0.03/0.12 % Problem : SLH719^1 : TPTP v7.5.0. Released v7.5.0. 0.03/0.13 % Command : run_E %s %d THM 0.13/0.34 % Computer : n016.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 30 0.13/0.34 % WCLimit : 30 0.13/0.34 % DateTime : Tue Aug 9 03:53:42 EDT 2022 0.13/0.35 % CPUTime : 0.20/0.46 The problem SPC is TH0_THM_EQU_NAR 0.20/0.46 Running higher-order on 1 cores theorem proving 0.20/0.46 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=1 --cpu-limit=30 /export/starexec/sandbox/benchmark/theBenchmark.p 0.20/0.47 # Version: 3.0pre003-ho 1.07/1.26 # Preprocessing class: HSLSSMSSSSSNHSA. 1.07/1.26 # Scheduled 1 strats onto 1 cores with 30 seconds (30 total) 1.07/1.26 # Starting full_lambda_9 with 30s (1) cores 1.07/1.26 # full_lambda_9 with pid 32360 completed with status 0 1.07/1.26 # Result found by full_lambda_9 1.07/1.26 # Preprocessing class: HSLSSMSSSSSNHSA. 1.07/1.26 # Scheduled 1 strats onto 1 cores with 30 seconds (30 total) 1.07/1.26 # Starting full_lambda_9 with 30s (1) cores 1.07/1.26 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true) 1.07/1.26 # ...ProofStateSinE()=222/261 1.07/1.26 # Search class: HGHSM-FSLM31-DHSFFFBN 1.07/1.26 # Scheduled 6 strats onto 1 cores with 30 seconds (30 total) 1.07/1.26 # Starting sh1l with 9s (1) cores 1.07/1.26 # sh1l with pid 32361 completed with status 0 1.07/1.26 # Result found by sh1l 1.07/1.26 # Preprocessing class: HSLSSMSSSSSNHSA. 1.07/1.26 # Scheduled 1 strats onto 1 cores with 30 seconds (30 total) 1.07/1.26 # Starting full_lambda_9 with 30s (1) cores 1.07/1.26 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true) 1.07/1.26 # ...ProofStateSinE()=222/261 1.07/1.26 # Search class: HGHSM-FSLM31-DHSFFFBN 1.07/1.26 # Scheduled 6 strats onto 1 cores with 30 seconds (30 total) 1.07/1.26 # Starting sh1l with 9s (1) cores 1.07/1.26 # Preprocessing time : 0.723 s 1.07/1.26 1.07/1.26 # Proof found! 1.07/1.26 # SZS status Theorem 1.07/1.26 # SZS output start CNFRefutation 1.07/1.26 thf(decl_22, type, edmond1517640972ysis_a: (product_prod_nat_nat > a) > $o). 1.07/1.26 thf(decl_23, type, edmond1517640973ysis_b: (product_prod_nat_nat > b) > $o). 1.07/1.26 thf(decl_24, type, edmond1022345716sure_a: (product_prod_nat_nat > a) > nat > nat > nat). 1.07/1.26 thf(decl_25, type, edmond1022345717sure_b: (product_prod_nat_nat > b) > nat > nat > nat). 1.07/1.26 thf(decl_26, type, edmond475474835dges_a: (product_prod_nat_nat > a) > nat > nat > set_Pr1986765409at_nat). 1.07/1.26 thf(decl_27, type, edmond475474836dges_b: (product_prod_nat_nat > b) > nat > nat > set_Pr1986765409at_nat). 1.07/1.26 thf(decl_28, type, edmond771116670s_uE_a: (product_prod_nat_nat > a) > set_Pr1986765409at_nat). 1.07/1.26 thf(decl_29, type, edmond771116671s_uE_b: (product_prod_nat_nat > b) > set_Pr1986765409at_nat). 1.07/1.26 thf(decl_30, type, finite_card_nat: set_nat > nat). 1.07/1.26 thf(decl_31, type, finite447719721at_nat: set_Pr1986765409at_nat > nat). 1.07/1.26 thf(decl_32, type, v_a: (product_prod_nat_nat > a) > set_nat). 1.07/1.26 thf(decl_33, type, v_b: (product_prod_nat_nat > b) > set_nat). 1.07/1.26 thf(decl_34, type, connected_a: (product_prod_nat_nat > a) > nat > nat > $o). 1.07/1.26 thf(decl_35, type, connected_b: (product_prod_nat_nat > b) > nat > nat > $o). 1.07/1.26 thf(decl_36, type, min_dist_a: (product_prod_nat_nat > a) > nat > nat > nat). 1.07/1.26 thf(decl_37, type, min_dist_b: (product_prod_nat_nat > b) > nat > nat > nat). 1.07/1.26 thf(decl_38, type, minus_minus_nat: nat > nat > nat). 1.07/1.26 thf(decl_39, type, one_one_nat: nat). 1.07/1.26 thf(decl_40, type, plus_plus_nat: nat > nat > nat). 1.07/1.26 thf(decl_41, type, times_times_nat: nat > nat > nat). 1.07/1.26 thf(decl_42, type, zero_zero_nat: nat). 1.07/1.26 thf(decl_43, type, if_nat: $o > nat > nat > nat). 1.07/1.26 thf(decl_44, type, ord_less_nat: nat > nat > $o). 1.07/1.26 thf(decl_45, type, ord_less_eq_nat: nat > nat > $o). 1.07/1.26 thf(decl_46, type, collect_nat: (nat > $o) > set_nat). 1.07/1.26 thf(decl_47, type, member_nat: nat > set_nat > $o). 1.07/1.26 thf(decl_48, type, c: product_prod_nat_nat > a). 1.07/1.26 thf(decl_49, type, c2: product_prod_nat_nat > b). 1.07/1.26 thf(decl_50, type, s: nat). 1.07/1.26 thf(decl_51, type, t: nat). 1.07/1.26 thf(decl_52, type, esk1_1: (nat > nat) > nat). 1.07/1.26 thf(decl_53, type, esk2_1: (nat > nat) > nat). 1.07/1.26 thf(decl_54, type, esk3_2: (nat > $o) > nat > nat). 1.07/1.26 thf(decl_55, type, esk4_1: (nat > nat) > nat). 1.07/1.26 thf(decl_56, type, esk5_1: (nat > nat) > nat). 1.07/1.26 thf(decl_57, type, esk6_2: nat > nat > nat). 1.07/1.26 thf(decl_58, type, esk7_2: nat > nat > nat). 1.07/1.26 thf(decl_59, type, esk8_4: nat > nat > nat > nat > nat). 1.07/1.26 thf(decl_60, type, esk9_3: nat > nat > nat > nat). 1.07/1.26 thf(decl_61, type, esk10_4: nat > nat > nat > nat > nat). 1.07/1.26 thf(decl_62, type, esk11_3: nat > nat > nat > nat). 1.07/1.26 thf(decl_63, type, esk12_2: (nat > $o) > nat > nat). 1.07/1.26 thf(decl_64, type, esk13_1: (nat > $o) > nat). 1.07/1.26 thf(decl_65, type, esk14_2: (nat > $o) > (nat > $o) > nat). 1.07/1.26 thf(decl_66, type, epred1_1: set_nat > nat > $o). 1.07/1.26 thf(decl_67, type, esk15_2: nat > nat > nat). 1.07/1.26 thf(fact_22_ekMeasure__def, axiom, (((connected_a @ c @ s @ t)=>((edmond1022345716sure_a @ c @ s @ t)=(plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t)))))&(~((connected_a @ c @ s @ t))=>((edmond1022345716sure_a @ c @ s @ t)=(zero_zero_nat)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_22_ekMeasure__def)). 1.07/1.26 thf(conj_0, conjecture, (ord_less_nat @ (if_nat @ ((connected_b @ c2 @ s @ t)) @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ ((connected_a @ c @ s @ t)) @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_0)). 1.07/1.26 thf(fact_2_CONN, axiom, (connected_a @ c @ s @ t), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_2_CONN)). 1.07/1.26 thf(fact_3_NCONN2, axiom, ~((connected_b @ c2 @ s @ t)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_3_NCONN2)). 1.07/1.26 thf(help_If_2_1_If_001t__Nat__Onat_T, axiom, ![X28:nat, X29:nat]:(((if_nat @ (~($true)) @ X28 @ X29)=(X29))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', help_If_2_1_If_001t__Nat__Onat_T)). 1.07/1.26 thf(fact_77_less__nat__zero__code, axiom, ![X19:nat]:(~((ord_less_nat @ X19 @ zero_zero_nat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_77_less__nat__zero__code)). 1.07/1.26 thf(fact_20_Veq, axiom, ((v_b @ c2)=(v_a @ c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_20_Veq)). 1.07/1.26 thf(fact_21_uE__eq, axiom, ((edmond771116671s_uE_b @ c2)=(edmond771116670s_uE_a @ c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_21_uE__eq)). 1.07/1.26 thf(help_If_1_1_If_001t__Nat__Onat_T, axiom, ![X28:nat, X29:nat]:(((if_nat @ (($true)) @ X28 @ X29)=(X28))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', help_If_1_1_If_001t__Nat__Onat_T)). 1.07/1.26 thf(fact_102_add__less__same__cancel1, axiom, ![X12:nat, X10:nat]:(((ord_less_nat @ (plus_plus_nat @ X12 @ X10) @ X12)<=>(ord_less_nat @ X10 @ zero_zero_nat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_102_add__less__same__cancel1)). 1.07/1.26 thf(fact_57_zero__eq__add__iff__both__eq__0, axiom, ![X28:nat, X29:nat]:((((zero_zero_nat)=(plus_plus_nat @ X28 @ X29))<=>(((X28)=(zero_zero_nat))&((X29)=(zero_zero_nat))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_57_zero__eq__add__iff__both__eq__0)). 1.07/1.26 thf(fact_136_le__neq__implies__less, axiom, ![X20:nat, X19:nat]:(((ord_less_eq_nat @ X20 @ X19)=>(((X20)!=(X19))=>(ord_less_nat @ X20 @ X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_136_le__neq__implies__less)). 1.07/1.26 thf(fact_79_bot__nat__0_Oextremum, axiom, ![X10:nat]:((ord_less_eq_nat @ zero_zero_nat @ X10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_79_bot__nat__0_Oextremum)). 1.07/1.26 thf(fact_34_nat__0__less__mult__iff, axiom, ![X20:nat, X19:nat]:(((ord_less_nat @ zero_zero_nat @ (times_times_nat @ X20 @ X19))<=>((ord_less_nat @ zero_zero_nat @ X20)&(ord_less_nat @ zero_zero_nat @ X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_34_nat__0__less__mult__iff)). 1.07/1.26 thf(fact_14_card__spEdges__less, axiom, (ord_less_nat @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_14_card__spEdges__less)). 1.07/1.26 thf(fact_63_add_Oright__neutral, axiom, ![X10:nat]:(((plus_plus_nat @ X10 @ zero_zero_nat)=(X10))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_63_add_Oright__neutral)). 1.07/1.26 thf(fact_38_zero__less__diff, axiom, ![X19:nat, X20:nat]:(((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ X19 @ X20))<=>(ord_less_nat @ X20 @ X19))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_38_zero__less__diff)). 1.07/1.26 thf(fact_10_min__dist__less__V, axiom, ![X8:nat, X1:nat]:(((member_nat @ X8 @ (v_a @ c))=>((connected_a @ c @ X8 @ X1)=>(ord_less_nat @ (min_dist_a @ c @ X8 @ X1) @ (finite_card_nat @ (v_a @ c)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_10_min__dist__less__V)). 1.07/1.26 thf(fact_4_SV, axiom, (member_nat @ s @ (v_a @ c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_4_SV)). 1.07/1.26 thf(c_0_19, plain, (((connected_a @ c @ s @ t)=>((edmond1022345716sure_a @ c @ s @ t)=(plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t)))))&(~(connected_a @ c @ s @ t)=>((edmond1022345716sure_a @ c @ s @ t)=(zero_zero_nat)))), inference(fof_simplification,[status(thm)],[fact_22_ekMeasure__def])). 1.07/1.26 thf(c_0_20, negated_conjecture, ~(((~(connected_b @ c2 @ s @ t)|((~(connected_a @ c @ s @ t)|(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat)))&((connected_a @ c @ s @ t)|(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat)))))&((connected_b @ c2 @ s @ t)|((~(connected_a @ c @ s @ t)|(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat)))&((connected_a @ c @ s @ t)|(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))))))), inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])])). 1.07/1.26 thf(c_0_21, plain, ((~(connected_a @ c @ s @ t)|((edmond1022345716sure_a @ c @ s @ t)=(plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t)))))&((connected_a @ c @ s @ t)|((edmond1022345716sure_a @ c @ s @ t)=(zero_zero_nat)))), inference(fof_nnf,[status(thm)],[c_0_19])). 1.07/1.26 thf(c_0_22, negated_conjecture, (((~(connected_b @ c2 @ s @ t)|(connected_b @ c2 @ s @ t))&(((~(connected_a @ c @ s @ t)|(connected_a @ c @ s @ t)|(connected_b @ c2 @ s @ t))&(~(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|(connected_a @ c @ s @ t)|(connected_b @ c2 @ s @ t)))&((~(connected_a @ c @ s @ t)|~(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|(connected_b @ c2 @ s @ t))&(~(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|~(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|(connected_b @ c2 @ s @ t)))))&((((~(connected_b @ c2 @ s @ t)|(~(connected_a @ c @ s @ t)|(connected_a @ c @ s @ t)))&(((~(connected_a @ c @ s @ t)|(connected_a @ c @ s @ t)|(~(connected_a @ c @ s @ t)|(connected_a @ c @ s @ t)))&(~(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ 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(plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat)))))))&((~(connected_b @ c2 @ s @ t)|(~(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|~(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))))&(((~(connected_a @ c @ s @ t)|(connected_a @ c @ s @ t)|(~(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|~(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))))&(~(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|(connected_a @ c @ s @ t)|(~(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|~(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat)))))&((~(connected_a @ c @ s @ t)|~(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|(~(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|~(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))))&(~(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|~(ord_less_nat @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|(~(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $false @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat))|~(ord_less_nat @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ $true @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat)))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])). 1.07/1.26 thf(c_0_23, plain, (((edmond1022345716sure_a @ c @ s @ t)=(plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))))|~((connected_a @ c @ s @ t))), inference(split_conjunct,[status(thm)],[c_0_21])). 1.07/1.26 thf(c_0_24, plain, (connected_a @ c @ s @ t), inference(split_conjunct,[status(thm)],[fact_2_CONN])). 1.07/1.26 thf(c_0_25, plain, ~(connected_b @ c2 @ s @ t), inference(fof_simplification,[status(thm)],[fact_3_NCONN2])). 1.07/1.26 thf(c_0_26, plain, ![X654:nat, X655:nat]:(((if_nat @ (~($true)) @ X654 @ X655)=(X655))), inference(variable_rename,[status(thm)],[help_If_2_1_If_001t__Nat__Onat_T])). 1.07/1.26 thf(c_0_27, plain, ![X19:nat]:(~(ord_less_nat @ X19 @ zero_zero_nat)), inference(fof_simplification,[status(thm)],[fact_77_less__nat__zero__code])). 1.07/1.26 thf(c_0_28, negated_conjecture, ((connected_b @ c2 @ s @ t)|~((connected_a @ c @ s @ t))|~((ord_less_nat @ (if_nat @ (~($true)) @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_b @ c2)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116671s_uE_b @ c2)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ (($true)) @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))) @ zero_zero_nat)))), inference(split_conjunct,[status(thm)],[c_0_22])). 1.07/1.26 thf(c_0_29, plain, ((v_b @ c2)=(v_a @ c)), inference(split_conjunct,[status(thm)],[fact_20_Veq])). 1.07/1.26 thf(c_0_30, plain, ((edmond771116671s_uE_b @ c2)=(edmond771116670s_uE_a @ c)), inference(split_conjunct,[status(thm)],[fact_21_uE__eq])). 1.07/1.26 thf(c_0_31, plain, ((plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t)))=(edmond1022345716sure_a @ c @ s @ t)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])). 1.07/1.26 thf(c_0_32, plain, ~((connected_b @ c2 @ s @ t)), inference(split_conjunct,[status(thm)],[c_0_25])). 1.07/1.26 thf(c_0_33, plain, ![X656:nat, X657:nat]:(((if_nat @ (($true)) @ X656 @ X657)=(X656))), inference(variable_rename,[status(thm)],[help_If_1_1_If_001t__Nat__Onat_T])). 1.07/1.26 thf(c_0_34, plain, ![X1:nat, X2:nat]:(((if_nat @ (((($true))!=(($true)))) @ X1 @ X2)=(X2))), inference(split_conjunct,[status(thm)],[c_0_26])). 1.07/1.26 thf(c_0_35, plain, ![X570:nat, X571:nat]:(((~(ord_less_nat @ (plus_plus_nat @ X570 @ X571) @ X570)|(ord_less_nat @ X571 @ zero_zero_nat))&(~(ord_less_nat @ X571 @ zero_zero_nat)|(ord_less_nat @ (plus_plus_nat @ X570 @ X571) @ X570)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_102_add__less__same__cancel1])])). 1.07/1.26 thf(c_0_36, plain, ![X559:nat]:(~(ord_less_nat @ X559 @ zero_zero_nat)), inference(variable_rename,[status(thm)],[c_0_27])). 1.07/1.26 thf(c_0_37, plain, ![X671:nat, X672:nat]:((((((X671)=(zero_zero_nat))|((zero_zero_nat)!=(plus_plus_nat @ X671 @ X672)))&(((X672)=(zero_zero_nat))|((zero_zero_nat)!=(plus_plus_nat @ X671 @ X672))))&(((X671)!=(zero_zero_nat))|((X672)!=(zero_zero_nat))|((zero_zero_nat)=(plus_plus_nat @ X671 @ X672))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_57_zero__eq__add__iff__both__eq__0])])])). 1.07/1.26 thf(c_0_38, negated_conjecture, ~((ord_less_nat @ (if_nat @ (~($true)) @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_b @ c2 @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)) @ (finite447719721at_nat @ (edmond475474836dges_b @ c2 @ s @ t))) @ zero_zero_nat) @ (if_nat @ (($true)) @ (edmond1022345716sure_a @ c @ s @ t) @ zero_zero_nat))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_24]), c_0_29]), c_0_30]), c_0_31])]), c_0_32])). 1.07/1.26 thf(c_0_39, plain, ![X2:nat, X1:nat]:(((if_nat @ (($true)) @ X1 @ X2)=(X1))), inference(split_conjunct,[status(thm)],[c_0_33])). 1.07/1.26 thf(c_0_40, plain, ![X1:nat, X2:nat]:(((if_nat @ (~($true)) @ X1 @ X2)=(X2))), inference(cn,[status(thm)],[c_0_34])). 1.07/1.26 thf(c_0_41, plain, ![X583:nat, X584:nat]:((~(ord_less_eq_nat @ X583 @ X584)|(((X583)=(X584))|(ord_less_nat @ X583 @ X584)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_136_le__neq__implies__less])])). 1.07/1.26 thf(c_0_42, plain, ![X688:nat]:((ord_less_eq_nat @ zero_zero_nat @ X688)), inference(variable_rename,[status(thm)],[fact_79_bot__nat__0_Oextremum])). 1.07/1.26 thf(c_0_43, plain, ![X2:nat, X1:nat]:(((ord_less_nat @ X2 @ zero_zero_nat)|~((ord_less_nat @ (plus_plus_nat @ X1 @ X2) @ X1)))), inference(split_conjunct,[status(thm)],[c_0_35])). 1.07/1.26 thf(c_0_44, plain, ![X1:nat]:(~((ord_less_nat @ X1 @ zero_zero_nat))), inference(split_conjunct,[status(thm)],[c_0_36])). 1.07/1.26 thf(c_0_45, plain, ![X2:nat, X1:nat]:((((X1)=(zero_zero_nat))|((zero_zero_nat)!=(plus_plus_nat @ X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_37])). 1.07/1.26 thf(c_0_46, negated_conjecture, ~((ord_less_nat @ zero_zero_nat @ (edmond1022345716sure_a @ c @ s @ t))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39]), c_0_40])). 1.07/1.26 thf(c_0_47, plain, ![X1:nat, X2:nat]:((((X1)=(X2))|(ord_less_nat @ X1 @ X2)|~((ord_less_eq_nat @ X1 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_41])). 1.07/1.26 thf(c_0_48, plain, ![X1:nat]:((ord_less_eq_nat @ zero_zero_nat @ X1)), inference(split_conjunct,[status(thm)],[c_0_42])). 1.07/1.26 thf(c_0_49, plain, ![X2:nat, X1:nat]:(~((ord_less_nat @ (plus_plus_nat @ X1 @ X2) @ X1))), inference(sr,[status(thm)],[c_0_43, c_0_44])). 1.07/1.26 thf(c_0_50, plain, (((finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))=(zero_zero_nat))|((edmond1022345716sure_a @ c @ s @ t)!=(zero_zero_nat))), inference(spm,[status(thm)],[c_0_45, c_0_31])). 1.07/1.26 thf(c_0_51, negated_conjecture, ((edmond1022345716sure_a @ c @ s @ t)=(zero_zero_nat)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47]), c_0_48])])). 1.07/1.26 thf(c_0_52, plain, ~((ord_less_nat @ (edmond1022345716sure_a @ c @ s @ t) @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)))), inference(spm,[status(thm)],[c_0_49, c_0_31])). 1.07/1.26 thf(c_0_53, plain, ![X542:nat, X543:nat]:(((((ord_less_nat @ zero_zero_nat @ X542)|~(ord_less_nat @ zero_zero_nat @ (times_times_nat @ X542 @ X543)))&((ord_less_nat @ zero_zero_nat @ X543)|~(ord_less_nat @ zero_zero_nat @ (times_times_nat @ X542 @ X543))))&(~(ord_less_nat @ zero_zero_nat @ X542)|~(ord_less_nat @ zero_zero_nat @ X543)|(ord_less_nat @ zero_zero_nat @ (times_times_nat @ X542 @ X543))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_34_nat__0__less__mult__iff])])])). 1.07/1.26 thf(c_0_54, plain, (ord_less_nat @ (finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)), inference(split_conjunct,[status(thm)],[fact_14_card__spEdges__less])). 1.07/1.26 thf(c_0_55, plain, ((finite447719721at_nat @ (edmond475474835dges_a @ c @ s @ t))=(zero_zero_nat)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])). 1.07/1.26 thf(c_0_56, plain, ~((ord_less_nat @ zero_zero_nat @ (times_times_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)) @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)))), inference(rw,[status(thm)],[c_0_52, c_0_51])). 1.07/1.26 thf(c_0_57, plain, ![X1:nat, X2:nat]:(((ord_less_nat @ zero_zero_nat @ (times_times_nat @ X1 @ X2))|~((ord_less_nat @ zero_zero_nat @ X1))|~((ord_less_nat @ zero_zero_nat @ X2)))), inference(split_conjunct,[status(thm)],[c_0_53])). 1.07/1.26 thf(c_0_58, plain, (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ (finite447719721at_nat @ (edmond771116670s_uE_a @ c)) @ one_one_nat)), inference(rw,[status(thm)],[c_0_54, c_0_55])). 1.07/1.26 thf(c_0_59, plain, ![X683:nat]:(((plus_plus_nat @ X683 @ zero_zero_nat)=(X683))), inference(variable_rename,[status(thm)],[fact_63_add_Oright__neutral])). 1.07/1.26 thf(c_0_60, plain, ![X547:nat, X548:nat]:(((~(ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ X547 @ X548))|(ord_less_nat @ X548 @ X547))&(~(ord_less_nat @ X548 @ X547)|(ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ X547 @ X548))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_38_zero__less__diff])])). 1.07/1.26 thf(c_0_61, plain, ~((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_58])])). 1.07/1.26 thf(c_0_62, plain, ![X1:nat]:(((plus_plus_nat @ X1 @ zero_zero_nat)=(X1))), inference(split_conjunct,[status(thm)],[c_0_59])). 1.07/1.26 thf(c_0_63, plain, ![X1:nat, X2:nat]:(((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ X2 @ X1))|~((ord_less_nat @ X1 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_60])). 1.07/1.26 thf(c_0_64, plain, ((minus_minus_nat @ (finite_card_nat @ (v_a @ c)) @ (min_dist_a @ c @ s @ t))=(zero_zero_nat)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_47]), c_0_48])])). 1.07/1.26 thf(c_0_65, plain, ![X1:nat]:(~((ord_less_nat @ X1 @ X1))), inference(spm,[status(thm)],[c_0_49, c_0_62])). 1.07/1.26 thf(c_0_66, plain, ![X927:nat, X928:nat]:((~(member_nat @ X927 @ (v_a @ c))|(~(connected_a @ c @ X927 @ X928)|(ord_less_nat @ (min_dist_a @ c @ X927 @ X928) @ (finite_card_nat @ (v_a @ c)))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_10_min__dist__less__V])])). 1.07/1.26 thf(c_0_67, plain, ~((ord_less_nat @ (min_dist_a @ c @ s @ t) @ (finite_card_nat @ (v_a @ c)))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_64]), c_0_65])). 1.07/1.26 thf(c_0_68, plain, ![X1:nat, X2:nat]:(((ord_less_nat @ (min_dist_a @ c @ X1 @ X2) @ (finite_card_nat @ (v_a @ c)))|~((member_nat @ X1 @ (v_a @ c)))|~((connected_a @ c @ X1 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_66])). 1.07/1.26 thf(c_0_69, plain, (member_nat @ s @ (v_a @ c)), inference(split_conjunct,[status(thm)],[fact_4_SV])). 1.07/1.26 thf(c_0_70, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_69]), c_0_24])]), ['proof']). 1.07/1.26 # SZS output end CNFRefutation 1.07/1.26 # Parsed axioms : 261 1.07/1.26 # Removed by relevancy pruning/SinE : 39 1.07/1.26 # Initial clauses : 346 1.07/1.26 # Removed in clause preprocessing : 25 1.07/1.26 # Initial clauses in saturation : 321 1.07/1.26 # Processed clauses : 451 1.07/1.26 # ...of these trivial : 22 1.07/1.26 # ...subsumed : 165 1.07/1.26 # ...remaining for further processing : 264 1.07/1.26 # Other redundant clauses eliminated : 29 1.07/1.26 # Clauses deleted for lack of memory : 0 1.07/1.26 # Backward-subsumed : 11 1.07/1.26 # Backward-rewritten : 17 1.07/1.26 # Generated clauses : 3373 1.07/1.26 # ...of the previous two non-redundant : 2804 1.07/1.26 # ...aggressively subsumed : 0 1.07/1.26 # Contextual simplify-reflections : 0 1.07/1.26 # Paramodulations : 3253 1.07/1.26 # Factorizations : 4 1.07/1.26 # NegExts : 0 1.07/1.26 # Equation resolutions : 37 1.07/1.26 # Propositional unsat checks : 0 1.07/1.26 # Propositional check models : 0 1.07/1.26 # Propositional check unsatisfiable : 0 1.07/1.26 # Propositional clauses : 0 1.07/1.26 # Propositional clauses after purity: 0 1.07/1.26 # Propositional unsat core size : 0 1.07/1.26 # Propositional preprocessing time : 0.000 1.07/1.26 # Propositional encoding time : 0.000 1.07/1.26 # Propositional solver time : 0.000 1.07/1.26 # Success case prop preproc time : 0.000 1.07/1.26 # Success case prop encoding time : 0.000 1.07/1.26 # Success case prop solver time : 0.000 1.07/1.26 # Current number of processed clauses : 227 1.07/1.26 # Positive orientable unit clauses : 50 1.07/1.26 # Positive unorientable unit clauses: 5 1.07/1.26 # Negative unit clauses : 17 1.07/1.26 # Non-unit-clauses : 155 1.07/1.26 # Current number of unprocessed clauses: 2649 1.07/1.26 # ...number of literals in the above : 7941 1.07/1.26 # Current number of archived formulas : 0 1.07/1.26 # Current number of archived clauses : 31 1.07/1.26 # Clause-clause subsumption calls (NU) : 16335 1.07/1.26 # Rec. Clause-clause subsumption calls : 7603 1.07/1.26 # Non-unit clause-clause subsumptions : 104 1.07/1.26 # Unit Clause-clause subsumption calls : 1392 1.07/1.26 # Rewrite failures with RHS unbound : 0 1.07/1.26 # BW rewrite match attempts : 33 1.07/1.26 # BW rewrite match successes : 8 1.07/1.26 # Condensation attempts : 0 1.07/1.26 # Condensation successes : 0 1.07/1.26 # Termbank termtop insertions : 120100 1.07/1.26 1.07/1.26 # ------------------------------------------------- 1.07/1.26 # User time : 0.774 s 1.07/1.26 # System time : 0.012 s 1.07/1.26 # Total time : 0.786 s 1.07/1.26 # Maximum resident set size: 3212 pages 1.07/1.26 1.07/1.26 # ------------------------------------------------- 1.07/1.26 # User time : 0.781 s 1.07/1.26 # System time : 0.014 s 1.07/1.26 # Total time : 0.795 s 1.07/1.26 # Maximum resident set size: 2052 pages 1.07/1.26 EOF