TSTP Solution File: GRA007+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRA007+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 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 : Thu Aug 31 00:00:31 EDT 2023
% Result : Theorem 31.14s 31.34s
% Output : Proof 31.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRA007+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.08/0.15 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun Aug 27 03:16:09 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.22/0.51 %----Proving TF0_NAR, FOF, or CNF
% 31.14/31.34 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8xOaXlwvUm/cvc5---1.0.5_18592.p...
% 31.14/31.34 ------- get file name : TPTP file name is GRA007+1
% 31.14/31.34 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_18592.smt2...
% 31.14/31.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.14/31.34 --- Run --no-e-matching --full-saturate-quant at 5...
% 31.14/31.34 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.14/31.34 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.14/31.34 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.14/31.34 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.14/31.34 % SZS status Theorem for GRA007+1
% 31.14/31.34 % SZS output start Proof for GRA007+1
% 31.14/31.34 (
% 31.14/31.34 (let ((_let_1 (not (=> tptp.complete (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (=> (and (tptp.shortest_path V1 V2 P) (tptp.precedes E1 E2 P)) (exists ((E3 $$unsorted)) (and (tptp.edge E3) (= (tptp.tail_of E3) (tptp.head_of E2)) (= (tptp.head_of E3) (tptp.tail_of E1)))))))))) (let ((_let_2 (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (=> (and (tptp.shortest_path V1 V2 P) (tptp.precedes E1 E2 P)) (and (not (exists ((E3 $$unsorted)) (and (= (tptp.tail_of E3) (tptp.tail_of E1)) (= (tptp.head_of E3) (tptp.head_of E2))))) (not (tptp.precedes E2 E1 P))))))) (let ((_let_3 (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (tptp.shortest_path V1 V2 SP) (and (tptp.path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (=> (tptp.path V1 V2 P) (tptp.less_or_equal (tptp.length_of SP) (tptp.length_of P))))))))) (let ((_let_4 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.path V1 V2 P) (forall ((E1 $$unsorted) (E2 $$unsorted)) (=> (tptp.precedes E1 E2 P) (and (tptp.on_path E1 P) (tptp.on_path E2 P) (xor (tptp.sequential E1 E2) (exists ((E3 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))))))))) (let ((_let_5 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (tptp.path V1 V2 P) (forall ((E1 $$unsorted) (E2 $$unsorted)) (=> (and (tptp.on_path E1 P) (tptp.on_path E2 P) (or (tptp.sequential E1 E2) (exists ((E3 $$unsorted)) (and (tptp.sequential E1 E3) (tptp.precedes E3 E2 P))))) (tptp.precedes E1 E2 P))))))) (let ((_let_6 (forall ((E1 $$unsorted) (E2 $$unsorted)) (= (tptp.sequential E1 E2) (and (tptp.edge E1) (tptp.edge E2) (not (= E1 E2)) (= (tptp.head_of E1) (tptp.tail_of E2))))))) (let ((_let_7 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (E $$unsorted)) (=> (and (tptp.path V1 V2 P) (tptp.on_path E P)) (and (tptp.edge E) (tptp.in_path (tptp.head_of E) P) (tptp.in_path (tptp.tail_of E) P)))))) (let ((_let_8 (=> tptp.complete (forall ((V1 $$unsorted) (V2 $$unsorted)) (=> (and (tptp.vertex V1) (tptp.vertex V2) (not (= V1 V2))) (exists ((E $$unsorted)) (let ((_let_1 (tptp.tail_of E))) (let ((_let_2 (tptp.head_of E))) (and (tptp.edge E) (xor (and (= V1 _let_2) (= V2 _let_1)) (and (= V2 _let_2) (= V1 _let_1)))))))))))) (let ((_let_9 (forall ((E $$unsorted)) (=> (tptp.edge E) (and (tptp.vertex (tptp.head_of E)) (tptp.vertex (tptp.tail_of E))))))) (let ((_let_10 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_11 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (= _let_11 _let_10))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_15 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_13))) (let ((_let_19 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_20 (not _let_19))) (let ((_let_21 (and _let_18 _let_20))) (let ((_let_22 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.shortest_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_21))) (let ((_let_27 (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_1250 $$unsorted)) (or (not (tptp.shortest_path V1 V2 P)) (not (tptp.precedes E1 E2 P)) (and (or (not (= (tptp.tail_of E1) (tptp.tail_of BOUND_VARIABLE_1250))) (not (= (tptp.head_of E2) (tptp.head_of BOUND_VARIABLE_1250)))) (not (tptp.precedes E2 E1 P))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (_let_27))) (let ((_let_30 (forall ((E3 $$unsorted)) (or (not (tptp.edge E3)) (not (= (tptp.tail_of E3) (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (not (= (tptp.head_of E3) (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_25 _let_23 _let_31))) (let ((_let_33 (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (or (not (tptp.shortest_path V1 V2 P)) (not (tptp.precedes E1 E2 P)) (not (forall ((E3 $$unsorted)) (or (not (tptp.edge E3)) (not (= (tptp.tail_of E3) (tptp.head_of E2))) (not (= (tptp.head_of E3) (tptp.tail_of E1)))))))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)))) (let ((_let_36 (ASSUME :args (_let_1)))) (let ((_let_37 (MACRO_SR_PRED_TRANSFORM (NOT_IMPLIES_ELIM1 (EQ_RESOLVE _let_36 _let_35)) :args ((= tptp.complete true))))) (let ((_let_38 (EQ_RESOLVE _let_36 (TRANS _let_35 (MACRO_SR_EQ_INTRO _let_37 :args ((not (=> tptp.complete _let_33)) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_39 (or))) (let ((_let_40 (not _let_33))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_38) :args (_let_40))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_33))) (REFL :args (_let_34)) :args _let_39)) _let_38 :args (_let_34 true _let_33)))) (let ((_let_42 (REFL :args (_let_32)))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 1)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_39)) :args ((or _let_22 _let_32))) _let_41 :args (_let_22 true _let_32)))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 0)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_39)) :args ((or _let_24 _let_32))) _let_41 :args (_let_24 true _let_32)))) (let ((_let_45 (and _let_12 _let_16))) (let ((_let_46 (= _let_11 _let_14))) (let ((_let_47 (= _let_15 _let_10))) (let ((_let_48 (and _let_47 _let_46))) (let ((_let_49 (= _let_45 _let_48))) (let ((_let_50 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49))) (let ((_let_53 (forall ((E $$unsorted)) (let ((_let_1 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_2 (tptp.tail_of E))) (let ((_let_3 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_4 (tptp.head_of E))) (or (not (tptp.edge E)) (= (and (= _let_4 _let_1) (= _let_2 _let_3)) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (not _let_53))) (let ((_let_56 (= _let_11 _let_15))) (let ((_let_57 (tptp.vertex _let_15))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.vertex _let_11))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_60 _let_58 _let_56 _let_55))) (let ((_let_62 (forall ((V1 $$unsorted) (V2 $$unsorted)) (or (not (tptp.vertex V1)) (not (tptp.vertex V2)) (= V1 V2) (not (forall ((E $$unsorted)) (let ((_let_1 (tptp.tail_of E))) (let ((_let_2 (tptp.head_of E))) (or (not (tptp.edge E)) (= (and (= V1 _let_2) (= V2 _let_1)) (and (= V2 _let_2) (= V1 _let_1)))))))))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_37 :args ((=> tptp.complete _let_62) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_64 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_65 (and _let_59 (tptp.vertex _let_64)))) (let ((_let_66 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_65))) (let ((_let_69 (forall ((E $$unsorted)) (or (not (tptp.edge E)) (and (tptp.vertex (tptp.head_of E)) (tptp.vertex (tptp.tail_of E))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (_let_69))) (let ((_let_72 ((not (= (tptp.edge E) false))))) (let ((_let_73 (and _let_66 (tptp.in_path _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in_path _let_64 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_74 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_75 (not _let_74))) (let ((_let_76 (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_77 _let_75 _let_73))) (let ((_let_79 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (E $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.on_path E P)) (and (tptp.edge E) (tptp.in_path (tptp.head_of E) P) (tptp.in_path (tptp.tail_of E) P)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (_let_79))) (let ((_let_82 (tptp.on_path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_83 (and _let_82 _let_74 (= (not (forall ((E3 $$unsorted)) (or (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 E3)) (not (tptp.precedes E3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_84 (or _let_77 _let_23 _let_83))) (let ((_let_85 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_1201 $$unsorted) (BOUND_VARIABLE_1199 $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.precedes BOUND_VARIABLE_1199 BOUND_VARIABLE_1201 P)) (and (tptp.on_path BOUND_VARIABLE_1199 P) (tptp.on_path BOUND_VARIABLE_1201 P) (= (not (forall ((E3 $$unsorted)) (or (not (tptp.sequential BOUND_VARIABLE_1199 E3)) (not (tptp.precedes E3 BOUND_VARIABLE_1201 P))))) (not (tptp.sequential BOUND_VARIABLE_1199 BOUND_VARIABLE_1201)))))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (and _let_76 (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (forall ((P $$unsorted)) (or (not (tptp.path SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 P)) (tptp.less_or_equal (tptp.length_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.length_of P))))))) (let ((_let_88 (= _let_24 _let_87))) (let ((_let_89 (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (tptp.shortest_path V1 V2 SP) (and (tptp.path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (or (not (tptp.path V1 V2 P)) (tptp.less_or_equal (tptp.length_of SP) (tptp.length_of P))))))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_87 0)) :args ((or _let_76 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_88)) :args ((or _let_25 _let_87 (not _let_88)))) _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.shortest_path V1 V2 SP)))) :args (_let_89))) _let_90 :args (_let_88 false _let_89)) :args (_let_87 false _let_24 false _let_88)) :args (_let_76 false _let_87)))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_23 _let_77 _let_83 (not _let_84)))) _let_43 _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.path V1 V2 P) false)) (not (= (tptp.precedes BOUND_VARIABLE_1199 BOUND_VARIABLE_1201 P) false))))) :args (_let_85))) _let_86 :args (_let_84 false _let_85)) :args (_let_83 false _let_22 false _let_76 false _let_84)))) (let ((_let_93 (not _let_83))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_83 1)) :args ((or _let_74 _let_93))) _let_92 :args (_let_74 false _let_83)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_73 0)) :args ((or _let_66 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_77 _let_75 _let_73 (not _let_78)))) _let_91 _let_94 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_81)) _let_80 :args (_let_78 false _let_79)) :args (_let_73 false _let_76 false _let_74 false _let_78)) :args (_let_66 false _let_73)))) (let ((_let_96 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_97 (and (tptp.vertex _let_96) _let_57))) (let ((_let_98 (tptp.edge SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_99 (not _let_98))) (let ((_let_100 (or _let_99 _let_97))) (let ((_let_101 (and _let_98 (tptp.in_path _let_96 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in_path _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_102 (not _let_82))) (let ((_let_103 (or _let_77 _let_102 _let_101))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 0)) :args ((or _let_98 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_77 _let_102 _let_101 (not _let_103)))) _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_83 0)) :args ((or _let_82 _let_93))) _let_92 :args (_let_82 false _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.path V1 V2 P) false)) (not (= (tptp.on_path E P) false))))) :args _let_81)) _let_80 :args (_let_103 false _let_79)) :args (_let_101 false _let_76 false _let_82 false _let_103)) :args (_let_98 false _let_101)))) (let ((_let_105 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_106 (not _let_105))) (let ((_let_107 (and _let_66 _let_98 _let_106 _let_56))) (let ((_let_108 (not _let_56))) (let ((_let_109 (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_110 (= _let_109 _let_107))) (let ((_let_111 (not _let_107))) (let ((_let_112 (_let_6))) (let ((_let_113 (ASSUME :args _let_112))) (let ((_let_114 (not _let_109))) (let ((_let_115 (or _let_114 _let_23))) (let ((_let_116 (and (not (tptp.sequential SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_115))) (let ((_let_117 (tptp.precedes SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_118 (or _let_77 _let_75 _let_75 _let_116 _let_117))) (let ((_let_119 (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted) (BOUND_VARIABLE_1148 $$unsorted) (BOUND_VARIABLE_1146 $$unsorted)) (or (not (tptp.path V1 V2 P)) (not (tptp.on_path BOUND_VARIABLE_1146 P)) (not (tptp.on_path BOUND_VARIABLE_1148 P)) (and (not (tptp.sequential BOUND_VARIABLE_1146 BOUND_VARIABLE_1148)) (or (not (tptp.sequential BOUND_VARIABLE_1146 BOUND_VARIABLE_1150)) (not (tptp.precedes BOUND_VARIABLE_1150 BOUND_VARIABLE_1148 P)))) (tptp.precedes BOUND_VARIABLE_1146 BOUND_VARIABLE_1148 P))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (not _let_117))) (let ((_let_122 (and (or (not (= _let_64 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (not (= _let_11 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) _let_121))) (let ((_let_123 (or _let_25 _let_121 _let_122))) (let ((_let_124 (and (or (not (= _let_15 (tptp.tail_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (not (= _let_11 (tptp.head_of SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) _let_20))) (let ((_let_125 (or _let_25 _let_23 _let_124))) (let ((_let_126 (SYMM (ASSUME :args (_let_105))))) (let ((_let_127 (_let_107))) (let ((_let_128 (_let_55))) (let ((_let_129 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_128)) :args _let_128) (REWRITE :args ((=> _let_55 (not (or _let_51 (= (and (= _let_10 _let_11) (= _let_14 _let_15)) (and (= _let_10 _let_15) (= _let_14 _let_11)))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_53))) (REFL :args (_let_54)) :args _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_56 _let_58 _let_60 _let_55 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_127) (CONG (REFL :args _let_127) (REFL :args (_let_67)) (REFL :args (_let_99)) (MACRO_SR_PRED_INTRO :args ((= (not _let_106) _let_105))) (REFL :args (_let_108)) :args _let_39)) :args ((or _let_105 _let_99 _let_67 _let_108 _let_107))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_20)))) (CONG _let_126 (SYMM _let_126) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args (APPLY_UF tptp.precedes)) (TRUE_INTRO (ASSUME :args (_let_22))))) :args (_let_22 _let_105 _let_20))) (CONG (REFL :args (_let_23)) (REFL :args (_let_106)) (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_124 1)) :args ((or _let_20 (not _let_124)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_125)) :args ((or _let_25 _let_23 _let_124 (not _let_125)))) _let_44 _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.shortest_path V1 V2 P) false)) (not (= (tptp.precedes E1 E2 P) false)) (tptp.tail_of BOUND_VARIABLE_1250)))) :args _let_29)) _let_28 :args (_let_125 false _let_27)) :args (_let_124 false _let_24 false _let_22 false _let_125)) :args (_let_20 false _let_124)) _let_43 :args (_let_106 true _let_19 false _let_22)) _let_104 _let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_110)) :args ((or _let_109 _let_111 (not _let_110)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_115)) :args ((or _let_23 _let_114 (not _let_115)))) _let_43 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_116 1)) :args ((or _let_115 (not _let_116)))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_118))) :args ((or _let_77 _let_75 _let_116 _let_117 (not _let_118)))) _let_91 _let_94 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_25 _let_121 _let_122 (not _let_123)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_29)) _let_28 :args (_let_123 false _let_27)) _let_44 (REORDERING (CNF_AND_POS :args (_let_122 1)) :args ((or _let_121 (not _let_122)))) :args (_let_121 false _let_123 false _let_24 true _let_122)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((tptp.sequential BOUND_VARIABLE_1146 BOUND_VARIABLE_1148) (not (= (tptp.path V1 V2 P) false)) (tptp.precedes BOUND_VARIABLE_1150 BOUND_VARIABLE_1148 P)))) :args (_let_119))) _let_120 :args (_let_118 false _let_119)) :args (_let_116 false _let_76 false _let_74 true _let_117 false _let_118)) :args (_let_115 false _let_116)) :args (_let_114 false _let_22 false _let_115)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sequential E1 E2)))) :args _let_112))) _let_113 :args (_let_110 false _let_6)) :args (_let_111 true _let_109 false _let_110)) :args (_let_108 true _let_105 false _let_98 false _let_66 true _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_97 1)) :args ((or _let_57 (not _let_97)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_99 _let_97 (not _let_100)))) _let_104 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_72)) :args _let_71)) _let_70 :args (_let_100 false _let_69)) :args (_let_97 false _let_98 false _let_100)) :args (_let_57 false _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_65 0)) :args ((or _let_59 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_65 (not _let_68)))) _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_72)) :args _let_71)) _let_70 :args (_let_68 false _let_69)) :args (_let_65 false _let_66 false _let_68)) :args (_let_59 false _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_63 :args (_let_11 _let_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.vertex V1) false)) (not (= (tptp.vertex V2) false))))) :args (_let_62)))) _let_63 :args (_let_61 false _let_62)) :args (_let_55 true _let_56 false _let_57 false _let_59 false _let_61)) :args (_let_54 true _let_53)))) (let ((_let_130 (not _let_47))) (let ((_let_131 (not _let_46))) (let ((_let_132 (or _let_51 _let_131 _let_130))) (let ((_let_133 (not _let_48))) (let ((_let_134 (_let_30))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args (_let_49)) :args ((or _let_45 _let_48 _let_49))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_132)) :args ((or _let_51 _let_130 _let_131 (not _let_132)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_134) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_134))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 2)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_39)) :args ((or _let_30 _let_32))) _let_41 :args (_let_30 true _let_32)) :args (_let_132 false _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 0)) (CONG (REFL :args (_let_52)) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_39)) :args ((or _let_50 _let_52))) _let_129 :args (_let_50 true _let_52)) (REORDERING (CNF_AND_POS :args (_let_48 1)) :args ((or _let_46 _let_133))) (REORDERING (CNF_AND_POS :args (_let_48 0)) :args ((or _let_47 _let_133))) :args (_let_133 false _let_132 false _let_50 false _let_46 false _let_47)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_52 1)) _let_129 :args ((not _let_49) true _let_52)) :args (_let_45 true _let_48 true _let_49)))) (let ((_let_136 (not _let_45))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_13 _let_17 (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 1)) :args ((or _let_16 _let_136))) _let_135 :args (_let_16 false _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_45 0)) :args ((or _let_12 _let_136))) _let_135 :args (_let_12 false _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 0)) :args ((or _let_18 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_23 _let_21 (not _let_26)))) _let_44 _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_29)) _let_28 :args (_let_26 false _let_27)) :args (_let_21 false _let_24 false _let_22 false _let_26)) :args (_let_18 false _let_21)) :args (false false _let_16 false _let_12 false _let_18)) :args ((forall ((E $$unsorted)) (=> (tptp.edge E) (not (= (tptp.head_of E) (tptp.tail_of E))))) _let_9 _let_8 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (and (tptp.vertex V1) (tptp.vertex V2) (exists ((E $$unsorted)) (and (tptp.edge E) (= V1 (tptp.tail_of E)) (or (and (= V2 (tptp.head_of E)) (= P (tptp.path_cons E tptp.empty))) (exists ((TP $$unsorted)) (and (tptp.path (tptp.head_of E) V2 TP) (= P (tptp.path_cons E TP)))))))) (tptp.path V1 V2 P))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (tptp.path V1 V2 P) (and (tptp.vertex V1) (tptp.vertex V2) (exists ((E $$unsorted)) (and (tptp.edge E) (= V1 (tptp.tail_of E)) (xor (and (= V2 (tptp.head_of E)) (= P (tptp.path_cons E tptp.empty))) (exists ((TP $$unsorted)) (and (tptp.path (tptp.head_of E) V2 TP) (= P (tptp.path_cons E TP)))))))))) _let_7 (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (V $$unsorted)) (=> (and (tptp.path V1 V2 P) (tptp.in_path V P)) (and (tptp.vertex V) (exists ((E $$unsorted)) (and (tptp.on_path E P) (or (= V (tptp.head_of E)) (= V (tptp.tail_of E)))))))) _let_6 _let_5 _let_4 _let_3 _let_2 (forall ((E1 $$unsorted) (E2 $$unsorted) (E3 $$unsorted)) (= (tptp.triangle E1 E2 E3) (and (tptp.edge E1) (tptp.edge E2) (tptp.edge E3) (tptp.sequential E1 E2) (tptp.sequential E2 E3) (tptp.sequential E3 E1)))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (tptp.path V1 V2 P) (= (tptp.length_of P) (tptp.number_of_in tptp.edges P)))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (=> (tptp.path V1 V2 P) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.minus (tptp.length_of P) tptp.n1)))) (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (=> (and (tptp.path V1 V2 P) (forall ((E1 $$unsorted) (E2 $$unsorted)) (=> (and (tptp.on_path E1 P) (tptp.on_path E2 P) (tptp.sequential E1 E2)) (exists ((E3 $$unsorted)) (tptp.triangle E1 E2 E3))))) (= (tptp.number_of_in tptp.sequential_pairs P) (tptp.number_of_in tptp.triangles P)))) (forall ((Things $$unsorted) (InThese $$unsorted)) (tptp.less_or_equal (tptp.number_of_in Things InThese) (tptp.number_of_in Things tptp.graph))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.14/31.34 )
% 31.14/31.34 % SZS output end Proof for GRA007+1
% 31.14/31.34 % cvc5---1.0.5 exiting
% 31.14/31.34 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------