
% 0.17/0.39 % Computer : n003.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Sun Aug 27 22:43:40 EDT 2023
% 0.17/0.39 % CPUTime :
% 0.25/0.56 %----Proving TF0_ARI
% 58.15/58.36 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.YJVWiVJJ78/cvc5---1.0.5_30754.p...
% 58.15/58.36 ------- get file name : TPTP file name is SWW577_2
% 58.15/58.36 ------- cvc5-tfa : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30754.smt2...
% 58.15/58.36 --- Run --finite-model-find --decision=internal at 15...
% 58.15/58.36 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 58.15/58.36 --- Run --no-e-matching --full-saturate-quant at 15...
% 58.15/58.36 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 15...
% 58.15/58.36 % SZS status Theorem for SWW577_2
% 58.15/58.36 % SZS output start Proof for SWW577_2
% 58.15/58.36 (
% 58.15/58.36 (let ((_let_1 (tptp.cardinal1 tptp.vertices))) (let ((_let_2 (- _let_1 1))) (let ((_let_3 (not (=> (or (< 1 _let_2) (= 1 _let_2)) (forall ((M tptp.map_vertex_t19) (I Int)) (let ((_let_1 (- (tptp.cardinal1 tptp.vertices) 1))) (=> (and (or (< 1 I) (= 1 I)) (or (< I _let_1) (= I _let_1))) (=> (forall ((V tptp.vertex)) (=> (tptp.mem1 V tptp.vertices) (or (exists ((X Int)) (and (= (tptp.get1 M V) (tptp.finite X)) (exists ((L tptp.list_vertex)) (and (tptp.path tptp.s L V) (= (tptp.path_weight L V) X))) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (=> (< (tptp.length1 L) I) (<= X (tptp.path_weight L V))))) (forall ((U tptp.vertex) (L tptp.list_vertex)) (=> (tptp.path tptp.s L U) (=> (< (tptp.length1 L) I) (=> (tptp.mem2 (tptp.tuple22 U V) tptp.empty2) (<= X (+ (tptp.path_weight L U) (tptp.weight U V))))))))) (and (= (tptp.get1 M V) tptp.infinite) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (<= I (tptp.length1 L)))) (forall ((U tptp.vertex)) (=> (tptp.mem2 (tptp.tuple22 U V) tptp.empty2) (forall ((Lu tptp.list_vertex)) (=> (tptp.path tptp.s Lu U) (<= I (tptp.length1 Lu)))))))))) (forall ((Es tptp.set_lpvertexcm_vertexrp)) (=> (= Es tptp.edges) (forall ((Es1 tptp.set_lpvertexcm_vertexrp) (M1 tptp.map_vertex_t19)) (=> (and (forall ((X tptp.lpvertexcm_vertexrp)) (=> (tptp.mem2 X Es1) (tptp.mem2 X tptp.edges))) (forall ((V tptp.vertex)) (=> (tptp.mem1 V tptp.vertices) (or (exists ((X Int)) (and (= (tptp.get1 M1 V) (tptp.finite X)) (exists ((L tptp.list_vertex)) (and (tptp.path tptp.s L V) (= (tptp.path_weight L V) X))) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (=> (< (tptp.length1 L) I) (<= X (tptp.path_weight L V))))) (forall ((U tptp.vertex) (L tptp.list_vertex)) (=> (tptp.path tptp.s L U) (=> (< (tptp.length1 L) I) (=> (tptp.mem2 (tptp.tuple22 U V) (tptp.diff2 tptp.edges Es1)) (<= X (+ (tptp.path_weight L U) (tptp.weight U V))))))))) (and (= (tptp.get1 M1 V) tptp.infinite) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (<= I (tptp.length1 L)))) (forall ((U tptp.vertex)) (=> (tptp.mem2 (tptp.tuple22 U V) (tptp.diff2 tptp.edges Es1)) (forall ((Lu tptp.list_vertex)) (=> (tptp.path tptp.s Lu U) (<= I (tptp.length1 Lu))))))))))) (forall ((O tptp.bool)) (let ((_let_1 (= O tptp.true))) (=> (= _let_1 (forall ((X tptp.lpvertexcm_vertexrp)) (not (tptp.mem2 X Es1)))) (=> (not _let_1) (=> (not (forall ((X tptp.lpvertexcm_vertexrp)) (not (tptp.mem2 X Es1)))) (forall ((Es2 tptp.set_lpvertexcm_vertexrp) (Result tptp.vertex) (Result1 tptp.vertex)) (let ((_let_1 (tptp.tuple22 Result Result1))) (=> (and (tptp.mem2 _let_1 Es1) (= Es2 (tptp.remove2 _let_1 Es1))) (=> (and (or (< 1 I) (= 1 I)) (tptp.mem2 _let_1 tptp.edges) (not (tptp.mem2 _let_1 (tptp.diff2 tptp.edges Es1))) (forall ((V tptp.vertex)) (=> (tptp.mem1 V tptp.vertices) (or (exists ((X Int)) (and (= (tptp.get1 M1 V) (tptp.finite X)) (exists ((L tptp.list_vertex)) (and (tptp.path tptp.s L V) (= (tptp.path_weight L V) X))) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (=> (< (tptp.length1 L) I) (<= X (tptp.path_weight L V))))) (forall ((U tptp.vertex) (L tptp.list_vertex)) (=> (tptp.path tptp.s L U) (=> (< (tptp.length1 L) I) (=> (tptp.mem2 (tptp.tuple22 U V) (tptp.diff2 tptp.edges Es1)) (<= X (+ (tptp.path_weight L U) (tptp.weight U V))))))))) (and (= (tptp.get1 M1 V) tptp.infinite) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (<= I (tptp.length1 L)))) (forall ((U tptp.vertex)) (=> (tptp.mem2 (tptp.tuple22 U V) (tptp.diff2 tptp.edges Es1)) (forall ((Lu tptp.list_vertex)) (=> (tptp.path tptp.s Lu U) (<= I (tptp.length1 Lu))))))))))) (forall ((M2 tptp.map_vertex_t19)) (=> (forall ((V tptp.vertex)) (=> (tptp.mem1 V tptp.vertices) (or (exists ((X Int)) (and (= (tptp.get1 M2 V) (tptp.finite X)) (exists ((L tptp.list_vertex)) (and (tptp.path tptp.s L V) (= (tptp.path_weight L V) X))) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (=> (< (tptp.length1 L) I) (<= X (tptp.path_weight L V))))) (forall ((U tptp.vertex) (L tptp.list_vertex)) (=> (tptp.path tptp.s L U) (=> (< (tptp.length1 L) I) (=> (tptp.mem2 (tptp.tuple22 U V) (tptp.add2 (tptp.tuple22 Result Result1) (tptp.diff2 tptp.edges Es1))) (<= X (+ (tptp.path_weight L U) (tptp.weight U V))))))))) (and (= (tptp.get1 M2 V) tptp.infinite) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (<= I (tptp.length1 L)))) (forall ((U tptp.vertex)) (=> (tptp.mem2 (tptp.tuple22 U V) (tptp.add2 (tptp.tuple22 Result Result1) (tptp.diff2 tptp.edges Es1))) (forall ((Lu tptp.list_vertex)) (=> (tptp.path tptp.s Lu U) (<= I (tptp.length1 Lu)))))))))) (forall ((V tptp.vertex)) (=> (tptp.mem1 V tptp.vertices) (forall ((X Int)) (=> (= (tptp.get1 M2 V) (tptp.finite X)) (forall ((U tptp.vertex) (L tptp.list_vertex)) (=> (tptp.path tptp.s L U) (=> (< (tptp.length1 L) I) (=> (tptp.mem2 (tptp.tuple22 U V) (tptp.diff2 tptp.edges Es2)) (<= X (+ (tptp.path_weight L U) (tptp.weight U V)))))))))))))))))))))))))))))))))) (let ((_let_4 (forall ((U Int)) (= (tptp.finite_proj_1 (tptp.finite U)) U)))) (let ((_let_5 (forall ((U Int)) (not (= (tptp.finite U) tptp.infinite))))) (let ((_let_6 (forall ((S1 tptp.set_lpvertexcm_vertexrp) (S2 tptp.set_lpvertexcm_vertexrp) (X tptp.lpvertexcm_vertexrp)) (= (tptp.mem2 X (tptp.diff2 S1 S2)) (and (tptp.mem2 X S1) (not (tptp.mem2 X S2))))))) (let ((_let_7 (forall ((X tptp.lpvertexcm_vertexrp) (Y tptp.lpvertexcm_vertexrp) (S tptp.set_lpvertexcm_vertexrp)) (= (tptp.mem2 X (tptp.remove2 Y S)) (and (not (= X Y)) (tptp.mem2 X S)))))) (let ((_let_8 (forall ((X tptp.lpvertexcm_vertexrp) (Y tptp.lpvertexcm_vertexrp) (S tptp.set_lpvertexcm_vertexrp)) (= (tptp.mem2 X (tptp.add2 Y S)) (or (= X Y) (tptp.mem2 X S)))))) (let ((_let_9 (tptp.tuple22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_266 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_265))) (let ((_let_10 (tptp.mem2 _let_9 tptp.edges))) (let ((_let_11 (tptp.mem2 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272))) (let ((_let_12 (not _let_11))) (let ((_let_13 (and _let_10 _let_12))) (let ((_let_14 (tptp.tuple22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_263 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_264))) (let ((_let_15 (tptp.remove2 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272))) (let ((_let_16 (tptp.mem2 _let_9 _let_15))) (let ((_let_17 (not _let_16))) (let ((_let_18 (and _let_10 _let_17))) (let ((_let_19 (tptp.mem2 _let_9 (tptp.diff2 tptp.edges _let_15)))) (let ((_let_20 (= _let_19 _let_18))) (let ((_let_21 (_let_6))) (let ((_let_22 (ASSUME :args _let_21))) (let ((_let_23 (= tptp.true SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_270))) (let ((_let_24 (= (not (forall ((X tptp.lpvertexcm_vertexrp)) (not (tptp.mem2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272)))) _let_23))) (let ((_let_25 (tptp.weight SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_266 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_265))) (let ((_let_26 (tptp.path_weight SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_267 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_266))) (let ((_let_27 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_268 (* (- 1) _let_26) (* (- 1) _let_25)) 1))) (let ((_let_28 (not _let_27))) (let ((_let_29 (not _let_19))) (let ((_let_30 (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_267))) 1))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.path tptp.s SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_267 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_266))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.finite SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_268))) (let ((_let_35 (tptp.get1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_269 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_265))) (let ((_let_36 (= _let_35 _let_34))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.mem1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_265 tptp.vertices))) (let ((_let_39 (not _let_38))) (let ((_let_40 (forall ((V tptp.vertex) (BOUND_VARIABLE_6326 tptp.list_vertex) (BOUND_VARIABLE_6324 tptp.vertex) (BOUND_VARIABLE_6314 tptp.list_vertex)) (or (not (tptp.mem1 V tptp.vertices)) (not (forall ((BOUND_VARIABLE_6212 tptp.list_vertex)) (or (not (= (tptp.finite (tptp.path_weight BOUND_VARIABLE_6212 V)) (tptp.get1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_269 V))) (not (forall ((L tptp.list_vertex)) (or (not (tptp.path tptp.s L V)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 L))) 1)) (>= (+ (tptp.path_weight L V) (* (- 1) (tptp.path_weight BOUND_VARIABLE_6212 V))) 0)))) (not (forall ((U tptp.vertex) (L tptp.list_vertex)) (or (not (tptp.path tptp.s L U)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 L))) 1)) (not (tptp.mem2 (tptp.tuple22 U V) (tptp.add2 (tptp.tuple22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_263 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_264) (tptp.diff2 tptp.edges SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272)))) (>= (+ (tptp.path_weight L U) (tptp.weight U V) (* (- 1) (tptp.path_weight BOUND_VARIABLE_6212 V))) 0)))) (not (tptp.path tptp.s BOUND_VARIABLE_6212 V))))) (and (= tptp.infinite (tptp.get1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_269 V)) (or (not (tptp.path tptp.s BOUND_VARIABLE_6314 V)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 BOUND_VARIABLE_6314))) 1))) (or (not (tptp.mem2 (tptp.tuple22 BOUND_VARIABLE_6324 V) (tptp.add2 (tptp.tuple22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_263 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_264) (tptp.diff2 tptp.edges SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272)))) (not (tptp.path tptp.s BOUND_VARIABLE_6326 BOUND_VARIABLE_6324)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 BOUND_VARIABLE_6326))) 1)))))))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.diff2 tptp.edges SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272))) (let ((_let_43 (tptp.mem2 _let_14 _let_42))) (let ((_let_44 (not (tptp.mem2 _let_14 tptp.edges)))) (let ((_let_45 (not (tptp.mem2 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272)))) (let ((_let_46 (not (forall ((V tptp.vertex) (BOUND_VARIABLE_6133 tptp.list_vertex) (BOUND_VARIABLE_6131 tptp.vertex) (BOUND_VARIABLE_6121 tptp.list_vertex)) (or (not (tptp.mem1 V tptp.vertices)) (not (forall ((BOUND_VARIABLE_6019 tptp.list_vertex)) (or (not (= (tptp.finite (tptp.path_weight BOUND_VARIABLE_6019 V)) (tptp.get1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_271 V))) (not (forall ((L tptp.list_vertex)) (or (not (tptp.path tptp.s L V)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 L))) 1)) (>= (+ (tptp.path_weight L V) (* (- 1) (tptp.path_weight BOUND_VARIABLE_6019 V))) 0)))) (not (forall ((U tptp.vertex) (L tptp.list_vertex)) (or (not (tptp.path tptp.s L U)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 L))) 1)) (not (tptp.mem2 (tptp.tuple22 U V) (tptp.diff2 tptp.edges SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272))) (>= (+ (tptp.path_weight L U) (tptp.weight U V) (* (- 1) (tptp.path_weight BOUND_VARIABLE_6019 V))) 0)))) (not (tptp.path tptp.s BOUND_VARIABLE_6019 V))))) (and (= tptp.infinite (tptp.get1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_271 V)) (or (not (tptp.path tptp.s BOUND_VARIABLE_6121 V)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 BOUND_VARIABLE_6121))) 1))) (or (not (tptp.mem2 (tptp.tuple22 BOUND_VARIABLE_6131 V) (tptp.diff2 tptp.edges SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272))) (not (tptp.path tptp.s BOUND_VARIABLE_6133 BOUND_VARIABLE_6131)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 BOUND_VARIABLE_6133))) 1))))))))) (let ((_let_47 (not (tptp.mem2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_262 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272)))) (let ((_let_48 (not (forall ((V tptp.vertex) (BOUND_VARIABLE_5936 tptp.list_vertex) (BOUND_VARIABLE_5934 tptp.vertex) (BOUND_VARIABLE_5924 tptp.list_vertex)) (or (not (tptp.mem1 V tptp.vertices)) (not (forall ((BOUND_VARIABLE_5822 tptp.list_vertex)) (or (not (= (tptp.finite (tptp.path_weight BOUND_VARIABLE_5822 V)) (tptp.get1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_271 V))) (not (forall ((L tptp.list_vertex)) (or (not (tptp.path tptp.s L V)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 L))) 1)) (>= (+ (tptp.path_weight L V) (* (- 1) (tptp.path_weight BOUND_VARIABLE_5822 V))) 0)))) (not (forall ((U tptp.vertex) (L tptp.list_vertex)) (or (not (tptp.path tptp.s L U)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 L))) 1)) (not (tptp.mem2 (tptp.tuple22 U V) (tptp.diff2 tptp.edges SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272))) (>= (+ (tptp.path_weight L U) (tptp.weight U V) (* (- 1) (tptp.path_weight BOUND_VARIABLE_5822 V))) 0)))) (not (tptp.path tptp.s BOUND_VARIABLE_5822 V))))) (and (= tptp.infinite (tptp.get1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_271 V)) (or (not (tptp.path tptp.s BOUND_VARIABLE_5924 V)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 BOUND_VARIABLE_5924))) 1))) (or (not (tptp.mem2 (tptp.tuple22 BOUND_VARIABLE_5934 V) (tptp.diff2 tptp.edges SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272))) (not (tptp.path tptp.s BOUND_VARIABLE_5936 BOUND_VARIABLE_5934)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 BOUND_VARIABLE_5936))) 1))))))))) (let ((_let_49 (not (forall ((X tptp.lpvertexcm_vertexrp)) (or (not (tptp.mem2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_272)) (tptp.mem2 X tptp.edges)))))) (let ((_let_50 (and (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) _let_1)) (- 1)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (+ (- 1) _let_1)))))) (let ((_let_51 (and (not (>= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 2)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 1))))) (let ((_let_52 (or _let_51 _let_50 (not (forall ((V tptp.vertex) (BOUND_VARIABLE_5740 tptp.list_vertex) (BOUND_VARIABLE_5738 tptp.vertex) (BOUND_VARIABLE_5728 tptp.list_vertex)) (or (not (tptp.mem1 V tptp.vertices)) (not (forall ((BOUND_VARIABLE_5626 tptp.list_vertex)) (or (not (= (tptp.finite (tptp.path_weight BOUND_VARIABLE_5626 V)) (tptp.get1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_260 V))) (not (forall ((L tptp.list_vertex)) (or (not (tptp.path tptp.s L V)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 L))) 1)) (>= (+ (tptp.path_weight L V) (* (- 1) (tptp.path_weight BOUND_VARIABLE_5626 V))) 0)))) (not (forall ((U tptp.vertex) (L tptp.list_vertex)) (or (not (tptp.path tptp.s L U)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 L))) 1)) (not (tptp.mem2 (tptp.tuple22 U V) tptp.empty2)) (>= (+ (tptp.path_weight L U) (tptp.weight U V) (* (- 1) (tptp.path_weight BOUND_VARIABLE_5626 V))) 0)))) (not (tptp.path tptp.s BOUND_VARIABLE_5626 V))))) (and (= tptp.infinite (tptp.get1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_260 V)) (or (not (tptp.path tptp.s BOUND_VARIABLE_5728 V)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 BOUND_VARIABLE_5728))) 1))) (or (not (tptp.mem2 (tptp.tuple22 BOUND_VARIABLE_5738 V) tptp.empty2)) (not (tptp.path tptp.s BOUND_VARIABLE_5740 BOUND_VARIABLE_5738)) (not (>= (+ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_261 (* (- 1) (tptp.length1 BOUND_VARIABLE_5740))) 1))))))) _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_41 _let_39 _let_37 _let_33 _let_31 _let_29 _let_28 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tptp.uni)) (tptp.sort (tptp.list A) (tptp.cons_proj_2 A X))) (forall ((A tptp.ty) (U tptp.uni) (U1 tptp.uni)) (= (tptp.cons_proj_2 A (tptp.cons A U U1)) U1)) (forall ((A tptp.ty) (U tptp.uni)) (or (= U (tptp.nil A)) (= U (tptp.cons A (tptp.cons_proj_1 A U) (tptp.cons_proj_2 A U))))) (forall ((X tptp.list_vertex)) (tptp.sort (tptp.list tptp.vertex1) (tptp.t2tb3 X))) (forall ((I tptp.list_vertex)) (= (tptp.tb2t3 (tptp.t2tb3 I)) I)) (forall ((J tptp.uni)) (= (tptp.t2tb3 (tptp.tb2t3 J)) J)) (and (= (tptp.length1 (tptp.tb2t3 (tptp.nil tptp.vertex1))) 0) (forall ((X tptp.vertex) (X1 tptp.list_vertex)) (= (tptp.length1 (tptp.tb2t3 (tptp.cons tptp.vertex1 (tptp.t2tb X) (tptp.t2tb3 X1)))) (+ 1 (tptp.length1 X1))))) (forall ((A tptp.ty)) (and (= (tptp.length A (tptp.nil A)) 0) (forall ((X tptp.uni) (X1 tptp.uni)) (= (tptp.length A (tptp.cons A X X1)) (+ 1 (tptp.length A X1)))))) (forall ((L tptp.list_vertex)) (<= 0 (tptp.length1 L))) (forall ((A tptp.ty) (L tptp.uni)) (<= 0 (tptp.length A L))) (forall ((L tptp.list_vertex)) (= (= (tptp.length1 L) 0) (= L (tptp.tb2t3 (tptp.nil tptp.vertex1))))) (forall ((A tptp.ty) (L tptp.uni)) (= (= (tptp.length A L) 0) (= L (tptp.nil A)))) (forall ((X tptp.set_lpvertexcm_vertexrp)) (tptp.sort (tptp.set1 (tptp.tuple2 tptp.vertex1 tptp.vertex1)) (tptp.t2tb4 X))) (forall ((I tptp.set_lpvertexcm_vertexrp)) (= (tptp.tb2t4 (tptp.t2tb4 I)) I)) (forall ((J tptp.uni)) (=> (tptp.sort (tptp.set1 (tptp.tuple2 tptp.vertex1 tptp.vertex1)) J) (= (tptp.t2tb4 (tptp.tb2t4 J)) J))) (forall ((S1 tptp.set_lpvertexcm_vertexrp) (S2 tptp.set_lpvertexcm_vertexrp)) (= (tptp.infix_eqeq (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 S1) (tptp.t2tb4 S2)) (forall ((X tptp.lpvertexcm_vertexrp)) (= (tptp.mem2 X S1) (tptp.mem2 X S2))))) (forall ((X tptp.set_vertex)) (tptp.sort (tptp.set1 tptp.vertex1) (tptp.t2tb5 X))) (forall ((I tptp.set_vertex)) (= (tptp.tb2t5 (tptp.t2tb5 I)) I)) (forall ((J tptp.uni)) (=> (tptp.sort (tptp.set1 tptp.vertex1) J) (= (tptp.t2tb5 (tptp.tb2t5 J)) J))) (forall ((S1 tptp.set_vertex) (S2 tptp.set_vertex)) (= (tptp.infix_eqeq tptp.vertex1 (tptp.t2tb5 S1) (tptp.t2tb5 S2)) (forall ((X tptp.vertex)) (= (tptp.mem1 X S1) (tptp.mem1 X S2))))) (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.sort 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.set1 A))) (=> (tptp.sort _let_1 S1) (=> (tptp.sort _let_1 S2) (=> (tptp.infix_eqeq A S1 S2) (= S1 S2)))))) (forall ((S1 tptp.set_lpvertexcm_vertexrp) (S2 tptp.set_lpvertexcm_vertexrp)) (= (tptp.subset (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 S1) (tptp.t2tb4 S2)) (forall ((X tptp.lpvertexcm_vertexrp)) (=> (tptp.mem2 X S1) (tptp.mem2 X S2))))) (forall ((S1 tptp.set_vertex) (S2 tptp.set_vertex)) (= (tptp.subset tptp.vertex1 (tptp.t2tb5 S1) (tptp.t2tb5 S2)) (forall ((X tptp.vertex)) (=> (tptp.mem1 X S1) (tptp.mem1 X 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.sort 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.sort (tptp.set1 A) (tptp.empty A))) (forall ((S tptp.set_lpvertexcm_vertexrp)) (= (tptp.is_empty (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 S)) (forall ((X tptp.lpvertexcm_vertexrp)) (not (tptp.mem2 X S))))) (forall ((S tptp.set_vertex)) (= (tptp.is_empty tptp.vertex1 (tptp.t2tb5 S)) (forall ((X tptp.vertex)) (not (tptp.mem1 X S))))) (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.sort A X) (not (tptp.mem A X S)))) _let_1)))) (tptp.is_empty (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 tptp.empty2)) (tptp.is_empty tptp.vertex1 (tptp.t2tb5 tptp.empty1)) (forall ((A tptp.ty)) (tptp.is_empty A (tptp.empty A))) (forall ((X tptp.lpvertexcm_vertexrp)) (= (tptp.mem2 X tptp.empty2) false)) (forall ((X tptp.vertex)) (= (tptp.mem1 X tptp.empty1) false)) (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.sort (tptp.set1 A) (tptp.add A X X1))) _let_8 (forall ((X tptp.vertex) (Y tptp.vertex) (S tptp.set_vertex)) (= (tptp.mem1 X (tptp.add1 Y S)) (or (= X Y) (tptp.mem1 X S)))) (forall ((A tptp.ty) (X tptp.uni) (Y tptp.uni)) (=> (tptp.sort A X) (=> (tptp.sort 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.sort (tptp.set1 A) (tptp.remove A X X1))) _let_7 (forall ((X tptp.vertex) (Y tptp.vertex) (S tptp.set_vertex)) (= (tptp.mem1 X (tptp.remove1 Y S)) (and (not (= X Y)) (tptp.mem1 X S)))) (forall ((A tptp.ty) (X tptp.uni) (Y tptp.uni) (S tptp.uni)) (=> (tptp.sort A X) (=> (tptp.sort A Y) (= (tptp.mem A X (tptp.remove A Y S)) (and (not (= X Y)) (tptp.mem A X S)))))) (forall ((X tptp.lpvertexcm_vertexrp) (S tptp.set_lpvertexcm_vertexrp)) (=> (tptp.mem2 X S) (= (tptp.add2 X (tptp.remove2 X S)) S))) (forall ((X tptp.vertex) (S tptp.set_vertex)) (=> (tptp.mem1 X S) (= (tptp.add1 X (tptp.remove1 X S)) S))) (forall ((A tptp.ty) (X tptp.uni) (S tptp.uni)) (=> (tptp.sort (tptp.set1 A) S) (=> (tptp.mem A X S) (= (tptp.add A X (tptp.remove A X S)) S)))) (forall ((X tptp.lpvertexcm_vertexrp) (S tptp.set_lpvertexcm_vertexrp)) (= (tptp.remove2 X (tptp.add2 X S)) (tptp.remove2 X S))) (forall ((X tptp.vertex) (S tptp.set_vertex)) (= (tptp.remove1 X (tptp.add1 X S)) (tptp.remove1 X 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 ((X tptp.lpvertexcm_vertexrp) (S tptp.set_lpvertexcm_vertexrp)) (tptp.subset (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 (tptp.remove2 X S)) (tptp.t2tb4 S))) (forall ((X tptp.vertex) (S tptp.set_vertex)) (tptp.subset tptp.vertex1 (tptp.t2tb5 (tptp.remove1 X S)) (tptp.t2tb5 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.sort (tptp.set1 A) (tptp.union A X X1))) (forall ((S1 tptp.set_lpvertexcm_vertexrp) (S2 tptp.set_lpvertexcm_vertexrp) (X tptp.lpvertexcm_vertexrp)) (= (tptp.mem2 X (tptp.tb2t4 (tptp.union (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 S1) (tptp.t2tb4 S2)))) (or (tptp.mem2 X S1) (tptp.mem2 X S2)))) (forall ((S1 tptp.set_vertex) (S2 tptp.set_vertex) (X tptp.vertex)) (= (tptp.mem1 X (tptp.tb2t5 (tptp.union tptp.vertex1 (tptp.t2tb5 S1) (tptp.t2tb5 S2)))) (or (tptp.mem1 X S1) (tptp.mem1 X S2)))) (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.sort (tptp.set1 A) (tptp.inter A X X1))) (forall ((S1 tptp.set_lpvertexcm_vertexrp) (S2 tptp.set_lpvertexcm_vertexrp) (X tptp.lpvertexcm_vertexrp)) (= (tptp.mem2 X (tptp.tb2t4 (tptp.inter (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 S1) (tptp.t2tb4 S2)))) (and (tptp.mem2 X S1) (tptp.mem2 X S2)))) (forall ((S1 tptp.set_vertex) (S2 tptp.set_vertex) (X tptp.vertex)) (= (tptp.mem1 X (tptp.tb2t5 (tptp.inter tptp.vertex1 (tptp.t2tb5 S1) (tptp.t2tb5 S2)))) (and (tptp.mem1 X S1) (tptp.mem1 X S2)))) (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.sort (tptp.set1 A) (tptp.diff A X X1))) _let_6 (forall ((S1 tptp.set_vertex) (S2 tptp.set_vertex) (X tptp.vertex)) (= (tptp.mem1 X (tptp.diff1 S1 S2)) (and (tptp.mem1 X S1) (not (tptp.mem1 X S2))))) (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 ((S1 tptp.set_lpvertexcm_vertexrp) (S2 tptp.set_lpvertexcm_vertexrp)) (tptp.subset (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 (tptp.diff2 S1 S2)) (tptp.t2tb4 S1))) (forall ((S1 tptp.set_vertex) (S2 tptp.set_vertex)) (tptp.subset tptp.vertex1 (tptp.t2tb5 (tptp.diff1 S1 S2)) (tptp.t2tb5 S1))) (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.sort A (tptp.choose A X))) (forall ((X tptp.lpvertexcm_vertexrp)) (tptp.sort (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb6 X))) (forall ((I tptp.lpvertexcm_vertexrp)) (= (tptp.tb2t6 (tptp.t2tb6 I)) I)) (forall ((J tptp.uni)) (=> (tptp.sort (tptp.tuple2 tptp.vertex1 tptp.vertex1) J) (= (tptp.t2tb6 (tptp.tb2t6 J)) J))) (forall ((S tptp.set_lpvertexcm_vertexrp)) (let ((_let_1 (tptp.t2tb4 S))) (let ((_let_2 (tptp.tuple2 tptp.vertex1 tptp.vertex1))) (=> (not (tptp.is_empty _let_2 _let_1)) (tptp.mem2 (tptp.tb2t6 (tptp.choose _let_2 _let_1)) S))))) (forall ((S tptp.set_vertex)) (let ((_let_1 (tptp.t2tb5 S))) (=> (not (tptp.is_empty tptp.vertex1 _let_1)) (tptp.mem1 (tptp.tb2t (tptp.choose tptp.vertex1 _let_1)) S)))) (forall ((A tptp.ty) (S tptp.uni)) (=> (not (tptp.is_empty A S)) (tptp.mem A (tptp.choose A S) S))) (forall ((S tptp.set_lpvertexcm_vertexrp)) (<= 0 (tptp.cardinal2 S))) (forall ((S tptp.set_vertex)) (<= 0 (tptp.cardinal1 S))) (forall ((A tptp.ty) (S tptp.uni)) (<= 0 (tptp.cardinal A S))) (forall ((S tptp.set_lpvertexcm_vertexrp)) (= (= (tptp.cardinal2 S) 0) (tptp.is_empty (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 S)))) (forall ((S tptp.set_vertex)) (= (= (tptp.cardinal1 S) 0) (tptp.is_empty tptp.vertex1 (tptp.t2tb5 S)))) (forall ((A tptp.ty) (S tptp.uni)) (= (= (tptp.cardinal A S) 0) (tptp.is_empty A S))) (forall ((X tptp.lpvertexcm_vertexrp) (S tptp.set_lpvertexcm_vertexrp)) (=> (not (tptp.mem2 X S)) (= (tptp.cardinal2 (tptp.add2 X S)) (+ 1 (tptp.cardinal2 S))))) (forall ((X tptp.vertex) (S tptp.set_vertex)) (=> (not (tptp.mem1 X S)) (= (tptp.cardinal1 (tptp.add1 X S)) (+ 1 (tptp.cardinal1 S))))) (forall ((A tptp.ty) (X tptp.uni) (S tptp.uni)) (=> (not (tptp.mem A X S)) (= (tptp.cardinal A (tptp.add A X S)) (+ 1 (tptp.cardinal A S))))) (forall ((X tptp.lpvertexcm_vertexrp) (S tptp.set_lpvertexcm_vertexrp)) (=> (tptp.mem2 X S) (= (tptp.cardinal2 S) (+ 1 (tptp.cardinal2 (tptp.remove2 X S)))))) (forall ((X tptp.vertex) (S tptp.set_vertex)) (=> (tptp.mem1 X S) (= (tptp.cardinal1 S) (+ 1 (tptp.cardinal1 (tptp.remove1 X S)))))) (forall ((A tptp.ty) (X tptp.uni) (S tptp.uni)) (=> (tptp.mem A X S) (= (tptp.cardinal A S) (+ 1 (tptp.cardinal A (tptp.remove A X S)))))) (forall ((S1 tptp.set_lpvertexcm_vertexrp) (S2 tptp.set_lpvertexcm_vertexrp)) (=> (tptp.subset (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 S1) (tptp.t2tb4 S2)) (<= (tptp.cardinal2 S1) (tptp.cardinal2 S2)))) (forall ((S1 tptp.set_vertex) (S2 tptp.set_vertex)) (=> (tptp.subset tptp.vertex1 (tptp.t2tb5 S1) (tptp.t2tb5 S2)) (<= (tptp.cardinal1 S1) (tptp.cardinal1 S2)))) (forall ((A tptp.ty) (S1 tptp.uni) (S2 tptp.uni)) (=> (tptp.subset A S1 S2) (<= (tptp.cardinal A S1) (tptp.cardinal A S2)))) (forall ((S tptp.set_lpvertexcm_vertexrp)) (=> (= (tptp.cardinal2 S) 1) (forall ((X tptp.lpvertexcm_vertexrp)) (=> (tptp.mem2 X S) (= X (tptp.tb2t6 (tptp.choose (tptp.tuple2 tptp.vertex1 tptp.vertex1) (tptp.t2tb4 S)))))))) (forall ((S tptp.set_vertex)) (=> (= (tptp.cardinal1 S) 1) (forall ((X tptp.vertex)) (=> (tptp.mem1 X S) (= X (tptp.tb2t (tptp.choose tptp.vertex1 (tptp.t2tb5 S)))))))) (forall ((A tptp.ty) (S tptp.uni)) (=> (= (tptp.cardinal A S) 1) (forall ((X tptp.uni)) (=> (tptp.sort A X) (=> (tptp.mem A X S) (= X (tptp.choose A S))))))) (forall ((A tptp.ty) (A1 tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort (tptp.tuple2 A1 A) (tptp.tuple21 A1 A X X1))) (forall ((A tptp.ty) (A1 tptp.ty) (X tptp.uni)) (tptp.sort A1 (tptp.tuple2_proj_1 A1 A X))) (forall ((U tptp.vertex) (U1 tptp.vertex)) (= (tptp.tb2t (tptp.tuple2_proj_1 tptp.vertex1 tptp.vertex1 (tptp.t2tb6 (tptp.tuple22 U U1)))) U)) (forall ((A tptp.ty) (A1 tptp.ty) (U tptp.uni) (U1 tptp.uni)) (=> (tptp.sort A1 U) (= (tptp.tuple2_proj_1 A1 A (tptp.tuple21 A1 A U U1)) U))) (forall ((A tptp.ty) (A1 tptp.ty) (X tptp.uni)) (tptp.sort A (tptp.tuple2_proj_2 A1 A X))) (forall ((U tptp.vertex) (U1 tptp.vertex)) (= (tptp.tb2t (tptp.tuple2_proj_2 tptp.vertex1 tptp.vertex1 (tptp.t2tb6 (tptp.tuple22 U U1)))) U1)) (forall ((A tptp.ty) (A1 tptp.ty) (U tptp.uni) (U1 tptp.uni)) (=> (tptp.sort A U1) (= (tptp.tuple2_proj_2 A1 A (tptp.tuple21 A1 A U U1)) U1))) (forall ((U tptp.lpvertexcm_vertexrp)) (let ((_let_1 (tptp.t2tb6 U))) (= U (tptp.tuple22 (tptp.tb2t (tptp.tuple2_proj_1 tptp.vertex1 tptp.vertex1 _let_1)) (tptp.tb2t (tptp.tuple2_proj_2 tptp.vertex1 tptp.vertex1 _let_1)))))) (forall ((A tptp.ty) (A1 tptp.ty) (U tptp.uni)) (=> (tptp.sort (tptp.tuple2 A1 A) U) (= U (tptp.tuple21 A1 A (tptp.tuple2_proj_1 A1 A U) (tptp.tuple2_proj_2 A1 A U))))) (forall ((X tptp.vertex) (Y tptp.vertex)) (= (tptp.edge X Y) (tptp.mem2 (tptp.tuple22 X Y) tptp.edges))) (forall ((X tptp.vertex) (Y tptp.vertex)) (=> (tptp.mem2 (tptp.tuple22 X Y) tptp.edges) (and (tptp.mem1 X tptp.vertices) (tptp.mem1 Y tptp.vertices)))) (tptp.mem1 tptp.s tptp.vertices) (< 0 _let_1) (forall ((A tptp.ty) (X tptp.uni) (X1 tptp.uni)) (tptp.sort (tptp.list A) (tptp.infix_plpl A X X1))) (forall ((A tptp.ty) (L2 tptp.uni)) (and (= (tptp.infix_plpl A (tptp.nil A) L2) L2) (forall ((X tptp.uni) (X1 tptp.uni)) (= (tptp.infix_plpl A (tptp.cons A X X1) L2) (tptp.cons A X (tptp.infix_plpl A X1 L2)))))) (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni) (L3 tptp.uni)) (= (tptp.infix_plpl A L1 (tptp.infix_plpl A L2 L3)) (tptp.infix_plpl A (tptp.infix_plpl A L1 L2) L3))) (forall ((A tptp.ty) (L tptp.uni)) (= (tptp.infix_plpl A L (tptp.nil A)) L)) (forall ((L1 tptp.list_vertex) (L2 tptp.list_vertex)) (= (tptp.length1 (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.t2tb3 L2)))) (+ (tptp.length1 L1) (tptp.length1 L2)))) (forall ((A tptp.ty) (L1 tptp.uni) (L2 tptp.uni)) (= (tptp.length A (tptp.infix_plpl A L1 L2)) (+ (tptp.length A L1) (tptp.length A L2)))) (forall ((A tptp.ty) (X tptp.uni)) (=> (tptp.sort A X) (and (not (tptp.mem3 A X (tptp.nil A))) (forall ((X1 tptp.uni) (X2 tptp.uni)) (=> (tptp.sort A X1) (= (tptp.mem3 A X (tptp.cons A X1 X2)) (or (= X X1) (tptp.mem3 A X X2)))))))) (forall ((A tptp.ty) (X tptp.uni) (L1 tptp.uni) (L2 tptp.uni)) (= (tptp.mem3 A X (tptp.infix_plpl A L1 L2)) (or (tptp.mem3 A X L1) (tptp.mem3 A X L2)))) (forall ((A tptp.ty) (X tptp.uni) (L tptp.uni)) (=> (tptp.mem3 A X L) (exists ((L1 tptp.uni) (L2 tptp.uni)) (let ((_let_1 (tptp.list A))) (and (tptp.sort _let_1 L1) (tptp.sort _let_1 L2) (= L (tptp.infix_plpl A L1 (tptp.cons A X L2)))))))) (forall ((X tptp.vertex)) (tptp.path X (tptp.tb2t3 (tptp.nil tptp.vertex1)) X)) (forall ((X tptp.vertex) (Y tptp.vertex) (Z tptp.vertex) (L tptp.list_vertex)) (=> (tptp.edge X Y) (=> (tptp.path Y L Z) (tptp.path X (tptp.tb2t3 (tptp.cons tptp.vertex1 (tptp.t2tb X) (tptp.t2tb3 L))) Z)))) (forall ((Z tptp.vertex) (Z1 tptp.list_vertex) (Z2 tptp.vertex)) (=> (tptp.path Z Z1 Z2) (or (exists ((X tptp.vertex)) (and (= Z X) (= Z1 (tptp.tb2t3 (tptp.nil tptp.vertex1))) (= Z2 X))) (exists ((X tptp.vertex) (Y tptp.vertex) (Z3 tptp.vertex) (L tptp.list_vertex)) (and (tptp.edge X Y) (tptp.path Y L Z3) (= Z X) (= Z1 (tptp.tb2t3 (tptp.cons tptp.vertex1 (tptp.t2tb X) (tptp.t2tb3 L)))) (= Z2 Z3)))))) (forall ((X tptp.vertex) (Y tptp.vertex) (Z tptp.vertex) (L tptp.list_vertex)) (=> (tptp.path X L Y) (=> (tptp.edge Y Z) (tptp.path X (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L) (tptp.cons tptp.vertex1 (tptp.t2tb Y) (tptp.nil tptp.vertex1)))) Z)))) (forall ((X tptp.vertex) (Z tptp.vertex) (L tptp.list_vertex)) (=> (tptp.path X L Z) (or (and (= X Z) (= L (tptp.tb2t3 (tptp.nil tptp.vertex1)))) (exists ((Y tptp.vertex) (Lqt tptp.list_vertex)) (and (tptp.path X Lqt Y) (tptp.edge Y Z) (= L (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 Lqt) (tptp.cons tptp.vertex1 (tptp.t2tb Y) (tptp.nil tptp.vertex1)))))))))) (forall ((X tptp.vertex) (Y tptp.vertex) (Z tptp.vertex) (L1 tptp.list_vertex) (L2 tptp.list_vertex)) (=> (tptp.path X L1 Y) (=> (tptp.path Y L2 Z) (tptp.path X (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.t2tb3 L2))) Z)))) (forall ((X tptp.vertex) (Y tptp.vertex)) (=> (tptp.path X (tptp.tb2t3 (tptp.nil tptp.vertex1)) Y) (= X Y))) (forall ((X tptp.vertex) (Y tptp.vertex) (Z tptp.vertex) (L1 tptp.list_vertex) (L2 tptp.list_vertex)) (let ((_let_1 (tptp.cons tptp.vertex1 (tptp.t2tb Y) (tptp.t2tb3 L2)))) (=> (tptp.path X (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) _let_1)) Z) (and (tptp.path X L1 Y) (tptp.path Y (tptp.tb2t3 _let_1) Z))))) (forall ((Dst tptp.vertex)) (and (= (tptp.path_weight (tptp.tb2t3 (tptp.nil tptp.vertex1)) Dst) 0) (forall ((X tptp.vertex) (X1 tptp.list_vertex)) (and (=> (= X1 (tptp.tb2t3 (tptp.nil tptp.vertex1))) (= (tptp.path_weight (tptp.tb2t3 (tptp.cons tptp.vertex1 (tptp.t2tb X) (tptp.t2tb3 X1))) Dst) (tptp.weight X Dst))) (forall ((X2 tptp.vertex) (X3 tptp.list_vertex)) (=> (= X1 (tptp.tb2t3 (tptp.cons tptp.vertex1 (tptp.t2tb X2) (tptp.t2tb3 X3)))) (= (tptp.path_weight (tptp.tb2t3 (tptp.cons tptp.vertex1 (tptp.t2tb X) (tptp.t2tb3 X1))) Dst) (+ (tptp.weight X X2) (tptp.path_weight X1 Dst))))))))) (forall ((X tptp.vertex) (Y tptp.vertex) (L tptp.list_vertex)) (= (tptp.path_weight (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L) (tptp.cons tptp.vertex1 (tptp.t2tb X) (tptp.nil tptp.vertex1)))) Y) (+ (tptp.path_weight L X) (tptp.weight X Y)))) (forall ((Y tptp.vertex) (Z tptp.vertex) (L1 tptp.list_vertex) (L2 tptp.list_vertex)) (let ((_let_1 (tptp.cons tptp.vertex1 (tptp.t2tb Y) (tptp.t2tb3 L2)))) (= (tptp.path_weight (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) _let_1)) Z) (+ (tptp.path_weight L1 Y) (tptp.path_weight (tptp.tb2t3 _let_1) Z))))) (forall ((V1 tptp.vertex) (V2 tptp.vertex) (L tptp.list_vertex)) (=> (tptp.mem1 V1 tptp.vertices) (=> (tptp.path V1 L V2) (tptp.mem1 V2 tptp.vertices)))) (forall ((S tptp.set_vertex)) (= (tptp.pigeon_set S) (forall ((L tptp.list_vertex)) (=> (forall ((E tptp.vertex)) (=> (tptp.mem3 tptp.vertex1 (tptp.t2tb E) (tptp.t2tb3 L)) (tptp.mem1 E S))) (=> (< (tptp.cardinal1 S) (tptp.length1 L)) (exists ((E tptp.vertex) (L1 tptp.list_vertex) (L2 tptp.list_vertex) (L3 tptp.list_vertex)) (let ((_let_1 (tptp.t2tb E))) (= L (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.cons tptp.vertex1 _let_1 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L2) (tptp.cons tptp.vertex1 _let_1 (tptp.t2tb3 L3)))))))))))))) (=> (forall ((S tptp.set_vertex)) (=> (tptp.is_empty tptp.vertex1 (tptp.t2tb5 S)) (tptp.pigeon_set S))) (=> (forall ((S tptp.set_vertex)) (=> (tptp.pigeon_set S) (forall ((T tptp.vertex)) (=> (not (tptp.mem1 T S)) (tptp.pigeon_set (tptp.add1 T S)))))) (forall ((S tptp.set_vertex)) (tptp.pigeon_set S)))) (forall ((S tptp.set_vertex) (L tptp.list_vertex)) (=> (= (tptp.length1 L) (tptp.cardinal1 S)) (=> (forall ((E tptp.vertex)) (=> (tptp.mem3 tptp.vertex1 (tptp.t2tb E) (tptp.t2tb3 L)) (tptp.mem1 E S))) (or (exists ((E tptp.vertex) (L1 tptp.list_vertex) (L2 tptp.list_vertex) (L3 tptp.list_vertex)) (let ((_let_1 (tptp.t2tb E))) (= L (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.cons tptp.vertex1 _let_1 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L2) (tptp.cons tptp.vertex1 _let_1 (tptp.t2tb3 L3))))))))) (forall ((E tptp.vertex)) (=> (tptp.mem1 E S) (tptp.mem3 tptp.vertex1 (tptp.t2tb E) (tptp.t2tb3 L)))))))) (tptp.pigeon_set tptp.empty1) (forall ((S tptp.set_vertex)) (=> (tptp.pigeon_set S) (forall ((T tptp.vertex)) (tptp.pigeon_set (tptp.add1 T S))))) (forall ((S tptp.set_vertex)) (tptp.pigeon_set S)) (forall ((S tptp.set_vertex) (L tptp.list_vertex)) (=> (forall ((E tptp.vertex)) (=> (tptp.mem3 tptp.vertex1 (tptp.t2tb E) (tptp.t2tb3 L)) (tptp.mem1 E S))) (=> (< (tptp.cardinal1 S) (tptp.length1 L)) (exists ((E tptp.vertex) (L1 tptp.list_vertex) (L2 tptp.list_vertex) (L3 tptp.list_vertex)) (let ((_let_1 (tptp.t2tb E))) (= L (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.cons tptp.vertex1 _let_1 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L2) (tptp.cons tptp.vertex1 _let_1 (tptp.t2tb3 L3)))))))))))) (forall ((L tptp.list_vertex) (V tptp.vertex)) (=> (tptp.path tptp.s L V) (=> (not (= L (tptp.tb2t3 (tptp.nil tptp.vertex1)))) (forall ((V1 tptp.vertex)) (=> (tptp.mem3 tptp.vertex1 (tptp.t2tb V1) (tptp.cons tptp.vertex1 (tptp.t2tb V) (tptp.t2tb3 L))) (tptp.mem1 V1 tptp.vertices)))))) (forall ((L tptp.list_vertex) (V tptp.vertex)) (=> (forall ((V1 tptp.vertex)) (=> (tptp.mem3 tptp.vertex1 (tptp.t2tb V1) (tptp.cons tptp.vertex1 (tptp.t2tb V) (tptp.t2tb3 L))) (tptp.mem1 V1 tptp.vertices))) (=> (< (tptp.cardinal1 tptp.vertices) (tptp.length1 (tptp.tb2t3 (tptp.cons tptp.vertex1 (tptp.t2tb V) (tptp.t2tb3 L))))) (exists ((E tptp.vertex) (L1 tptp.list_vertex) (L2 tptp.list_vertex) (L3 tptp.list_vertex)) (let ((_let_1 (tptp.t2tb E))) (= (tptp.tb2t3 (tptp.cons tptp.vertex1 (tptp.t2tb V) (tptp.t2tb3 L))) (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.cons tptp.vertex1 _let_1 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L2) (tptp.cons tptp.vertex1 _let_1 (tptp.t2tb3 L3)))))))))))) (forall ((L tptp.list_vertex) (V tptp.vertex)) (=> (exists ((E tptp.vertex) (L1 tptp.list_vertex) (L2 tptp.list_vertex) (L3 tptp.list_vertex)) (let ((_let_1 (tptp.t2tb E))) (= (tptp.tb2t3 (tptp.cons tptp.vertex1 (tptp.t2tb V) (tptp.t2tb3 L))) (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.cons tptp.vertex1 _let_1 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L2) (tptp.cons tptp.vertex1 _let_1 (tptp.t2tb3 L3))))))))) (or (exists ((L1 tptp.list_vertex) (L2 tptp.list_vertex)) (= L (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.cons tptp.vertex1 (tptp.t2tb V) (tptp.t2tb3 L2)))))) (exists ((N tptp.vertex) (L1 tptp.list_vertex) (L2 tptp.list_vertex) (L3 tptp.list_vertex)) (let ((_let_1 (tptp.t2tb N))) (= L (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.cons tptp.vertex1 _let_1 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L2) (tptp.cons tptp.vertex1 _let_1 (tptp.t2tb3 L3)))))))))))) (forall ((L tptp.list_vertex) (V tptp.vertex)) (=> (tptp.path tptp.s L V) (=> (<= (tptp.cardinal1 tptp.vertices) (tptp.length1 L)) (or (exists ((L1 tptp.list_vertex) (L2 tptp.list_vertex)) (= L (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.cons tptp.vertex1 (tptp.t2tb V) (tptp.t2tb3 L2)))))) (exists ((N tptp.vertex) (L1 tptp.list_vertex) (L2 tptp.list_vertex) (L3 tptp.list_vertex)) (let ((_let_1 (tptp.t2tb N))) (= L (tptp.tb2t3 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L1) (tptp.cons tptp.vertex1 _let_1 (tptp.infix_plpl tptp.vertex1 (tptp.t2tb3 L2) (tptp.cons tptp.vertex1 _let_1 (tptp.t2tb3 L3))))))))))))) (forall ((V tptp.vertex) (L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (exists ((Lqt tptp.list_vertex)) (and (tptp.path tptp.s Lqt V) (< (tptp.length1 Lqt) (tptp.cardinal1 tptp.vertices)))))) (forall ((V tptp.vertex)) (= (tptp.negative_cycle V) (and (tptp.mem1 V tptp.vertices) (exists ((L1 tptp.list_vertex)) (tptp.path tptp.s L1 V)) (exists ((L2 tptp.list_vertex)) (and (tptp.path V L2 V) (< (tptp.path_weight L2 V) 0)))))) (forall ((V tptp.vertex) (N Int)) (=> (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (=> (< (tptp.length1 L) (tptp.cardinal1 tptp.vertices)) (<= N (tptp.path_weight L V))))) (=> (exists ((L tptp.list_vertex)) (and (tptp.path tptp.s L V) (< (tptp.path_weight L V) N))) (exists ((U tptp.vertex)) (tptp.negative_cycle U))))) (forall ((A tptp.ty) (X tptp.t) (X1 tptp.uni) (X2 tptp.uni)) (tptp.sort A (tptp.match_t A X X1 X2))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni) (U Int)) (=> (tptp.sort A Z) (= (tptp.match_t A (tptp.finite U) Z Z1) Z))) (forall ((A tptp.ty) (Z tptp.uni) (Z1 tptp.uni)) (=> (tptp.sort A Z1) (= (tptp.match_t A tptp.infinite Z Z1) Z1))) _let_5 _let_4 (forall ((U tptp.t)) (or (= U (tptp.finite (tptp.finite_proj_1 U))) (= U tptp.infinite))) (forall ((Y tptp.t)) (and (forall ((X Int)) (and (forall ((Y1 Int)) (= (tptp.add3 (tptp.finite X) (tptp.finite Y1)) (tptp.finite (+ X Y1)))) (= (tptp.add3 (tptp.finite X) tptp.infinite) tptp.infinite))) (= (tptp.add3 tptp.infinite Y) tptp.infinite))) (forall ((Y tptp.t)) (and (forall ((X Int)) (and (forall ((Y1 Int)) (= (tptp.lt (tptp.finite X) (tptp.finite Y1)) (< X Y1))) (tptp.lt (tptp.finite X) tptp.infinite))) (not (tptp.lt tptp.infinite Y)))) (forall ((X tptp.t) (Y tptp.t)) (= (tptp.le X Y) (or (tptp.lt X Y) (= X Y)))) (forall ((X tptp.t)) (tptp.le X X)) (forall ((X tptp.t) (Y tptp.t) (Z tptp.t)) (=> (tptp.le X Y) (=> (tptp.le Y Z) (tptp.le X Z)))) (forall ((X tptp.t) (Y tptp.t)) (=> (tptp.le X Y) (=> (tptp.le Y X) (= X Y)))) (forall ((X tptp.t) (Y tptp.t)) (or (tptp.le X Y) (tptp.le Y X))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort (tptp.ref A) (tptp.mk_ref A X))) (forall ((A tptp.ty) (X tptp.uni)) (tptp.sort A (tptp.contents A X))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort A U) (= (tptp.contents A (tptp.mk_ref A U)) U))) (forall ((A tptp.ty) (U tptp.uni)) (=> (tptp.sort (tptp.ref A) U) (= U (tptp.mk_ref A (tptp.contents A U))))) (forall ((M tptp.map_vertex_t19) (Pass Int) (Via tptp.set_lpvertexcm_vertexrp)) (let ((_let_1 (tptp.inv1 M Pass Via))) (and (=> _let_1 (forall ((V tptp.vertex)) (=> (tptp.mem1 V tptp.vertices) (and (forall ((X Int)) (=> (= (tptp.get1 M V) (tptp.finite X)) (and (exists ((L tptp.list_vertex)) (and (tptp.path tptp.s L V) (= (tptp.path_weight L V) X))) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (=> (< (tptp.length1 L) Pass) (<= X (tptp.path_weight L V))))) (forall ((U tptp.vertex) (L tptp.list_vertex)) (=> (tptp.path tptp.s L U) (=> (< (tptp.length1 L) Pass) (=> (tptp.mem2 (tptp.tuple22 U V) Via) (<= X (+ (tptp.path_weight L U) (tptp.weight U V)))))))))) (=> (= (tptp.get1 M V) tptp.infinite) (and (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (<= Pass (tptp.length1 L)))) (forall ((U tptp.vertex)) (=> (tptp.mem2 (tptp.tuple22 U V) Via) (forall ((Lu tptp.list_vertex)) (=> (tptp.path tptp.s Lu U) (<= Pass (tptp.length1 Lu)))))))))))) (=> (forall ((V tptp.vertex)) (=> (tptp.mem1 V tptp.vertices) (or (exists ((X Int)) (and (= (tptp.get1 M V) (tptp.finite X)) (exists ((L tptp.list_vertex)) (and (tptp.path tptp.s L V) (= (tptp.path_weight L V) X))) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (=> (< (tptp.length1 L) Pass) (<= X (tptp.path_weight L V))))) (forall ((U tptp.vertex) (L tptp.list_vertex)) (=> (tptp.path tptp.s L U) (=> (< (tptp.length1 L) Pass) (=> (tptp.mem2 (tptp.tuple22 U V) Via) (<= X (+ (tptp.path_weight L U) (tptp.weight U V))))))))) (and (= (tptp.get1 M V) tptp.infinite) (forall ((L tptp.list_vertex)) (=> (tptp.path tptp.s L V) (<= Pass (tptp.length1 L)))) (forall ((U tptp.vertex)) (=> (tptp.mem2 (tptp.tuple22 U V) Via) (forall ((Lu tptp.list_vertex)) (=> (tptp.path tptp.s Lu U) (<= Pass (tptp.length1 Lu)))))))))) _let_1)))) (forall ((M tptp.map_vertex_t19) (Via tptp.set_lpvertexcm_vertexrp)) (= (tptp.inv2 M Via) (forall ((U tptp.vertex) (V tptp.vertex)) (=> (tptp.mem2 (tptp.tuple22 U V) Via) (tptp.le (tptp.get1 M V) (tptp.add3 (tptp.get1 M U) (tptp.finite (tptp.weight U V)))))))) (forall ((M tptp.map_vertex_t19)) (=> (tptp.inv1 M (tptp.cardinal1 tptp.vertices) tptp.empty2) (=> (tptp.inv2 M tptp.edges) (forall ((V tptp.vertex)) (not (tptp.negative_cycle V)))))) _let_3 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 58.15/58.38 )
% 58.15/58.38 % SZS output end Proof for SWW577_2
% 58.15/58.38 % cvc5---1.0.5 exiting
% 58.15/58.38 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------