%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP052^1 : TPTP v9.2.1. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n025.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 : Wed Jun 3 08:24:54 AM UTC 2026 % Result : Theorem 155.07s 155.73s % Output : Proof 155.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP052^1 : TPTP v9.2.1. Released v7.5.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n025.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 04:12:31 EDT 2026 % 0.17/0.34 % CPUTime : % 0.39/0.57 %----Proving TH0 % 155.07/155.73 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 155.07/155.73 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 155.07/155.73 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 155.07/155.73 --- Run --ho-elim --full-saturate-quant at 18s... % 155.07/155.73 % SZS status Theorem % 155.07/155.73 % SZS output start Proof % 155.07/155.73 ( % 155.07/155.73 (declare-sort tptp.product_prod_nat_nat 0) % 155.07/155.73 (declare-sort tptp.capacity 0) % 155.07/155.73 (declare-sort tptp.nat 0) % 155.07/155.73 (declare-sort tptp.set_Pr1986765409at_nat 0) % 155.07/155.73 (declare-sort tptp.set_nat 0) % 155.07/155.73 (declare-sort tptp.list_P559422087at_nat 0) % 155.07/155.73 (declare-const tptp.bot_bot_set_nat tptp.set_nat) % 155.07/155.73 (declare-const tptp.member_nat (-> tptp.nat tptp.set_nat Bool)) % 155.07/155.73 (declare-const tptp.bot_bo2130386637at_nat tptp.set_Pr1986765409at_nat) % 155.07/155.73 (declare-const tptp.member701585322at_nat (-> tptp.product_prod_nat_nat tptp.set_Pr1986765409at_nat Bool)) % 155.07/155.73 (declare-const tptp.inf_in586391887at_nat (-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (declare-const tptp.cap_capacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.set_nat tptp.capacity)) % 155.07/155.73 (declare-const tptp.ord_less_eq_capacity (-> tptp.capacity tptp.capacity Bool)) % 155.07/155.73 (declare-const tptp.nCut_capacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat tptp.set_nat Bool)) % 155.07/155.73 (declare-const tptp.flow_capacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat (-> tptp.product_prod_nat_nat tptp.capacity) Bool)) % 155.07/155.73 (declare-const tptp.preflow_capacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat (-> tptp.product_prod_nat_nat tptp.capacity) Bool)) % 155.07/155.73 (declare-const tptp.network_capacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat Bool)) % 155.07/155.73 (declare-const tptp.finite217307323pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) Bool)) % 155.07/155.73 (declare-const tptp.p tptp.list_P559422087at_nat) % 155.07/155.73 (declare-const tptp.ord_le1015898640_nat_o (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) Bool)) % 155.07/155.73 (declare-const tptp.ord_less_capacity (-> tptp.capacity tptp.capacity Bool)) % 155.07/155.73 (declare-const tptp.excess_capacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.capacity)) % 155.07/155.73 (declare-const tptp.zero_zero_capacity tptp.capacity) % 155.07/155.73 (declare-const tptp.product_Pair_nat_nat (-> tptp.nat tptp.nat tptp.product_prod_nat_nat)) % 155.07/155.73 (declare-const tptp.ord_le1039616028_nat_o (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) Bool)) % 155.07/155.73 (declare-const tptp.augmen1090971539pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat (-> tptp.product_prod_nat_nat tptp.capacity) tptp.list_P559422087at_nat Bool)) % 155.07/155.73 (declare-const tptp.converse_nat_nat (-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (declare-const tptp.is_max2144541363pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat tptp.capacity Bool)) % 155.07/155.73 (declare-const tptp.augmen72931474pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) (-> tptp.product_prod_nat_nat tptp.capacity) tptp.list_P559422087at_nat tptp.product_prod_nat_nat tptp.capacity)) % 155.07/155.73 (declare-const tptp.product_swap_nat_nat (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) % 155.07/155.73 (declare-const tptp.isMaxFlow_capacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat (-> tptp.product_prod_nat_nat tptp.capacity) Bool)) % 155.07/155.73 (declare-const tptp.residu164581374pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat (-> tptp.product_prod_nat_nat tptp.capacity) Bool)) % 155.07/155.73 (declare-const tptp.isSimp1359852763pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)) % 155.07/155.73 (declare-const tptp.isShor1936442771pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)) % 155.07/155.73 (declare-const tptp.collect_nat (-> (-> tptp.nat Bool) tptp.set_nat)) % 155.07/155.73 (declare-const tptp.f (-> tptp.product_prod_nat_nat tptp.capacity)) % 155.07/155.73 (declare-const tptp.s tptp.nat) % 155.07/155.73 (declare-const tptp.residu203630698pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) (-> tptp.product_prod_nat_nat tptp.capacity) tptp.product_prod_nat_nat tptp.capacity)) % 155.07/155.73 (declare-const tptp.set_Pr2131844118at_nat (-> tptp.list_P559422087at_nat tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (declare-const tptp.t tptp.nat) % 155.07/155.73 (declare-const tptp.c (-> tptp.product_prod_nat_nat tptp.capacity)) % 155.07/155.73 (declare-const tptp.inf_in2138576462_nat_o (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat Bool)) % 155.07/155.73 (declare-const tptp.residu1549650759pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) (-> tptp.product_prod_nat_nat tptp.capacity) tptp.product_prod_nat_nat tptp.capacity)) % 155.07/155.73 (declare-const tptp.residu800046103pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.nat (-> tptp.product_prod_nat_nat tptp.capacity) Bool)) % 155.07/155.73 (declare-const tptp.augmen68920357pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) (-> tptp.product_prod_nat_nat tptp.capacity) tptp.list_P559422087at_nat tptp.capacity)) % 155.07/155.73 (declare-const tptp.augmen887209518pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) (-> tptp.product_prod_nat_nat tptp.capacity) (-> tptp.product_prod_nat_nat tptp.capacity) tptp.product_prod_nat_nat tptp.capacity)) % 155.07/155.73 (declare-const tptp.collec7649004at_nat (-> (-> tptp.product_prod_nat_nat Bool) tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (declare-const tptp.plus_plus_capacity (-> tptp.capacity tptp.capacity tptp.capacity)) % 155.07/155.73 (declare-const tptp.val_capacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat (-> tptp.product_prod_nat_nat tptp.capacity) tptp.capacity)) % 155.07/155.73 (declare-const tptp.bot_bot_o Bool) % 155.07/155.73 (define tptp.bot_bot_nat_o () (let ((_let_1 (@var "X3" tptp.nat))) (lambda (@list _let_1) (_ (_ tptp.member_nat _let_1) tptp.bot_bot_set_nat)))) % 155.07/155.73 (define tptp.bot_bo513358416_nat_o () (let ((_let_1 (@var "X3" tptp.product_prod_nat_nat))) (lambda (@list _let_1) (_ (_ tptp.member701585322at_nat _let_1) tptp.bot_bo2130386637at_nat)))) % 155.07/155.73 (define tptp.ord_le841296385at_nat () (let ((_let_1 (@var "B2" tptp.set_Pr1986765409at_nat))) (let ((_let_2 (@var "A2" tptp.set_Pr1986765409at_nat))) (lambda (@list _let_1 _let_2) (= (_ (_ tptp.inf_in586391887at_nat _let_2) _let_1) _let_1))))) % 155.07/155.73 (define tptp.isMinCut_capacity () (let ((_let_1 (@var "K5" tptp.set_nat))) (let ((_let_2 (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (let ((_let_3 (_ tptp.cap_capacity _let_2))) (let ((_let_4 (@var "K2" tptp.set_nat))) (let ((_let_5 (@var "T2" tptp.nat))) (let ((_let_6 (@var "S2" tptp.nat))) (let ((_let_7 (_ (_ (_ tptp.nCut_capacity _let_2) _let_6) _let_5))) (lambda (@list _let_2 _let_6 _let_5 _let_4) (and (_ _let_7 _let_4) (forall (@list _let_1) (=> (_ _let_7 _let_1) (_ (_ tptp.ord_less_eq_capacity (_ _let_3 _let_4)) (_ _let_3 _let_1)))))))))))))) % 155.07/155.73 (define tptp.nPreflow_capacity () (let ((_let_1 (@var "F2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (let ((_let_2 (@var "T2" tptp.nat))) (let ((_let_3 (@var "S2" tptp.nat))) (let ((_let_4 (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (lambda (@list _let_4 _let_3 _let_2 _let_1) (and (_ (_ (_ tptp.network_capacity _let_4) _let_3) _let_2) (_ (_ (_ (_ tptp.preflow_capacity _let_4) _let_3) _let_2) _let_1)))))))) % 155.07/155.73 (define tptp.nFlow_capacity () (let ((_let_1 (@var "F2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (let ((_let_2 (@var "T2" tptp.nat))) (let ((_let_3 (@var "S2" tptp.nat))) (let ((_let_4 (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (lambda (@list _let_4 _let_3 _let_2 _let_1) (and (_ (_ (_ (_ tptp.nPreflow_capacity _let_4) _let_3) _let_2) _let_1) (_ (_ (_ (_ tptp.flow_capacity _let_4) _let_3) _let_2) _let_1)))))))) % 155.07/155.73 (define tptp.finite1387368318pacity () (let ((_let_1 (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (let ((_let_2 (@var "F2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (let ((_let_3 (@var "T2" tptp.nat))) (let ((_let_4 (@var "S2" tptp.nat))) (lambda (@list _let_1 _let_4 _let_3 _let_2) (and (_ (_ (_ (_ tptp.preflow_capacity _let_1) _let_4) _let_3) _let_2) (_ tptp.finite217307323pacity _let_1)))))))) % 155.07/155.73 (define tptp.ord_le116442893at_nat () (let ((_let_1 (@var "B2" tptp.set_Pr1986765409at_nat))) (let ((_let_2 (@var "A2" tptp.set_Pr1986765409at_nat))) (lambda (@list _let_2 _let_1) (and (= _let_2 (_ (_ tptp.inf_in586391887at_nat _let_2) _let_1)) (not (= _let_2 _let_1))))))) % 155.07/155.73 (define @t1 () (@var "P" tptp.list_P559422087at_nat)) % 155.07/155.73 (define @t2 () (_ tptp.set_Pr2131844118at_nat @t1)) % 155.07/155.73 (define @t3 () (_ tptp.converse_nat_nat @t2)) % 155.07/155.73 (define @t4 () (_ (_ tptp.inf_in586391887at_nat @t2) @t3)) % 155.07/155.73 (define @t5 () (= @t4 tptp.bot_bo2130386637at_nat)) % 155.07/155.73 (define @t6 () (@var "T" tptp.nat)) % 155.07/155.73 (define @t7 () (@var "S" tptp.nat)) % 155.07/155.73 (define @t8 () (_ (_ tptp.residu203630698pacity tptp.c) tptp.f)) % 155.07/155.73 (define @t9 () (_ tptp.isSimp1359852763pacity @t8)) % 155.07/155.73 (define @t10 () (_ (_ (_ @t9 @t7) @t1) @t6)) % 155.07/155.73 (define @t11 () (=> @t10 @t5)) % 155.07/155.73 (define @t12 () (@list @t7 @t1 @t6)) % 155.07/155.73 (define @t13 () (forall @t12 @t11)) % 155.07/155.73 (define @t14 () (_ tptp.isSimp1359852763pacity tptp.c)) % 155.07/155.73 (define @t15 () (_ (_ (_ @t14 @t7) @t1) @t6)) % 155.07/155.73 (define @t16 () (_ (_ (_ tptp.nFlow_capacity tptp.c) tptp.s) tptp.t)) % 155.07/155.73 (define @t17 () (@var "Fv2" tptp.capacity)) % 155.07/155.73 (define @t18 () (@var "Fv1" tptp.capacity)) % 155.07/155.73 (define @t19 () (= @t18 @t17)) % 155.07/155.73 (define @t20 () (_ (_ (_ tptp.is_max2144541363pacity tptp.c) tptp.s) tptp.t)) % 155.07/155.73 (define @t21 () (_ (_ (_ @t9 tptp.s) @t1) tptp.t)) % 155.07/155.73 (define @t22 () (_ (_ (_ (_ tptp.augmen1090971539pacity tptp.c) tptp.s) tptp.t) tptp.f)) % 155.07/155.73 (define @t23 () (_ @t22 @t1)) % 155.07/155.73 (define @t24 () (= @t23 @t21)) % 155.07/155.73 (define @t25 () (@list @t1)) % 155.07/155.73 (define @t26 () (forall @t25 @t24)) % 155.07/155.73 (define @t27 () (@var "X_1" tptp.list_P559422087at_nat)) % 155.07/155.73 (define @t28 () (@list @t27)) % 155.07/155.73 (define @t29 () (_ (_ (_ tptp.isMaxFlow_capacity tptp.c) tptp.s) tptp.t)) % 155.07/155.73 (define @t30 () (_ @t29 tptp.f)) % 155.07/155.73 (define @t31 () (@var "X" tptp.list_P559422087at_nat)) % 155.07/155.73 (define @t32 () (@list @t31)) % 155.07/155.73 (define @t33 () (not (exists @t32 (_ @t22 @t31)))) % 155.07/155.73 (define @t34 () (_ (_ (_ tptp.flow_capacity tptp.c) tptp.s) tptp.t)) % 155.07/155.73 (define @t35 () (@var "X2" (-> tptp.product_prod_nat_nat Bool))) % 155.07/155.73 (define @t36 () (@list @t35)) % 155.07/155.73 (define @t37 () (@var "X2" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t38 () (@list @t37)) % 155.07/155.73 (define @t39 () (_ tptp.inf_in586391887at_nat @t37)) % 155.07/155.73 (define @t40 () (@var "Y" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t41 () (_ @t39 @t40)) % 155.07/155.73 (define @t42 () (_ tptp.inf_in586391887at_nat @t41)) % 155.07/155.73 (define @t43 () (@list @t37 @t40)) % 155.07/155.73 (define @t44 () (@var "B" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t45 () (@var "A" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t46 () (_ tptp.inf_in586391887at_nat @t45)) % 155.07/155.73 (define @t47 () (_ @t46 @t44)) % 155.07/155.73 (define @t48 () (_ tptp.inf_in586391887at_nat @t47)) % 155.07/155.73 (define @t49 () (@list @t45 @t44)) % 155.07/155.73 (define @t50 () (@list @t45)) % 155.07/155.73 (define @t51 () (@var "R" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t52 () (_ tptp.converse_nat_nat @t51)) % 155.07/155.73 (define @t53 () (@var "S" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t54 () (_ tptp.converse_nat_nat @t53)) % 155.07/155.73 (define @t55 () (@list @t51 @t53)) % 155.07/155.73 (define @t56 () (_ (_ (_ tptp.augmen72931474pacity tptp.c) tptp.f) @t1)) % 155.07/155.73 (define @t57 () (_ (_ (_ tptp.flow_capacity @t8) tptp.s) tptp.t)) % 155.07/155.73 (define @t58 () (@var "Z" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t59 () (_ tptp.inf_in586391887at_nat @t40)) % 155.07/155.73 (define @t60 () (_ @t59 @t58)) % 155.07/155.73 (define @t61 () (_ @t39 @t60)) % 155.07/155.73 (define @t62 () (@list @t37 @t40 @t58)) % 155.07/155.73 (define @t63 () (@var "C" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t64 () (_ tptp.inf_in586391887at_nat @t44)) % 155.07/155.73 (define @t65 () (_ @t64 @t63)) % 155.07/155.73 (define @t66 () (_ @t46 @t65)) % 155.07/155.73 (define @t67 () (@list @t44 @t45 @t63)) % 155.07/155.73 (define @t68 () (@var "X3" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t69 () (@var "Y2" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t70 () (@list @t68 @t69)) % 155.07/155.73 (define @t71 () (@var "A2" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t72 () (@var "B2" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t73 () (@list @t71 @t72)) % 155.07/155.73 (define @t74 () (@list @t45 @t44 @t63)) % 155.07/155.73 (define @t75 () (@var "K" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t76 () (_ tptp.inf_in586391887at_nat @t75)) % 155.07/155.73 (define @t77 () (_ @t76 @t47)) % 155.07/155.73 (define @t78 () (@var "B3" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t79 () (@var "A3" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t80 () (@var "F" (-> tptp.product_prod_nat_nat tptp.capacity))) % 155.07/155.73 (define @t81 () (_ (_ (_ tptp.augmen887209518pacity tptp.c) tptp.f) @t80)) % 155.07/155.73 (define @t82 () (_ @t57 @t80)) % 155.07/155.73 (define @t83 () (@list @t80)) % 155.07/155.73 (define @t84 () (@var "A" tptp.nat)) % 155.07/155.73 (define @t85 () (@var "P2" (-> tptp.nat Bool))) % 155.07/155.73 (define @t86 () (@var "A" tptp.product_prod_nat_nat)) % 155.07/155.73 (define @t87 () (@var "P2" (-> tptp.product_prod_nat_nat Bool))) % 155.07/155.73 (define @t88 () (_ tptp.collec7649004at_nat @t87)) % 155.07/155.73 (define @t89 () (@var "A3" tptp.set_nat)) % 155.07/155.73 (define @t90 () (@var "X3" tptp.nat)) % 155.07/155.73 (define @t91 () (_ tptp.member_nat @t90)) % 155.07/155.73 (define @t92 () (@list @t90)) % 155.07/155.73 (define @t93 () (@var "X3" tptp.product_prod_nat_nat)) % 155.07/155.73 (define @t94 () (_ tptp.member701585322at_nat @t93)) % 155.07/155.73 (define @t95 () (@list @t93)) % 155.07/155.73 (define @t96 () (@var "Q" (-> tptp.product_prod_nat_nat Bool))) % 155.07/155.73 (define @t97 () (@var "X4" tptp.product_prod_nat_nat)) % 155.07/155.73 (define @t98 () (@var "E" tptp.product_prod_nat_nat)) % 155.07/155.73 (define @t99 () (=> (_ (_ tptp.member701585322at_nat @t98) @t2) (not (_ (_ tptp.member701585322at_nat (_ tptp.product_swap_nat_nat @t98)) @t2)))) % 155.07/155.73 (define @t100 () (@list @t7 @t1 @t6 @t98)) % 155.07/155.73 (define @t101 () (@var "F2" (-> tptp.product_prod_nat_nat tptp.capacity))) % 155.07/155.73 (define @t102 () (_ (_ tptp.val_capacity tptp.c) tptp.s)) % 155.07/155.73 (define @t103 () (@var "Fv" tptp.capacity)) % 155.07/155.73 (define @t104 () (@list @t101)) % 155.07/155.73 (define @t105 () (_ tptp.isShor1936442771pacity @t8)) % 155.07/155.73 (define @t106 () (_ @t105 tptp.s)) % 155.07/155.73 (define @t107 () (@var "P3" tptp.list_P559422087at_nat)) % 155.07/155.73 (define @t108 () (@list @t107)) % 155.07/155.73 (define @t109 () (@var "C" (-> tptp.product_prod_nat_nat tptp.capacity))) % 155.07/155.73 (define @t110 () (_ tptp.isSimp1359852763pacity @t109)) % 155.07/155.73 (define @t111 () (_ (_ (_ @t110 @t7) @t1) @t6)) % 155.07/155.73 (define @t112 () (@list @t109 @t7 @t1 @t6)) % 155.07/155.73 (define @t113 () (@var "Cf" (-> tptp.product_prod_nat_nat tptp.capacity))) % 155.07/155.73 (define @t114 () (_ (_ (_ tptp.residu800046103pacity @t109) @t7) @t6)) % 155.07/155.73 (define @t115 () (_ @t114 @t113)) % 155.07/155.73 (define @t116 () (_ tptp.residu1549650759pacity @t109)) % 155.07/155.73 (define @t117 () (_ @t116 @t113)) % 155.07/155.73 (define @t118 () (_ (_ (_ tptp.isMaxFlow_capacity @t109) @t7) @t6)) % 155.07/155.73 (define @t119 () (_ (_ (_ tptp.residu164581374pacity @t109) @t7) @t6)) % 155.07/155.73 (define @t120 () (_ @t119 @t113)) % 155.07/155.73 (define @t121 () (@list @t109 @t7 @t6 @t113)) % 155.07/155.73 (define @t122 () (@var "F3" (-> tptp.product_prod_nat_nat tptp.capacity))) % 155.07/155.73 (define @t123 () (_ (_ (_ (_ tptp.augmen1090971539pacity @t109) @t7) @t6) @t122)) % 155.07/155.73 (define @t124 () (_ @t123 @t1)) % 155.07/155.73 (define @t125 () (_ tptp.residu203630698pacity @t109)) % 155.07/155.73 (define @t126 () (_ @t125 @t122)) % 155.07/155.73 (define @t127 () (_ (_ tptp.isShor1936442771pacity @t126) @t7)) % 155.07/155.73 (define @t128 () (_ (_ (_ tptp.nFlow_capacity @t109) @t7) @t6)) % 155.07/155.73 (define @t129 () (_ @t128 @t122)) % 155.07/155.73 (define @t130 () (@list @t109 @t7 @t6 @t122 @t1)) % 155.07/155.73 (define @t131 () (_ (_ (_ tptp.network_capacity @t109) @t7) @t6)) % 155.07/155.73 (define @t132 () (_ (_ (_ tptp.nPreflow_capacity @t109) @t7) @t6)) % 155.07/155.73 (define @t133 () (_ @t132 @t122)) % 155.07/155.73 (define @t134 () (@list @t109 @t7 @t6 @t122)) % 155.07/155.73 (define @t135 () (@var "F4" (-> tptp.product_prod_nat_nat tptp.capacity))) % 155.07/155.73 (define @t136 () (= @t113 (_ @t125 @t135))) % 155.07/155.73 (define @t137 () (@list @t135)) % 155.07/155.73 (define @t138 () (_ (_ (_ tptp.augmen68920357pacity tptp.c) tptp.f) @t1)) % 155.07/155.73 (define @t139 () (_ (_ tptp.val_capacity @t8) tptp.s)) % 155.07/155.73 (define @t140 () (_ @t102 tptp.f)) % 155.07/155.73 (define @t141 () (_ @t102 @t122)) % 155.07/155.73 (define @t142 () (@var "F5" (-> tptp.product_prod_nat_nat tptp.capacity))) % 155.07/155.73 (define @t143 () (_ (_ tptp.ord_less_eq_capacity (_ @t102 @t142)) @t141)) % 155.07/155.73 (define @t144 () (@list @t142)) % 155.07/155.73 (define @t145 () (_ @t29 @t122)) % 155.07/155.73 (define @t146 () (@list @t122)) % 155.07/155.73 (define @t147 () (_ (_ (_ tptp.augmen72931474pacity @t109) @t122) @t1)) % 155.07/155.73 (define @t148 () (_ (_ (_ tptp.flow_capacity @t126) @t7) @t6)) % 155.07/155.73 (define @t149 () (@var "K" tptp.set_nat)) % 155.07/155.73 (define @t150 () (_ tptp.cap_capacity tptp.c)) % 155.07/155.73 (define @t151 () (_ tptp.ord_le841296385at_nat @t37)) % 155.07/155.73 (define @t152 () (@var "X2" tptp.capacity)) % 155.07/155.73 (define @t153 () (_ tptp.ord_less_eq_capacity @t152)) % 155.07/155.73 (define @t154 () (_ tptp.ord_le841296385at_nat @t45)) % 155.07/155.73 (define @t155 () (_ @t154 @t63)) % 155.07/155.73 (define @t156 () (_ @t154 @t44)) % 155.07/155.73 (define @t157 () (_ @t154 @t65)) % 155.07/155.73 (define @t158 () (_ @t151 @t58)) % 155.07/155.73 (define @t159 () (_ @t151 @t40)) % 155.07/155.73 (define @t160 () (_ @t151 @t60)) % 155.07/155.73 (define @t161 () (@var "A" (-> tptp.product_prod_nat_nat Bool))) % 155.07/155.73 (define @t162 () (@list @t161)) % 155.07/155.73 (define @t163 () (= @t161 tptp.bot_bo513358416_nat_o)) % 155.07/155.73 (define @t164 () (_ (_ tptp.ord_le1039616028_nat_o @t161) tptp.bot_bo513358416_nat_o)) % 155.07/155.73 (define @t165 () (= @t45 tptp.bot_bo2130386637at_nat)) % 155.07/155.73 (define @t166 () (_ @t154 tptp.bot_bo2130386637at_nat)) % 155.07/155.73 (define @t167 () (@var "F3" (-> tptp.set_Pr1986765409at_nat tptp.capacity))) % 155.07/155.73 (define @t168 () (@var "A" tptp.capacity)) % 155.07/155.73 (define @t169 () (_ tptp.ord_less_eq_capacity @t168)) % 155.07/155.73 (define @t170 () (@var "Y3" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t171 () (@var "X4" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t172 () (_ tptp.ord_le841296385at_nat @t171)) % 155.07/155.73 (define @t173 () (_ @t172 @t170)) % 155.07/155.73 (define @t174 () (@list @t171 @t170)) % 155.07/155.73 (define @t175 () (forall @t174 (=> @t173 (_ (_ tptp.ord_less_eq_capacity (_ @t167 @t171)) (_ @t167 @t170))))) % 155.07/155.73 (define @t176 () (_ tptp.ord_le841296385at_nat @t44)) % 155.07/155.73 (define @t177 () (_ @t176 @t63)) % 155.07/155.73 (define @t178 () (=> @t177 (=> @t175 (_ @t169 (_ @t167 @t63))))) % 155.07/155.73 (define @t179 () (_ @t167 @t44)) % 155.07/155.73 (define @t180 () (@list @t168 @t167 @t44 @t63)) % 155.07/155.73 (define @t181 () (@var "C" tptp.capacity)) % 155.07/155.73 (define @t182 () (@var "F3" (-> tptp.capacity tptp.set_Pr1986765409at_nat))) % 155.07/155.73 (define @t183 () (@var "Y3" tptp.capacity)) % 155.07/155.73 (define @t184 () (@var "X4" tptp.capacity)) % 155.07/155.73 (define @t185 () (_ (_ tptp.ord_less_eq_capacity @t184) @t183)) % 155.07/155.73 (define @t186 () (@list @t184 @t183)) % 155.07/155.73 (define @t187 () (forall @t186 (=> @t185 (_ (_ tptp.ord_le841296385at_nat (_ @t182 @t184)) (_ @t182 @t183))))) % 155.07/155.73 (define @t188 () (@var "B" tptp.capacity)) % 155.07/155.73 (define @t189 () (_ tptp.ord_less_eq_capacity @t188)) % 155.07/155.73 (define @t190 () (_ @t189 @t181)) % 155.07/155.73 (define @t191 () (=> @t190 (=> @t187 (_ @t154 (_ @t182 @t181))))) % 155.07/155.73 (define @t192 () (_ @t182 @t188)) % 155.07/155.73 (define @t193 () (@list @t45 @t182 @t188 @t181)) % 155.07/155.73 (define @t194 () (@var "F3" (-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat))) % 155.07/155.73 (define @t195 () (forall @t174 (=> @t173 (_ (_ tptp.ord_le841296385at_nat (_ @t194 @t171)) (_ @t194 @t170))))) % 155.07/155.73 (define @t196 () (=> @t177 (=> @t195 (_ @t154 (_ @t194 @t63))))) % 155.07/155.73 (define @t197 () (_ @t194 @t44)) % 155.07/155.73 (define @t198 () (@list @t45 @t194 @t44 @t63)) % 155.07/155.73 (define @t199 () (@var "F3" (-> tptp.capacity tptp.capacity))) % 155.07/155.73 (define @t200 () (forall @t186 (=> @t185 (_ (_ tptp.ord_less_eq_capacity (_ @t199 @t184)) (_ @t199 @t183))))) % 155.07/155.73 (define @t201 () (=> @t190 (=> @t200 (_ @t169 (_ @t199 @t181))))) % 155.07/155.73 (define @t202 () (_ @t199 @t188)) % 155.07/155.73 (define @t203 () (@list @t168 @t199 @t188 @t181)) % 155.07/155.73 (define @t204 () (=> @t187 (_ (_ tptp.ord_le841296385at_nat (_ @t182 @t168)) @t63))) % 155.07/155.73 (define @t205 () (_ @t169 @t188)) % 155.07/155.73 (define @t206 () (@list @t168 @t188 @t182 @t63)) % 155.07/155.73 (define @t207 () (=> @t175 (_ (_ tptp.ord_less_eq_capacity (_ @t167 @t45)) @t181))) % 155.07/155.73 (define @t208 () (@list @t45 @t44 @t167 @t181)) % 155.07/155.73 (define @t209 () (=> @t195 (_ (_ tptp.ord_le841296385at_nat (_ @t194 @t45)) @t63))) % 155.07/155.73 (define @t210 () (@list @t45 @t44 @t194 @t63)) % 155.07/155.73 (define @t211 () (=> @t200 (_ (_ tptp.ord_less_eq_capacity (_ @t199 @t168)) @t181))) % 155.07/155.73 (define @t212 () (@list @t168 @t188 @t199 @t181)) % 155.07/155.73 (define @t213 () (@var "Z2" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t214 () (@var "Y4" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t215 () (lambda (@list @t214 @t213) (= @t214 @t213))) % 155.07/155.73 (define @t216 () (@var "X3" tptp.capacity)) % 155.07/155.73 (define @t217 () (@var "Y2" tptp.capacity)) % 155.07/155.73 (define @t218 () (@var "Z2" tptp.capacity)) % 155.07/155.73 (define @t219 () (@var "Y4" tptp.capacity)) % 155.07/155.73 (define @t220 () (lambda (@list @t219 @t218) (= @t219 @t218))) % 155.07/155.73 (define @t221 () (= @t37 @t40)) % 155.07/155.73 (define @t222 () (_ tptp.ord_le841296385at_nat @t40)) % 155.07/155.73 (define @t223 () (_ @t222 @t37)) % 155.07/155.73 (define @t224 () (@var "Y" tptp.capacity)) % 155.07/155.73 (define @t225 () (= @t152 @t224)) % 155.07/155.73 (define @t226 () (_ tptp.ord_less_eq_capacity @t224)) % 155.07/155.73 (define @t227 () (_ @t226 @t152)) % 155.07/155.73 (define @t228 () (_ @t153 @t224)) % 155.07/155.73 (define @t229 () (@list @t152 @t224)) % 155.07/155.73 (define @t230 () (not @t228)) % 155.07/155.73 (define @t231 () (=> @t177 @t155)) % 155.07/155.73 (define @t232 () (_ @t169 @t181)) % 155.07/155.73 (define @t233 () (=> @t190 @t232)) % 155.07/155.73 (define @t234 () (@list @t168 @t188 @t181)) % 155.07/155.73 (define @t235 () (@var "Z" tptp.capacity)) % 155.07/155.73 (define @t236 () (_ tptp.ord_less_eq_capacity @t235)) % 155.07/155.73 (define @t237 () (_ @t236 @t152)) % 155.07/155.73 (define @t238 () (_ @t226 @t235)) % 155.07/155.73 (define @t239 () (_ @t236 @t224)) % 155.07/155.73 (define @t240 () (_ @t153 @t235)) % 155.07/155.73 (define @t241 () (@list @t152 @t224 @t235)) % 155.07/155.73 (define @t242 () (@list @t40 @t37)) % 155.07/155.73 (define @t243 () (_ (_ tptp.ord_le841296385at_nat @t72) @t71)) % 155.07/155.73 (define @t244 () (_ (_ tptp.ord_le841296385at_nat @t71) @t72)) % 155.07/155.73 (define @t245 () (@var "A2" tptp.capacity)) % 155.07/155.73 (define @t246 () (@var "B2" tptp.capacity)) % 155.07/155.73 (define @t247 () (_ (_ tptp.ord_less_eq_capacity @t246) @t245)) % 155.07/155.73 (define @t248 () (_ (_ tptp.ord_less_eq_capacity @t245) @t246)) % 155.07/155.73 (define @t249 () (@list @t245 @t246)) % 155.07/155.73 (define @t250 () (= @t45 @t44)) % 155.07/155.73 (define @t251 () (= @t168 @t188)) % 155.07/155.73 (define @t252 () (_ @t176 @t45)) % 155.07/155.73 (define @t253 () (_ @t189 @t168)) % 155.07/155.73 (define @t254 () (@list @t168 @t188)) % 155.07/155.73 (define @t255 () (@var "P2" (-> tptp.capacity tptp.capacity Bool))) % 155.07/155.73 (define @t256 () (@var "B4" tptp.capacity)) % 155.07/155.73 (define @t257 () (@var "A4" tptp.capacity)) % 155.07/155.73 (define @t258 () (_ (_ @t255 @t257) @t256)) % 155.07/155.73 (define @t259 () (@list @t257 @t256)) % 155.07/155.73 (define @t260 () (_ tptp.ord_le841296385at_nat @t63)) % 155.07/155.73 (define @t261 () (_ tptp.ord_less_eq_capacity @t181)) % 155.07/155.73 (define @t262 () (@list @t44 @t45)) % 155.07/155.73 (define @t263 () (@list @t188 @t168)) % 155.07/155.73 (define @t264 () (_ tptp.ord_le841296385at_nat @t47)) % 155.07/155.73 (define @t265 () (_ @t264 @t63)) % 155.07/155.73 (define @t266 () (@list @t44 @t63 @t45)) % 155.07/155.73 (define @t267 () (@list @t45 @t63 @t44)) % 155.07/155.73 (define @t268 () (_ (_ tptp.inf_in586391887at_nat @t71) @t72)) % 155.07/155.73 (define @t269 () (= @t71 @t268)) % 155.07/155.73 (define @t270 () (@var "F3" (-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat))) % 155.07/155.73 (define @t271 () (@var "Z3" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t272 () (_ tptp.ord_le841296385at_nat (_ (_ @t270 @t171) @t170))) % 155.07/155.73 (define @t273 () (= @t45 @t47)) % 155.07/155.73 (define @t274 () (_ @t264 @t37)) % 155.07/155.73 (define @t275 () (@list @t44 @t37 @t45)) % 155.07/155.73 (define @t276 () (@list @t45 @t37 @t44)) % 155.07/155.73 (define @t277 () (@var "D" tptp.set_Pr1986765409at_nat)) % 155.07/155.73 (define @t278 () (_ @t151 @t47)) % 155.07/155.73 (define @t279 () (_ @t151 @t44)) % 155.07/155.73 (define @t280 () (_ @t151 @t45)) % 155.07/155.73 (define @t281 () (@list @t37 @t45 @t44)) % 155.07/155.73 (define @t282 () (_ tptp.ord_le841296385at_nat @t41)) % 155.07/155.73 (define @t283 () (_ (_ tptp.val_capacity @t126) @t7)) % 155.07/155.73 (define @t284 () (@var "K2" tptp.set_nat)) % 155.07/155.73 (define @t285 () (_ (_ (_ tptp.nCut_capacity tptp.c) tptp.s) tptp.t)) % 155.07/155.73 (define @t286 () (@list @t284)) % 155.07/155.73 (define @t287 () (@var "K3" tptp.set_nat)) % 155.07/155.73 (define @t288 () (@list @t287)) % 155.07/155.73 (define @t289 () (@var "K4" tptp.set_nat)) % 155.07/155.73 (define @t290 () (@list @t289)) % 155.07/155.73 (define @t291 () (@var "X_12" tptp.list_P559422087at_nat)) % 155.07/155.73 (define @t292 () (@list @t291)) % 155.07/155.73 (define @t293 () (_ (_ tptp.val_capacity @t109) @t7)) % 155.07/155.73 (define @t294 () (_ @t293 @t122)) % 155.07/155.73 (define @t295 () (_ (_ (_ tptp.augmen887209518pacity @t109) @t122) @t80)) % 155.07/155.73 (define @t296 () (_ @t148 @t80)) % 155.07/155.73 (define @t297 () (@list @t109 @t7 @t6 @t122 @t80)) % 155.07/155.73 (define @t298 () (_ tptp.cap_capacity @t109)) % 155.07/155.73 (define @t299 () (_ @t118 @t122)) % 155.07/155.73 (define @t300 () (_ (_ tptp.ord_less_eq_capacity (_ @t293 @t142)) @t294)) % 155.07/155.73 (define @t301 () (_ tptp.ord_le841296385at_nat @t51)) % 155.07/155.73 (define @t302 () (_ @t301 @t53)) % 155.07/155.73 (define @t303 () (_ tptp.ord_le841296385at_nat @t52)) % 155.07/155.73 (define @t304 () (_ (_ (_ tptp.nCut_capacity @t109) @t7) @t6)) % 155.07/155.73 (define @t305 () (_ @t304 @t149)) % 155.07/155.73 (define @t306 () (@list @t109 @t7 @t6 @t149)) % 155.07/155.73 (define @t307 () (@list @t109 @t7 @t6)) % 155.07/155.73 (define @t308 () (not (exists @t32 (_ @t123 @t31)))) % 155.07/155.73 (define @t309 () (_ (_ (_ tptp.flow_capacity @t109) @t7) @t6)) % 155.07/155.73 (define @t310 () (_ @t309 @t122)) % 155.07/155.73 (define @t311 () (_ (_ (_ (_ tptp.preflow_capacity @t109) @t7) @t6) @t122)) % 155.07/155.73 (define @t312 () (_ (_ (_ tptp.is_max2144541363pacity @t109) @t7) @t6)) % 155.07/155.73 (define @t313 () (_ tptp.finite217307323pacity @t109)) % 155.07/155.73 (define @t314 () (_ (_ (_ (_ tptp.finite1387368318pacity @t109) @t7) @t6) @t122)) % 155.07/155.73 (define @t315 () (@var "U1" tptp.nat)) % 155.07/155.73 (define @t316 () (_ tptp.product_Pair_nat_nat @t315)) % 155.07/155.73 (define @t317 () (not (_ (_ tptp.member701585322at_nat (_ @t316 @t315)) @t2))) % 155.07/155.73 (define @t318 () (@var "V" tptp.nat)) % 155.07/155.73 (define @t319 () (@var "U" tptp.nat)) % 155.07/155.73 (define @t320 () (_ (_ (_ @t9 @t319) @t1) @t318)) % 155.07/155.73 (define @t321 () (@list @t319 @t1 @t318 @t315)) % 155.07/155.73 (define @t322 () (@var "V1" tptp.nat)) % 155.07/155.73 (define @t323 () (@var "U2" tptp.nat)) % 155.07/155.73 (define @t324 () (_ (_ tptp.member701585322at_nat (_ @t316 @t322)) @t2)) % 155.07/155.73 (define @t325 () (=> @t324 (=> (not (= @t315 @t323)) (not (_ (_ tptp.member701585322at_nat (_ (_ tptp.product_Pair_nat_nat @t323) @t322)) @t2))))) % 155.07/155.73 (define @t326 () (@list @t319 @t1 @t318 @t315 @t322 @t323)) % 155.07/155.73 (define @t327 () (@var "V2" tptp.nat)) % 155.07/155.73 (define @t328 () (=> @t324 (=> (not (= @t322 @t327)) (not (_ (_ tptp.member701585322at_nat (_ @t316 @t327)) @t2))))) % 155.07/155.73 (define @t329 () (@list @t319 @t1 @t318 @t315 @t322 @t327)) % 155.07/155.73 (define @t330 () (_ (_ (_ @t14 @t319) @t1) @t318)) % 155.07/155.73 (define @t331 () (@var "B" tptp.nat)) % 155.07/155.73 (define @t332 () (_ tptp.member701585322at_nat (_ (_ tptp.product_Pair_nat_nat @t331) @t84))) % 155.07/155.73 (define @t333 () (_ @t332 @t51)) % 155.07/155.73 (define @t334 () (_ (_ tptp.product_Pair_nat_nat @t84) @t331)) % 155.07/155.73 (define @t335 () (_ tptp.member701585322at_nat @t334)) % 155.07/155.73 (define @t336 () (_ @t335 @t52)) % 155.07/155.73 (define @t337 () (@list @t84 @t331 @t51)) % 155.07/155.73 (define @t338 () (@var "Y3" tptp.nat)) % 155.07/155.73 (define @t339 () (@var "X4" tptp.nat)) % 155.07/155.73 (define @t340 () (_ (_ tptp.product_Pair_nat_nat @t339) @t338)) % 155.07/155.73 (define @t341 () (_ tptp.member701585322at_nat @t340)) % 155.07/155.73 (define @t342 () (_ @t341 @t51)) % 155.07/155.73 (define @t343 () (@list @t339 @t338)) % 155.07/155.73 (define @t344 () (@var "Yx" tptp.product_prod_nat_nat)) % 155.07/155.73 (define @t345 () (@var "A1" tptp.nat)) % 155.07/155.73 (define @t346 () (@var "A22" tptp.nat)) % 155.07/155.73 (define @t347 () (_ (_ tptp.member701585322at_nat (_ (_ tptp.product_Pair_nat_nat @t345) @t346)) @t52)) % 155.07/155.73 (define @t348 () (@list @t345 @t346 @t51)) % 155.07/155.73 (define @t349 () (@var "B2" tptp.nat)) % 155.07/155.73 (define @t350 () (@var "A2" tptp.nat)) % 155.07/155.73 (define @t351 () (@var "X22" tptp.nat)) % 155.07/155.73 (define @t352 () (@var "X1" tptp.nat)) % 155.07/155.73 (define @t353 () (@var "P2" (-> tptp.nat tptp.nat Bool))) % 155.07/155.73 (define @t354 () (@var "A4" tptp.nat)) % 155.07/155.73 (define @t355 () (@var "B4" tptp.nat)) % 155.07/155.73 (define @t356 () (_ (_ tptp.product_Pair_nat_nat @t354) @t355)) % 155.07/155.73 (define @t357 () (@list @t354 @t355)) % 155.07/155.73 (define @t358 () (_ (_ tptp.product_Pair_nat_nat @t352) @t351)) % 155.07/155.73 (define @t359 () (_ (_ (_ @t110 @t319) @t1) @t318)) % 155.07/155.73 (define @t360 () (_ (_ tptp.product_Pair_nat_nat @t319) @t318)) % 155.07/155.73 (define @t361 () (_ @t81 @t360)) % 155.07/155.73 (define @t362 () (_ tptp.ord_less_eq_capacity tptp.zero_zero_capacity)) % 155.07/155.73 (define @t363 () (@var "X2" tptp.nat)) % 155.07/155.73 (define @t364 () (@var "Y" tptp.nat)) % 155.07/155.73 (define @t365 () (@list @t98)) % 155.07/155.73 (define @t366 () (@var "B5" tptp.nat)) % 155.07/155.73 (define @t367 () (= @t331 @t366)) % 155.07/155.73 (define @t368 () (@var "A5" tptp.nat)) % 155.07/155.73 (define @t369 () (= @t84 @t368)) % 155.07/155.73 (define @t370 () (= @t334 (_ (_ tptp.product_Pair_nat_nat @t368) @t366))) % 155.07/155.73 (define @t371 () (@list @t84 @t331 @t368 @t366)) % 155.07/155.73 (define @t372 () (@var "Y22" tptp.nat)) % 155.07/155.73 (define @t373 () (@var "Y1" tptp.nat)) % 155.07/155.73 (define @t374 () (@var "V3" tptp.nat)) % 155.07/155.73 (define @t375 () (@var "U3" tptp.nat)) % 155.07/155.73 (define @t376 () (_ (_ tptp.product_Pair_nat_nat @t375) @t374)) % 155.07/155.73 (define @t377 () (@list @t375 @t374)) % 155.07/155.73 (define @t378 () (@var "E2" tptp.product_prod_nat_nat)) % 155.07/155.73 (define @t379 () (_ tptp.f @t378)) % 155.07/155.73 (define @t380 () (@list @t378)) % 155.07/155.73 (define @t381 () (@var "P" tptp.product_prod_nat_nat)) % 155.07/155.73 (define @t382 () (@list @t381)) % 155.07/155.73 (define @t383 () (_ @t122 @t378)) % 155.07/155.73 (define @t384 () (@list @t109 @t7 @t6 @t122 @t98)) % 155.07/155.73 (define @t385 () (@var "Prod" tptp.product_prod_nat_nat)) % 155.07/155.73 (define @t386 () (forall @t357 (_ @t87 @t356))) % 155.07/155.73 (define @t387 () (@var "Y" tptp.product_prod_nat_nat)) % 155.07/155.73 (define @t388 () (_ @t295 @t360)) % 155.07/155.73 (define @t389 () (_ tptp.ord_le116442893at_nat @t45)) % 155.07/155.73 (define @t390 () (_ tptp.ord_le116442893at_nat @t47)) % 155.07/155.73 (define @t391 () (_ @t390 @t37)) % 155.07/155.73 (define @t392 () (_ tptp.ord_le116442893at_nat @t44)) % 155.07/155.73 (define @t393 () (_ @t389 @t63)) % 155.07/155.73 (define @t394 () (_ @t389 @t44)) % 155.07/155.73 (define @t395 () (_ @t390 @t63)) % 155.07/155.73 (define @t396 () (not @t250)) % 155.07/155.73 (define @t397 () (not @t251)) % 155.07/155.73 (define @t398 () (_ @t22 tptp.p)) % 155.07/155.73 (define @t399 () (_ tptp.set_Pr2131844118at_nat tptp.p)) % 155.07/155.73 (define @t400 () (_ (_ tptp.inf_in586391887at_nat @t399) (_ tptp.converse_nat_nat @t399))) % 155.07/155.73 (define @t401 () (not (= @t400 tptp.bot_bo2130386637at_nat))) % 155.07/155.73 (define @t402 () (lambda @t92 (_ @t91 tptp.bot_bot_set_nat))) % 155.07/155.73 (define @t403 () (lambda @t95 (_ @t94 tptp.bot_bo2130386637at_nat))) % 155.07/155.73 (define @t404 () (lambda (@list @t72 @t71) (= @t268 @t72))) % 155.07/155.73 (define @t405 () (@var "K5" tptp.set_nat)) % 155.07/155.73 (define @t406 () (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity))) % 155.07/155.73 (define @t407 () (_ tptp.cap_capacity @t406)) % 155.07/155.73 (define @t408 () (@var "T2" tptp.nat)) % 155.07/155.73 (define @t409 () (@var "S2" tptp.nat)) % 155.07/155.73 (define @t410 () (_ (_ (_ tptp.nCut_capacity @t406) @t409) @t408)) % 155.07/155.73 (define @t411 () (lambda (@list @t406 @t409 @t408 @t284) (and (_ @t410 @t284) (forall (@list @t405) (=> (_ @t410 @t405) (_ (_ tptp.ord_less_eq_capacity (_ @t407 @t284)) (_ @t407 @t405))))))) % 155.07/155.73 (define @t412 () (@list @t406 @t409 @t408 @t101)) % 155.07/155.73 (define @t413 () (lambda @t412 (and (_ (_ (_ (_ tptp.nPreflow_capacity @t406) @t409) @t408) @t101) (_ (_ (_ (_ tptp.flow_capacity @t406) @t409) @t408) @t101)))) % 155.07/155.73 (define @t414 () (_ (_ (_ (_ tptp.preflow_capacity @t406) @t409) @t408) @t101)) % 155.07/155.73 (define @t415 () (lambda @t412 (and (_ (_ (_ tptp.network_capacity @t406) @t409) @t408) @t414))) % 155.07/155.73 (define @t416 () (lambda @t412 (and @t414 (_ tptp.finite217307323pacity @t406)))) % 155.07/155.73 (define @t417 () (lambda @t73 (and @t269 (not (= @t71 @t72))))) % 155.07/155.73 (define @t418 () (@const 0 (@ho-elim-sort (-> tptp.list_P559422087at_nat tptp.set_Pr1986765409at_nat)))) % 155.07/155.73 (define @t419 () (@const 1 (-> (@ho-elim-sort (-> tptp.list_P559422087at_nat tptp.set_Pr1986765409at_nat)) tptp.list_P559422087at_nat tptp.set_Pr1986765409at_nat))) % 155.07/155.73 (define @t420 () (_ @t419 @t418 @t1)) % 155.07/155.73 (define @t421 () (@const 2 (@ho-elim-sort (-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)))) % 155.07/155.73 (define @t422 () (@const 3 (-> (@ho-elim-sort (-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)) tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat))) % 155.07/155.73 (define @t423 () (@const 4 (@ho-elim-sort (-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)))) % 155.07/155.73 (define @t424 () (@const 5 (-> (@ho-elim-sort (-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat)) tptp.set_Pr1986765409at_nat (@ho-elim-sort (-> tptp.set_Pr1986765409at_nat tptp.set_Pr1986765409at_nat))))) % 155.07/155.73 (define @t425 () (@const 6 (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)))) % 155.07/155.73 (define @t426 () (@const 7 (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)))) % 155.07/155.73 (define @t427 () (_ (@const 12 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)) (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) (@ho-elim-sort (-> tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)))) (@const 11 (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.nat tptp.list_P559422087at_nat tptp.nat Bool))) (_ (@const 10 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.product_prod_nat_nat tptp.capacity)) (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)))) (_ (@const 9 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.product_prod_nat_nat tptp.capacity)) (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.product_prod_nat_nat tptp.capacity)))) (@const 8 (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.product_prod_nat_nat tptp.capacity))) @t426) @t425))) % 155.07/155.73 (define @t428 () (@const 13 (-> (@ho-elim-sort (-> tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)) tptp.nat (@ho-elim-sort (-> tptp.list_P559422087at_nat tptp.nat Bool))))) % 155.07/155.73 (define @t429 () (@const 14 (-> (@ho-elim-sort (-> tptp.list_P559422087at_nat tptp.nat Bool)) tptp.list_P559422087at_nat (@ho-elim-sort (-> tptp.nat Bool))))) % 155.07/155.73 (define @t430 () (@const 15 (-> (@ho-elim-sort (-> tptp.nat Bool)) tptp.nat Bool))) % 155.07/155.73 (define @t431 () (forall @t12 (or (not (_ @t430 (_ @t429 (_ @t428 @t427 @t7) @t1) @t6)) (= tptp.bot_bo2130386637at_nat (_ @t422 (_ @t424 @t423 @t420) (_ @t422 @t421 @t420)))))) % 155.07/155.73 (define @t432 () (tptp.set_Pr2131844118at_nat @t1)) % 155.07/155.73 (define @t433 () (tptp.converse_nat_nat @t432)) % 155.07/155.73 (define @t434 () (tptp.inf_in586391887at_nat @t432 @t433)) % 155.07/155.73 (define @t435 () (tptp.isSimp1359852763pacity @t8 @t7 @t1 @t6)) % 155.07/155.73 (define @t436 () (= tptp.bot_bo2130386637at_nat @t4)) % 155.07/155.73 (define @t437 () (not @t10)) % 155.07/155.73 (define @t438 () (or @t437 @t436)) % 155.07/155.73 (define @t439 () (_ (@const 20 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.list_P559422087at_nat Bool)) (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) (@ho-elim-sort (-> tptp.list_P559422087at_nat Bool)))) (_ (@const 19 (-> (@ho-elim-sort (-> tptp.nat (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.list_P559422087at_nat Bool)) tptp.nat (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.list_P559422087at_nat Bool)))) (_ (@const 18 (-> (@ho-elim-sort (-> tptp.nat tptp.nat (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.list_P559422087at_nat Bool)) tptp.nat (@ho-elim-sort (-> tptp.nat (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.list_P559422087at_nat Bool)))) (_ (@const 17 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.nat tptp.nat (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.list_P559422087at_nat Bool)) (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) (@ho-elim-sort (-> tptp.nat tptp.nat (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.list_P559422087at_nat Bool)))) (@const 16 (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.nat tptp.nat (@ho-elim-sort (-> tptp.product_prod_nat_nat tptp.capacity)) tptp.list_P559422087at_nat Bool))) @t426) tptp.s) tptp.t) @t425)) % 155.07/155.73 (define @t440 () (@const 21 (-> (@ho-elim-sort (-> tptp.list_P559422087at_nat Bool)) tptp.list_P559422087at_nat Bool))) % 155.07/155.73 (define @t441 () (_ @t440 @t439 @t1)) % 155.07/155.73 (define @t442 () (_ @t428 @t427 tptp.s)) % 155.07/155.73 (define @t443 () (_ @t430 (_ @t429 @t442 @t1) tptp.t)) % 155.07/155.73 (define @t444 () (forall @t25 (= @t441 @t443))) % 155.07/155.73 (define @t445 () (tptp.isSimp1359852763pacity @t8 tptp.s @t1 tptp.t)) % 155.07/155.73 (define @t446 () (tptp.augmen1090971539pacity tptp.c tptp.s tptp.t tptp.f @t1)) % 155.07/155.73 (define @t447 () (_ @t430 (_ @t429 @t442 tptp.p) tptp.t)) % 155.07/155.73 (define @t448 () (_ @t440 @t439 tptp.p)) % 155.07/155.73 (define @t449 () (forall @t25 (= @t443 @t441))) % 155.07/155.73 (define @t450 () (= @t447 @t448)) % 155.07/155.73 (define @t451 () (= @t448 @t447)) % 155.07/155.73 (define @t452 () (_ @t419 @t418 tptp.p)) % 155.07/155.73 (define @t453 () (= tptp.bot_bo2130386637at_nat (_ @t422 (_ @t424 @t423 @t452) (_ @t422 @t421 @t452)))) % 155.07/155.73 (define @t454 () (not @t447)) % 155.07/155.73 (define @t455 () (or @t454 @t453)) % 155.07/155.73 (define @t456 () (not @t455)) % 155.07/155.73 (define @t457 () (@list true false)) % 155.07/155.73 (assume @p1 (not (= tptp.t tptp.s))) % 155.07/155.73 (assume @p2 @t13) % 155.07/155.73 (assume @p3 (forall @t12 (=> @t15 @t5))) % 155.07/155.73 (assume @p4 (_ @t16 tptp.f)) % 155.07/155.73 (assume @p5 (forall (@list @t18 @t17) (=> (_ @t20 @t18) (=> (_ @t20 @t17) @t19)))) % 155.07/155.73 (assume @p6 @t26) % 155.07/155.73 (assume @p7 (_ (_ (_ (_ tptp.finite1387368318pacity tptp.c) tptp.s) tptp.t) tptp.f)) % 155.07/155.73 (assume @p8 (=> @t30 (not (exists @t28 (_ @t22 @t27))))) % 155.07/155.73 (assume @p9 (= @t33 @t30)) % 155.07/155.73 (assume @p10 (_ (_ (_ (_ tptp.preflow_capacity tptp.c) tptp.s) tptp.t) tptp.f)) % 155.07/155.73 (assume @p11 (_ (_ (_ (_ tptp.residu800046103pacity tptp.c) tptp.s) tptp.t) @t8)) % 155.07/155.73 (assume @p12 (_ @t34 tptp.f)) % 155.07/155.73 (assume @p13 (_ (_ (_ (_ tptp.nPreflow_capacity tptp.c) tptp.s) tptp.t) tptp.f)) % 155.07/155.73 (assume @p14 (= (_ tptp.converse_nat_nat tptp.bot_bo2130386637at_nat) tptp.bot_bo2130386637at_nat)) % 155.07/155.73 (assume @p15 (forall @t36 (= (_ (_ tptp.inf_in2138576462_nat_o tptp.bot_bo513358416_nat_o) @t35) tptp.bot_bo513358416_nat_o))) % 155.07/155.73 (assume @p16 (forall @t38 (= (_ (_ tptp.inf_in586391887at_nat tptp.bot_bo2130386637at_nat) @t37) tptp.bot_bo2130386637at_nat))) % 155.07/155.73 (assume @p17 (forall @t36 (= (_ (_ tptp.inf_in2138576462_nat_o @t35) tptp.bot_bo513358416_nat_o) tptp.bot_bo513358416_nat_o))) % 155.07/155.73 (assume @p18 (forall @t38 (= (_ @t39 tptp.bot_bo2130386637at_nat) tptp.bot_bo2130386637at_nat))) % 155.07/155.73 (assume @p19 (_ (_ (_ (_ tptp.residu164581374pacity tptp.c) tptp.s) tptp.t) @t8)) % 155.07/155.73 (assume @p20 (_ (_ (_ tptp.network_capacity tptp.c) tptp.s) tptp.t)) % 155.07/155.73 (assume @p21 (= (_ (_ tptp.residu1549650759pacity tptp.c) @t8) tptp.f)) % 155.07/155.73 (assume @p22 (forall @t43 (= (_ @t42 @t40) @t41))) % 155.07/155.73 (assume @p23 (forall @t49 (= (_ @t48 @t44) @t47))) % 155.07/155.73 (assume @p24 (forall @t43 (= (_ @t39 @t41) @t41))) % 155.07/155.73 (assume @p25 (forall @t49 (= (_ @t46 @t47) @t47))) % 155.07/155.73 (assume @p26 (forall @t38 (= (_ @t39 @t37) @t37))) % 155.07/155.73 (assume @p27 (forall @t50 (= (_ @t46 @t45) @t45))) % 155.07/155.73 (assume @p28 (forall (@list @t51) (= (_ tptp.converse_nat_nat @t52) @t51))) % 155.07/155.73 (assume @p29 (forall @t55 (= (= @t52 @t54) (= @t51 @t53)))) % 155.07/155.73 (assume @p30 (forall @t25 (=> @t23 (_ @t57 @t56)))) % 155.07/155.73 (assume @p31 (forall @t62 (= @t61 (_ @t59 (_ @t39 @t58))))) % 155.07/155.73 (assume @p32 (forall @t67 (= (_ @t64 (_ @t46 @t63)) @t66))) % 155.07/155.73 (assume @p33 (= tptp.inf_in586391887at_nat (lambda @t70 (_ (_ tptp.inf_in586391887at_nat @t69) @t68)))) % 155.07/155.73 (assume @p34 (= tptp.inf_in586391887at_nat (lambda @t73 (_ (_ tptp.inf_in586391887at_nat @t72) @t71)))) % 155.07/155.73 (assume @p35 (forall @t62 (= (_ @t42 @t58) @t61))) % 155.07/155.73 (assume @p36 (forall @t74 (= (_ @t48 @t63) @t66))) % 155.07/155.73 (assume @p37 (forall (@list @t78 @t75 @t44 @t45) (=> (= @t78 (_ @t76 @t44)) (= (_ @t46 @t78) @t77)))) % 155.07/155.73 (assume @p38 (forall (@list @t79 @t75 @t45 @t44) (=> (= @t79 (_ @t76 @t45)) (= (_ (_ tptp.inf_in586391887at_nat @t79) @t44) @t77)))) % 155.07/155.73 (assume @p39 (forall @t55 (= (_ tptp.converse_nat_nat (_ (_ tptp.inf_in586391887at_nat @t51) @t53)) (_ (_ tptp.inf_in586391887at_nat @t52) @t54)))) % 155.07/155.73 (assume @p40 (forall @t83 (=> @t82 (_ @t34 @t81)))) % 155.07/155.73 (assume @p41 (forall (@list @t84 @t85) (= (_ (_ tptp.member_nat @t84) (_ tptp.collect_nat @t85)) (_ @t85 @t84)))) % 155.07/155.73 (assume @p42 (forall (@list @t86 @t87) (= (_ (_ tptp.member701585322at_nat @t86) @t88) (_ @t87 @t86)))) % 155.07/155.73 (assume @p43 (forall (@list @t89) (= (_ tptp.collect_nat (lambda @t92 (_ @t91 @t89))) @t89))) % 155.07/155.73 (assume @p44 (forall (@list @t79) (= (_ tptp.collec7649004at_nat (lambda @t95 (_ @t94 @t79))) @t79))) % 155.07/155.73 (assume @p45 (forall (@list @t87 @t96) (=> (forall (@list @t97) (= (_ @t87 @t97) (_ @t96 @t97))) (= @t88 (_ tptp.collec7649004at_nat @t96))))) % 155.07/155.73 (assume @p46 (forall @t100 (=> @t10 @t99))) % 155.07/155.73 (assume @p47 (forall (@list @t103) (= (_ @t20 @t103) (exists @t104 (and (_ @t29 @t101) (= @t103 (_ @t102 @t101))))))) % 155.07/155.73 (assume @p48 (_ tptp.finite217307323pacity @t8)) % 155.07/155.73 (assume @p49 (= @t30 @t33)) % 155.07/155.73 (assume @p50 (forall @t25 (=> (_ (_ @t106 @t1) tptp.t) @t23))) % 155.07/155.73 (assume @p51 (forall @t25 (=> @t23 (exists @t108 (_ (_ @t106 @t107) tptp.t))))) % 155.07/155.73 (assume @p52 (forall @t112 (=> @t111 @t5))) % 155.07/155.73 (assume @p53 (forall @t121 (=> @t120 (=> (_ @t118 @t117) @t115)))) % 155.07/155.73 (assume @p54 (forall @t100 (=> @t15 @t99))) % 155.07/155.73 (assume @p55 (_ tptp.finite217307323pacity tptp.c)) % 155.07/155.73 (assume @p56 (forall @t12 (=> (_ (_ (_ (_ tptp.isShor1936442771pacity tptp.c) @t7) @t1) @t6) @t15))) % 155.07/155.73 (assume @p57 (forall @t12 (=> (_ (_ (_ @t105 @t7) @t1) @t6) @t10))) % 155.07/155.73 (assume @p58 (= tptp.isShor1936442771pacity tptp.isShor1936442771pacity)) % 155.07/155.73 (assume @p59 (forall @t112 (=> (_ (_ (_ (_ tptp.isShor1936442771pacity @t109) @t7) @t1) @t6) @t111))) % 155.07/155.73 (assume @p60 (forall (@list @t109 @t7 @t1 @t6 @t98) (=> @t111 @t99))) % 155.07/155.73 (assume @p61 (= tptp.isSimp1359852763pacity tptp.isSimp1359852763pacity)) % 155.07/155.73 (assume @p62 (forall @t121 (=> @t120 @t120))) % 155.07/155.73 (assume @p63 (forall @t130 (=> @t129 (=> (_ (_ @t127 @t1) @t6) @t124)))) % 155.07/155.73 (assume @p64 (forall @t130 (=> @t129 (=> @t124 (exists @t108 (_ (_ @t127 @t107) @t6)))))) % 155.07/155.73 (assume @p65 (forall @t121 (=> @t115 @t115))) % 155.07/155.73 (assume @p66 (= tptp.residu1549650759pacity tptp.residu1549650759pacity)) % 155.07/155.73 (assume @p67 (forall @t121 (=> @t120 @t131))) % 155.07/155.73 (assume @p68 (forall @t121 (=> @t115 @t131))) % 155.07/155.73 (assume @p69 (forall @t121 (=> @t115 @t120))) % 155.07/155.73 (assume @p70 (forall @t134 (=> @t133 (_ @t119 @t126)))) % 155.07/155.73 (assume @p71 (forall @t121 (=> @t120 (exists @t137 (and (_ @t132 @t135) @t136))))) % 155.07/155.73 (assume @p72 (forall @t134 (=> @t129 (_ @t114 @t126)))) % 155.07/155.73 (assume @p73 (forall @t121 (=> @t115 (exists @t137 (and (_ @t128 @t135) @t136))))) % 155.07/155.73 (assume @p74 (forall @t134 (=> @t133 (= (_ @t116 @t126) @t122)))) % 155.07/155.73 (assume @p75 (forall @t121 (=> @t120 (= (_ @t125 @t117) @t113)))) % 155.07/155.73 (assume @p76 (forall @t121 (=> @t120 (_ @t132 @t117)))) % 155.07/155.73 (assume @p77 (forall @t121 (=> @t115 (_ @t128 @t117)))) % 155.07/155.73 (assume @p78 (forall @t25 (=> @t23 (= (_ @t139 @t56) @t138)))) % 155.07/155.73 (assume @p79 (forall @t83 (=> @t82 (= (_ @t102 @t81) (_ (_ tptp.plus_plus_capacity @t140) (_ @t139 @t80)))))) % 155.07/155.73 (assume @p80 (forall @t146 (= @t145 (and (_ @t16 @t122) (forall @t144 (=> (_ @t16 @t142) @t143)))))) % 155.07/155.73 (assume @p81 (forall @t146 (= @t145 (and (_ @t34 @t122) (forall @t144 (=> (_ @t34 @t142) @t143)))))) % 155.07/155.73 (assume @p82 (forall @t130 (=> @t133 (=> @t124 (_ @t148 @t147))))) % 155.07/155.73 (assume @p83 (= tptp.bot_bo513358416_nat_o (lambda @t95 tptp.bot_bot_o))) % 155.07/155.73 (assume @p84 (forall (@list @t122 @t149) (=> @t145 (=> (_ (_ (_ (_ tptp.isMinCut_capacity tptp.c) tptp.s) tptp.t) @t149) (= @t141 (_ @t150 @t149)))))) % 155.07/155.73 (assume @p85 (forall @t38 (_ @t151 @t37))) % 155.07/155.73 (assume @p86 (forall (@list @t152) (_ @t153 @t152))) % 155.07/155.73 (assume @p87 (forall @t74 (= @t157 (and @t156 @t155)))) % 155.07/155.73 (assume @p88 (forall @t62 (= @t160 (and @t159 @t158)))) % 155.07/155.73 (assume @p89 (forall @t162 (_ (_ tptp.ord_le1039616028_nat_o tptp.bot_bo513358416_nat_o) @t161))) % 155.07/155.73 (assume @p90 (forall @t50 (_ (_ tptp.ord_le841296385at_nat tptp.bot_bo2130386637at_nat) @t45))) % 155.07/155.73 (assume @p91 (forall @t162 (= @t164 @t163))) % 155.07/155.73 (assume @p92 (forall @t50 (= @t166 @t165))) % 155.07/155.73 (assume @p93 (forall @t162 (=> @t164 @t163))) % 155.07/155.73 (assume @p94 (forall @t50 (=> @t166 @t165))) % 155.07/155.73 (assume @p95 (forall @t180 (=> (_ @t169 @t179) @t178))) % 155.07/155.73 (assume @p96 (forall @t193 (=> (_ @t154 @t192) @t191))) % 155.07/155.73 (assume @p97 (forall @t198 (=> (_ @t154 @t197) @t196))) % 155.07/155.73 (assume @p98 (forall @t203 (=> (_ @t169 @t202) @t201))) % 155.07/155.73 (assume @p99 (forall @t206 (=> @t205 (=> (_ (_ tptp.ord_le841296385at_nat @t192) @t63) @t204)))) % 155.07/155.73 (assume @p100 (forall @t208 (=> @t156 (=> (_ (_ tptp.ord_less_eq_capacity @t179) @t181) @t207)))) % 155.07/155.73 (assume @p101 (forall @t210 (=> @t156 (=> (_ (_ tptp.ord_le841296385at_nat @t197) @t63) @t209)))) % 155.07/155.73 (assume @p102 (forall @t212 (=> @t205 (=> (_ (_ tptp.ord_less_eq_capacity @t202) @t181) @t211)))) % 155.07/155.73 (assume @p103 (forall @t193 (=> (= @t45 @t192) @t191))) % 155.07/155.73 (assume @p104 (forall @t180 (=> (= @t168 @t179) @t178))) % 155.07/155.74 (assume @p105 (forall @t198 (=> (= @t45 @t197) @t196))) % 155.07/155.74 (assume @p106 (forall @t203 (=> (= @t168 @t202) @t201))) % 155.07/155.74 (assume @p107 (forall @t206 (=> @t205 (=> (= @t192 @t63) @t204)))) % 155.07/155.74 (assume @p108 (forall @t208 (=> @t156 (=> (= @t179 @t181) @t207)))) % 155.07/155.74 (assume @p109 (forall @t210 (=> @t156 (=> (= @t197 @t63) @t209)))) % 155.07/155.74 (assume @p110 (forall @t212 (=> @t205 (=> (= @t202 @t181) @t211)))) % 155.07/155.74 (assume @p111 (= @t215 (lambda @t70 (and (_ (_ tptp.ord_le841296385at_nat @t68) @t69) (_ (_ tptp.ord_le841296385at_nat @t69) @t68))))) % 155.07/155.74 (assume @p112 (= @t220 (lambda (@list @t216 @t217) (and (_ (_ tptp.ord_less_eq_capacity @t216) @t217) (_ (_ tptp.ord_less_eq_capacity @t217) @t216))))) % 155.07/155.74 (assume @p113 (forall @t43 (=> @t159 (=> @t223 @t221)))) % 155.07/155.74 (assume @p114 (forall @t229 (=> @t228 (=> @t227 @t225)))) % 155.07/155.74 (assume @p115 (forall @t229 (or @t228 @t227))) % 155.07/155.74 (assume @p116 (forall @t43 (=> @t221 @t159))) % 155.07/155.74 (assume @p117 (forall @t229 (=> @t225 @t228))) % 155.07/155.74 (assume @p118 (forall @t229 (=> @t230 @t227))) % 155.07/155.74 (assume @p119 (forall @t74 (=> @t156 @t231))) % 155.07/155.74 (assume @p120 (forall @t234 (=> @t205 @t233))) % 155.07/155.74 (assume @p121 (forall @t241 (=> (=> @t228 (not @t238)) (=> (=> @t227 (not @t240)) (=> (=> @t240 (not @t239)) (=> (=> @t239 (not @t227)) (=> (=> @t238 (not @t237)) (not (=> @t237 @t230))))))))) % 155.07/155.74 (assume @p122 (forall @t242 (=> @t223 (= @t159 @t221)))) % 155.07/155.74 (assume @p123 (forall (@list @t224 @t152) (=> @t227 (= @t228 @t225)))) % 155.07/155.74 (assume @p124 (= @t215 (lambda @t73 (and @t244 @t243)))) % 155.07/155.74 (assume @p125 (= @t220 (lambda @t249 (and @t248 @t247)))) % 155.07/155.74 (assume @p126 (forall @t74 (=> @t250 @t231))) % 155.07/155.74 (assume @p127 (forall @t234 (=> @t251 @t233))) % 155.07/155.74 (assume @p128 (forall @t74 (=> @t156 (=> (= @t44 @t63) @t155)))) % 155.07/155.74 (assume @p129 (forall @t234 (=> @t205 (=> (= @t188 @t181) @t232)))) % 155.07/155.74 (assume @p130 (forall @t49 (=> @t156 (=> @t252 @t250)))) % 155.07/155.74 (assume @p131 (forall @t254 (=> @t205 (=> @t253 @t251)))) % 155.07/155.74 (assume @p132 (= tptp.augmen68920357pacity tptp.augmen68920357pacity)) % 155.07/155.74 (assume @p133 (forall @t62 (=> @t159 (=> (_ @t222 @t58) @t158)))) % 155.07/155.74 (assume @p134 (forall @t241 (=> @t228 (=> @t238 @t240)))) % 155.07/155.74 (assume @p135 (forall @t50 (_ @t154 @t45))) % 155.07/155.74 (assume @p136 (forall (@list @t168) (_ @t169 @t168))) % 155.07/155.74 (assume @p137 (forall (@list @t255 @t168 @t188) (=> (forall @t259 (=> (_ (_ tptp.ord_less_eq_capacity @t257) @t256) @t258)) (=> (forall @t259 (=> (_ (_ @t255 @t256) @t257) @t258)) (_ (_ @t255 @t168) @t188))))) % 155.07/155.74 (assume @p138 (forall @t67 (=> @t252 (=> (_ @t260 @t44) (_ @t260 @t45))))) % 155.07/155.74 (assume @p139 (forall (@list @t188 @t168 @t181) (=> @t253 (=> (_ @t261 @t188) (_ @t261 @t168))))) % 155.07/155.74 (assume @p140 (= @t215 (lambda @t73 (and @t243 @t244)))) % 155.07/155.74 (assume @p141 (= @t220 (lambda @t249 (and @t247 @t248)))) % 155.07/155.74 (assume @p142 (forall @t262 (=> @t252 (=> @t156 @t250)))) % 155.07/155.74 (assume @p143 (forall @t263 (=> @t253 (=> @t205 @t251)))) % 155.07/155.74 (assume @p144 (forall @t266 (=> @t177 @t265))) % 155.07/155.74 (assume @p145 (forall @t267 (=> @t155 @t265))) % 155.07/155.74 (assume @p146 (= tptp.ord_le841296385at_nat (lambda @t73 (= @t268 @t71)))) % 155.07/155.74 (assume @p147 (forall @t49 (_ @t264 @t44))) % 155.07/155.74 (assume @p148 (forall @t49 (_ @t264 @t45))) % 155.07/155.74 (assume @p149 (= tptp.ord_le841296385at_nat (lambda @t73 @t269))) % 155.07/155.74 (assume @p150 (forall @t62 (=> @t159 (=> @t158 @t160)))) % 155.07/155.74 (assume @p151 (forall @t74 (=> @t156 (=> @t155 @t157)))) % 155.07/155.74 (assume @p152 (forall @t74 (=> @t157 (not (=> @t156 (not @t155)))))) % 155.07/155.74 (assume @p153 (forall @t242 (=> @t223 (= @t41 @t40)))) % 155.07/155.74 (assume @p154 (forall @t43 (=> @t159 (= @t41 @t37)))) % 155.07/155.74 (assume @p155 (forall @t262 (=> @t252 (= @t47 @t44)))) % 155.07/155.74 (assume @p156 (forall @t49 (=> @t156 (= @t47 @t45)))) % 155.07/155.74 (assume @p157 (= tptp.ord_le841296385at_nat (lambda @t70 (= (_ (_ tptp.inf_in586391887at_nat @t68) @t69) @t68)))) % 155.07/155.74 (assume @p158 (forall (@list @t270 @t37 @t40) (=> (forall @t174 (_ @t272 @t171)) (=> (forall @t174 (_ @t272 @t170)) (=> (forall (@list @t171 @t170 @t271) (=> @t173 (=> (_ @t172 @t271) (_ @t172 (_ (_ @t270 @t170) @t271))))) (= @t41 (_ (_ @t270 @t37) @t40))))))) % 155.07/155.74 (assume @p159 (forall @t49 (=> @t273 @t156))) % 155.07/155.74 (assume @p160 (forall @t49 (=> @t156 @t273))) % 155.07/155.74 (assume @p161 (forall @t275 (=> (_ @t176 @t37) @t274))) % 155.07/155.74 (assume @p162 (forall @t276 (=> (_ @t154 @t37) @t274))) % 155.07/155.74 (assume @p163 (forall (@list @t45 @t63 @t44 @t277) (=> @t155 (=> (_ @t176 @t277) (_ @t264 (_ (_ tptp.inf_in586391887at_nat @t63) @t277)))))) % 155.07/155.74 (assume @p164 (forall @t281 (=> @t280 (=> @t279 @t278)))) % 155.07/155.74 (assume @p165 (forall @t281 (=> @t278 (not (=> @t280 (not @t279)))))) % 155.07/155.74 (assume @p166 (forall @t43 (_ @t282 @t40))) % 155.07/155.74 (assume @p167 (forall @t43 (_ @t282 @t37))) % 155.07/155.74 (assume @p168 (= tptp.augmen1090971539pacity tptp.augmen1090971539pacity)) % 155.07/155.74 (assume @p169 (= tptp.augmen72931474pacity tptp.augmen72931474pacity)) % 155.07/155.74 (assume @p170 (forall @t130 (=> @t133 (=> @t124 (= (_ @t283 @t147) (_ (_ (_ tptp.augmen68920357pacity @t109) @t122) @t1)))))) % 155.07/155.74 (assume @p171 (forall @t130 (=> @t133 (= @t124 (_ (_ (_ (_ tptp.isSimp1359852763pacity @t126) @t7) @t1) @t6))))) % 155.07/155.74 (assume @p172 (= @t33 (exists @t286 (and (_ @t285 @t284) (= @t140 (_ @t150 @t284)))))) % 155.07/155.74 (assume @p173 (=> (exists @t288 (and (_ @t285 @t287) (= @t140 (_ @t150 @t287)))) @t30)) % 155.07/155.74 (assume @p174 (=> (not (exists @t292 (_ @t22 @t291))) (exists @t290 (and (_ @t285 @t289) (= @t140 (_ @t150 @t289)))))) % 155.07/155.74 (assume @p175 (forall @t297 (=> @t129 (=> @t296 (= (_ @t293 @t295) (_ (_ tptp.plus_plus_capacity @t294) (_ @t283 @t80))))))) % 155.07/155.74 (assume @p176 (forall (@list @t109 @t7 @t6 @t122 @t149) (=> @t131 (=> @t299 (=> (_ (_ (_ (_ tptp.isMinCut_capacity @t109) @t7) @t6) @t149) (= @t294 (_ @t298 @t149))))))) % 155.07/155.74 (assume @p177 (forall @t134 (=> @t131 (= @t299 (and @t129 (forall @t144 (=> (_ @t128 @t142) @t300))))))) % 155.07/155.74 (assume @p178 (forall @t55 (= (_ @t303 @t54) @t302))) % 155.07/155.74 (assume @p179 (forall @t306 (=> @t305 @t131))) % 155.07/155.74 (assume @p180 (forall @t306 (=> @t305 (not (_ (_ tptp.member_nat @t6) @t149))))) % 155.07/155.74 (assume @p181 (forall @t306 (=> @t305 (_ (_ tptp.member_nat @t7) @t149)))) % 155.07/155.74 (assume @p182 (forall @t55 (= (_ @t301 @t54) (_ @t303 @t53)))) % 155.07/155.74 (assume @p183 (forall @t307 (=> @t131 (not (= @t6 @t7))))) % 155.07/155.74 (assume @p184 (forall @t307 (=> @t131 (not (= @t7 @t6))))) % 155.07/155.74 (assume @p185 (= tptp.val_capacity tptp.val_capacity)) % 155.07/155.74 (assume @p186 (= tptp.isMaxFlow_capacity tptp.isMaxFlow_capacity)) % 155.07/155.74 (assume @p187 (= tptp.augmen887209518pacity tptp.augmen887209518pacity)) % 155.07/155.74 (assume @p188 (= tptp.cap_capacity tptp.cap_capacity)) % 155.07/155.74 (assume @p189 (forall @t134 (=> @t129 (=> (not (exists @t292 (_ @t123 @t291))) (exists @t290 (and (_ @t304 @t289) (= @t294 (_ @t298 @t289)))))))) % 155.07/155.74 (assume @p190 (forall @t134 (=> @t129 (=> (exists @t288 (and (_ @t304 @t287) (= @t294 (_ @t298 @t287)))) @t299)))) % 155.07/155.74 (assume @p191 (= tptp.is_max2144541363pacity tptp.is_max2144541363pacity)) % 155.07/155.74 (assume @p192 (forall @t134 (=> @t129 (= @t308 (exists @t286 (and (_ @t304 @t284) (= @t294 (_ @t298 @t284)))))))) % 155.07/155.74 (assume @p193 (forall @t134 (=> @t133 @t131))) % 155.07/155.74 (assume @p194 (forall @t134 (=> @t129 @t133))) % 155.07/155.74 (assume @p195 (forall @t134 (=> @t129 @t310))) % 155.07/155.74 (assume @p196 (forall @t134 (=> @t133 @t311))) % 155.07/155.74 (assume @p197 (forall @t134 (=> @t310 @t311))) % 155.07/155.74 (assume @p198 (forall (@list @t109 @t7 @t6 @t18 @t17) (=> @t131 (=> (_ @t312 @t18) (=> (_ @t312 @t17) @t19))))) % 155.07/155.74 (assume @p199 (forall @t134 (=> @t314 @t313))) % 155.07/155.74 (assume @p200 (forall @t134 (=> @t314 @t311))) % 155.07/155.74 (assume @p201 (forall @t134 (=> @t133 (=> @t310 @t129)))) % 155.07/155.74 (assume @p202 (forall @t134 (=> @t131 (=> @t311 @t133)))) % 155.07/155.74 (assume @p203 (forall @t134 (=> @t129 (=> @t299 (not (exists @t28 (_ @t123 @t27))))))) % 155.07/155.74 (assume @p204 (forall @t134 (=> @t129 (= @t308 @t299)))) % 155.07/155.74 (assume @p205 (forall @t134 (=> @t311 (=> @t313 @t314)))) % 155.07/155.74 (assume @p206 (forall @t297 (=> @t129 (=> @t296 (_ @t309 @t295))))) % 155.07/155.74 (assume @p207 (forall @t134 (=> @t129 (= @t299 @t308)))) % 155.07/155.74 (assume @p208 (forall (@list @t109 @t7 @t6 @t103) (=> @t131 (= (_ @t312 @t103) (exists @t104 (and (_ @t118 @t101) (= @t103 (_ @t293 @t101)))))))) % 155.07/155.74 (assume @p209 (forall @t134 (=> @t131 (= @t299 (and @t310 (forall @t144 (=> (_ @t309 @t142) @t300))))))) % 155.07/155.74 (assume @p210 (forall @t321 (=> @t320 @t317))) % 155.07/155.74 (assume @p211 (forall @t326 (=> @t320 @t325))) % 155.07/155.74 (assume @p212 (forall @t329 (=> @t320 @t328))) % 155.07/155.74 (assume @p213 (forall @t329 (=> @t330 @t328))) % 155.07/155.74 (assume @p214 (forall @t326 (=> @t330 @t325))) % 155.07/155.74 (assume @p215 (forall @t321 (=> @t330 @t317))) % 155.07/155.74 (assume @p216 (forall @t337 (= @t336 @t333))) % 155.07/155.74 (assume @p217 (forall @t55 (=> (forall @t343 (=> @t342 (_ @t341 @t53))) @t302))) % 155.07/155.74 (assume @p218 (forall @t337 (=> @t336 @t333))) % 155.07/155.74 (assume @p219 (forall (@list @t344 @t51) (=> (_ (_ tptp.member701585322at_nat @t344) @t52) (not (forall @t343 (=> (= @t344 (_ (_ tptp.product_Pair_nat_nat @t338) @t339)) (not @t342))))))) % 155.07/155.74 (assume @p220 (forall @t348 (=> @t347 (_ (_ tptp.member701585322at_nat (_ (_ tptp.product_Pair_nat_nat @t346) @t345)) @t51)))) % 155.07/155.74 (assume @p221 (forall @t348 (= @t347 (exists (@list @t350 @t349) (and (= @t345 @t349) (= @t346 @t350) (_ (_ tptp.member701585322at_nat (_ (_ tptp.product_Pair_nat_nat @t350) @t349)) @t51)))))) % 155.07/155.74 (assume @p222 (forall @t337 (=> (_ @t335 @t51) (_ @t332 @t52)))) % 155.07/155.74 (assume @p223 (forall (@list @t352 @t351 @t51 @t353) (=> (_ (_ tptp.member701585322at_nat @t358) @t52) (=> (forall @t357 (=> (_ (_ tptp.member701585322at_nat @t356) @t51) (_ (_ @t353 @t355) @t354))) (_ (_ @t353 @t352) @t351))))) % 155.07/155.74 (assume @p224 (forall (@list @t109 @t319 @t1 @t318 @t315 @t322 @t327) (=> @t359 @t328))) % 155.07/155.74 (assume @p225 (forall (@list @t109 @t319 @t1 @t318 @t315 @t322 @t323) (=> @t359 @t325))) % 155.07/155.74 (assume @p226 (forall (@list @t109 @t319 @t1 @t318 @t315) (=> @t359 @t317))) % 155.07/155.74 (assume @p227 (forall (@list @t80 @t319 @t318) (=> @t82 (and (_ @t362 @t361) (_ (_ tptp.ord_less_eq_capacity @t361) (_ tptp.c @t360)))))) % 155.07/155.74 (assume @p228 (forall (@list @t363 @t364) (= (_ tptp.product_swap_nat_nat (_ (_ tptp.product_Pair_nat_nat @t363) @t364)) (_ (_ tptp.product_Pair_nat_nat @t364) @t363)))) % 155.07/155.74 (assume @p229 (forall @t365 (_ @t362 (_ tptp.f @t98)))) % 155.07/155.74 (assume @p230 (forall @t371 (= @t370 (and @t369 @t367)))) % 155.07/155.74 (assume @p231 (forall (@list @t352 @t351 @t373 @t372) (= (= @t358 (_ (_ tptp.product_Pair_nat_nat @t373) @t372)) (and (= @t352 @t373) (= @t351 @t372))))) % 155.07/155.74 (assume @p232 (forall @t377 (_ @t362 (_ tptp.c @t376)))) % 155.07/155.74 (assume @p233 (forall @t380 (and (_ @t362 @t379) (_ (_ tptp.ord_less_eq_capacity @t379) (_ tptp.c @t378))))) % 155.07/155.74 (assume @p234 (forall @t382 (= (_ tptp.product_swap_nat_nat (_ tptp.product_swap_nat_nat @t381)) @t381))) % 155.07/155.74 (assume @p235 (forall @t365 (_ @t362 (_ @t8 @t98)))) % 155.07/155.74 (assume @p236 (forall (@list @t109 @t7 @t6 @t113 @t98) (=> @t120 (_ @t362 (_ @t113 @t98))))) % 155.07/155.74 (assume @p237 (forall @t134 (=> @t311 (forall @t380 (and (_ @t362 @t383) (_ (_ tptp.ord_less_eq_capacity @t383) (_ @t109 @t378))))))) % 155.07/155.74 (assume @p238 (forall @t384 (=> @t311 (_ @t362 (_ @t122 @t98))))) % 155.07/155.74 (assume @p239 (forall (@list @t87 @t385) (=> @t386 (_ @t87 @t385)))) % 155.07/155.74 (assume @p240 (forall (@list @t387) (not (forall @t357 (not (= @t387 @t356)))))) % 155.07/155.74 (assume @p241 (forall @t371 (=> @t370 (not (=> @t369 (not @t367)))))) % 155.07/155.74 (assume @p242 (forall (@list @t87 @t381) (=> @t386 (_ @t87 @t381)))) % 155.07/155.74 (assume @p243 (forall @t382 (exists @t343 (= @t381 @t340)))) % 155.07/155.74 (assume @p244 (forall @t307 (=> @t131 (forall @t377 (_ @t362 (_ @t109 @t376)))))) % 155.07/155.74 (assume @p245 (forall @t384 (=> @t133 (_ @t362 (_ @t126 @t98))))) % 155.07/155.74 (assume @p246 (forall (@list @t109 @t7 @t6 @t122 @t80 @t319 @t318) (=> @t129 (=> @t296 (and (_ @t362 @t388) (_ (_ tptp.ord_less_eq_capacity @t388) (_ @t109 @t360))))))) % 155.07/155.74 (assume @p247 (_ (_ tptp.ord_less_eq_capacity (_ (_ (_ tptp.excess_capacity tptp.c) tptp.f) tptp.s)) tptp.zero_zero_capacity)) % 155.07/155.74 (assume @p248 (forall @t25 (=> @t23 (_ (_ tptp.ord_less_capacity tptp.zero_zero_capacity) @t138)))) % 155.07/155.74 (assume @p249 (= tptp.excess_capacity tptp.excess_capacity)) % 155.07/155.74 (assume @p250 (forall @t162 (= (not @t163) (_ (_ tptp.ord_le1015898640_nat_o tptp.bot_bo513358416_nat_o) @t161)))) % 155.07/155.74 (assume @p251 (forall @t50 (= (not @t165) (_ (_ tptp.ord_le116442893at_nat tptp.bot_bo2130386637at_nat) @t45)))) % 155.07/155.74 (assume @p252 (forall @t162 (not (_ (_ tptp.ord_le1015898640_nat_o @t161) tptp.bot_bo513358416_nat_o)))) % 155.07/155.74 (assume @p253 (forall @t50 (not (_ @t389 tptp.bot_bo2130386637at_nat)))) % 155.07/155.74 (assume @p254 (forall @t276 (=> (_ @t389 @t37) @t391))) % 155.07/155.74 (assume @p255 (forall @t275 (=> (_ @t392 @t37) @t391))) % 155.07/155.74 (assume @p256 (forall @t74 (=> (_ @t389 @t65) (not (=> @t394 (not @t393)))))) % 155.07/155.74 (assume @p257 (forall @t267 (=> @t393 @t395))) % 155.07/155.74 (assume @p258 (forall @t266 (=> (_ @t392 @t63) @t395))) % 155.07/155.74 (assume @p259 (forall @t262 (=> (_ @t392 @t45) @t396))) % 155.07/155.74 (assume @p260 (forall @t263 (=> (_ (_ tptp.ord_less_capacity @t188) @t168) @t397))) % 155.07/155.74 (assume @p261 (forall @t49 (=> @t394 @t396))) % 155.07/155.74 (assume @p262 (forall @t254 (=> (_ (_ tptp.ord_less_capacity @t168) @t188) @t397))) % 155.07/155.74 (assume @p263 (forall @t229 (= (not (_ (_ tptp.ord_less_capacity @t152) @t224)) (or (_ (_ tptp.ord_less_capacity @t224) @t152) @t225)))) % 155.07/155.74 (assume @p264 @t398) % 155.07/155.74 (assume @p265 @t401) % 155.07/155.74 (assume @p266 true) % 155.07/155.74 (step @p267 (= tptp.bot_bot_nat_o @t402) :rule refl :args (@t402)) % 155.07/155.74 (step @p268 (= tptp.bot_bo513358416_nat_o @t403) :rule refl :args (@t403)) % 155.07/155.74 (step @p269 (= tptp.ord_le841296385at_nat @t404) :rule refl :args (@t404)) % 155.07/155.74 (step @p270 (= tptp.isMinCut_capacity @t411) :rule refl :args (@t411)) % 155.07/155.74 (step @p271 (= tptp.nFlow_capacity @t413) :rule refl :args (@t413)) % 155.07/155.74 (step @p272 (= tptp.nPreflow_capacity @t415) :rule refl :args (@t415)) % 155.07/155.74 (step @p273 (= tptp.finite1387368318pacity @t416) :rule refl :args (@t416)) % 155.07/155.74 (step @p274 (= tptp.ord_le116442893at_nat @t417) :rule refl :args (@t417)) % 155.07/155.74 ; WARNING: add trust step for TRUST % 155.07/155.74 ; trust TRUST PREPROCESS_HO_ELIM % 155.07/155.74 (step @p275 :rule trust :premises () :args ((= (forall @t12 (or (not @t435) (= tptp.bot_bo2130386637at_nat @t434))) @t431))) % 155.07/155.74 (step @p276 :rule refl :args ((tptp.inf_in586391887at_nat @t2 @t3))) % 155.07/155.74 (step @p277 :rule refl :args ((tptp.converse_nat_nat @t2))) % 155.07/155.74 (step @p278 :rule refl :args (@t432)) % 155.07/155.74 (step @p279 :rule cong :premises (@p278) :args (@t433)) % 155.07/155.74 (step @p280 :rule trans :premises (@p279 @p277)) % 155.07/155.74 (step @p281 :rule cong :premises (@p278 @p280) :args (@t434)) % 155.07/155.74 (step @p282 :rule trans :premises (@p281 @p276)) % 155.07/155.74 (step @p283 :rule refl :args (tptp.inf_in586391887at_nat)) % 155.07/155.74 (step @p284 :rule ho_cong :premises (@p283 @p278)) % 155.07/155.74 (step @p285 :rule ho_cong :premises (@p284 @p280)) % 155.07/155.74 (step @p286 :rule cong :premises (@p285 @p282) :args ((= (_ (_ tptp.inf_in586391887at_nat @t432) @t433) @t434))) % 155.07/155.74 (step @p287 :rule symm :premises (@p286)) % 155.07/155.74 (step @p288 :rule refl :args (@t4)) % 155.07/155.74 (step @p289 :rule eq_resolve :premises (@p288 @p287)) % 155.07/155.74 (step @p290 :rule refl :args (tptp.converse_nat_nat)) % 155.07/155.74 (step @p291 :rule ho_cong :premises (@p290 @p278)) % 155.07/155.74 (step @p292 :rule cong :premises (@p291 @p280) :args ((= (_ tptp.converse_nat_nat @t432) @t433))) % 155.07/155.74 (step @p293 :rule symm :premises (@p292)) % 155.07/155.74 (step @p294 :rule refl :args (@t3)) % 155.07/155.74 (step @p295 :rule eq_resolve :premises (@p294 @p293)) % 155.07/155.74 (step @p296 :rule refl :args (@t2)) % 155.07/155.74 (step @p297 :rule cong :premises (@p296 @p278) :args ((= @t2 @t432))) % 155.07/155.74 (step @p298 :rule symm :premises (@p297)) % 155.07/155.74 (step @p299 :rule eq_resolve :premises (@p296 @p298)) % 155.07/155.74 (step @p300 :rule ho_cong :premises (@p290 @p299)) % 155.07/155.74 (step @p301 :rule trans :premises (@p300 @p295)) % 155.07/155.74 (step @p302 :rule ho_cong :premises (@p283 @p299)) % 155.07/155.74 (step @p303 :rule ho_cong :premises (@p302 @p301)) % 155.07/155.74 (step @p304 :rule trans :premises (@p303 @p289)) % 155.07/155.74 (step @p305 :rule refl :args (tptp.bot_bo2130386637at_nat)) % 155.07/155.74 (step @p306 :rule cong :premises (@p305 @p304) :args (@t436)) % 155.07/155.74 (step @p307 :rule refl :args (@t435)) % 155.07/155.74 (step @p308 :rule refl :args (@t10)) % 155.07/155.74 (step @p309 :rule cong :premises (@p308 @p307) :args ((= @t10 @t435))) % 155.07/155.74 (step @p310 :rule symm :premises (@p309)) % 155.07/155.74 (step @p311 :rule eq_resolve :premises (@p308 @p310)) % 155.07/155.74 (step @p312 :rule cong :premises (@p311) :args (@t437)) % 155.07/155.74 (step @p313 :rule nary_cong :premises (@p312 @p306) :args (@t438)) % 155.07/155.74 (step @p314 :rule cong :premises (@p313) :args ((forall @t12 @t438))) % 155.07/155.74 (step @p315 :rule bool-impl-elim :args (@t10 @t436)) % 155.07/155.74 (step @p316 :rule cong :premises (@p315) :args ((forall @t12 (=> @t10 @t436)))) % 155.07/155.74 (step @p317 :rule trans :premises (@p316 @p314)) % 155.07/155.74 (step @p318 :rule eq-symm :args (@t4 tptp.bot_bo2130386637at_nat)) % 155.07/155.74 (step @p319 :rule refl :args (@t10)) % 155.07/155.74 (step @p320 :rule cong :premises (@p319 @p318) :args (@t11)) % 155.07/155.74 (step @p321 :rule cong :premises (@p320) :args (@t13)) % 155.07/155.74 (step @p322 :rule trans :premises (@p321 @p317)) % 155.07/155.74 (step @p323 :rule trans :premises (@p322 @p275)) % 155.07/155.74 (step @p324 :rule eq_resolve :premises (@p2 @p323)) % 155.07/155.74 (step @p325 :rule eq-symm :args (@t441 @t443)) % 155.07/155.74 (step @p326 :rule cong :premises (@p325) :args (@t444)) % 155.07/155.74 ; trust TRUST PREPROCESS_HO_ELIM % 155.07/155.74 (step @p327 :rule trust :premises () :args ((= (forall @t25 (= @t446 @t445)) @t444))) % 155.07/155.74 (step @p328 :rule refl :args (@t445)) % 155.07/155.74 (step @p329 :rule refl :args (@t21)) % 155.07/155.74 (step @p330 :rule cong :premises (@p329 @p328) :args ((= @t21 @t445))) % 155.07/155.74 (step @p331 :rule symm :premises (@p330)) % 155.07/155.74 (step @p332 :rule eq_resolve :premises (@p329 @p331)) % 155.07/155.74 (step @p333 :rule refl :args (@t446)) % 155.07/155.74 (step @p334 :rule refl :args (@t23)) % 155.07/155.74 (step @p335 :rule cong :premises (@p334 @p333) :args ((= @t23 @t446))) % 155.07/155.74 (step @p336 :rule symm :premises (@p335)) % 155.07/155.74 (step @p337 :rule eq_resolve :premises (@p334 @p336)) % 155.07/155.74 (step @p338 :rule cong :premises (@p337 @p332) :args (@t24)) % 155.07/155.74 (step @p339 :rule cong :premises (@p338) :args (@t26)) % 155.07/155.74 (step @p340 :rule trans :premises (@p339 @p327 @p326)) % 155.07/155.74 (step @p341 :rule eq_resolve :premises (@p6 @p340)) % 155.07/155.74 (step @p342 :rule eq-symm :args (@t447 @t448)) % 155.07/155.74 (step @p343 :rule refl :args (@t449)) % 155.07/155.74 (step @p344 :rule cong :premises (@p343 @p342) :args ((=> @t449 @t450))) % 155.07/155.74 (assume-push @p371 @t449) % 155.07/155.74 (step @p346 :rule instantiate :premises (@p341) :args ((@list tptp.p))) % 155.07/155.74 (step-pop @p372 :rule scope :premises (@p346)) % 155.07/155.74 (step @p347 :rule process_scope :premises (@p372) :args (@t450)) % 155.07/155.74 (step @p349 :rule eq_resolve :premises (@p347 @p344)) % 155.07/155.74 (step @p350 :rule implies_elim :premises (@p349)) % 155.07/155.74 (step @p351 :rule chain_m_resolution :premises (@p350 @p341) :args (@t451 (@list false) (@list @t449))) % 155.07/155.74 ; trust TRUST PREPROCESS_HO_ELIM % 155.07/155.74 (step @p352 :rule trust :premises () :args ((= @t398 @t448))) % 155.07/155.74 (step @p353 :rule eq_resolve :premises (@p264 @p352)) % 155.07/155.74 (step @p354 :rule cnf_equiv_pos1 :args (@t451)) % 155.07/155.74 (step @p355 :rule reordering :premises (@p354) :args ((or (not @t448) @t447 (not @t451)))) % 155.07/155.74 (step @p356 :rule chain_m_resolution :premises (@p355 @p353 @p351) :args (@t447 (@list false false) (@list @t448 @t451))) % 155.07/155.74 ; trust TRUST PREPROCESS_HO_ELIM % 155.07/155.74 (step @p357 :rule trust :premises () :args ((= (not (= tptp.bot_bo2130386637at_nat @t400)) (not @t453)))) % 155.07/155.74 (step @p358 :rule eq-symm :args (@t400 tptp.bot_bo2130386637at_nat)) % 155.07/155.74 (step @p359 :rule cong :premises (@p358) :args (@t401)) % 155.07/155.74 (step @p360 :rule trans :premises (@p359 @p357)) % 155.07/155.74 (step @p361 :rule eq_resolve :premises (@p265 @p360)) % 155.07/155.74 (step @p362 :rule cnf_or_pos :args (@t455)) % 155.07/155.74 (step @p363 :rule reordering :premises (@p362) :args ((or @t453 @t454 @t456))) % 155.07/155.74 (step @p364 :rule chain_m_resolution :premises (@p363 @p361 @p356) :args (@t456 @t457 (@list @t453 @t447))) % 155.07/155.74 (assume-push @p373 @t431) % 155.07/155.74 (step @p366 :rule instantiate :premises (@p324) :args ((@list tptp.s tptp.p tptp.t))) % 155.07/155.74 (step-pop @p374 :rule scope :premises (@p366)) % 155.07/155.74 (step @p367 :rule process_scope :premises (@p374) :args (@t455)) % 155.07/155.74 (step @p369 :rule implies_elim :premises (@p367)) % 155.07/155.74 (step @p370 false :rule chain_m_resolution :premises (@p369 @p364 @p324) :args (false @t457 (@list @t455 @t431))) % 155.07/155.74 ) % 155.07/155.74 % SZS output end Proof % 155.07/155.74 % cvc5 exiting %------------------------------------------------------------------------------