%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP048^1 : TPTP v9.2.1. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n015.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 151.05s 151.86s % Output : Proof 151.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP048^1 : TPTP v9.2.1. Released v7.5.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n015.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 04:12:04 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.55 %----Proving TH0 % 151.05/151.86 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 151.05/151.86 --- 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... % 151.05/151.86 --- 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... % 151.05/151.86 --- Run --ho-elim --full-saturate-quant at 18s... % 151.05/151.86 % SZS status Theorem % 151.05/151.86 % SZS output start Proof % 151.05/151.86 ( % 151.05/151.86 (declare-sort tptp.nat 0) % 151.05/151.86 (declare-sort tptp.product_prod_nat_nat 0) % 151.05/151.86 (declare-sort tptp.capacity 0) % 151.05/151.86 (declare-sort tptp.list_P559422087at_nat 0) % 151.05/151.86 (declare-sort tptp.set_nat 0) % 151.05/151.86 (declare-sort tptp.a 0) % 151.05/151.86 (declare-const tptp.plus_plus_nat (-> tptp.nat tptp.nat tptp.nat)) % 151.05/151.86 (declare-const tptp.ord_Least_nat (-> (-> tptp.nat Bool) tptp.nat)) % 151.05/151.86 (declare-const tptp.size_s1990949619at_nat (-> tptp.list_P559422087at_nat tptp.nat)) % 151.05/151.86 (declare-const tptp.isPath_capacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)) % 151.05/151.86 (declare-const tptp.isPath_a (-> (-> tptp.product_prod_nat_nat tptp.a) tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)) % 151.05/151.86 (declare-const tptp.collect_nat (-> (-> tptp.nat Bool) tptp.set_nat)) % 151.05/151.86 (declare-const tptp.u tptp.nat) % 151.05/151.86 (declare-const tptp.p3 tptp.list_P559422087at_nat) % 151.05/151.86 (declare-const tptp.c2 (-> tptp.product_prod_nat_nat tptp.a)) % 151.05/151.86 (declare-const tptp.p2 tptp.list_P559422087at_nat) % 151.05/151.86 (declare-const tptp.isSimplePath_a (-> (-> tptp.product_prod_nat_nat tptp.a) tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)) % 151.05/151.86 (declare-const tptp.t tptp.nat) % 151.05/151.86 (declare-const tptp.ua tptp.nat) % 151.05/151.86 (declare-const tptp.c (-> tptp.product_prod_nat_nat tptp.capacity)) % 151.05/151.86 (declare-const tptp.va tptp.nat) % 151.05/151.86 (declare-const tptp.s tptp.nat) % 151.05/151.86 (declare-const tptp.isSimp1359852763pacity (-> (-> tptp.product_prod_nat_nat tptp.capacity) tptp.nat tptp.list_P559422087at_nat tptp.nat Bool)) % 151.05/151.86 (declare-const tptp.p2_a tptp.list_P559422087at_nat) % 151.05/151.86 (declare-const tptp.p tptp.list_P559422087at_nat) % 151.05/151.86 (declare-const tptp.p1a tptp.list_P559422087at_nat) % 151.05/151.86 (declare-const tptp.v tptp.nat) % 151.05/151.86 (declare-const tptp.member_nat (-> tptp.nat tptp.set_nat Bool)) % 151.05/151.86 (declare-const tptp.p1 tptp.list_P559422087at_nat) % 151.05/151.86 (define tptp.ord_less_eq_nat () (let ((_let_1 (@var "C2" tptp.nat))) (let ((_let_2 (@var "A2" tptp.nat))) (let ((_let_3 (@var "B2" tptp.nat))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (= _let_3 (_ (_ tptp.plus_plus_nat _let_2) _let_1)))))))) % 151.05/151.86 (define tptp.ord_less_nat () (let ((_let_1 (@var "N2" tptp.nat))) (let ((_let_2 (@var "M2" tptp.nat))) (lambda (@list _let_2 _let_1) (and (_ (_ tptp.ord_less_eq_nat _let_2) _let_1) (not (= _let_2 _let_1))))))) % 151.05/151.86 (define tptp.dist_capacity () (let ((_let_1 (@var "D4" tptp.nat))) (let ((_let_2 (@var "P" tptp.list_P559422087at_nat))) (let ((_let_3 (@var "V5" tptp.nat))) (let ((_let_4 (@var "V4" tptp.nat))) (let ((_let_5 (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (lambda (@list _let_5 _let_4 _let_1 _let_3) (exists (@list _let_2) (and (_ (_ (_ (_ tptp.isPath_capacity _let_5) _let_4) _let_2) _let_3) (= (_ tptp.size_s1990949619at_nat _let_2) _let_1)))))))))) % 151.05/151.86 (define tptp.min_dist_capacity () (let ((_let_1 (@var "V5" tptp.nat))) (let ((_let_2 (@var "D4" tptp.nat))) (let ((_let_3 (@var "V4" tptp.nat))) (let ((_let_4 (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (lambda (@list _let_4 _let_3 _let_1) (_ tptp.ord_Least_nat (lambda (@list _let_2) (_ (_ (_ (_ tptp.dist_capacity _let_4) _let_3) _let_2) _let_1))))))))) % 151.05/151.86 (define tptp.isShor1936442771pacity () (let ((_let_1 (@var "V4" tptp.nat))) (let ((_let_2 (@var "U2" tptp.nat))) (let ((_let_3 (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (let ((_let_4 (@var "P" tptp.list_P559422087at_nat))) (lambda (@list _let_3 _let_2 _let_4 _let_1) (and (_ (_ (_ (_ tptp.isPath_capacity _let_3) _let_2) _let_4) _let_1) (= (_ tptp.size_s1990949619at_nat _let_4) (_ (_ (_ tptp.min_dist_capacity _let_3) _let_2) _let_1))))))))) % 151.05/151.86 (define tptp.dist_a () (let ((_let_1 (@var "D4" tptp.nat))) (let ((_let_2 (@var "P" tptp.list_P559422087at_nat))) (let ((_let_3 (@var "V5" tptp.nat))) (let ((_let_4 (@var "V4" tptp.nat))) (let ((_let_5 (@var "C2" (-> tptp.product_prod_nat_nat tptp.a)))) (lambda (@list _let_5 _let_4 _let_1 _let_3) (exists (@list _let_2) (and (_ (_ (_ (_ tptp.isPath_a _let_5) _let_4) _let_2) _let_3) (= (_ tptp.size_s1990949619at_nat _let_2) _let_1)))))))))) % 151.05/151.86 (define tptp.min_dist_a () (let ((_let_1 (@var "V5" tptp.nat))) (let ((_let_2 (@var "D4" tptp.nat))) (let ((_let_3 (@var "V4" tptp.nat))) (let ((_let_4 (@var "C2" (-> tptp.product_prod_nat_nat tptp.a)))) (lambda (@list _let_4 _let_3 _let_1) (_ tptp.ord_Least_nat (lambda (@list _let_2) (_ (_ (_ (_ tptp.dist_a _let_4) _let_3) _let_2) _let_1))))))))) % 151.05/151.86 (define tptp.isShortestPath_a () (let ((_let_1 (@var "V4" tptp.nat))) (let ((_let_2 (@var "U2" tptp.nat))) (let ((_let_3 (@var "C2" (-> tptp.product_prod_nat_nat tptp.a)))) (let ((_let_4 (@var "P" tptp.list_P559422087at_nat))) (lambda (@list _let_3 _let_2 _let_4 _let_1) (and (_ (_ (_ (_ tptp.isPath_a _let_3) _let_2) _let_4) _let_1) (= (_ tptp.size_s1990949619at_nat _let_4) (_ (_ (_ tptp.min_dist_a _let_3) _let_2) _let_1))))))))) % 151.05/151.86 (define tptp.connected_capacity () (let ((_let_1 (@var "V4" tptp.nat))) (let ((_let_2 (@var "P" tptp.list_P559422087at_nat))) (let ((_let_3 (@var "U2" tptp.nat))) (let ((_let_4 (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (lambda (@list _let_4 _let_3 _let_1) (exists (@list _let_2) (_ (_ (_ (_ tptp.isPath_capacity _let_4) _let_3) _let_2) _let_1)))))))) % 151.05/151.86 (define tptp.reacha1693770334pacity () (let ((_let_1 (@var "U2" tptp.nat))) (let ((_let_2 (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity)))) (lambda (@list _let_2 _let_1) (_ tptp.collect_nat (_ (_ tptp.connected_capacity _let_2) _let_1)))))) % 151.05/151.86 (define tptp.connected_a () (let ((_let_1 (@var "V4" tptp.nat))) (let ((_let_2 (@var "P" tptp.list_P559422087at_nat))) (let ((_let_3 (@var "U2" tptp.nat))) (let ((_let_4 (@var "C2" (-> tptp.product_prod_nat_nat tptp.a)))) (lambda (@list _let_4 _let_3 _let_1) (exists (@list _let_2) (_ (_ (_ (_ tptp.isPath_a _let_4) _let_3) _let_2) _let_1)))))))) % 151.05/151.86 (define tptp.reachableNodes_a () (let ((_let_1 (@var "U2" tptp.nat))) (let ((_let_2 (@var "C2" (-> tptp.product_prod_nat_nat tptp.a)))) (lambda (@list _let_2 _let_1) (_ tptp.collect_nat (_ (_ tptp.connected_a _let_2) _let_1)))))) % 151.05/151.86 (define @t1 () (_ tptp.min_dist_capacity tptp.c)) % 151.05/151.86 (define @t2 () (_ (_ @t1 tptp.ua) tptp.t)) % 151.05/151.86 (define @t3 () (_ @t1 tptp.s)) % 151.05/151.86 (define @t4 () (_ @t3 tptp.ua)) % 151.05/151.86 (define @t5 () (_ @t3 tptp.t)) % 151.05/151.86 (define @t6 () (= @t5 (_ (_ tptp.plus_plus_nat @t4) @t2))) % 151.05/151.86 (define @t7 () (_ tptp.size_s1990949619at_nat tptp.p1a)) % 151.05/151.86 (define @t8 () (_ tptp.size_s1990949619at_nat tptp.p2_a)) % 151.05/151.86 (define @t9 () (@var "N" tptp.nat)) % 151.05/151.86 (define @t10 () (@var "M" tptp.nat)) % 151.05/151.86 (define @t11 () (_ (_ tptp.ord_less_nat @t10) @t9)) % 151.05/151.86 (define @t12 () (@var "K" tptp.nat)) % 151.05/151.86 (define @t13 () (_ tptp.plus_plus_nat @t12)) % 151.05/151.86 (define @t14 () (_ @t13 @t9)) % 151.05/151.86 (define @t15 () (_ @t13 @t10)) % 151.05/151.86 (define @t16 () (@list @t12 @t10 @t9)) % 151.05/151.86 (define @t17 () (@var "B" tptp.nat)) % 151.05/151.86 (define @t18 () (@var "A" tptp.nat)) % 151.05/151.86 (define @t19 () (_ tptp.ord_less_nat @t18)) % 151.05/151.86 (define @t20 () (_ @t19 @t17)) % 151.05/151.86 (define @t21 () (@var "C" tptp.nat)) % 151.05/151.86 (define @t22 () (_ tptp.plus_plus_nat @t21)) % 151.05/151.86 (define @t23 () (_ @t22 @t17)) % 151.05/151.86 (define @t24 () (_ @t22 @t18)) % 151.05/151.86 (define @t25 () (_ (_ tptp.ord_less_nat @t24) @t23)) % 151.05/151.86 (define @t26 () (@list @t21 @t18 @t17)) % 151.05/151.86 (define @t27 () (_ tptp.plus_plus_nat @t17)) % 151.05/151.86 (define @t28 () (_ @t27 @t21)) % 151.05/151.86 (define @t29 () (_ tptp.plus_plus_nat @t18)) % 151.05/151.86 (define @t30 () (_ @t29 @t21)) % 151.05/151.86 (define @t31 () (_ tptp.ord_less_nat @t30)) % 151.05/151.86 (define @t32 () (_ @t31 @t28)) % 151.05/151.86 (define @t33 () (@list @t18 @t21 @t17)) % 151.05/151.86 (define @t34 () (_ tptp.isPath_capacity tptp.c)) % 151.05/151.86 (define @t35 () (_ @t34 tptp.s)) % 151.05/151.86 (define @t36 () (_ tptp.isShor1936442771pacity tptp.c)) % 151.05/151.86 (define @t37 () (@var "D2" tptp.nat)) % 151.05/151.86 (define @t38 () (@var "V" tptp.nat)) % 151.05/151.86 (define @t39 () (@var "W" tptp.nat)) % 151.05/151.86 (define @t40 () (@var "D1" tptp.nat)) % 151.05/151.86 (define @t41 () (_ (_ tptp.plus_plus_nat @t40) @t37)) % 151.05/151.86 (define @t42 () (@var "U" tptp.nat)) % 151.05/151.86 (define @t43 () (_ @t1 @t42)) % 151.05/151.86 (define @t44 () (_ @t43 @t38)) % 151.05/151.86 (define @t45 () (= @t44 @t41)) % 151.05/151.86 (define @t46 () (_ tptp.dist_capacity tptp.c)) % 151.05/151.86 (define @t47 () (_ (_ (_ @t46 @t39) @t37) @t38)) % 151.05/151.86 (define @t48 () (_ @t46 @t42)) % 151.05/151.86 (define @t49 () (_ (_ @t48 @t40) @t39)) % 151.05/151.86 (define @t50 () (@list @t42 @t40 @t39 @t37 @t38)) % 151.05/151.86 (define @t51 () (@var "D3" tptp.nat)) % 151.05/151.86 (define @t52 () (@var "V2" tptp.nat)) % 151.05/151.86 (define @t53 () (@var "Src" tptp.nat)) % 151.05/151.86 (define @t54 () (_ @t1 @t53)) % 151.05/151.86 (define @t55 () (_ tptp.connected_capacity tptp.c)) % 151.05/151.86 (define @t56 () (_ @t55 @t53)) % 151.05/151.86 (define @t57 () (@list @t52)) % 151.05/151.86 (define @t58 () (exists @t57 (and (_ @t56 @t52) (= (_ @t54 @t52) @t51)))) % 151.05/151.86 (define @t59 () (@var "D" tptp.nat)) % 151.05/151.86 (define @t60 () (_ (_ tptp.ord_less_nat @t51) @t59)) % 151.05/151.86 (define @t61 () (_ @t54 @t38)) % 151.05/151.86 (define @t62 () (_ @t56 @t38)) % 151.05/151.86 (define @t63 () (@list @t53 @t38 @t59 @t51)) % 151.05/151.86 (define @t64 () (= @t17 @t21)) % 151.05/151.86 (define @t65 () (_ @t29 @t17)) % 151.05/151.86 (define @t66 () (= @t65 @t30)) % 151.05/151.86 (define @t67 () (@list @t18 @t17 @t21)) % 151.05/151.86 (define @t68 () (= (_ @t27 @t18) @t24)) % 151.05/151.86 (define @t69 () (@list @t17 @t18 @t21)) % 151.05/151.86 (define @t70 () (_ @t34 tptp.ua)) % 151.05/151.86 (define @t71 () (@var "P" tptp.list_P559422087at_nat)) % 151.05/151.86 (define @t72 () (_ @t34 @t42)) % 151.05/151.86 (define @t73 () (@list @t71)) % 151.05/151.86 (define @t74 () (_ @t55 @t42)) % 151.05/151.86 (define @t75 () (_ @t74 @t38)) % 151.05/151.86 (define @t76 () (@list @t42 @t38)) % 151.05/151.86 (define @t77 () (@var "P2" tptp.list_P559422087at_nat)) % 151.05/151.86 (define @t78 () (_ (_ @t72 @t77) @t38)) % 151.05/151.86 (define @t79 () (_ @t36 @t42)) % 151.05/151.86 (define @t80 () (_ (_ @t79 @t77) @t38)) % 151.05/151.86 (define @t81 () (@list @t42 @t77 @t38)) % 151.05/151.86 (define @t82 () (@var "V3" tptp.nat)) % 151.05/151.86 (define @t83 () (@var "D4" tptp.nat)) % 151.05/151.86 (define @t84 () (_ @t46 @t38)) % 151.05/151.86 (define @t85 () (_ (_ @t84 @t83) @t82)) % 151.05/151.86 (define @t86 () (@list @t83)) % 151.05/151.86 (define @t87 () (_ @t55 @t38)) % 151.05/151.86 (define @t88 () (_ @t87 @t82)) % 151.05/151.86 (define @t89 () (@list @t38 @t82)) % 151.05/151.86 (define @t90 () (@var "P3" tptp.list_P559422087at_nat)) % 151.05/151.86 (define @t91 () (@list @t90)) % 151.05/151.86 (define @t92 () (_ tptp.ord_less_eq_nat @t51)) % 151.05/151.86 (define @t93 () (@list @t53 @t38 @t51)) % 151.05/151.86 (define @t94 () (_ (_ @t1 @t38) @t82)) % 151.05/151.86 (define @t95 () (_ (_ @t84 @t59) @t82)) % 151.05/151.86 (define @t96 () (@list @t38 @t59 @t82)) % 151.05/151.86 (define @t97 () (@var "D5" tptp.nat)) % 151.05/151.86 (define @t98 () (_ (_ tptp.ord_less_eq_nat @t59) @t97)) % 151.05/151.86 (define @t99 () (@list @t97)) % 151.05/151.86 (define @t100 () (_ tptp.size_s1990949619at_nat @t77)) % 151.05/151.86 (define @t101 () (_ tptp.size_s1990949619at_nat @t71)) % 151.05/151.86 (define @t102 () (= @t101 @t59)) % 151.05/151.86 (define @t103 () (@var "P4" tptp.list_P559422087at_nat)) % 151.05/151.86 (define @t104 () (_ tptp.size_s1990949619at_nat @t103)) % 151.05/151.86 (define @t105 () (_ (_ tptp.ord_less_eq_nat @t100) @t104)) % 151.05/151.86 (define @t106 () (@list @t103)) % 151.05/151.86 (define @t107 () (@var "Q" (-> tptp.nat Bool))) % 151.05/151.86 (define @t108 () (@var "D6" tptp.nat)) % 151.05/151.86 (define @t109 () (_ @t107 @t108)) % 151.05/151.86 (define @t110 () (@var "D7" tptp.nat)) % 151.05/151.86 (define @t111 () (_ (_ tptp.ord_less_eq_nat @t108) @t110)) % 151.05/151.86 (define @t112 () (@list @t110)) % 151.05/151.86 (define @t113 () (@list @t108)) % 151.05/151.86 (define @t114 () (@list @t38 @t82 @t107)) % 151.05/151.86 (define @t115 () (= @t100 @t44)) % 151.05/151.86 (define @t116 () (_ tptp.ord_less_eq_nat @t18)) % 151.05/151.86 (define @t117 () (_ @t116 @t17)) % 151.05/151.86 (define @t118 () (_ tptp.ord_less_eq_nat @t30)) % 151.05/151.86 (define @t119 () (_ @t118 @t28)) % 151.05/151.86 (define @t120 () (_ (_ tptp.ord_less_eq_nat @t24) @t23)) % 151.05/151.86 (define @t121 () (_ (_ tptp.ord_less_eq_nat @t10) @t9)) % 151.05/151.86 (define @t122 () (@list @t38)) % 151.05/151.86 (define @t123 () (_ tptp.ord_less_eq_nat @t9)) % 151.05/151.86 (define @t124 () (@list @t9)) % 151.05/151.86 (define @t125 () (@var "I" tptp.nat)) % 151.05/151.86 (define @t126 () (_ tptp.ord_less_eq_nat @t125)) % 151.05/151.86 (define @t127 () (@var "J" tptp.nat)) % 151.05/151.86 (define @t128 () (_ @t126 @t127)) % 151.05/151.86 (define @t129 () (@list @t125 @t127 @t12)) % 151.05/151.86 (define @t130 () (= @t10 @t9)) % 151.05/151.86 (define @t131 () (@list @t10 @t9)) % 151.05/151.86 (define @t132 () (_ @t123 @t10)) % 151.05/151.86 (define @t133 () (@var "X" tptp.nat)) % 151.05/151.86 (define @t134 () (@var "Y2" tptp.nat)) % 151.05/151.86 (define @t135 () (@var "P5" (-> tptp.nat Bool))) % 151.05/151.86 (define @t136 () (_ @t135 @t134)) % 151.05/151.86 (define @t137 () (@list @t134)) % 151.05/151.86 (define @t138 () (_ @t135 @t133)) % 151.05/151.86 (define @t139 () (@list @t133)) % 151.05/151.86 (define @t140 () (@var "Y" tptp.nat)) % 151.05/151.86 (define @t141 () (_ @t135 @t12)) % 151.05/151.86 (define @t142 () (_ @t135 @t18)) % 151.05/151.86 (define @t143 () (_ tptp.collect_nat @t135)) % 151.05/151.86 (define @t144 () (@var "A3" tptp.set_nat)) % 151.05/151.86 (define @t145 () (@var "X2" tptp.nat)) % 151.05/151.86 (define @t146 () (_ @t107 @t133)) % 151.05/151.86 (define @t147 () (@list @t135 @t107)) % 151.05/151.86 (define @t148 () (@var "C3" tptp.nat)) % 151.05/151.86 (define @t149 () (@list @t18 @t17)) % 151.05/151.86 (define @t150 () (_ @t27 @t59)) % 151.05/151.86 (define @t151 () (_ tptp.ord_less_eq_nat @t21)) % 151.05/151.86 (define @t152 () (_ @t151 @t59)) % 151.05/151.86 (define @t153 () (@list @t18 @t17 @t21 @t59)) % 151.05/151.86 (define @t154 () (@var "L" tptp.nat)) % 151.05/151.86 (define @t155 () (_ tptp.plus_plus_nat @t127)) % 151.05/151.86 (define @t156 () (_ @t155 @t154)) % 151.05/151.86 (define @t157 () (_ tptp.plus_plus_nat @t125)) % 151.05/151.86 (define @t158 () (_ @t157 @t12)) % 151.05/151.86 (define @t159 () (_ tptp.ord_less_eq_nat @t158)) % 151.05/151.86 (define @t160 () (_ @t159 @t156)) % 151.05/151.86 (define @t161 () (_ tptp.ord_less_eq_nat @t12)) % 151.05/151.86 (define @t162 () (_ @t161 @t154)) % 151.05/151.86 (define @t163 () (@list @t125 @t127 @t12 @t154)) % 151.05/151.86 (define @t164 () (= @t125 @t127)) % 151.05/151.86 (define @t165 () (= @t12 @t154)) % 151.05/151.86 (define @t166 () (@var "F" (-> tptp.nat tptp.nat))) % 151.05/151.86 (define @t167 () (@var "J2" tptp.nat)) % 151.05/151.86 (define @t168 () (@var "I2" tptp.nat)) % 151.05/151.86 (define @t169 () (not @t130)) % 151.05/151.86 (define @t170 () (@var "N2" tptp.nat)) % 151.05/151.86 (define @t171 () (@var "M2" tptp.nat)) % 151.05/151.86 (define @t172 () (= @t171 @t170)) % 151.05/151.86 (define @t173 () (_ (_ tptp.ord_less_nat @t171) @t170)) % 151.05/151.86 (define @t174 () (@list @t171 @t170)) % 151.05/151.86 (define @t175 () (@var "K2" tptp.nat)) % 151.05/151.86 (define @t176 () (_ tptp.plus_plus_nat @t10)) % 151.05/151.86 (define @t177 () (_ @t176 @t127)) % 151.05/151.86 (define @t178 () (@list @t125 @t127 @t10)) % 151.05/151.86 (define @t179 () (_ @t155 @t10)) % 151.05/151.86 (define @t180 () (_ @t155 @t12)) % 151.05/151.86 (define @t181 () (@var "N3" tptp.nat)) % 151.05/151.86 (define @t182 () (@list @t181)) % 151.05/151.86 (define @t183 () (_ @t161 @t9)) % 151.05/151.86 (define @t184 () (_ @t176 @t12)) % 151.05/151.86 (define @t185 () (_ (_ tptp.ord_less_eq_nat @t184) @t9)) % 151.05/151.86 (define @t186 () (@list @t10 @t12 @t9)) % 151.05/151.86 (define @t187 () (@list @t9 @t10)) % 151.05/151.86 (define @t188 () (_ @t29 @t28)) % 151.05/151.86 (define @t189 () (@var "A2" tptp.nat)) % 151.05/151.86 (define @t190 () (@var "B2" tptp.nat)) % 151.05/151.86 (define @t191 () (@list @t189 @t190)) % 151.05/151.86 (define @t192 () (_ @t13 @t65)) % 151.05/151.86 (define @t193 () (@var "B3" tptp.nat)) % 151.05/151.86 (define @t194 () (@var "A3" tptp.nat)) % 151.05/151.86 (define @t195 () (@var "X3" tptp.nat)) % 151.05/151.86 (define @t196 () (@var "Y3" tptp.nat)) % 151.05/151.86 (define @t197 () (_ tptp.ord_less_nat @t196)) % 151.05/151.86 (define @t198 () (_ @t197 @t195)) % 151.05/151.86 (define @t199 () (_ tptp.ord_less_nat @t195)) % 151.05/151.86 (define @t200 () (_ @t199 @t196)) % 151.05/151.86 (define @t201 () (not @t200)) % 151.05/151.86 (define @t202 () (= @t195 @t196)) % 151.05/151.86 (define @t203 () (not @t202)) % 151.05/151.86 (define @t204 () (@list @t195 @t196)) % 151.05/151.86 (define @t205 () (_ @t135 @t9)) % 151.05/151.86 (define @t206 () (@var "M3" tptp.nat)) % 151.05/151.86 (define @t207 () (_ @t135 @t206)) % 151.05/151.86 (define @t208 () (_ (_ tptp.ord_less_nat @t206) @t181)) % 151.05/151.86 (define @t209 () (@list @t206)) % 151.05/151.86 (define @t210 () (_ @t135 @t181)) % 151.05/151.86 (define @t211 () (@list @t135 @t9)) % 151.05/151.86 (define @t212 () (_ tptp.ord_less_nat @t9)) % 151.05/151.86 (define @t213 () (@var "T" tptp.nat)) % 151.05/151.86 (define @t214 () (@var "S" tptp.nat)) % 151.05/151.86 (define @t215 () (_ @t212 @t10)) % 151.05/151.86 (define @t216 () (@var "Y3" tptp.list_P559422087at_nat)) % 151.05/151.86 (define @t217 () (@var "X3" tptp.list_P559422087at_nat)) % 151.05/151.86 (define @t218 () (_ @t31 @t150)) % 151.05/151.86 (define @t219 () (=> @t152 @t218)) % 151.05/151.86 (define @t220 () (=> @t20 @t219)) % 151.05/151.86 (define @t221 () (forall @t153 @t220)) % 151.05/151.86 (define @t222 () (_ tptp.ord_less_nat @t21)) % 151.05/151.86 (define @t223 () (=> (_ @t222 @t59) @t218)) % 151.05/151.86 (define @t224 () (_ tptp.ord_less_nat @t158)) % 151.05/151.86 (define @t225 () (_ @t224 @t156)) % 151.05/151.86 (define @t226 () (_ tptp.ord_less_nat @t125)) % 151.05/151.86 (define @t227 () (_ @t226 @t127)) % 151.05/151.86 (define @t228 () (_ tptp.ord_less_nat @t12)) % 151.05/151.86 (define @t229 () (_ @t228 @t154)) % 151.05/151.86 (define @t230 () (@var "M4" tptp.nat)) % 151.05/151.86 (define @t231 () (_ tptp.ord_less_nat (_ @t157 @t127))) % 151.05/151.86 (define @t232 () (@list @t42)) % 151.05/151.86 (define @t233 () (_ (_ tptp.ord_less_eq_nat @t101) @t104)) % 151.05/151.86 (define @t234 () (@var "V4" tptp.nat)) % 151.05/151.86 (define @t235 () (@var "U2" tptp.nat)) % 151.05/151.86 (define @t236 () (@var "C2" (-> tptp.product_prod_nat_nat tptp.capacity))) % 151.05/151.86 (define @t237 () (_ tptp.isPath_capacity @t236)) % 151.05/151.86 (define @t238 () (_ @t237 @t235)) % 151.05/151.86 (define @t239 () (_ (_ @t238 @t71) @t234)) % 151.05/151.86 (define @t240 () (@list @t236 @t235 @t71 @t234)) % 151.05/151.86 (define @t241 () (@var "C2" (-> tptp.product_prod_nat_nat tptp.a))) % 151.05/151.86 (define @t242 () (_ tptp.isPath_a @t241)) % 151.05/151.86 (define @t243 () (_ @t242 @t235)) % 151.05/151.86 (define @t244 () (_ (_ @t243 @t71) @t234)) % 151.05/151.86 (define @t245 () (@list @t241 @t235 @t71 @t234)) % 151.05/151.86 (define @t246 () (@var "C" (-> tptp.product_prod_nat_nat tptp.capacity))) % 151.05/151.86 (define @t247 () (_ tptp.min_dist_capacity @t246)) % 151.05/151.86 (define @t248 () (_ (_ @t247 @t38) @t82)) % 151.05/151.86 (define @t249 () (_ tptp.dist_capacity @t246)) % 151.05/151.86 (define @t250 () (_ @t249 @t38)) % 151.05/151.86 (define @t251 () (_ tptp.connected_capacity @t246)) % 151.05/151.86 (define @t252 () (_ @t251 @t38)) % 151.05/151.86 (define @t253 () (_ @t252 @t82)) % 151.05/151.86 (define @t254 () (@var "C" (-> tptp.product_prod_nat_nat tptp.a))) % 151.05/151.86 (define @t255 () (_ tptp.min_dist_a @t254)) % 151.05/151.86 (define @t256 () (_ (_ @t255 @t38) @t82)) % 151.05/151.86 (define @t257 () (_ tptp.dist_a @t254)) % 151.05/151.86 (define @t258 () (_ @t257 @t38)) % 151.05/151.86 (define @t259 () (_ tptp.connected_a @t254)) % 151.05/151.86 (define @t260 () (_ @t259 @t38)) % 151.05/151.86 (define @t261 () (_ @t260 @t82)) % 151.05/151.86 (define @t262 () (_ tptp.isSimp1359852763pacity tptp.c)) % 151.05/151.86 (define @t263 () (_ @t249 @t42)) % 151.05/151.86 (define @t264 () (_ tptp.isPath_capacity @t246)) % 151.05/151.86 (define @t265 () (_ (_ (_ @t264 @t42) @t77) @t38)) % 151.05/151.86 (define @t266 () (@list @t246 @t42 @t77 @t38)) % 151.05/151.86 (define @t267 () (_ @t257 @t42)) % 151.05/151.86 (define @t268 () (_ tptp.isPath_a @t254)) % 151.05/151.86 (define @t269 () (_ (_ (_ @t268 @t42) @t77) @t38)) % 151.05/151.86 (define @t270 () (@list @t254 @t42 @t77 @t38)) % 151.05/151.86 (define @t271 () (_ @t247 @t42)) % 151.05/151.86 (define @t272 () (= (_ @t271 @t38) @t41)) % 151.05/151.86 (define @t273 () (_ (_ (_ @t249 @t39) @t37) @t38)) % 151.05/151.86 (define @t274 () (_ (_ @t263 @t40) @t39)) % 151.05/151.86 (define @t275 () (@list @t246 @t42 @t40 @t39 @t37 @t38)) % 151.05/151.86 (define @t276 () (_ @t255 @t42)) % 151.05/151.86 (define @t277 () (= (_ @t276 @t38) @t41)) % 151.05/151.86 (define @t278 () (_ (_ (_ @t257 @t39) @t37) @t38)) % 151.05/151.86 (define @t279 () (_ (_ @t267 @t40) @t39)) % 151.05/151.86 (define @t280 () (@list @t254 @t42 @t40 @t39 @t37 @t38)) % 151.05/151.86 (define @t281 () (@var "P6" tptp.list_P559422087at_nat)) % 151.05/151.86 (define @t282 () (_ @t262 @t214)) % 151.05/151.86 (define @t283 () (@list @t281)) % 151.05/151.86 (define @t284 () (@list @t214 @t77 @t213)) % 151.05/151.86 (define @t285 () (_ (_ tptp.isSimp1359852763pacity @t246) @t214)) % 151.05/151.86 (define @t286 () (@list @t246 @t214 @t77 @t213)) % 151.05/151.86 (define @t287 () (_ (_ tptp.isSimplePath_a @t254) @t214)) % 151.05/151.86 (define @t288 () (@list @t254 @t214 @t77 @t213)) % 151.05/151.86 (define @t289 () (_ tptp.isShor1936442771pacity @t246)) % 151.05/151.86 (define @t290 () (_ tptp.isShortestPath_a @t254)) % 151.05/151.86 (define @t291 () (= @t101 (_ (_ (_ tptp.min_dist_capacity @t236) @t235) @t234))) % 151.05/151.86 (define @t292 () (= @t101 (_ (_ (_ tptp.min_dist_a @t241) @t235) @t234))) % 151.05/151.86 (define @t293 () (_ @t289 @t42)) % 151.05/151.86 (define @t294 () (_ @t290 @t42)) % 151.05/151.86 (define @t295 () (@var "V5" tptp.nat)) % 151.05/151.86 (define @t296 () (_ (_ (_ (_ tptp.dist_capacity @t236) @t234) @t83) @t295)) % 151.05/151.86 (define @t297 () (@list @t236 @t234 @t295)) % 151.05/151.86 (define @t298 () (_ (_ (_ (_ tptp.dist_a @t241) @t234) @t83) @t295)) % 151.05/151.86 (define @t299 () (@list @t241 @t234 @t295)) % 151.05/151.86 (define @t300 () (_ (_ @t250 @t59) @t82)) % 151.05/151.86 (define @t301 () (@list @t246 @t38 @t59 @t82)) % 151.05/151.86 (define @t302 () (_ (_ @t258 @t59) @t82)) % 151.05/151.86 (define @t303 () (@list @t254 @t38 @t59 @t82)) % 151.05/151.86 (define @t304 () (_ @t247 @t53)) % 151.05/151.86 (define @t305 () (_ @t251 @t53)) % 151.05/151.86 (define @t306 () (exists @t57 (and (_ @t305 @t52) (= (_ @t304 @t52) @t51)))) % 151.05/151.86 (define @t307 () (_ @t304 @t38)) % 151.05/151.86 (define @t308 () (_ @t305 @t38)) % 151.05/151.86 (define @t309 () (_ @t255 @t53)) % 151.05/151.86 (define @t310 () (_ @t259 @t53)) % 151.05/151.86 (define @t311 () (exists @t57 (and (_ @t310 @t52) (= (_ @t309 @t52) @t51)))) % 151.05/151.86 (define @t312 () (_ @t309 @t38)) % 151.05/151.86 (define @t313 () (_ @t310 @t38)) % 151.05/151.86 (define @t314 () (_ tptp.isPath_a tptp.c2)) % 151.05/151.86 (define @t315 () (_ tptp.ord_Least_nat @t135)) % 151.05/151.86 (define @t316 () (@list @t135 @t12)) % 151.05/151.86 (define @t317 () (_ tptp.dist_a tptp.c2)) % 151.05/151.86 (define @t318 () (_ @t317 @t38)) % 151.05/151.86 (define @t319 () (_ (_ @t318 @t83) @t82)) % 151.05/151.86 (define @t320 () (_ tptp.connected_a tptp.c2)) % 151.05/151.86 (define @t321 () (_ @t320 @t38)) % 151.05/151.86 (define @t322 () (_ @t321 @t82)) % 151.05/151.86 (define @t323 () (_ tptp.min_dist_a tptp.c2)) % 151.05/151.86 (define @t324 () (_ (_ @t323 @t38) @t82)) % 151.05/151.86 (define @t325 () (_ tptp.isShortestPath_a tptp.c2)) % 151.05/151.86 (define @t326 () (_ @t325 @t42)) % 151.05/151.86 (define @t327 () (_ @t320 @t42)) % 151.05/151.86 (define @t328 () (_ @t327 @t38)) % 151.05/151.86 (define @t329 () (_ tptp.isSimplePath_a tptp.c2)) % 151.05/151.86 (define @t330 () (_ @t329 @t214)) % 151.05/151.86 (define @t331 () (_ @t323 @t53)) % 151.05/151.86 (define @t332 () (_ @t320 @t53)) % 151.05/151.86 (define @t333 () (exists @t57 (and (_ @t332 @t52) (= (_ @t331 @t52) @t51)))) % 151.05/151.86 (define @t334 () (_ @t331 @t38)) % 151.05/151.86 (define @t335 () (_ @t332 @t38)) % 151.05/151.86 (define @t336 () (_ (_ @t318 @t59) @t82)) % 151.05/151.86 (define @t337 () (_ @t323 @t42)) % 151.05/151.86 (define @t338 () (_ @t337 @t38)) % 151.05/151.86 (define @t339 () (= @t338 @t41)) % 151.05/151.86 (define @t340 () (_ (_ (_ @t317 @t39) @t37) @t38)) % 151.05/151.86 (define @t341 () (_ @t317 @t42)) % 151.05/151.86 (define @t342 () (_ (_ @t341 @t40) @t39)) % 151.05/151.86 (define @t343 () (_ @t314 @t42)) % 151.05/151.86 (define @t344 () (_ (_ @t343 @t77) @t38)) % 151.05/151.86 (define @t345 () (_ (_ @t326 @t77) @t38)) % 151.05/151.86 (define @t346 () (= @t100 @t338)) % 151.05/151.86 (define @t347 () (_ tptp.ord_less_eq_nat @t195)) % 151.05/151.86 (define @t348 () (@list @t195)) % 151.05/151.86 (define @t349 () (_ @t166 @t21)) % 151.05/151.86 (define @t350 () (_ @t166 @t140)) % 151.05/151.86 (define @t351 () (_ @t166 @t133)) % 151.05/151.86 (define @t352 () (@list @t133 @t140)) % 151.05/151.86 (define @t353 () (forall @t352 (=> (_ (_ tptp.ord_less_eq_nat @t133) @t140) (_ (_ tptp.ord_less_eq_nat @t351) @t350)))) % 151.05/151.86 (define @t354 () (_ tptp.ord_less_eq_nat @t17)) % 151.05/151.86 (define @t355 () (_ @t354 @t21)) % 151.05/151.86 (define @t356 () (=> @t355 (=> @t353 (_ @t116 @t349)))) % 151.05/151.86 (define @t357 () (_ @t166 @t17)) % 151.05/151.86 (define @t358 () (@list @t18 @t166 @t17 @t21)) % 151.05/151.86 (define @t359 () (_ @t166 @t18)) % 151.05/151.86 (define @t360 () (=> @t353 (_ (_ tptp.ord_less_eq_nat @t359) @t21))) % 151.05/151.86 (define @t361 () (@list @t18 @t17 @t166 @t21)) % 151.05/151.86 (define @t362 () (= @t18 @t357)) % 151.05/151.86 (define @t363 () (= @t357 @t21)) % 151.05/151.86 (define @t364 () (@var "Y5" tptp.nat)) % 151.05/151.86 (define @t365 () (@var "Z" tptp.nat)) % 151.05/151.86 (define @t366 () (@var "Y4" tptp.nat)) % 151.05/151.86 (define @t367 () (lambda (@list @t366 @t365) (= @t366 @t365))) % 151.05/151.86 (define @t368 () (_ tptp.ord_less_eq_nat @t196)) % 151.05/151.86 (define @t369 () (_ @t368 @t195)) % 151.05/151.86 (define @t370 () (_ @t347 @t196)) % 151.05/151.86 (define @t371 () (not @t370)) % 151.05/151.86 (define @t372 () (_ @t116 @t21)) % 151.05/151.86 (define @t373 () (=> @t355 @t372)) % 151.05/151.86 (define @t374 () (@var "Z2" tptp.nat)) % 151.05/151.86 (define @t375 () (_ tptp.ord_less_eq_nat @t374)) % 151.05/151.86 (define @t376 () (_ @t375 @t195)) % 151.05/151.86 (define @t377 () (_ @t368 @t374)) % 151.05/151.86 (define @t378 () (_ @t375 @t196)) % 151.05/151.86 (define @t379 () (_ @t347 @t374)) % 151.05/151.86 (define @t380 () (@list @t195 @t196 @t374)) % 151.05/151.86 (define @t381 () (@list @t196 @t195)) % 151.05/151.86 (define @t382 () (_ (_ tptp.ord_less_eq_nat @t190) @t189)) % 151.05/151.86 (define @t383 () (_ (_ tptp.ord_less_eq_nat @t189) @t190)) % 151.05/151.86 (define @t384 () (= @t18 @t17)) % 151.05/151.86 (define @t385 () (_ @t354 @t18)) % 151.05/151.86 (define @t386 () (@list @t18)) % 151.05/151.86 (define @t387 () (@var "P5" (-> tptp.nat tptp.nat Bool))) % 151.05/151.86 (define @t388 () (@var "B4" tptp.nat)) % 151.05/151.86 (define @t389 () (@var "A4" tptp.nat)) % 151.05/151.86 (define @t390 () (_ @t387 @t389)) % 151.05/151.86 (define @t391 () (_ @t390 @t388)) % 151.05/151.86 (define @t392 () (@list @t389 @t388)) % 151.05/151.86 (define @t393 () (=> (forall @t392 (=> (_ (_ @t387 @t388) @t389) @t391)) (_ (_ @t387 @t18) @t17))) % 151.05/151.86 (define @t394 () (@list @t387 @t18 @t17)) % 151.05/151.86 (define @t395 () (@list @t17 @t18)) % 151.05/151.86 (define @t396 () (not @t384)) % 151.05/151.86 (define @t397 () (_ tptp.ord_less_nat @t17)) % 151.05/151.86 (define @t398 () (_ @t397 @t18)) % 151.05/151.86 (define @t399 () (@var "P8" (-> tptp.nat Bool))) % 151.05/151.86 (define @t400 () (@list @t170)) % 151.05/151.86 (define @t401 () (@var "X4" tptp.nat)) % 151.05/151.86 (define @t402 () (@var "P7" (-> tptp.nat Bool))) % 151.05/151.86 (define @t403 () (not @t198)) % 151.05/151.86 (define @t404 () (_ @t19 @t21)) % 151.05/151.86 (define @t405 () (_ @t397 @t21)) % 151.05/151.86 (define @t406 () (=> @t405 @t404)) % 151.05/151.86 (define @t407 () (@var "P5" Bool)) % 151.05/151.86 (define @t408 () (@var "X_1" tptp.nat)) % 151.05/151.86 (define @t409 () (forall @t352 (=> (_ (_ tptp.ord_less_nat @t133) @t140) (_ (_ tptp.ord_less_nat @t351) @t350)))) % 151.05/151.86 (define @t410 () (=> @t409 (_ (_ tptp.ord_less_nat @t359) @t21))) % 151.05/151.86 (define @t411 () (=> @t405 (=> @t409 (_ @t19 @t349)))) % 151.05/151.86 (define @t412 () (=> (forall @t139 (=> @t138 @t146)) (_ @t107 @t315))) % 151.05/151.86 (define @t413 () (_ @t135 @t315)) % 151.05/151.86 (define @t414 () (@var "X_12" tptp.nat)) % 151.05/151.86 (define @t415 () (exists (@list @t414) (_ @t135 @t414))) % 151.05/151.86 (define @t416 () (= @t189 @t190)) % 151.05/151.86 (define @t417 () (@list @t190 @t189)) % 151.05/151.86 (define @t418 () (_ (_ tptp.plus_plus_nat @t7) @t8)) % 151.05/151.86 (define @t419 () (not (_ (_ tptp.ord_less_nat @t5) @t418))) % 151.05/151.86 (define @t420 () (@var "C2" tptp.nat)) % 151.05/151.86 (define @t421 () (_ (_ tptp.plus_plus_nat @t189) @t420)) % 151.05/151.86 (define @t422 () (= @t190 @t421)) % 151.05/151.86 (define @t423 () (@list @t420)) % 151.05/151.86 (define @t424 () (exists @t423 @t422)) % 151.05/151.86 (define @t425 () (lambda @t191 @t424)) % 151.05/151.86 (define @t426 () (not @t172)) % 151.05/151.86 (define @t427 () (and (_ (_ tptp.ord_less_eq_nat @t171) @t170) @t426)) % 151.05/151.86 (define @t428 () (lambda @t174 @t427)) % 151.05/151.86 (define @t429 () (lambda @t240 (and @t239 @t291))) % 151.05/151.86 (define @t430 () (lambda @t245 (and @t244 @t292))) % 151.05/151.86 (define @t431 () (= @t101 @t83)) % 151.05/151.86 (define @t432 () (_ (_ (_ @t237 @t234) @t71) @t295)) % 151.05/151.86 (define @t433 () (and @t432 @t431)) % 151.05/151.86 (define @t434 () (exists @t73 @t433)) % 151.05/151.86 (define @t435 () (@list @t236 @t234 @t83 @t295)) % 151.05/151.86 (define @t436 () (lambda @t435 @t434)) % 151.05/151.86 (define @t437 () (lambda (@list @t241 @t234 @t83 @t295) (exists @t73 (and (_ (_ (_ @t242 @t234) @t71) @t295) @t431)))) % 151.05/151.86 (define @t438 () (lambda (@list @t236 @t235) (_ tptp.collect_nat (_ (_ tptp.connected_capacity @t236) @t235)))) % 151.05/151.86 (define @t439 () (lambda (@list @t241 @t235) (_ tptp.collect_nat (_ (_ tptp.connected_a @t241) @t235)))) % 151.05/151.86 (define @t440 () (lambda @t86 @t296)) % 151.05/151.86 (define @t441 () (lambda @t297 (_ tptp.ord_Least_nat @t440))) % 151.05/151.86 (define @t442 () (lambda @t299 (_ tptp.ord_Least_nat (lambda @t86 @t298)))) % 151.05/151.86 (define @t443 () (lambda (@list @t236 @t235 @t234) (exists @t73 @t239))) % 151.05/151.86 (define @t444 () (lambda (@list @t241 @t235 @t234) (exists @t73 @t244))) % 151.05/151.86 (define @t445 () (@const 1 (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.nat Bool)) tptp.nat)))) % 151.05/151.86 (define @t446 () (@const 2 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.nat Bool)) tptp.nat)) (@ho-elim-sort (-> tptp.nat Bool)) tptp.nat))) % 151.05/151.86 (define @t447 () (_ @t446 @t445 (@const 0 (@ho-elim-sort (-> tptp.nat Bool))))) % 151.05/151.86 (define @t448 () (_ @t446 @t445 (@const 3 (@ho-elim-sort (-> tptp.nat Bool))))) % 151.05/151.86 (define @t449 () (@const 4 (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat)))) % 151.05/151.86 (define @t450 () (@const 5 (-> (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat)) tptp.nat (@ho-elim-sort (-> tptp.nat tptp.nat))))) % 151.05/151.86 (define @t451 () (_ @t450 @t449 @t448)) % 151.05/151.86 (define @t452 () (@const 6 (-> (@ho-elim-sort (-> tptp.nat tptp.nat)) tptp.nat tptp.nat))) % 151.05/151.86 (define @t453 () (_ @t452 @t451 @t447)) % 151.05/151.86 (define @t454 () (_ @t446 @t445 (@const 7 (@ho-elim-sort (-> tptp.nat Bool))))) % 151.05/151.86 (define @t455 () (@const 8 (-> tptp.nat Bool))) % 151.05/151.86 (define @t456 () (_ tptp.ord_Least_nat @t455)) % 151.05/151.86 (define @t457 () (@const 9 (-> tptp.nat Bool))) % 151.05/151.86 (define @t458 () (@const 10 (-> tptp.nat Bool))) % 151.05/151.86 (define @t459 () (_ tptp.ord_Least_nat @t458)) % 151.05/151.86 (define @t460 () (_ (_ tptp.plus_plus_nat @t459) (_ tptp.ord_Least_nat @t457))) % 151.05/151.86 (define @t461 () (tptp.size_s1990949619at_nat @t71)) % 151.05/151.86 (define @t462 () (= @t83 @t461)) % 151.05/151.86 (define @t463 () (not @t462)) % 151.05/151.86 (define @t464 () (tptp.isPath_capacity tptp.c tptp.ua @t71 tptp.t)) % 151.05/151.86 (define @t465 () (not @t464)) % 151.05/151.86 (define @t466 () (or @t465 @t463)) % 151.05/151.86 (define @t467 () (forall @t73 @t466)) % 151.05/151.86 (define @t468 () (not @t467)) % 151.05/151.86 (define @t469 () (lambda @t86 @t468)) % 151.05/151.86 (define @t470 () (_ tptp.ord_Least_nat @t469)) % 151.05/151.86 (define @t471 () (tptp.isPath_capacity tptp.c tptp.s @t71 tptp.ua)) % 151.05/151.86 (define @t472 () (not @t471)) % 151.05/151.86 (define @t473 () (or @t472 @t463)) % 151.05/151.86 (define @t474 () (forall @t73 @t473)) % 151.05/151.86 (define @t475 () (not @t474)) % 151.05/151.86 (define @t476 () (lambda @t86 @t475)) % 151.05/151.86 (define @t477 () (_ tptp.ord_Least_nat @t476)) % 151.05/151.86 (define @t478 () (tptp.isPath_capacity tptp.c tptp.s @t71 tptp.t)) % 151.05/151.86 (define @t479 () (not @t478)) % 151.05/151.86 (define @t480 () (or @t479 @t463)) % 151.05/151.86 (define @t481 () (forall @t73 @t480)) % 151.05/151.86 (define @t482 () (not @t481)) % 151.05/151.86 (define @t483 () (lambda @t86 @t482)) % 151.05/151.86 (define @t484 () (_ tptp.ord_Least_nat @t483)) % 151.05/151.86 (define @t485 () (@list @t295)) % 151.05/151.86 (define @t486 () (lambda @t485 (_ tptp.ord_Least_nat (lambda @t86 (not (forall @t73 (or (not (tptp.isPath_capacity tptp.c tptp.ua @t71 @t295)) @t463))))))) % 151.05/151.86 (define @t487 () (lambda (@list @t234 @t295) (_ tptp.ord_Least_nat (lambda @t86 (not (forall @t73 (or (not (tptp.isPath_capacity tptp.c @t234 @t71 @t295)) @t463))))))) % 151.05/151.86 (define @t488 () (tptp.isPath_capacity @t236 @t234 @t71 @t295)) % 151.05/151.86 (define @t489 () (not (forall @t73 (or (not @t488) @t463)))) % 151.05/151.86 (define @t490 () (_ (lambda @t297 (_ tptp.ord_Least_nat (lambda @t86 @t489))) tptp.c)) % 151.05/151.86 (define @t491 () (lambda @t485 (_ tptp.ord_Least_nat (lambda @t86 (not (forall @t73 (or (not (tptp.isPath_capacity tptp.c tptp.s @t71 @t295)) @t463))))))) % 151.05/151.86 (define @t492 () (_ @t490 tptp.s)) % 151.05/151.86 (define @t493 () (_ @t492 tptp.t)) % 151.05/151.86 (define @t494 () (lambda @t485 @t489)) % 151.05/151.86 (define @t495 () (lambda (@list @t83 @t295) @t489)) % 151.05/151.86 (define @t496 () (lambda (@list @t234 @t83 @t295) @t489)) % 151.05/151.86 (define @t497 () (_ (lambda @t435 @t489) @t236)) % 151.05/151.86 (define @t498 () (= @t83 @t101)) % 151.05/151.86 (define @t499 () (not @t498)) % 151.05/151.86 (define @t500 () (not @t432)) % 151.05/151.86 (define @t501 () (or @t500 @t499)) % 151.05/151.86 (define @t502 () (and @t432 @t498)) % 151.05/151.86 (define @t503 () (forall @t73 (not @t502))) % 151.05/151.86 (define @t504 () (not @t503)) % 151.05/151.86 (define @t505 () (@const 11 (@ho-elim-sort (-> tptp.list_P559422087at_nat tptp.nat)))) % 151.05/151.86 (define @t506 () (@const 12 (-> (@ho-elim-sort (-> tptp.list_P559422087at_nat tptp.nat)) tptp.list_P559422087at_nat tptp.nat))) % 151.05/151.86 (define @t507 () (_ @t506 @t505 tptp.p1a)) % 151.05/151.86 (define @t508 () (not (= @t507 @t448))) % 151.05/151.86 (define @t509 () (forall @t423 (not (= @t507 (_ @t452 @t451 @t420))))) % 151.05/151.86 (define @t510 () (not @t509)) % 151.05/151.86 (define @t511 () (and @t510 @t508)) % 151.05/151.86 (define @t512 () (not (= @t7 @t459))) % 151.05/151.86 (define @t513 () (tptp.plus_plus_nat (tptp.ord_Least_nat @t458) @t420)) % 151.05/151.86 (define @t514 () (tptp.size_s1990949619at_nat tptp.p1a)) % 151.05/151.86 (define @t515 () (not (= @t513 @t514))) % 151.05/151.86 (define @t516 () (forall @t423 @t515)) % 151.05/151.86 (define @t517 () (not @t516)) % 151.05/151.86 (define @t518 () (and @t517 @t512)) % 151.05/151.86 (define @t519 () (not (= @t7 @t477))) % 151.05/151.86 (define @t520 () (tptp.ord_Least_nat @t476)) % 151.05/151.86 (define @t521 () (tptp.plus_plus_nat @t520 @t420)) % 151.05/151.86 (define @t522 () (not (= @t514 @t521))) % 151.05/151.86 (define @t523 () (= @t7 @t521)) % 151.05/151.86 (define @t524 () (not @t523)) % 151.05/151.86 (define @t525 () (forall @t423 @t524)) % 151.05/151.86 (define @t526 () (not @t525)) % 151.05/151.86 (define @t527 () (and @t526 @t519)) % 151.05/151.86 (define @t528 () (not (= @t477 @t170))) % 151.05/151.86 (define @t529 () (_ @t35 @t71)) % 151.05/151.86 (define @t530 () (lambda @t86 (not (forall @t73 (or (not (_ @t529 tptp.ua)) @t499))))) % 151.05/151.86 (define @t531 () (tptp.plus_plus_nat @t477 @t420)) % 151.05/151.86 (define @t532 () (= @t170 @t531)) % 151.05/151.86 (define @t533 () (not @t532)) % 151.05/151.86 (define @t534 () (forall @t423 @t533)) % 151.05/151.86 (define @t535 () (not @t534)) % 151.05/151.86 (define @t536 () (and @t535 @t528)) % 151.05/151.86 (define @t537 () (lambda @t400 @t536)) % 151.05/151.86 (define @t538 () (tptp.plus_plus_nat @t171 @t420)) % 151.05/151.86 (define @t539 () (not (forall @t423 (not (= @t170 @t538))))) % 151.05/151.86 (define @t540 () (lambda @t174 (and @t539 @t426))) % 151.05/151.86 (define @t541 () (@list @t190)) % 151.05/151.86 (define @t542 () (lambda @t541 (not (forall @t423 (not (= @t190 @t538)))))) % 151.05/151.86 (define @t543 () (tptp.plus_plus_nat @t189 @t420)) % 151.05/151.86 (define @t544 () (lambda @t191 (not (forall @t423 (not (= @t190 @t543)))))) % 151.05/151.86 (define @t545 () (_ @t544 @t171)) % 151.05/151.86 (define @t546 () (not @t422)) % 151.05/151.86 (define @t547 () (forall @t423 @t546)) % 151.05/151.86 (define @t548 () (not @t547)) % 151.05/151.86 (define @t549 () (@quantifiers_skolemize @t509 0)) % 151.05/151.86 (define @t550 () (_ @t452 @t451 @t549)) % 151.05/151.86 (define @t551 () (= @t507 @t550)) % 151.05/151.86 (define @t552 () (not @t551)) % 151.05/151.86 (define @t553 () (not @t552)) % 151.05/151.86 (define @t554 () (@list true)) % 151.05/151.86 (define @t555 () (_ @t506 @t505 tptp.p2_a)) % 151.05/151.86 (define @t556 () (_ @t450 @t449 @t447)) % 151.05/151.86 (define @t557 () (_ @t452 @t556 @t420)) % 151.05/151.86 (define @t558 () (not (= @t555 @t557))) % 151.05/151.86 (define @t559 () (forall @t423 @t558)) % 151.05/151.86 (define @t560 () (not @t559)) % 151.05/151.86 (define @t561 () (tptp.plus_plus_nat (tptp.ord_Least_nat @t457) @t420)) % 151.05/151.86 (define @t562 () (tptp.size_s1990949619at_nat tptp.p2_a)) % 151.05/151.86 (define @t563 () (not (= @t561 @t562))) % 151.05/151.86 (define @t564 () (forall @t423 @t563)) % 151.05/151.86 (define @t565 () (not @t564)) % 151.05/151.86 (define @t566 () (tptp.ord_Least_nat @t469)) % 151.05/151.86 (define @t567 () (tptp.plus_plus_nat @t566 @t420)) % 151.05/151.86 (define @t568 () (not (= @t562 @t567))) % 151.05/151.86 (define @t569 () (= @t8 @t567)) % 151.05/151.86 (define @t570 () (not @t569)) % 151.05/151.86 (define @t571 () (forall @t423 @t570)) % 151.05/151.86 (define @t572 () (not @t571)) % 151.05/151.86 (define @t573 () (lambda @t86 (not (forall @t73 (or (not (_ (_ @t70 @t71) tptp.t)) @t499))))) % 151.05/151.86 (define @t574 () (tptp.plus_plus_nat @t470 @t420)) % 151.05/151.86 (define @t575 () (= @t190 @t574)) % 151.05/151.86 (define @t576 () (not @t575)) % 151.05/151.86 (define @t577 () (forall @t423 @t576)) % 151.05/151.86 (define @t578 () (not @t577)) % 151.05/151.86 (define @t579 () (lambda @t541 @t578)) % 151.05/151.86 (define @t580 () (forall @t423 (not (= @t557 @t555)))) % 151.05/151.86 (define @t581 () (@quantifiers_skolemize @t580 0)) % 151.05/151.86 (define @t582 () (_ @t452 @t556 @t581)) % 151.05/151.86 (define @t583 () (= @t555 @t582)) % 151.05/151.86 (define @t584 () (not @t580)) % 151.05/151.86 (define @t585 () (= @t582 @t555)) % 151.05/151.86 (define @t586 () (not (not @t585))) % 151.05/151.86 (define @t587 () (@var "BOUND_VARIABLE_12776" tptp.nat)) % 151.05/151.86 (define @t588 () (@var "BOUND_VARIABLE_12771" tptp.nat)) % 151.05/151.86 (define @t589 () (_ @t450 @t449 @t18)) % 151.05/151.86 (define @t590 () (_ @t452 @t589 @t588)) % 151.05/151.86 (define @t591 () (_ @t452 (_ @t450 @t449 @t590) (_ @t452 (_ @t450 @t449 @t21) @t587))) % 151.05/151.86 (define @t592 () (_ @t452 @t589 @t21)) % 151.05/151.86 (define @t593 () (@list @t18 @t21 @t588 @t587)) % 151.05/151.86 (define @t594 () (tptp.plus_plus_nat @t21 @t587)) % 151.05/151.86 (define @t595 () (tptp.plus_plus_nat @t18 @t588)) % 151.05/151.86 (define @t596 () (tptp.plus_plus_nat @t595 @t594)) % 151.05/151.86 (define @t597 () (tptp.plus_plus_nat @t18 @t21)) % 151.05/151.86 (define @t598 () (tptp.plus_plus_nat @t597 @t420)) % 151.05/151.86 (define @t599 () (and (not (forall @t423 (not (= @t598 @t596)))) (not (= @t597 @t596)))) % 151.05/151.86 (define @t600 () (= @t18 @t595)) % 151.05/151.86 (define @t601 () (or @t600 @t599)) % 151.05/151.86 (define @t602 () (not (= @t594 @t594))) % 151.05/151.86 (define @t603 () (or @t600 @t602 @t599)) % 151.05/151.86 (define @t604 () (tptp.plus_plus_nat @t595 @t59)) % 151.05/151.86 (define @t605 () (and (not (forall @t423 (not (= @t598 @t604)))) (not (= @t597 @t604)))) % 151.05/151.86 (define @t606 () (not (= @t59 @t594))) % 151.05/151.86 (define @t607 () (or @t606 @t600 @t606 @t605)) % 151.05/151.86 (define @t608 () (@list @t59)) % 151.05/151.86 (define @t609 () (or @t600 @t606 @t605)) % 151.05/151.86 (define @t610 () (forall @t608 @t609)) % 151.05/151.86 (define @t611 () (forall @t593 @t610)) % 151.05/151.86 (define @t612 () (forall (@list @t18 @t21 @t588 @t587 @t59) @t609)) % 151.05/151.86 (define @t613 () (@list @t18 @t21 @t59 @t588 @t587)) % 151.05/151.86 (define @t614 () (not (= @t595 @t595))) % 151.05/151.86 (define @t615 () (or @t614 @t600 @t606 @t605)) % 151.05/151.86 (define @t616 () (tptp.plus_plus_nat @t17 @t59)) % 151.05/151.86 (define @t617 () (not (forall @t423 (not (= @t598 @t616))))) % 151.05/151.86 (define @t618 () (and @t617 (not (= @t597 @t616)))) % 151.05/151.86 (define @t619 () (not (= @t17 @t595))) % 151.05/151.86 (define @t620 () (or @t619 @t619 @t384 @t606 @t618)) % 151.05/151.86 (define @t621 () (@list @t17)) % 151.05/151.86 (define @t622 () (or @t619 @t384 @t606 @t618)) % 151.05/151.86 (define @t623 () (forall @t621 @t622)) % 151.05/151.86 (define @t624 () (forall @t613 @t623)) % 151.05/151.86 (define @t625 () (forall (@list @t18 @t21 @t59 @t588 @t587 @t17) @t622)) % 151.05/151.86 (define @t626 () (forall (@list @t18 @t17 @t21 @t59 @t588 @t587) @t622)) % 151.05/151.86 (define @t627 () (forall (@list @t588 @t587) @t622)) % 151.05/151.86 (define @t628 () (forall (@list @t587) @t606)) % 151.05/151.86 (define @t629 () (@list @t420)) % 151.05/151.86 (define @t630 () (forall (@list @t588) @t619)) % 151.05/151.86 (define @t631 () (or @t630 @t384 @t628 @t618)) % 151.05/151.86 (define @t632 () (tptp.plus_plus_nat @t21 @t420)) % 151.05/151.86 (define @t633 () (forall @t423 (not (= @t59 @t632)))) % 151.05/151.86 (define @t634 () (tptp.plus_plus_nat @t18 @t420)) % 151.05/151.86 (define @t635 () (forall @t423 (not (= @t17 @t634)))) % 151.05/151.86 (define @t636 () (= @t30 @t150)) % 151.05/151.86 (define @t637 () (not @t636)) % 151.05/151.86 (define @t638 () (and @t617 @t637)) % 151.05/151.86 (define @t639 () (or @t635 @t384 @t633 @t638)) % 151.05/151.86 (define @t640 () (not @t633)) % 151.05/151.86 (define @t641 () (not @t635)) % 151.05/151.86 (define @t642 () (=> @t640 @t638)) % 151.05/151.86 (define @t643 () (and @t641 @t396)) % 151.05/151.86 (define @t644 () (not (= @t616 @t598))) % 151.05/151.86 (define @t645 () (= @t150 @t598)) % 151.05/151.86 (define @t646 () (not @t645)) % 151.05/151.86 (define @t647 () (forall @t423 @t646)) % 151.05/151.86 (define @t648 () (not @t647)) % 151.05/151.86 (define @t649 () (and @t648 @t637)) % 151.05/151.86 (define @t650 () (not (= @t30 @t170))) % 151.05/151.86 (define @t651 () (tptp.plus_plus_nat @t30 @t420)) % 151.05/151.86 (define @t652 () (= @t170 @t651)) % 151.05/151.86 (define @t653 () (not @t652)) % 151.05/151.86 (define @t654 () (forall @t423 @t653)) % 151.05/151.86 (define @t655 () (not @t654)) % 151.05/151.86 (define @t656 () (and @t655 @t650)) % 151.05/151.86 (define @t657 () (lambda @t400 @t656)) % 151.05/151.86 (define @t658 () (_ @t540 @t30)) % 151.05/151.86 (define @t659 () (lambda @t541 (not (forall @t423 (not (= @t190 @t632)))))) % 151.05/151.86 (define @t660 () (_ @t544 @t21)) % 151.05/151.86 (define @t661 () (=> (_ @t660 @t59) (_ @t658 @t150))) % 151.05/151.86 (define @t662 () (lambda @t400 (and (not (forall @t423 (not (= @t170 @t634)))) (not (= @t18 @t170))))) % 151.05/151.86 (define @t663 () (_ @t540 @t18)) % 151.05/151.86 (define @t664 () (=> (_ @t663 @t17) @t661)) % 151.05/151.86 (define @t665 () (= @t448 @t550)) % 151.05/151.86 (define @t666 () (_ @t452 (_ @t450 @t449 @t550) @t582)) % 151.05/151.86 (define @t667 () (not (= @t453 @t666))) % 151.05/151.86 (define @t668 () (_ @t450 @t449 @t453)) % 151.05/151.86 (define @t669 () (forall @t423 (not (= (_ @t452 @t668 @t420) @t666)))) % 151.05/151.86 (define @t670 () (not @t669)) % 151.05/151.86 (define @t671 () (and @t670 @t667)) % 151.05/151.86 (define @t672 () (or @t665 @t671)) % 151.05/151.86 (define @t673 () (not @t671)) % 151.05/151.86 (define @t674 () (@list false)) % 151.05/151.86 (define @t675 () (@list @t671)) % 151.05/151.86 (define @t676 () (@quantifiers_skolemize @t669 0)) % 151.05/151.86 (define @t677 () (_ @t452 @t668 @t676)) % 151.05/151.86 (define @t678 () (= @t666 @t677)) % 151.05/151.86 (define @t679 () (= @t677 @t666)) % 151.05/151.86 (define @t680 () (not (not @t679))) % 151.05/151.86 (define @t681 () (@list @t669)) % 151.05/151.86 (define @t682 () (_ @t450 @t449 @t507)) % 151.05/151.86 (define @t683 () (_ @t452 @t682 @t555)) % 151.05/151.86 (define @t684 () (= @t454 @t683)) % 151.05/151.86 (define @t685 () (_ @t450 @t449 @t454)) % 151.05/151.86 (define @t686 () (forall @t423 (not (= @t683 (_ @t452 @t685 @t420))))) % 151.05/151.86 (define @t687 () (not @t686)) % 151.05/151.86 (define @t688 () (not (= @t683 @t454))) % 151.05/151.86 (define @t689 () (and @t687 @t688)) % 151.05/151.86 (define @t690 () (not @t689)) % 151.05/151.86 (define @t691 () (not (= @t418 @t456))) % 151.05/151.86 (define @t692 () (tptp.plus_plus_nat (tptp.ord_Least_nat @t455) @t420)) % 151.05/151.86 (define @t693 () (tptp.plus_plus_nat @t514 @t562)) % 151.05/151.86 (define @t694 () (not (= @t692 @t693))) % 151.05/151.86 (define @t695 () (forall @t423 @t694)) % 151.05/151.86 (define @t696 () (not @t695)) % 151.05/151.86 (define @t697 () (and @t696 @t691)) % 151.05/151.86 (define @t698 () (not @t697)) % 151.05/151.86 (define @t699 () (not (= @t418 @t484))) % 151.05/151.86 (define @t700 () (tptp.ord_Least_nat @t483)) % 151.05/151.86 (define @t701 () (tptp.plus_plus_nat @t700 @t420)) % 151.05/151.86 (define @t702 () (not (= @t693 @t701))) % 151.05/151.86 (define @t703 () (= @t418 @t701)) % 151.05/151.86 (define @t704 () (not @t703)) % 151.05/151.86 (define @t705 () (forall @t423 @t704)) % 151.05/151.86 (define @t706 () (not @t705)) % 151.05/151.86 (define @t707 () (and @t706 @t699)) % 151.05/151.86 (define @t708 () (not (= @t484 @t170))) % 151.05/151.86 (define @t709 () (lambda @t86 (not (forall @t73 (or (not (_ @t529 tptp.t)) @t499))))) % 151.05/151.86 (define @t710 () (tptp.plus_plus_nat @t484 @t420)) % 151.05/151.86 (define @t711 () (= @t170 @t710)) % 151.05/151.86 (define @t712 () (not @t711)) % 151.05/151.86 (define @t713 () (forall @t423 @t712)) % 151.05/151.86 (define @t714 () (not @t713)) % 151.05/151.86 (define @t715 () (and @t714 @t708)) % 151.05/151.86 (define @t716 () (lambda @t400 @t715)) % 151.05/151.86 (define @t717 () (= @t683 (_ @t452 @t685 @t676))) % 151.05/151.86 (define @t718 () (not @t678)) % 151.05/151.86 (define @t719 () (not @t583)) % 151.05/151.86 (define @t720 () (= @t454 @t453)) % 151.05/151.86 (define @t721 () (not @t720)) % 151.05/151.86 (define @t722 () (not @t717)) % 151.05/151.86 (define @t723 () (and @t717 @t722)) % 151.05/151.86 (assume @p1 @t6) % 151.05/151.86 (assume @p2 (_ (_ tptp.ord_less_nat @t4) @t7)) % 151.05/151.86 (assume @p3 (_ (_ tptp.ord_less_eq_nat @t2) @t8)) % 151.05/151.86 (assume @p4 (forall @t16 (= (_ (_ tptp.ord_less_nat @t15) @t14) @t11))) % 151.05/151.86 (assume @p5 (forall @t26 (= @t25 @t20))) % 151.05/151.86 (assume @p6 (forall @t33 (= @t32 @t20))) % 151.05/151.86 (assume @p7 (_ (_ @t35 tptp.p1a) tptp.va)) % 151.05/151.86 (assume @p8 (_ (_ (_ @t36 tptp.s) tptp.p) tptp.t)) % 151.05/151.86 (assume @p9 (forall @t50 (=> @t49 (=> @t47 (=> @t45 (= (_ (_ @t1 @t39) @t38) @t37)))))) % 151.05/151.86 (assume @p10 (forall @t50 (=> @t49 (=> @t47 (=> @t45 (= (_ @t43 @t39) @t40)))))) % 151.05/151.86 (assume @p11 (forall @t63 (=> @t62 (=> (= @t61 @t59) (=> @t60 @t58))))) % 151.05/151.86 (assume @p12 (forall @t67 (= @t66 @t64))) % 151.05/151.86 (assume @p13 (forall @t69 (= @t68 @t64))) % 151.05/151.86 (assume @p14 (_ (_ @t70 tptp.p2_a) tptp.t)) % 151.05/151.86 (assume @p15 (forall @t50 (=> @t49 (=> @t47 (_ (_ @t48 @t41) @t38))))) % 151.05/151.86 (assume @p16 (forall @t76 (= @t75 (exists @t73 (_ (_ @t72 @t71) @t38))))) % 151.05/151.86 (assume @p17 (forall @t81 (=> @t80 @t78))) % 151.05/151.86 (assume @p18 (forall @t89 (= @t88 (exists @t86 @t85)))) % 151.05/151.86 (assume @p19 (forall @t76 (=> @t75 (not (forall @t91 (not (_ (_ @t79 @t90) @t38))))))) % 151.05/151.86 (assume @p20 (forall @t93 (=> @t62 (=> (_ @t92 @t61) @t58)))) % 151.05/151.86 (assume @p21 (forall @t96 (=> @t95 (_ (_ tptp.ord_less_eq_nat @t94) @t59)))) % 151.05/151.86 (assume @p22 (forall @t96 (=> @t95 (=> (forall @t99 (=> (_ (_ @t84 @t97) @t82) @t98)) (= @t94 @t59))))) % 151.05/151.86 (assume @p23 (forall @t81 (=> @t78 (_ (_ @t48 @t100) @t38)))) % 151.05/151.86 (assume @p24 (forall @t96 (= @t95 (exists @t73 (and (_ (_ (_ @t34 @t38) @t71) @t82) @t102))))) % 151.05/151.86 (assume @p25 (_ (_ @t35 tptp.p1) tptp.v)) % 151.05/151.86 (assume @p26 (forall @t89 (=> @t88 (_ (_ @t84 @t94) @t82)))) % 151.05/151.86 (assume @p27 (forall @t81 (= @t80 (and @t78 (forall @t106 (=> (_ (_ @t72 @t103) @t38) @t105)))))) % 151.05/151.86 (assume @p28 (forall @t114 (=> @t88 (=> (forall @t113 (=> (_ (_ @t84 @t108) @t82) (=> (forall @t112 (=> (_ (_ @t84 @t110) @t82) @t111)) @t109))) (_ @t107 @t94))))) % 151.05/151.86 (assume @p29 (forall @t81 (= @t80 (and @t78 @t115)))) % 151.05/151.86 (assume @p30 (_ (_ @t55 tptp.s) tptp.ua)) % 151.05/151.86 (assume @p31 (forall @t33 (= @t119 @t117))) % 151.05/151.86 (assume @p32 (forall @t26 (= @t120 @t117))) % 151.05/151.86 (assume @p33 (forall @t16 (= (_ (_ tptp.ord_less_eq_nat @t15) @t14) @t121))) % 151.05/151.86 (assume @p34 (forall @t122 (_ @t87 @t38))) % 151.05/151.86 (assume @p35 (forall @t96 (=> @t95 @t88))) % 151.05/151.86 (assume @p36 (forall @t124 (_ @t123 @t9))) % 151.05/151.86 (assume @p37 (forall @t129 (=> @t128 (=> (_ (_ tptp.ord_less_eq_nat @t127) @t12) (_ @t126 @t12))))) % 151.05/151.86 (assume @p38 (forall @t131 (=> @t130 @t121))) % 151.05/151.86 (assume @p39 (forall @t131 (=> @t121 (=> @t132 @t130)))) % 151.05/151.86 (assume @p40 (forall @t131 (or @t121 @t132))) % 151.05/151.86 (assume @p41 (forall (@list @t135 @t12 @t17) (=> @t141 (=> (forall (@list @t140) (=> (_ @t135 @t140) (_ (_ tptp.ord_less_eq_nat @t140) @t17))) (exists @t139 (and @t138 (forall @t137 (=> @t136 (_ (_ tptp.ord_less_eq_nat @t134) @t133))))))))) % 151.05/151.86 (assume @p42 (forall @t33 (=> @t119 @t117))) % 151.05/151.86 (assume @p43 (forall @t26 (=> @t120 @t117))) % 151.05/151.86 (assume @p44 (forall (@list @t18 @t135) (= (_ (_ tptp.member_nat @t18) @t143) @t142))) % 151.05/151.86 (assume @p45 (forall (@list @t144) (= (_ tptp.collect_nat (lambda (@list @t145) (_ (_ tptp.member_nat @t145) @t144))) @t144))) % 151.05/151.86 (assume @p46 (forall @t147 (=> (forall @t139 (= @t138 @t146)) (= @t143 (_ tptp.collect_nat @t107))))) % 151.05/151.86 (assume @p47 (forall @t67 (=> @t117 @t119))) % 151.05/151.86 (assume @p48 (forall @t149 (=> @t117 (not (forall (@list @t148) (not (= @t17 (_ @t29 @t148)))))))) % 151.05/151.86 (assume @p49 (forall @t67 (=> @t117 @t120))) % 151.05/151.86 (assume @p50 (forall @t153 (=> @t117 (=> @t152 (_ @t118 @t150))))) % 151.05/151.86 (assume @p51 (forall @t163 (=> (and @t128 @t162) @t160))) % 151.05/151.86 (assume @p52 (forall @t163 (=> (and @t164 @t162) @t160))) % 151.05/151.86 (assume @p53 (forall @t163 (=> (and @t128 @t165) @t160))) % 151.05/151.86 (assume @p54 (forall (@list @t166 @t125 @t127) (=> (forall (@list @t168 @t167) (=> (_ (_ tptp.ord_less_nat @t168) @t167) (_ (_ tptp.ord_less_nat (_ @t166 @t168)) (_ @t166 @t167)))) (=> @t128 (_ (_ tptp.ord_less_eq_nat (_ @t166 @t125)) (_ @t166 @t127)))))) % 151.05/151.86 (assume @p55 (forall @t131 (=> @t121 (=> @t169 @t11)))) % 151.05/151.86 (assume @p56 (forall @t131 (=> (or @t11 @t130) @t121))) % 151.05/151.86 (assume @p57 (= tptp.ord_less_eq_nat (lambda @t174 (or @t173 @t172)))) % 151.05/151.86 (assume @p58 (forall @t131 (=> @t11 @t121))) % 151.05/151.86 (assume @p59 (= tptp.ord_less_eq_nat (lambda @t174 (exists (@list @t175) (= @t170 (_ (_ tptp.plus_plus_nat @t171) @t175)))))) % 151.05/151.86 (assume @p60 (forall @t178 (=> @t128 (_ @t126 @t177)))) % 151.05/151.86 (assume @p61 (forall @t178 (=> @t128 (_ @t126 @t179)))) % 151.05/151.86 (assume @p62 (forall @t129 (=> @t128 (_ @t159 @t180)))) % 151.05/151.86 (assume @p63 (forall @t163 (=> @t128 (=> @t162 @t160)))) % 151.05/151.86 (assume @p64 (forall (@list @t12 @t154) (=> @t162 (exists @t182 (= @t154 (_ @t13 @t181)))))) % 151.05/151.86 (assume @p65 (forall @t186 (=> @t185 @t183))) % 151.05/151.86 (assume @p66 (forall @t186 (=> @t185 @t121))) % 151.05/151.86 (assume @p67 (forall @t187 (_ @t123 (_ @t176 @t9)))) % 151.05/151.86 (assume @p68 (forall @t187 (_ @t123 (_ (_ tptp.plus_plus_nat @t9) @t10)))) % 151.05/151.86 (assume @p69 (forall @t186 (=> @t185 (not (=> @t121 (not @t183)))))) % 151.05/151.86 (assume @p70 (forall @t69 (=> @t68 @t64))) % 151.05/151.86 (assume @p71 (forall @t67 (=> @t66 @t64))) % 151.05/151.86 (assume @p72 (forall @t69 (= (_ @t27 @t30) @t188))) % 151.05/151.86 (assume @p73 (= tptp.plus_plus_nat (lambda @t191 (_ (_ tptp.plus_plus_nat @t190) @t189)))) % 151.05/151.86 (assume @p74 (forall @t67 (= (_ (_ tptp.plus_plus_nat @t65) @t21) @t188))) % 151.05/151.86 (assume @p75 (forall (@list @t193 @t12 @t17 @t18) (=> (= @t193 (_ @t13 @t17)) (= (_ @t29 @t193) @t192)))) % 151.05/151.86 (assume @p76 (forall (@list @t194 @t12 @t18 @t17) (=> (= @t194 (_ @t13 @t18)) (= (_ (_ tptp.plus_plus_nat @t194) @t17) @t192)))) % 151.05/151.86 (assume @p77 (forall @t163 (=> (and @t164 @t165) (= @t158 @t156)))) % 151.05/151.86 (assume @p78 (forall @t204 (=> @t203 (=> @t201 @t198)))) % 151.05/151.86 (assume @p79 (forall @t211 (=> (forall @t182 (=> (not @t210) (exists @t209 (and @t208 (not @t207))))) @t205))) % 151.05/151.86 (assume @p80 (forall @t211 (=> (forall @t182 (=> (forall @t209 (=> @t208 @t207)) @t210)) @t205))) % 151.05/151.86 (assume @p81 (forall @t124 (not (_ @t212 @t9)))) % 151.05/151.86 (assume @p82 (forall (@list @t214 @t213) (=> (_ (_ tptp.ord_less_nat @t214) @t213) (not (= @t214 @t213))))) % 151.05/151.86 (assume @p83 (forall @t187 (=> @t215 @t169))) % 151.05/151.86 (assume @p84 (forall @t131 (= @t169 (or @t11 @t215)))) % 151.05/151.86 (assume @p85 (forall (@list @t217 @t216) (=> (not (= (_ tptp.size_s1990949619at_nat @t217) (_ tptp.size_s1990949619at_nat @t216))) (not (= @t217 @t216))))) % 151.05/151.86 (assume @p86 @t221) % 151.05/151.86 (assume @p87 (forall @t153 (=> @t117 @t223))) % 151.05/151.86 (assume @p88 (forall @t163 (=> (and @t227 @t162) @t225))) % 151.05/151.86 (assume @p89 (forall @t163 (=> (and @t128 @t229) @t225))) % 151.05/151.86 (assume @p90 (forall (@list @t166 @t10 @t12) (=> (forall (@list @t230 @t181) (=> (_ (_ tptp.ord_less_nat @t230) @t181) (_ (_ tptp.ord_less_nat (_ @t166 @t230)) (_ @t166 @t181)))) (_ (_ tptp.ord_less_eq_nat (_ (_ tptp.plus_plus_nat (_ @t166 @t10)) @t12)) (_ @t166 @t184))))) % 151.05/151.86 (assume @p91 (forall @t33 (=> @t32 @t20))) % 151.05/151.86 (assume @p92 (forall @t26 (=> @t25 @t20))) % 151.05/151.86 (assume @p93 (forall @t67 (=> @t20 @t32))) % 151.05/151.86 (assume @p94 (forall @t67 (=> @t20 @t25))) % 151.05/151.86 (assume @p95 (forall @t153 (=> @t20 @t223))) % 151.05/151.86 (assume @p96 (forall @t163 (=> (and @t227 @t165) @t225))) % 151.05/151.86 (assume @p97 (forall @t163 (=> (and @t164 @t229) @t225))) % 151.05/151.86 (assume @p98 (forall @t163 (=> (and @t227 @t229) @t225))) % 151.05/151.86 (assume @p99 (forall (@list @t12 @t154 @t10 @t9) (=> @t229 (=> (= (_ @t176 @t154) @t14) @t11)))) % 151.05/151.86 (assume @p100 (forall @t178 (=> @t227 (_ @t226 @t177)))) % 151.05/151.86 (assume @p101 (forall @t178 (=> @t227 (_ @t226 @t179)))) % 151.05/151.86 (assume @p102 (forall @t129 (=> @t227 (_ @t224 @t180)))) % 151.05/151.86 (assume @p103 (forall (@list @t127 @t125) (not (_ (_ tptp.ord_less_nat (_ @t155 @t125)) @t125)))) % 151.05/151.86 (assume @p104 (forall (@list @t125 @t127) (not (_ @t231 @t125)))) % 151.05/151.86 (assume @p105 (forall @t163 (=> @t227 (=> @t229 @t225)))) % 151.05/151.86 (assume @p106 (forall @t129 (=> (_ @t231 @t12) (_ @t226 @t12)))) % 151.05/151.86 (assume @p107 (forall @t232 (= (_ (_ tptp.reacha1693770334pacity tptp.c) @t42) (_ tptp.collect_nat @t74)))) % 151.05/151.86 (assume @p108 (forall @t89 (= @t94 (_ tptp.ord_Least_nat (lambda @t86 @t85))))) % 151.05/151.86 (assume @p109 (= tptp.isShor1936442771pacity (lambda @t240 (and @t239 (forall @t106 (=> (_ (_ @t238 @t103) @t234) @t233)))))) % 151.05/151.86 (assume @p110 (= tptp.isShortestPath_a (lambda @t245 (and @t244 (forall @t106 (=> (_ (_ @t243 @t103) @t234) @t233)))))) % 151.05/151.86 (assume @p111 (forall (@list @t246 @t38 @t82 @t107) (=> @t253 (=> (forall @t113 (=> (_ (_ @t250 @t108) @t82) (=> (forall @t112 (=> (_ (_ @t250 @t110) @t82) @t111)) @t109))) (_ @t107 @t248))))) % 151.05/151.86 (assume @p112 (forall (@list @t254 @t38 @t82 @t107) (=> @t261 (=> (forall @t113 (=> (_ (_ @t258 @t108) @t82) (=> (forall @t112 (=> (_ (_ @t258 @t110) @t82) @t111)) @t109))) (_ @t107 @t256))))) % 151.05/151.86 (assume @p113 (forall @t81 (= @t80 (and (_ (_ (_ @t262 @t42) @t77) @t38) @t115)))) % 151.05/151.86 (assume @p114 (forall @t266 (=> @t265 (_ (_ @t263 @t100) @t38)))) % 151.05/151.86 (assume @p115 (forall @t270 (=> @t269 (_ (_ @t267 @t100) @t38)))) % 151.05/151.86 (assume @p116 (forall (@list @t246 @t38 @t82) (=> @t253 (_ (_ @t250 @t248) @t82)))) % 151.05/151.86 (assume @p117 (forall (@list @t254 @t38 @t82) (=> @t261 (_ (_ @t258 @t256) @t82)))) % 151.05/151.86 (assume @p118 (forall @t275 (=> @t274 (=> @t273 (=> @t272 (= (_ @t271 @t39) @t40)))))) % 151.05/151.86 (assume @p119 (forall @t280 (=> @t279 (=> @t278 (=> @t277 (= (_ @t276 @t39) @t40)))))) % 151.05/151.86 (assume @p120 (forall @t284 (=> (_ (_ (_ @t34 @t214) @t77) @t213) (exists @t283 (_ (_ @t282 @t281) @t213))))) % 151.05/151.86 (assume @p121 (forall @t284 (=> (_ (_ (_ @t36 @t214) @t77) @t213) (_ (_ @t282 @t77) @t213)))) % 151.05/151.86 (assume @p122 (= tptp.reacha1693770334pacity tptp.reacha1693770334pacity)) % 151.05/151.86 (assume @p123 (= tptp.reachableNodes_a tptp.reachableNodes_a)) % 151.05/151.86 (assume @p124 (= tptp.isSimp1359852763pacity tptp.isSimp1359852763pacity)) % 151.05/151.86 (assume @p125 (= tptp.isSimplePath_a tptp.isSimplePath_a)) % 151.05/151.86 (assume @p126 (forall @t286 (=> (_ (_ (_ @t264 @t214) @t77) @t213) (exists @t283 (_ (_ @t285 @t281) @t213))))) % 151.05/151.86 (assume @p127 (forall @t288 (=> (_ (_ (_ @t268 @t214) @t77) @t213) (exists @t283 (_ (_ @t287 @t281) @t213))))) % 151.05/151.86 (assume @p128 (forall @t286 (=> (_ (_ (_ @t289 @t214) @t77) @t213) (_ (_ @t285 @t77) @t213)))) % 151.05/151.86 (assume @p129 (forall @t288 (=> (_ (_ (_ @t290 @t214) @t77) @t213) (_ (_ @t287 @t77) @t213)))) % 151.05/151.86 (assume @p130 (= tptp.isShor1936442771pacity (lambda @t240 (and (_ (_ (_ (_ tptp.isSimp1359852763pacity @t236) @t235) @t71) @t234) @t291)))) % 151.05/151.86 (assume @p131 (= tptp.isShortestPath_a (lambda @t245 (and (_ (_ (_ (_ tptp.isSimplePath_a @t241) @t235) @t71) @t234) @t292)))) % 151.05/151.86 (assume @p132 (= tptp.isPath_capacity tptp.isPath_capacity)) % 151.05/151.86 (assume @p133 (= tptp.isPath_a tptp.isPath_a)) % 151.05/151.86 (assume @p134 (= tptp.min_dist_capacity tptp.min_dist_capacity)) % 151.05/151.86 (assume @p135 (= tptp.min_dist_a tptp.min_dist_a)) % 151.05/151.86 (assume @p136 (forall (@list @t246 @t38) (_ @t252 @t38))) % 151.05/151.86 (assume @p137 (forall (@list @t254 @t38) (_ @t260 @t38))) % 151.05/151.86 (assume @p138 (= tptp.connected_capacity tptp.connected_capacity)) % 151.05/151.86 (assume @p139 (= tptp.connected_a tptp.connected_a)) % 151.05/151.86 (assume @p140 (= tptp.dist_capacity tptp.dist_capacity)) % 151.05/151.86 (assume @p141 (= tptp.dist_a tptp.dist_a)) % 151.05/151.86 (assume @p142 (= tptp.isShor1936442771pacity tptp.isShor1936442771pacity)) % 151.05/151.86 (assume @p143 (= tptp.isShortestPath_a tptp.isShortestPath_a)) % 151.05/151.86 (assume @p144 (forall @t275 (=> @t274 (=> @t273 (_ (_ @t263 @t41) @t38))))) % 151.05/151.86 (assume @p145 (forall @t280 (=> @t279 (=> @t278 (_ (_ @t267 @t41) @t38))))) % 151.05/151.86 (assume @p146 (forall @t266 (=> (_ (_ @t293 @t77) @t38) @t265))) % 151.05/151.86 (assume @p147 (forall @t270 (=> (_ (_ @t294 @t77) @t38) @t269))) % 151.05/151.86 (assume @p148 (= tptp.connected_capacity (lambda @t297 (exists @t86 @t296)))) % 151.05/151.86 (assume @p149 (= tptp.connected_a (lambda @t299 (exists @t86 @t298)))) % 151.05/151.86 (assume @p150 (forall @t301 (=> @t300 @t253))) % 151.05/151.86 (assume @p151 (forall @t303 (=> @t302 @t261))) % 151.05/151.86 (assume @p152 (forall (@list @t246 @t42 @t38) (=> (_ (_ @t251 @t42) @t38) (not (forall @t91 (not (_ (_ @t293 @t90) @t38))))))) % 151.05/151.86 (assume @p153 (forall (@list @t254 @t42 @t38) (=> (_ (_ @t259 @t42) @t38) (not (forall @t91 (not (_ (_ @t294 @t90) @t38))))))) % 151.05/151.86 (assume @p154 (forall (@list @t246 @t53 @t38 @t59 @t51) (=> @t308 (=> (= @t307 @t59) (=> @t60 @t306))))) % 151.05/151.86 (assume @p155 (forall (@list @t254 @t53 @t38 @t59 @t51) (=> @t313 (=> (= @t312 @t59) (=> @t60 @t311))))) % 151.05/151.86 (assume @p156 (forall (@list @t246 @t53 @t38 @t51) (=> @t308 (=> (_ @t92 @t307) @t306)))) % 151.05/151.86 (assume @p157 (forall (@list @t254 @t53 @t38 @t51) (=> @t313 (=> (_ @t92 @t312) @t311)))) % 151.05/151.86 (assume @p158 (forall @t301 (=> @t300 (=> (forall @t99 (=> (_ (_ @t250 @t97) @t82) @t98)) (= @t248 @t59))))) % 151.05/151.86 (assume @p159 (forall @t303 (=> @t302 (=> (forall @t99 (=> (_ (_ @t258 @t97) @t82) @t98)) (= @t256 @t59))))) % 151.05/151.86 (assume @p160 (forall @t301 (=> @t300 (_ (_ tptp.ord_less_eq_nat @t248) @t59)))) % 151.05/151.86 (assume @p161 (forall @t303 (=> @t302 (_ (_ tptp.ord_less_eq_nat @t256) @t59)))) % 151.05/151.86 (assume @p162 (forall @t275 (=> @t274 (=> @t273 (=> @t272 (= (_ (_ @t247 @t39) @t38) @t37)))))) % 151.05/151.86 (assume @p163 (forall @t280 (=> @t279 (=> @t278 (=> @t277 (= (_ (_ @t255 @t39) @t38) @t37)))))) % 151.05/151.86 (assume @p164 (_ (_ (_ @t314 tptp.ua) tptp.p2_a) tptp.t)) % 151.05/151.86 (assume @p165 (forall (@list @t12 @t135) (=> (_ @t228 @t315) (not @t141)))) % 151.05/151.86 (assume @p166 (forall @t316 (=> @t141 (_ (_ tptp.ord_less_eq_nat @t315) @t12)))) % 151.05/151.86 (assume @p167 (forall @t89 (= @t322 (exists @t86 @t319)))) % 151.05/151.86 (assume @p168 (forall @t89 (=> @t322 (_ (_ @t318 @t324) @t82)))) % 151.05/151.86 (assume @p169 (forall @t76 (=> @t328 (not (forall @t91 (not (_ (_ @t326 @t90) @t38))))))) % 151.05/151.86 (assume @p170 (forall @t284 (=> (_ (_ (_ @t325 @t214) @t77) @t213) (_ (_ @t330 @t77) @t213)))) % 151.05/151.86 (assume @p171 (forall @t232 (= (_ (_ tptp.reachableNodes_a tptp.c2) @t42) (_ tptp.collect_nat @t327)))) % 151.05/151.86 (assume @p172 (forall @t63 (=> @t335 (=> (= @t334 @t59) (=> @t60 @t333))))) % 151.05/151.86 (assume @p173 (forall @t114 (=> @t322 (=> (forall @t113 (=> (_ (_ @t318 @t108) @t82) (=> (forall @t112 (=> (_ (_ @t318 @t110) @t82) @t111)) @t109))) (_ @t107 @t324))))) % 151.05/151.86 (assume @p174 (forall @t96 (=> @t336 (=> (forall @t99 (=> (_ (_ @t318 @t97) @t82) @t98)) (= @t324 @t59))))) % 151.05/151.86 (assume @p175 (forall @t93 (=> @t335 (=> (_ @t92 @t334) @t333)))) % 151.05/151.86 (assume @p176 (forall @t96 (=> @t336 (_ (_ tptp.ord_less_eq_nat @t324) @t59)))) % 151.05/151.86 (assume @p177 (forall @t50 (=> @t342 (=> @t340 (=> @t339 (= (_ (_ @t323 @t39) @t38) @t37)))))) % 151.05/151.86 (assume @p178 (forall @t50 (=> @t342 (=> @t340 (=> @t339 (= (_ @t337 @t39) @t40)))))) % 151.05/151.86 (assume @p179 (forall @t50 (=> @t342 (=> @t340 (_ (_ @t341 @t41) @t38))))) % 151.05/151.86 (assume @p180 (forall @t76 (= @t328 (exists @t73 (_ (_ @t343 @t71) @t38))))) % 151.05/151.86 (assume @p181 (forall @t284 (=> (_ (_ (_ @t314 @t214) @t77) @t213) (exists @t283 (_ (_ @t330 @t281) @t213))))) % 151.05/151.86 (assume @p182 (forall @t81 (=> @t345 @t344))) % 151.05/151.86 (assume @p183 (forall @t81 (= @t345 (and (_ (_ (_ @t329 @t42) @t77) @t38) @t346)))) % 151.05/151.86 (assume @p184 (forall @t89 (= @t324 (_ tptp.ord_Least_nat (lambda @t86 @t319))))) % 151.05/151.86 (assume @p185 (forall @t96 (= @t336 (exists @t73 (and (_ (_ (_ @t314 @t38) @t71) @t82) @t102))))) % 151.05/151.86 (assume @p186 (forall @t81 (=> @t344 (_ (_ @t341 @t100) @t38)))) % 151.05/151.86 (assume @p187 (forall @t81 (= @t345 (and @t344 @t346)))) % 151.05/151.86 (assume @p188 (forall @t348 (_ @t347 @t195))) % 151.05/151.86 (assume @p189 (forall @t81 (= @t345 (and @t344 (forall @t106 (=> (_ (_ @t343 @t103) @t38) @t105)))))) % 151.05/151.86 (assume @p190 (_ (_ (_ @t314 tptp.s) tptp.p3) tptp.t)) % 151.05/151.86 (assume @p191 (_ (_ (_ @t314 tptp.u) tptp.p2) tptp.t)) % 151.05/151.86 (assume @p192 (forall @t96 (=> @t336 @t322))) % 151.05/151.86 (assume @p193 (forall @t122 (_ @t321 @t38))) % 151.05/151.86 (assume @p194 (forall @t358 (=> (_ @t116 @t357) @t356))) % 151.05/151.86 (assume @p195 (forall @t361 (=> @t117 (=> (_ (_ tptp.ord_less_eq_nat @t357) @t21) @t360)))) % 151.05/151.86 (assume @p196 (forall @t358 (=> @t362 @t356))) % 151.05/151.86 (assume @p197 (forall @t361 (=> @t117 (=> @t363 @t360)))) % 151.05/151.86 (assume @p198 (= @t367 (lambda (@list @t145 @t364) (and (_ (_ tptp.ord_less_eq_nat @t145) @t364) (_ (_ tptp.ord_less_eq_nat @t364) @t145))))) % 151.05/151.86 (assume @p199 (forall @t204 (=> @t370 (=> @t369 @t202)))) % 151.05/151.86 (assume @p200 (forall @t204 (or @t370 @t369))) % 151.05/151.86 (assume @p201 (forall @t204 (=> @t202 @t370))) % 151.05/151.86 (assume @p202 (forall @t204 (=> @t371 @t369))) % 151.05/151.86 (assume @p203 (forall @t67 (=> @t117 @t373))) % 151.05/151.86 (assume @p204 (forall @t380 (=> (=> @t370 (not @t377)) (=> (=> @t369 (not @t379)) (=> (=> @t379 (not @t378)) (=> (=> @t378 (not @t369)) (=> (=> @t377 (not @t376)) (not (=> @t376 @t371))))))))) % 151.05/151.86 (assume @p205 (forall @t381 (=> @t369 (= @t370 @t202)))) % 151.05/151.86 (assume @p206 (= @t367 (lambda @t191 (and @t383 @t382)))) % 151.05/151.86 (assume @p207 (forall @t67 (=> @t384 @t373))) % 151.05/151.86 (assume @p208 (forall @t67 (=> @t117 (=> @t64 @t372)))) % 151.05/151.86 (assume @p209 (forall @t149 (=> @t117 (=> @t385 @t384)))) % 151.05/151.86 (assume @p210 (forall @t380 (=> @t370 (=> @t377 @t379)))) % 151.05/151.86 (assume @p211 (forall @t386 (_ @t116 @t18))) % 151.05/151.86 (assume @p212 (forall @t394 (=> (forall @t392 (=> (_ (_ tptp.ord_less_eq_nat @t389) @t388) @t391)) @t393))) % 151.05/151.86 (assume @p213 (forall @t69 (=> @t385 (=> (_ @t151 @t17) (_ @t151 @t18))))) % 151.05/151.86 (assume @p214 (= @t367 (lambda @t191 (and @t382 @t383)))) % 151.05/151.86 (assume @p215 (forall @t395 (=> @t385 (=> @t117 @t384)))) % 151.05/151.86 (assume @p216 (forall @t395 (=> @t398 @t396))) % 151.05/151.86 (assume @p217 (forall @t149 (=> @t20 @t396))) % 151.05/151.86 (assume @p218 (forall @t204 (= @t201 (or @t198 @t202)))) % 151.05/151.86 (assume @p219 (forall @t69 (=> @t398 (=> (_ @t222 @t17) (_ @t222 @t18))))) % 151.05/151.86 (assume @p220 (forall @t394 (=> (forall @t392 (=> (_ (_ tptp.ord_less_nat @t389) @t388) @t391)) (=> (forall (@list @t389) (_ @t390 @t389)) @t393)))) % 151.05/151.86 (assume @p221 (= (lambda (@list @t402) (exists (@list @t401) (_ @t402 @t401))) (lambda (@list @t399) (exists @t400 (and (_ @t399 @t170) (forall (@list @t171) (=> @t173 (not (_ @t399 @t171))))))))) % 151.05/151.86 (assume @p222 (forall @t204 (=> @t200 @t403))) % 151.05/151.86 (assume @p223 (forall @t67 (=> @t20 @t406))) % 151.05/151.86 (assume @p224 (forall @t386 (not (_ @t19 @t18)))) % 151.05/151.86 (assume @p225 (forall @t204 (=> @t201 (=> @t203 @t198)))) % 151.05/151.86 (assume @p226 (forall (@list @t195 @t196 @t407) (=> @t200 (=> @t198 @t407)))) % 151.05/151.86 (assume @p227 (forall @t204 (=> @t200 (not (= @t196 @t195))))) % 151.05/151.86 (assume @p228 (forall @t381 (=> @t403 (= @t201 @t202)))) % 151.05/151.86 (assume @p229 (forall (@list @t135 @t18) (=> (forall @t139 (=> (forall @t137 (=> (_ (_ tptp.ord_less_nat @t134) @t133) @t136)) @t138)) @t142))) % 151.05/151.86 (assume @p230 (forall @t204 (=> @t200 @t203))) % 151.05/151.86 (assume @p231 (forall @t395 (=> @t398 (not @t20)))) % 151.05/151.86 (assume @p232 (forall @t67 (=> @t20 (=> @t64 @t404)))) % 151.05/151.86 (assume @p233 (forall @t67 (=> @t384 @t406))) % 151.05/151.86 (assume @p234 (forall @t348 (not (_ @t199 @t195)))) % 151.05/151.86 (assume @p235 (forall @t204 (or @t200 @t202 @t198))) % 151.05/151.86 (assume @p236 (forall @t380 (=> @t200 (=> (_ @t197 @t374) (_ @t199 @t374))))) % 151.05/151.86 (assume @p237 (forall @t149 (=> @t20 (not @t398)))) % 151.05/151.86 (assume @p238 (forall @t204 (= @t203 (or @t200 @t198)))) % 151.05/151.86 (assume @p239 (forall @t348 (exists (@list @t408) (_ @t199 @t408)))) % 151.05/151.86 (assume @p240 (forall @t361 (=> @t20 (=> (_ (_ tptp.ord_less_nat @t357) @t21) @t410)))) % 151.05/151.86 (assume @p241 (forall @t358 (=> (_ @t19 @t357) @t411))) % 151.05/151.86 (assume @p242 (forall @t361 (=> @t20 (=> @t363 @t410)))) % 151.05/151.86 (assume @p243 (forall @t358 (=> @t362 @t411))) % 151.05/151.86 (assume @p244 (forall (@list @t135 @t18 @t107) (=> @t142 @t412))) % 151.05/151.86 (assume @p245 (forall (@list @t135) (=> @t415 @t413))) % 151.05/151.86 (assume @p246 (forall @t147 (=> @t415 @t412))) % 151.05/151.86 (assume @p247 (forall @t316 (=> @t141 @t413))) % 151.05/151.86 (assume @p248 (forall @t149 (=> @t396 (=> @t117 @t20)))) % 151.05/151.86 (assume @p249 (forall @t395 (=> @t398 @t385))) % 151.05/151.86 (assume @p250 (= tptp.ord_less_nat (lambda @t417 (and @t382 (not @t416))))) % 151.05/151.86 (assume @p251 (= tptp.ord_less_eq_nat (lambda @t417 (or (_ (_ tptp.ord_less_nat @t190) @t189) @t416)))) % 151.05/151.86 (assume @p252 (forall @t149 (=> @t20 @t117))) % 151.05/151.86 (assume @p253 @t419) % 151.05/151.86 (assume @p254 true) % 151.05/151.86 (step @p255 (= tptp.ord_less_eq_nat @t425) :rule refl :args (@t425)) % 151.05/151.86 (step @p256 (= tptp.ord_less_nat @t428) :rule refl :args (@t428)) % 151.05/151.86 (step @p257 (= tptp.isShor1936442771pacity @t429) :rule refl :args (@t429)) % 151.05/151.86 (step @p258 (= tptp.isShortestPath_a @t430) :rule refl :args (@t430)) % 151.05/151.86 (step @p259 (= tptp.dist_capacity @t436) :rule refl :args (@t436)) % 151.05/151.86 (step @p260 (= tptp.dist_a @t437) :rule refl :args (@t437)) % 151.05/151.86 (step @p261 (= tptp.reacha1693770334pacity @t438) :rule refl :args (@t438)) % 151.05/151.86 (step @p262 (= tptp.reachableNodes_a @t439) :rule refl :args (@t439)) % 151.05/151.86 (step @p263 (= tptp.min_dist_capacity @t441) :rule refl :args (@t441)) % 151.05/151.86 (step @p264 (= tptp.min_dist_a @t442) :rule refl :args (@t442)) % 151.05/151.86 (step @p265 (= tptp.connected_capacity @t443) :rule refl :args (@t443)) % 151.05/151.86 (step @p266 (= tptp.connected_a @t444) :rule refl :args (@t444)) % 151.05/151.86 (step @p267 :rule eq-symm :args (@t453 @t454)) % 151.05/151.86 ; WARNING: add trust step for TRUST % 151.05/151.86 ; trust TRUST PREPROCESS_HO_ELIM % 151.05/151.86 (step @p268 :rule trust :premises () :args ((= (= @t460 @t456) (= @t453 @t454)))) % 151.05/151.86 (step @p269 :rule eq-symm :args (@t456 @t460)) % 151.05/151.86 ; trust TRUST PREPROCESS_HO_ELIM % 151.05/151.86 (step @p270 :rule trust :premises () :args ((= (= @t484 (_ (_ tptp.plus_plus_nat @t477) @t470)) (= @t456 @t460)))) % 151.05/151.86 (step @p271 :rule beta-reduce :args ((= (_ @t486 tptp.t) @t470))) % 151.05/151.86 (step @p272 :rule refl :args (tptp.t)) % 151.05/151.86 (step @p273 :rule beta-reduce :args ((= (_ @t487 tptp.ua) @t486))) % 151.05/151.86 (step @p274 :rule refl :args (tptp.ua)) % 151.05/151.86 (step @p275 :rule beta-reduce :args ((= @t490 @t487))) % 151.05/151.86 (step @p276 :rule ho_cong :premises (@p275 @p274)) % 151.05/151.86 (step @p277 :rule trans :premises (@p276 @p273)) % 151.05/151.86 (step @p278 :rule ho_cong :premises (@p277 @p272)) % 151.05/151.86 (step @p279 :rule trans :premises (@p278 @p271)) % 151.05/151.86 (step @p280 :rule beta-reduce :args ((= (_ @t491 tptp.ua) @t477))) % 151.05/151.86 (step @p281 :rule beta-reduce :args ((= (_ @t487 tptp.s) @t491))) % 151.05/151.86 (step @p282 :rule refl :args (tptp.s)) % 151.05/151.86 (step @p283 :rule ho_cong :premises (@p275 @p282)) % 151.05/151.86 (step @p284 :rule trans :premises (@p283 @p281)) % 151.05/151.86 (step @p285 :rule ho_cong :premises (@p284 @p274)) % 151.05/151.86 (step @p286 :rule trans :premises (@p285 @p280)) % 151.05/151.86 (step @p287 :rule refl :args (tptp.plus_plus_nat)) % 151.05/151.86 (step @p288 :rule ho_cong :premises (@p287 @p286)) % 151.05/151.86 (step @p289 :rule ho_cong :premises (@p288 @p279)) % 151.05/151.86 (step @p290 :rule beta-reduce :args ((= (_ @t491 tptp.t) @t484))) % 151.05/151.86 (step @p291 :rule ho_cong :premises (@p284 @p272)) % 151.05/151.86 (step @p292 :rule trans :premises (@p291 @p290)) % 151.05/151.86 (step @p293 :rule cong :premises (@p292 @p289) :args ((= @t493 (_ (_ tptp.plus_plus_nat (_ @t492 tptp.ua)) (_ (_ @t490 tptp.ua) tptp.t))))) % 151.05/151.86 (step @p294 :rule refl :args (tptp.c)) % 151.05/151.86 (step @p295 :rule beta-reduce :args ((= (_ @t494 @t295) @t489))) % 151.05/151.86 (step @p296 :rule refl :args (@t295)) % 151.05/151.86 (step @p297 :rule beta-reduce :args ((= (_ @t495 @t83) @t494))) % 151.05/151.86 (step @p298 :rule refl :args (@t83)) % 151.05/151.86 (step @p299 :rule beta-reduce :args ((= (_ @t496 @t234) @t495))) % 151.05/151.86 (step @p300 :rule refl :args (@t234)) % 151.05/151.86 (step @p301 :rule beta-reduce :args ((= @t497 @t496))) % 151.05/151.86 (step @p302 :rule ho_cong :premises (@p301 @p300)) % 151.05/151.86 (step @p303 :rule trans :premises (@p302 @p299)) % 151.05/151.86 (step @p304 :rule ho_cong :premises (@p303 @p298)) % 151.05/151.86 (step @p305 :rule trans :premises (@p304 @p297)) % 151.05/151.86 (step @p306 :rule ho_cong :premises (@p305 @p296)) % 151.05/151.86 (step @p307 :rule trans :premises (@p306 @p295)) % 151.05/151.86 (step @p308 :rule cong :premises (@p307) :args ((lambda @t86 (_ (_ (_ @t497 @t234) @t83) @t295)))) % 151.05/151.86 (step @p309 :rule refl :args (tptp.ord_Least_nat)) % 151.05/151.86 (step @p310 :rule ho_cong :premises (@p309 @p308)) % 151.05/151.86 (step @p311 :rule refl :args (@t236)) % 151.05/151.86 (step @p312 :rule refl :args (@t461)) % 151.05/151.86 (step @p313 :rule refl :args (@t101)) % 151.05/151.86 (step @p314 :rule cong :premises (@p313 @p312) :args ((= @t101 @t461))) % 151.05/151.86 (step @p315 :rule symm :premises (@p314)) % 151.05/151.86 (step @p316 :rule eq_resolve :premises (@p313 @p315)) % 151.05/151.86 (step @p317 :rule refl :args (@t83)) % 151.05/151.86 (step @p318 :rule cong :premises (@p317 @p316) :args (@t498)) % 151.05/151.86 (step @p319 :rule cong :premises (@p318) :args (@t499)) % 151.05/151.86 (step @p320 :rule refl :args (@t488)) % 151.05/151.86 (step @p321 :rule refl :args (@t432)) % 151.05/151.86 (step @p322 :rule cong :premises (@p321 @p320) :args ((= @t432 @t488))) % 151.05/151.86 (step @p323 :rule symm :premises (@p322)) % 151.05/151.86 (step @p324 :rule eq_resolve :premises (@p321 @p323)) % 151.05/151.86 (step @p325 :rule cong :premises (@p324) :args (@t500)) % 151.05/151.86 (step @p326 :rule nary_cong :premises (@p325 @p319) :args (@t501)) % 151.05/151.86 (step @p327 :rule cong :premises (@p326) :args ((forall @t73 @t501))) % 151.05/151.86 (step @p328 :rule bool-and-de-morgan :args (@t432 @t498 true)) % 151.05/151.86 (step @p329 :rule cong :premises (@p328) :args (@t503)) % 151.05/151.86 (step @p330 :rule trans :premises (@p329 @p327)) % 151.05/151.86 (step @p331 :rule cong :premises (@p330) :args (@t504)) % 151.05/151.86 (step @p332 :rule exists-elim :args ((= (exists @t73 @t502) @t504))) % 151.05/151.86 (step @p333 :rule trans :premises (@p332 @p331)) % 151.05/151.86 (step @p334 :rule eq-symm :args (@t101 @t83)) % 151.05/151.86 (step @p335 :rule refl :args (@t432)) % 151.05/151.86 (step @p336 :rule nary_cong :premises (@p335 @p334) :args (@t433)) % 151.05/151.86 (step @p337 :rule cong :premises (@p336) :args (@t434)) % 151.05/151.86 (step @p338 :rule trans :premises (@p337 @p333)) % 151.05/151.86 (step @p339 :rule cong :premises (@p338) :args (@t436)) % 151.05/151.86 (step @p340 :rule trans :premises (@p259 @p339)) % 151.05/151.86 (step @p341 :rule ho_cong :premises (@p340 @p311)) % 151.05/151.86 (step @p342 :rule ho_cong :premises (@p341 @p300)) % 151.05/151.86 (step @p343 :rule ho_cong :premises (@p342 @p298)) % 151.05/151.86 (step @p344 :rule ho_cong :premises (@p343 @p296)) % 151.05/151.86 (step @p345 :rule cong :premises (@p344) :args (@t440)) % 151.05/151.86 (step @p346 :rule ho_cong :premises (@p309 @p345)) % 151.05/151.86 (step @p347 :rule trans :premises (@p346 @p310)) % 151.05/151.86 (step @p348 :rule cong :premises (@p347) :args (@t441)) % 151.05/151.86 (step @p349 :rule trans :premises (@p263 @p348)) % 151.05/151.86 (step @p350 :rule ho_cong :premises (@p349 @p294)) % 151.05/151.86 (step @p351 :rule ho_cong :premises (@p350 @p274)) % 151.05/151.86 (step @p352 :rule ho_cong :premises (@p351 @p272)) % 151.05/151.86 (step @p353 :rule ho_cong :premises (@p350 @p282)) % 151.05/151.86 (step @p354 :rule ho_cong :premises (@p353 @p274)) % 151.05/151.86 (step @p355 :rule ho_cong :premises (@p287 @p354)) % 151.05/151.86 (step @p356 :rule ho_cong :premises (@p355 @p352)) % 151.05/151.86 (step @p357 :rule ho_cong :premises (@p353 @p272)) % 151.05/151.86 (step @p358 :rule cong :premises (@p357 @p356) :args (@t6)) % 151.05/151.86 (step @p359 :rule trans :premises (@p358 @p293)) % 151.05/151.86 (step @p360 :rule trans :premises (@p359 @p270 @p269 @p268 @p267)) % 151.05/151.86 (step @p361 :rule eq_resolve :premises (@p1 @p360)) % 151.05/151.86 (step @p362 :rule eq-symm :args (@t507 @t448)) % 151.05/151.86 (step @p363 :rule cong :premises (@p362) :args (@t508)) % 151.05/151.86 (step @p364 :rule refl :args (@t510)) % 151.05/151.86 (step @p365 :rule nary_cong :premises (@p364 @p363) :args (@t511)) % 151.05/151.86 ; trust TRUST PREPROCESS_HO_ELIM % 151.05/151.86 (step @p366 :rule trust :premises () :args ((= (and (not (forall @t423 (not (= @t514 @t513)))) @t512) @t511))) % 151.05/151.86 (step @p367 :rule refl :args (@t512)) % 151.05/151.86 (step @p368 :rule eq-symm :args (@t513 @t514)) % 151.05/151.86 (step @p369 :rule cong :premises (@p368) :args (@t515)) % 151.05/151.86 (step @p370 :rule cong :premises (@p369) :args (@t516)) % 151.05/151.86 (step @p371 :rule cong :premises (@p370) :args (@t517)) % 151.05/151.86 (step @p372 :rule nary_cong :premises (@p371 @p367) :args (@t518)) % 151.05/151.86 ; trust TRUST PREPROCESS_HO_ELIM % 151.05/151.86 (step @p373 :rule trust :premises () :args ((= (and (not (forall @t423 (not (= @t521 @t514)))) @t519) @t518))) % 151.05/151.86 (step @p374 :rule refl :args (@t519)) % 151.05/151.86 (step @p375 :rule eq-symm :args (@t514 @t521)) % 151.05/151.86 (step @p376 :rule cong :premises (@p375) :args (@t522)) % 151.05/151.86 (step @p377 :rule cong :premises (@p376) :args ((forall @t423 @t522))) % 151.05/151.86 (step @p378 :rule refl :args (@t521)) % 151.05/151.86 (step @p379 :rule refl :args (@t514)) % 151.05/151.86 (step @p380 :rule refl :args (@t7)) % 151.05/151.86 (step @p381 :rule cong :premises (@p380 @p379) :args ((= @t7 @t514))) % 151.05/151.86 (step @p382 :rule symm :premises (@p381)) % 151.05/151.86 (step @p383 :rule eq_resolve :premises (@p380 @p382)) % 151.05/151.86 (step @p384 :rule cong :premises (@p383 @p378) :args (@t523)) % 151.05/151.86 (step @p385 :rule cong :premises (@p384) :args (@t524)) % 151.05/151.86 (step @p386 :rule cong :premises (@p385) :args (@t525)) % 151.05/151.86 (step @p387 :rule trans :premises (@p386 @p377)) % 151.05/151.86 (step @p388 :rule cong :premises (@p387) :args (@t526)) % 151.05/151.86 (step @p389 :rule nary_cong :premises (@p388 @p374) :args (@t527)) % 151.05/151.86 (step @p390 :rule beta-reduce :args ((= (_ (lambda @t400 (and (not (forall @t423 (not (= @t170 @t521)))) (not (= @t170 @t477)))) @t7) @t527))) % 151.05/151.86 (step @p391 :rule trans :premises (@p390 @p389)) % 151.05/151.86 (step @p392 :rule refl :args (@t7)) % 151.05/151.86 (step @p393 :rule eq-symm :args (@t477 @t170)) % 151.05/151.86 (step @p394 :rule cong :premises (@p393) :args (@t528)) % 151.05/151.86 (step @p395 :rule refl :args (@t420)) % 151.05/151.86 (step @p396 :rule refl :args ((tptp.ord_Least_nat @t530))) % 151.05/151.86 (step @p397 :rule cong :premises (@p317 @p312) :args (@t462)) % 151.05/151.86 (step @p398 :rule cong :premises (@p397) :args (@t463)) % 151.05/151.86 (step @p399 :rule refl :args (@t471)) % 151.05/151.86 (step @p400 :rule cong :premises (@p399) :args (@t472)) % 151.05/151.86 (step @p401 :rule nary_cong :premises (@p400 @p398) :args (@t473)) % 151.05/151.86 (step @p402 :rule cong :premises (@p401) :args (@t474)) % 151.05/151.86 (step @p403 :rule cong :premises (@p402) :args (@t475)) % 151.05/151.86 (step @p404 :rule cong :premises (@p403) :args (@t476)) % 151.05/151.86 (step @p405 :rule cong :premises (@p404) :args (@t520)) % 151.05/151.86 (step @p406 :rule trans :premises (@p405 @p396)) % 151.05/151.86 (step @p407 :rule refl :args (tptp.ord_Least_nat)) % 151.05/151.86 (step @p408 :rule ho_cong :premises (@p407 @p404)) % 151.05/151.86 (step @p409 :rule cong :premises (@p408 @p406) :args ((= @t477 @t520))) % 151.05/151.86 (step @p410 :rule symm :premises (@p409)) % 151.05/151.86 (step @p411 :rule refl :args ((_ tptp.ord_Least_nat @t530))) % 151.05/151.86 (step @p412 :rule eq_resolve :premises (@p411 @p410)) % 151.05/151.86 (step @p413 :rule cong :premises (@p412 @p395) :args (@t531)) % 151.05/151.86 (step @p414 :rule refl :args (@t170)) % 151.05/151.86 (step @p415 :rule cong :premises (@p414 @p413) :args (@t532)) % 151.05/151.86 (step @p416 :rule cong :premises (@p415) :args (@t533)) % 151.05/151.86 (step @p417 :rule cong :premises (@p416) :args (@t534)) % 151.05/151.86 (step @p418 :rule cong :premises (@p417) :args (@t535)) % 151.05/151.86 (step @p419 :rule nary_cong :premises (@p418 @p394) :args (@t536)) % 151.05/151.86 (step @p420 :rule cong :premises (@p419) :args (@t537)) % 151.05/151.86 (step @p421 :rule beta-reduce :args ((= (_ @t540 @t477) @t537))) % 151.05/151.86 (step @p422 :rule trans :premises (@p421 @p420)) % 151.05/151.86 (step @p423 :rule refl :args (@t540)) % 151.05/151.86 (step @p424 :rule ho_cong :premises (@p423 @p286)) % 151.05/151.86 (step @p425 :rule trans :premises (@p424 @p422)) % 151.05/151.86 (step @p426 :rule ho_cong :premises (@p425 @p392)) % 151.05/151.86 (step @p427 :rule trans :premises (@p426 @p391)) % 151.05/151.86 (step @p428 :rule refl :args (@t426)) % 151.05/151.86 (step @p429 :rule beta-reduce :args ((= (_ @t542 @t170) @t539))) % 151.05/151.86 (step @p430 :rule refl :args (@t170)) % 151.05/151.86 (step @p431 :rule beta-reduce :args ((= @t545 @t542))) % 151.05/151.86 (step @p432 :rule ho_cong :premises (@p431 @p430)) % 151.05/151.86 (step @p433 :rule trans :premises (@p432 @p429)) % 151.05/151.86 (step @p434 :rule nary_cong :premises (@p433 @p428) :args ((and (_ @t545 @t170) @t426))) % 151.05/151.86 (step @p435 :rule refl :args (@t171)) % 151.05/151.86 (step @p436 :rule refl :args (@t543)) % 151.05/151.86 (step @p437 :rule refl :args (@t421)) % 151.05/151.86 (step @p438 :rule cong :premises (@p437 @p436) :args ((= @t421 @t543))) % 151.05/151.86 (step @p439 :rule symm :premises (@p438)) % 151.05/151.86 (step @p440 :rule eq_resolve :premises (@p437 @p439)) % 151.05/151.86 (step @p441 :rule refl :args (@t190)) % 151.05/151.86 (step @p442 :rule cong :premises (@p441 @p440) :args (@t422)) % 151.05/151.86 (step @p443 :rule cong :premises (@p442) :args (@t546)) % 151.05/151.86 (step @p444 :rule cong :premises (@p443) :args (@t547)) % 151.05/151.86 (step @p445 :rule cong :premises (@p444) :args (@t548)) % 151.05/151.86 (step @p446 :rule exists-elim :args ((= @t424 @t548))) % 151.05/151.86 (step @p447 :rule trans :premises (@p446 @p445)) % 151.05/151.86 (step @p448 :rule cong :premises (@p447) :args (@t425)) % 151.05/151.86 (step @p449 :rule trans :premises (@p255 @p448)) % 151.05/151.86 (step @p450 :rule ho_cong :premises (@p449 @p435)) % 151.05/151.86 (step @p451 :rule ho_cong :premises (@p450 @p430)) % 151.05/151.86 (step @p452 :rule nary_cong :premises (@p451 @p428) :args (@t427)) % 151.05/151.86 (step @p453 :rule trans :premises (@p452 @p434)) % 151.05/151.86 (step @p454 :rule cong :premises (@p453) :args (@t428)) % 151.05/151.86 (step @p455 :rule trans :premises (@p256 @p454)) % 151.05/151.86 (step @p456 :rule ho_cong :premises (@p455 @p354)) % 151.05/151.86 (step @p457 :rule ho_cong :premises (@p456 @p392)) % 151.05/151.86 (step @p458 :rule trans :premises (@p457 @p427)) % 151.05/151.86 (step @p459 :rule trans :premises (@p458 @p373 @p372 @p366 @p365)) % 151.05/151.86 (step @p460 :rule eq_resolve :premises (@p2 @p459)) % 151.05/151.86 (step @p461 :rule and_elim :premises (@p460) :args (0)) % 151.05/151.86 (step @p462 :rule refl :args (@t551)) % 151.05/151.86 (step @p463 :rule bool-double-not-elim :args (@t509)) % 151.05/151.86 (step @p464 :rule nary_cong :premises (@p463 @p462) :args ((or (not @t510) @t551))) % 151.05/151.86 (step @p465 :rule bool-double-not-elim :args (@t551)) % 151.05/151.86 (step @p466 :rule cong :premises (@p364 @p465) :args ((=> @t510 @t553))) % 151.05/151.86 (assume-push @p860 @t510) % 151.05/151.86 (step @p468 :rule skolemize :premises (@p461)) % 151.05/151.86 (step-pop @p861 :rule scope :premises (@p468)) % 151.05/151.86 (step @p469 :rule process_scope :premises (@p861) :args (@t553)) % 151.05/151.86 (step @p471 :rule eq_resolve :premises (@p469 @p466)) % 151.05/151.86 (step @p472 :rule implies_elim :premises (@p471)) % 151.05/151.86 (step @p473 :rule eq_resolve :premises (@p472 @p464)) % 151.05/151.86 (step @p474 :rule chain_m_resolution :premises (@p473 @p461) :args (@t551 @t554 (@list @t509))) % 151.05/151.86 (step @p475 :rule eq-symm :args (@t555 @t557)) % 151.05/151.86 (step @p476 :rule cong :premises (@p475) :args (@t558)) % 151.05/151.86 (step @p477 :rule cong :premises (@p476) :args (@t559)) % 151.05/151.86 (step @p478 :rule cong :premises (@p477) :args (@t560)) % 151.05/151.86 ; trust TRUST PREPROCESS_HO_ELIM % 151.05/151.86 (step @p479 :rule trust :premises () :args ((= (not (forall @t423 (not (= @t562 @t561)))) @t560))) % 151.05/151.86 (step @p480 :rule eq-symm :args (@t561 @t562)) % 151.05/151.86 (step @p481 :rule cong :premises (@p480) :args (@t563)) % 151.05/151.86 (step @p482 :rule cong :premises (@p481) :args (@t564)) % 151.05/151.86 (step @p483 :rule cong :premises (@p482) :args (@t565)) % 151.05/151.86 ; trust TRUST PREPROCESS_HO_ELIM % 151.05/151.86 (step @p484 :rule trust :premises () :args ((= (not (forall @t423 (not (= @t567 @t562)))) @t565))) % 151.05/151.86 (step @p485 :rule eq-symm :args (@t562 @t567)) % 151.05/151.86 (step @p486 :rule cong :premises (@p485) :args (@t568)) % 151.05/151.86 (step @p487 :rule cong :premises (@p486) :args ((forall @t423 @t568))) % 151.05/151.86 (step @p488 :rule refl :args (@t567)) % 151.05/151.86 (step @p489 :rule refl :args (@t562)) % 151.05/151.86 (step @p490 :rule refl :args (@t8)) % 151.05/151.86 (step @p491 :rule cong :premises (@p490 @p489) :args ((= @t8 @t562))) % 151.05/151.86 (step @p492 :rule symm :premises (@p491)) % 151.05/151.86 (step @p493 :rule eq_resolve :premises (@p490 @p492)) % 151.05/151.86 (step @p494 :rule cong :premises (@p493 @p488) :args (@t569)) % 151.05/151.86 (step @p495 :rule cong :premises (@p494) :args (@t570)) % 151.05/151.86 (step @p496 :rule cong :premises (@p495) :args (@t571)) % 151.05/151.86 (step @p497 :rule trans :premises (@p496 @p487)) % 151.05/151.86 (step @p498 :rule cong :premises (@p497) :args (@t572)) % 151.05/151.86 (step @p499 :rule beta-reduce :args ((= (_ (lambda @t541 (not (forall @t423 (not (= @t190 @t567))))) @t8) @t572))) % 151.05/151.86 (step @p500 :rule trans :premises (@p499 @p498)) % 151.05/151.86 (step @p501 :rule refl :args (@t8)) % 151.05/151.86 (step @p502 :rule refl :args ((tptp.ord_Least_nat @t573))) % 151.05/151.86 (step @p503 :rule refl :args (@t464)) % 151.05/151.86 (step @p504 :rule cong :premises (@p503) :args (@t465)) % 151.05/151.86 (step @p505 :rule nary_cong :premises (@p504 @p398) :args (@t466)) % 151.05/151.86 (step @p506 :rule cong :premises (@p505) :args (@t467)) % 151.05/151.86 (step @p507 :rule cong :premises (@p506) :args (@t468)) % 151.05/151.86 (step @p508 :rule cong :premises (@p507) :args (@t469)) % 151.05/151.86 (step @p509 :rule cong :premises (@p508) :args (@t566)) % 151.05/151.86 (step @p510 :rule trans :premises (@p509 @p502)) % 151.05/151.86 (step @p511 :rule ho_cong :premises (@p407 @p508)) % 151.05/151.86 (step @p512 :rule cong :premises (@p511 @p510) :args ((= @t470 @t566))) % 151.05/151.86 (step @p513 :rule symm :premises (@p512)) % 151.05/151.86 (step @p514 :rule refl :args ((_ tptp.ord_Least_nat @t573))) % 151.05/151.86 (step @p515 :rule eq_resolve :premises (@p514 @p513)) % 151.05/151.86 (step @p516 :rule cong :premises (@p515 @p395) :args (@t574)) % 151.05/151.86 (step @p517 :rule cong :premises (@p441 @p516) :args (@t575)) % 151.05/151.86 (step @p518 :rule cong :premises (@p517) :args (@t576)) % 151.05/151.86 (step @p519 :rule cong :premises (@p518) :args (@t577)) % 151.05/151.86 (step @p520 :rule cong :premises (@p519) :args (@t578)) % 151.05/151.86 (step @p521 :rule cong :premises (@p520) :args (@t579)) % 151.05/151.86 (step @p522 :rule beta-reduce :args ((= (_ @t544 @t470) @t579))) % 151.05/151.86 (step @p523 :rule trans :premises (@p522 @p521)) % 151.05/151.86 (step @p524 :rule refl :args (@t544)) % 151.05/151.86 (step @p525 :rule ho_cong :premises (@p524 @p279)) % 151.05/151.86 (step @p526 :rule trans :premises (@p525 @p523)) % 151.05/151.86 (step @p527 :rule ho_cong :premises (@p526 @p501)) % 151.05/151.86 (step @p528 :rule trans :premises (@p527 @p500)) % 151.05/151.86 (step @p529 :rule ho_cong :premises (@p449 @p352)) % 151.05/151.86 (step @p530 :rule ho_cong :premises (@p529 @p501)) % 151.05/151.86 (step @p531 :rule trans :premises (@p530 @p528)) % 151.05/151.86 (step @p532 :rule trans :premises (@p531 @p484 @p483 @p479 @p478)) % 151.05/151.86 (step @p533 :rule eq_resolve :premises (@p3 @p532)) % 151.05/151.86 (step @p534 :rule refl :args (@t583)) % 151.05/151.86 (step @p535 :rule bool-double-not-elim :args (@t580)) % 151.05/151.86 (step @p536 :rule nary_cong :premises (@p535 @p534) :args ((or (not @t584) @t583))) % 151.05/151.86 (step @p537 :rule eq-symm :args (@t582 @t555)) % 151.05/151.86 (step @p538 :rule bool-double-not-elim :args (@t585)) % 151.05/151.86 (step @p539 :rule trans :premises (@p538 @p537)) % 151.05/151.86 (step @p540 :rule refl :args (@t584)) % 151.05/151.86 (step @p541 :rule cong :premises (@p540 @p539) :args ((=> @t584 @t586))) % 151.05/151.86 (assume-push @p862 @t584) % 151.05/151.86 (step @p543 :rule skolemize :premises (@p533)) % 151.05/151.86 (step-pop @p863 :rule scope :premises (@p543)) % 151.05/151.86 (step @p544 :rule process_scope :premises (@p863) :args (@t586)) % 151.05/151.86 (step @p546 :rule eq_resolve :premises (@p544 @p541)) % 151.05/151.86 (step @p547 :rule implies_elim :premises (@p546)) % 151.05/151.86 (step @p548 :rule eq_resolve :premises (@p547 @p536)) % 151.05/151.86 (step @p549 :rule chain_m_resolution :premises (@p548 @p533) :args (@t583 @t554 (@list @t580))) % 151.05/151.86 ; trust TRUST PREPROCESS_HO_ELIM % 151.05/151.86 (step @p550 :rule trust :premises () :args ((= (forall @t593 @t601) (forall @t593 (or (= @t18 @t590) (and (not (forall @t423 (not (= (_ @t452 (_ @t450 @t449 @t592) @t420) @t591)))) (not (= @t592 @t591)))))))) % 151.05/151.86 (step @p551 :rule aci_norm :args ((= (or @t600 false @t599) @t601))) % 151.05/151.86 (step @p552 :rule refl :args (@t599)) % 151.05/151.86 (step @p553 :rule evaluate :args ((not true))) % 151.05/151.86 (step @p554 :rule eq-refl :args (@t594)) % 151.05/151.86 (step @p555 :rule cong :premises (@p554) :args (@t602)) % 151.05/151.86 (step @p556 :rule trans :premises (@p555 @p553)) % 151.05/151.86 (step @p557 :rule refl :args (@t600)) % 151.05/151.86 (step @p558 :rule nary_cong :premises (@p557 @p556 @p552) :args (@t603)) % 151.05/151.86 (step @p559 :rule trans :premises (@p558 @p551)) % 151.05/151.86 (step @p560 :rule cong :premises (@p559) :args ((forall @t593 @t603))) % 151.05/151.86 (step @p561 :rule quant-var-elim-eq :args ((= (forall @t608 @t607) @t603))) % 151.05/151.86 (step @p562 :rule aci_norm :args ((= @t609 @t607))) % 151.05/151.86 (step @p563 :rule cong :premises (@p562) :args (@t610)) % 151.05/151.86 (step @p564 :rule trans :premises (@p563 @p561)) % 151.05/151.86 (step @p565 :rule cong :premises (@p564) :args (@t611)) % 151.05/151.86 (step @p566 :rule quant-merge-prenex :args ((= @t611 @t612))) % 151.05/151.86 (step @p567 :rule symm :premises (@p566)) % 151.05/151.86 (step @p568 :rule quant_var_reordering :args ((= (forall @t613 @t609) @t612))) % 151.05/151.86 (step @p569 :rule trans :premises (@p568 @p567 @p565)) % 151.05/151.86 (step @p570 :rule trans :premises (@p569 @p560)) % 151.05/151.86 (step @p571 :rule aci_norm :args ((= (or false @t600 @t606 @t605) @t609))) % 151.05/151.86 (step @p572 :rule refl :args (@t605)) % 151.05/151.86 (step @p573 :rule refl :args (@t606)) % 151.05/151.86 (step @p574 :rule eq-refl :args (@t595)) % 151.05/151.86 (step @p575 :rule cong :premises (@p574) :args (@t614)) % 151.05/151.86 (step @p576 :rule trans :premises (@p575 @p553)) % 151.05/151.86 (step @p577 :rule nary_cong :premises (@p576 @p557 @p573 @p572) :args (@t615)) % 151.05/151.86 (step @p578 :rule trans :premises (@p577 @p571)) % 151.05/151.86 (step @p579 :rule cong :premises (@p578) :args ((forall @t613 @t615))) % 151.05/151.86 (step @p580 :rule trans :premises (@p579 @p570)) % 151.05/151.86 (step @p581 :rule quant-var-elim-eq :args ((= (forall @t621 @t620) @t615))) % 151.05/151.86 (step @p582 :rule aci_norm :args ((= @t622 @t620))) % 151.05/151.86 (step @p583 :rule cong :premises (@p582) :args (@t623)) % 151.05/151.86 (step @p584 :rule trans :premises (@p583 @p581)) % 151.05/151.86 (step @p585 :rule cong :premises (@p584) :args (@t624)) % 151.05/151.86 (step @p586 :rule quant-merge-prenex :args ((= @t624 @t625))) % 151.05/151.86 (step @p587 :rule symm :premises (@p586)) % 151.05/151.86 (step @p588 :rule quant_var_reordering :args ((= @t626 @t625))) % 151.05/151.86 (step @p589 :rule trans :premises (@p588 @p587 @p585)) % 151.05/151.86 (step @p590 :rule trans :premises (@p589 @p580)) % 151.05/151.86 (step @p591 :rule quant-merge-prenex :args ((= (forall @t153 @t627) @t626))) % 151.05/151.86 (step @p592 :rule refl :args (@t618)) % 151.05/151.86 (step @p593 :rule alpha_equiv :args (@t628 (@list @t587) @t629)) % 151.05/151.86 (step @p594 :rule refl :args (@t384)) % 151.05/151.86 (step @p595 :rule alpha_equiv :args (@t630 (@list @t588) @t629)) % 151.05/151.86 (step @p596 :rule nary_cong :premises (@p595 @p594 @p593 @p592) :args (@t631)) % 151.05/151.86 (step @p597 :rule quant-miniscope-or :args ((= @t627 @t631))) % 151.05/151.86 (step @p598 :rule trans :premises (@p597 @p596)) % 151.05/151.86 (step @p599 :rule symm :premises (@p598)) % 151.05/151.86 (step @p600 :rule cong :premises (@p599) :args ((forall @t153 (or @t635 @t384 @t633 @t618)))) % 151.05/151.86 (step @p601 :rule trans :premises (@p600 @p591)) % 151.05/151.86 (step @p602 :rule trans :premises (@p601 @p590)) % 151.05/151.86 (step @p603 :rule refl :args (@t616)) % 151.05/151.86 (step @p604 :rule refl :args (@t150)) % 151.05/151.86 (step @p605 :rule cong :premises (@p604 @p603) :args ((= @t150 @t616))) % 151.05/151.86 (step @p606 :rule symm :premises (@p605)) % 151.05/151.86 (step @p607 :rule eq_resolve :premises (@p604 @p606)) % 151.05/151.86 (step @p608 :rule refl :args (@t597)) % 151.05/151.86 (step @p609 :rule refl :args (@t30)) % 151.05/151.86 (step @p610 :rule cong :premises (@p609 @p608) :args ((= @t30 @t597))) % 151.05/151.86 (step @p611 :rule symm :premises (@p610)) % 151.05/151.86 (step @p612 :rule eq_resolve :premises (@p609 @p611)) % 151.05/151.86 (step @p613 :rule cong :premises (@p612 @p607) :args (@t636)) % 151.05/151.86 (step @p614 :rule cong :premises (@p613) :args (@t637)) % 151.05/151.86 (step @p615 :rule refl :args (@t617)) % 151.05/151.86 (step @p616 :rule nary_cong :premises (@p615 @p614) :args (@t638)) % 151.05/151.86 (step @p617 :rule refl :args (@t633)) % 151.05/151.86 (step @p618 :rule refl :args (@t635)) % 151.05/151.86 (step @p619 :rule nary_cong :premises (@p618 @p594 @p617 @p616) :args (@t639)) % 151.05/151.86 (step @p620 :rule cong :premises (@p619) :args ((forall @t153 @t639))) % 151.05/151.86 (step @p621 :rule trans :premises (@p620 @p602)) % 151.05/151.86 (step @p622 :rule aci_norm :args ((= (or (or @t635 @t384) (or @t633 @t638)) @t639))) % 151.05/151.86 (step @p623 :rule refl :args (@t638)) % 151.05/151.86 (step @p624 :rule bool-double-not-elim :args (@t633)) % 151.05/151.86 (step @p625 :rule nary_cong :premises (@p624 @p623) :args ((or (not @t640) @t638))) % 151.05/151.86 (step @p626 :rule bool-impl-elim :args (@t640 @t638)) % 151.05/151.86 (step @p627 :rule trans :premises (@p626 @p625)) % 151.05/151.86 (step @p628 :rule bool-double-not-elim :args (@t384)) % 151.05/151.86 (step @p629 :rule bool-double-not-elim :args (@t635)) % 151.05/151.86 (step @p630 :rule nary_cong :premises (@p629 @p628) :args ((or (not @t641) (not @t396)))) % 151.05/151.86 (step @p631 :rule bool-and-de-morgan :args (@t641 @t396 true)) % 151.05/151.86 (step @p632 :rule trans :premises (@p631 @p630)) % 151.05/151.86 (step @p633 :rule nary_cong :premises (@p632 @p627) :args ((or (not @t643) @t642))) % 151.05/151.86 (step @p634 :rule trans :premises (@p633 @p622)) % 151.05/151.86 (step @p635 :rule bool-impl-elim :args (@t643 @t642)) % 151.05/151.86 (step @p636 :rule trans :premises (@p635 @p634)) % 151.05/151.86 (step @p637 :rule cong :premises (@p636) :args ((forall @t153 (=> @t643 @t642)))) % 151.05/151.86 (step @p638 :rule trans :premises (@p637 @p621)) % 151.05/151.86 (step @p639 :rule refl :args (@t637)) % 151.05/151.86 (step @p640 :rule eq-symm :args (@t616 @t598)) % 151.05/151.86 (step @p641 :rule cong :premises (@p640) :args (@t644)) % 151.05/151.86 (step @p642 :rule cong :premises (@p641) :args ((forall @t423 @t644))) % 151.05/151.86 (step @p643 :rule refl :args (@t598)) % 151.05/151.86 (step @p644 :rule cong :premises (@p607 @p643) :args (@t645)) % 151.05/151.86 (step @p645 :rule cong :premises (@p644) :args (@t646)) % 151.05/151.86 (step @p646 :rule cong :premises (@p645) :args (@t647)) % 151.05/151.86 (step @p647 :rule trans :premises (@p646 @p642)) % 151.05/151.86 (step @p648 :rule cong :premises (@p647) :args (@t648)) % 151.05/151.86 (step @p649 :rule nary_cong :premises (@p648 @p639) :args (@t649)) % 151.05/151.86 (step @p650 :rule beta-reduce :args ((= (_ (lambda @t400 (and (not (forall @t423 (not (= @t170 @t598)))) @t650)) @t150) @t649))) % 151.05/151.86 (step @p651 :rule trans :premises (@p650 @p649)) % 151.05/151.86 (step @p652 :rule refl :args (@t150)) % 151.05/151.86 (step @p653 :rule refl :args (@t650)) % 151.05/151.86 (step @p654 :rule cong :premises (@p612 @p395) :args (@t651)) % 151.05/151.86 (step @p655 :rule cong :premises (@p414 @p654) :args (@t652)) % 151.05/151.86 (step @p656 :rule cong :premises (@p655) :args (@t653)) % 151.05/151.86 (step @p657 :rule cong :premises (@p656) :args (@t654)) % 151.05/151.86 (step @p658 :rule cong :premises (@p657) :args (@t655)) % 151.05/151.86 (step @p659 :rule nary_cong :premises (@p658 @p653) :args (@t656)) % 151.05/151.86 (step @p660 :rule cong :premises (@p659) :args (@t657)) % 151.05/151.86 (step @p661 :rule beta-reduce :args ((= @t658 @t657))) % 151.05/151.86 (step @p662 :rule trans :premises (@p661 @p660)) % 151.05/151.86 (step @p663 :rule ho_cong :premises (@p662 @p652)) % 151.05/151.86 (step @p664 :rule trans :premises (@p663 @p651)) % 151.05/151.86 (step @p665 :rule beta-reduce :args ((= (_ @t659 @t59) @t640))) % 151.05/151.86 (step @p666 :rule refl :args (@t59)) % 151.05/151.86 (step @p667 :rule beta-reduce :args ((= @t660 @t659))) % 151.05/151.86 (step @p668 :rule ho_cong :premises (@p667 @p666)) % 151.05/151.86 (step @p669 :rule trans :premises (@p668 @p665)) % 151.05/151.86 (step @p670 :rule cong :premises (@p669 @p664) :args (@t661)) % 151.05/151.86 (step @p671 :rule beta-reduce :args ((= (_ @t662 @t17) @t643))) % 151.05/151.86 (step @p672 :rule refl :args (@t17)) % 151.05/151.86 (step @p673 :rule beta-reduce :args ((= @t663 @t662))) % 151.05/151.86 (step @p674 :rule ho_cong :premises (@p673 @p672)) % 151.05/151.86 (step @p675 :rule trans :premises (@p674 @p671)) % 151.05/151.86 (step @p676 :rule cong :premises (@p675 @p670) :args (@t664)) % 151.05/151.86 (step @p677 :rule cong :premises (@p676) :args ((forall @t153 @t664))) % 151.05/151.86 (step @p678 :rule trans :premises (@p677 @p638)) % 151.05/151.86 (step @p679 :rule refl :args (@t30)) % 151.05/151.86 (step @p680 :rule ho_cong :premises (@p455 @p679)) % 151.05/151.86 (step @p681 :rule ho_cong :premises (@p680 @p652)) % 151.05/151.86 (step @p682 :rule refl :args (@t21)) % 151.05/151.86 (step @p683 :rule ho_cong :premises (@p449 @p682)) % 151.05/151.86 (step @p684 :rule ho_cong :premises (@p683 @p666)) % 151.05/151.86 (step @p685 :rule cong :premises (@p684 @p681) :args (@t219)) % 151.05/151.86 (step @p686 :rule refl :args (@t18)) % 151.05/151.86 (step @p687 :rule ho_cong :premises (@p455 @p686)) % 151.05/151.86 (step @p688 :rule ho_cong :premises (@p687 @p672)) % 151.05/151.86 (step @p689 :rule cong :premises (@p688 @p685) :args (@t220)) % 151.05/151.86 (step @p690 :rule cong :premises (@p689) :args (@t221)) % 151.05/151.86 (step @p691 :rule trans :premises (@p690 @p678)) % 151.05/151.86 (step @p692 :rule trans :premises (@p691 @p550)) % 151.05/151.86 (step @p693 :rule eq_resolve :premises (@p86 @p692)) % 151.05/151.86 (step @p694 :rule instantiate :premises (@p693) :args ((@list @t448 @t447 @t549 @t581))) % 151.05/151.86 (step @p695 :rule and_elim :premises (@p460) :args (1)) % 151.05/151.86 (step @p696 :rule false_intro :premises (@p695)) % 151.05/151.86 (step @p697 :rule symm :premises (@p474)) % 151.05/151.86 (step @p698 :rule refl :args (@t448)) % 151.05/151.86 (step @p699 :rule cong :premises (@p698 @p697) :args (@t665)) % 151.05/151.86 (step @p700 :rule trans :premises (@p699 @p696)) % 151.05/151.86 (step @p701 :rule false_elim :premises (@p700)) % 151.05/151.86 (step @p702 :rule cnf_or_pos :args (@t672)) % 151.05/151.86 (step @p703 :rule reordering :premises (@p702) :args ((or @t665 @t671 (not @t672)))) % 151.05/151.86 (step @p704 :rule chain_m_resolution :premises (@p703 @p701 @p694) :args (@t671 (@list true false) (@list @t665 @t672))) % 151.05/151.86 (step @p705 :rule cnf_and_pos :args (@t671 0)) % 151.05/151.86 (step @p706 :rule reordering :premises (@p705) :args ((or @t670 @t673))) % 151.05/151.86 (step @p707 :rule chain_m_resolution :premises (@p706 @p704) :args (@t670 @t674 @t675)) % 151.05/151.86 (step @p708 :rule refl :args (@t678)) % 151.05/151.86 (step @p709 :rule bool-double-not-elim :args (@t669)) % 151.05/151.86 (step @p710 :rule nary_cong :premises (@p709 @p708) :args ((or (not @t670) @t678))) % 151.05/151.86 (step @p711 :rule eq-symm :args (@t677 @t666)) % 151.05/151.86 (step @p712 :rule bool-double-not-elim :args (@t679)) % 151.05/151.86 (step @p713 :rule trans :premises (@p712 @p711)) % 151.05/151.86 (step @p714 :rule refl :args (@t670)) % 151.05/151.86 (step @p715 :rule cong :premises (@p714 @p713) :args ((=> @t670 @t680))) % 151.05/151.86 (assume-push @p864 @t670) % 151.05/151.86 (step @p717 :rule skolemize :premises (@p707)) % 151.05/151.86 (step-pop @p865 :rule scope :premises (@p717)) % 151.05/151.86 (step @p718 :rule process_scope :premises (@p865) :args (@t680)) % 151.05/151.86 (step @p720 :rule eq_resolve :premises (@p718 @p715)) % 151.05/151.86 (step @p721 :rule implies_elim :premises (@p720)) % 151.05/151.86 (step @p722 :rule eq_resolve :premises (@p721 @p710)) % 151.05/151.86 (step @p723 :rule chain_m_resolution :premises (@p722 @p707) :args (@t678 @t554 @t681)) % 151.05/151.86 (step @p724 :rule cnf_and_pos :args (@t671 1)) % 151.05/151.86 (step @p725 :rule reordering :premises (@p724) :args ((or @t667 @t673))) % 151.05/151.86 (step @p726 :rule chain_m_resolution :premises (@p725 @p704) :args (@t667 @t674 @t675)) % 151.05/151.86 (step @p727 :rule false_intro :premises (@p726)) % 151.05/151.86 (step @p728 :rule refl :args (@t449)) % 151.05/151.86 (step @p729 :rule cong :premises (@p728 @p474) :args (@t682)) % 151.05/151.86 (step @p730 :rule cong :premises (@p729 @p549) :args (@t683)) % 151.05/151.86 (step @p731 :rule cong :premises (@p361 @p730) :args (@t684)) % 151.05/151.86 (step @p732 :rule trans :premises (@p731 @p727)) % 151.05/151.86 (step @p733 :rule false_elim :premises (@p732)) % 151.05/151.86 (step @p734 :rule bool-double-not-elim :args (@t684)) % 151.05/151.86 (step @p735 :rule bool-double-not-elim :args (@t686)) % 151.05/151.86 (step @p736 :rule nary_cong :premises (@p735 @p734) :args ((or (not @t687) (not (not @t684))))) % 151.05/151.86 (step @p737 :rule eq-symm :args (@t683 @t454)) % 151.05/151.86 (step @p738 :rule cong :premises (@p737) :args (@t688)) % 151.05/151.86 (step @p739 :rule refl :args (@t687)) % 151.05/151.86 (step @p740 :rule nary_cong :premises (@p739 @p738) :args (@t689)) % 151.05/151.86 (step @p741 :rule cong :premises (@p740) :args (@t690)) % 151.05/151.86 ; trust TRUST PREPROCESS_HO_ELIM % 151.05/151.86 (step @p742 :rule trust :premises () :args ((= (not (and (not (forall @t423 (not (= @t693 @t692)))) @t691)) @t690))) % 151.05/151.86 (step @p743 :rule refl :args (@t691)) % 151.05/151.86 (step @p744 :rule eq-symm :args (@t692 @t693)) % 151.05/151.86 (step @p745 :rule cong :premises (@p744) :args (@t694)) % 151.05/151.86 (step @p746 :rule cong :premises (@p745) :args (@t695)) % 151.05/151.86 (step @p747 :rule cong :premises (@p746) :args (@t696)) % 151.05/151.86 (step @p748 :rule nary_cong :premises (@p747 @p743) :args (@t697)) % 151.05/151.86 (step @p749 :rule cong :premises (@p748) :args (@t698)) % 151.05/151.86 ; trust TRUST PREPROCESS_HO_ELIM % 151.05/151.86 (step @p750 :rule trust :premises () :args ((= (not (and (not (forall @t423 (not (= @t701 @t693)))) @t699)) @t698))) % 151.05/151.86 (step @p751 :rule refl :args (@t699)) % 151.05/151.86 (step @p752 :rule eq-symm :args (@t693 @t701)) % 151.05/151.86 (step @p753 :rule cong :premises (@p752) :args (@t702)) % 151.05/151.86 (step @p754 :rule cong :premises (@p753) :args ((forall @t423 @t702))) % 151.05/151.86 (step @p755 :rule refl :args (@t701)) % 151.05/151.86 (step @p756 :rule refl :args ((tptp.plus_plus_nat @t7 @t8))) % 151.05/151.86 (step @p757 :rule cong :premises (@p379 @p489) :args (@t693)) % 151.05/151.86 (step @p758 :rule trans :premises (@p757 @p756)) % 151.05/151.86 (step @p759 :rule refl :args (tptp.plus_plus_nat)) % 151.05/151.86 (step @p760 :rule ho_cong :premises (@p759 @p379)) % 151.05/151.86 (step @p761 :rule ho_cong :premises (@p760 @p489)) % 151.05/151.86 (step @p762 :rule cong :premises (@p761 @p758) :args ((= (_ (_ tptp.plus_plus_nat @t514) @t562) @t693))) % 151.05/151.86 (step @p763 :rule symm :premises (@p762)) % 151.05/151.86 (step @p764 :rule refl :args (@t418)) % 151.05/151.86 (step @p765 :rule eq_resolve :premises (@p764 @p763)) % 151.05/151.86 (step @p766 :rule ho_cong :premises (@p759 @p383)) % 151.05/151.86 (step @p767 :rule ho_cong :premises (@p766 @p493)) % 151.05/151.86 (step @p768 :rule trans :premises (@p767 @p765)) % 151.05/151.86 (step @p769 :rule cong :premises (@p768 @p755) :args (@t703)) % 151.05/151.86 (step @p770 :rule cong :premises (@p769) :args (@t704)) % 151.05/151.86 (step @p771 :rule cong :premises (@p770) :args (@t705)) % 151.05/151.86 (step @p772 :rule trans :premises (@p771 @p754)) % 151.05/151.86 (step @p773 :rule cong :premises (@p772) :args (@t706)) % 151.05/151.86 (step @p774 :rule nary_cong :premises (@p773 @p751) :args (@t707)) % 151.05/151.86 (step @p775 :rule beta-reduce :args ((= (_ (lambda @t400 (and (not (forall @t423 (not (= @t170 @t701)))) (not (= @t170 @t484)))) @t418) @t707))) % 151.05/151.86 (step @p776 :rule trans :premises (@p775 @p774)) % 151.05/151.86 (step @p777 :rule refl :args (@t418)) % 151.05/151.86 (step @p778 :rule eq-symm :args (@t484 @t170)) % 151.05/151.86 (step @p779 :rule cong :premises (@p778) :args (@t708)) % 151.05/151.86 (step @p780 :rule refl :args ((tptp.ord_Least_nat @t709))) % 151.05/151.86 (step @p781 :rule refl :args (@t478)) % 151.05/151.86 (step @p782 :rule cong :premises (@p781) :args (@t479)) % 151.05/151.86 (step @p783 :rule nary_cong :premises (@p782 @p398) :args (@t480)) % 151.05/151.86 (step @p784 :rule cong :premises (@p783) :args (@t481)) % 151.05/151.86 (step @p785 :rule cong :premises (@p784) :args (@t482)) % 151.05/151.86 (step @p786 :rule cong :premises (@p785) :args (@t483)) % 151.05/151.86 (step @p787 :rule cong :premises (@p786) :args (@t700)) % 151.05/151.86 (step @p788 :rule trans :premises (@p787 @p780)) % 151.05/151.86 (step @p789 :rule ho_cong :premises (@p407 @p786)) % 151.05/151.86 (step @p790 :rule cong :premises (@p789 @p788) :args ((= @t484 @t700))) % 151.05/151.86 (step @p791 :rule symm :premises (@p790)) % 151.05/151.86 (step @p792 :rule refl :args ((_ tptp.ord_Least_nat @t709))) % 151.05/151.86 (step @p793 :rule eq_resolve :premises (@p792 @p791)) % 151.05/151.86 (step @p794 :rule cong :premises (@p793 @p395) :args (@t710)) % 151.05/151.86 (step @p795 :rule cong :premises (@p414 @p794) :args (@t711)) % 151.05/151.86 (step @p796 :rule cong :premises (@p795) :args (@t712)) % 151.05/151.86 (step @p797 :rule cong :premises (@p796) :args (@t713)) % 151.05/151.86 (step @p798 :rule cong :premises (@p797) :args (@t714)) % 151.05/151.86 (step @p799 :rule nary_cong :premises (@p798 @p779) :args (@t715)) % 151.05/151.86 (step @p800 :rule cong :premises (@p799) :args (@t716)) % 151.05/151.86 (step @p801 :rule beta-reduce :args ((= (_ @t540 @t484) @t716))) % 151.05/151.86 (step @p802 :rule trans :premises (@p801 @p800)) % 151.05/151.86 (step @p803 :rule ho_cong :premises (@p423 @p292)) % 151.05/151.86 (step @p804 :rule trans :premises (@p803 @p802)) % 151.05/151.86 (step @p805 :rule ho_cong :premises (@p804 @p777)) % 151.05/151.86 (step @p806 :rule trans :premises (@p805 @p776)) % 151.05/151.86 (step @p807 :rule cong :premises (@p806) :args ((not (_ (_ @t540 @t493) @t418)))) % 151.05/151.86 (step @p808 :rule ho_cong :premises (@p455 @p357)) % 151.05/151.86 (step @p809 :rule ho_cong :premises (@p808 @p777)) % 151.05/151.86 (step @p810 :rule cong :premises (@p809) :args (@t419)) % 151.05/151.86 (step @p811 :rule trans :premises (@p810 @p807)) % 151.05/151.86 (step @p812 :rule trans :premises (@p811 @p750 @p749 @p742 @p741)) % 151.05/151.86 (step @p813 :rule eq_resolve :premises (@p253 @p812)) % 151.05/151.86 (step @p814 :rule not_and :premises (@p813)) % 151.05/151.86 (step @p815 :rule eq_resolve :premises (@p814 @p736)) % 151.05/151.86 (step @p816 :rule chain_m_resolution :premises (@p815 @p733) :args (@t686 @t554 (@list @t684))) % 151.05/151.86 (step @p817 :rule instantiate :premises (@p816) :args ((@list @t676))) % 151.05/151.86 (step @p818 :rule bool-double-not-elim :args (@t717)) % 151.05/151.86 (step @p819 :rule refl :args (@t718)) % 151.05/151.86 (step @p820 :rule refl :args (@t719)) % 151.05/151.86 (step @p821 :rule refl :args (@t552)) % 151.05/151.86 (step @p822 :rule refl :args (@t721)) % 151.05/151.86 (step @p823 :rule nary_cong :premises (@p822 @p821 @p820 @p819 @p818) :args ((or @t721 @t552 @t719 @t718 (not @t722)))) % 151.05/151.86 (assume-push @p866 @t717) % 151.05/151.86 (assume-push @p867 @t722) % 151.05/151.86 (step @p826 :rule evaluate :args ((= true false))) % 151.05/151.86 (step @p827 :rule false_intro :premises (@p817)) % 151.05/151.86 (step @p828 :rule refl :args (@t676)) % 151.05/151.86 (step @p829 :rule symm :premises (@p361)) % 151.05/151.86 (step @p830 :rule cong :premises (@p728 @p829) :args (@t668)) % 151.05/151.86 (step @p831 :rule cong :premises (@p830 @p828) :args (@t677)) % 151.05/151.86 (step @p832 :rule chain_m_resolution :premises (@p722 @p707) :args (@t678 @t554 @t681)) % 151.05/151.86 (step @p833 :rule cong :premises (@p729 @p549) :args (@t683)) % 151.05/151.86 (step @p834 :rule trans :premises (@p833 @p832 @p831)) % 151.05/151.86 (step @p835 :rule true_intro :premises (@p834)) % 151.05/151.86 (step @p836 :rule symm :premises (@p835)) % 151.05/151.86 (step @p837 :rule trans :premises (@p836 @p827)) % 151.05/151.86 (step @p838 false :rule eq_resolve :premises (@p837 @p826)) % 151.05/151.86 (step-pop @p868 :rule scope :premises (@p838)) % 151.05/151.86 (step-pop @p869 :rule scope :premises (@p868)) % 151.05/151.86 (step @p839 :rule process_scope :premises (@p869) :args (false)) % 151.05/151.86 (assume-push @p870 @t720) % 151.05/151.86 (assume-push @p871 @t551) % 151.05/151.86 (assume-push @p872 @t583) % 151.05/151.86 (assume-push @p873 @t678) % 151.05/151.86 (assume-push @p874 @t722) % 151.05/151.86 (step @p828 :rule refl :args (@t676)) % 151.05/151.86 (step @p829 :rule symm :premises (@p361)) % 151.05/151.86 (step @p830 :rule cong :premises (@p728 @p829) :args (@t668)) % 151.05/151.86 (step @p831 :rule cong :premises (@p830 @p828) :args (@t677)) % 151.05/151.86 (step @p847 :rule trans :premises (@p730 @p723 @p831)) % 151.05/151.86 (step @p848 :rule and_intro :premises (@p847 @p817)) % 151.05/151.86 (step-pop @p875 :rule scope :premises (@p848)) % 151.05/151.86 (step-pop @p876 :rule scope :premises (@p875)) % 151.05/151.86 (step-pop @p877 :rule scope :premises (@p876)) % 151.05/151.86 (step-pop @p878 :rule scope :premises (@p877)) % 151.05/151.86 (step-pop @p879 :rule scope :premises (@p878)) % 151.05/151.86 (step @p849 :rule process_scope :premises (@p879) :args (@t723)) % 151.05/151.86 (step @p855 :rule implies_elim :premises (@p849)) % 151.05/151.86 (step @p856 :rule resolution :premises (@p855 @p839) :args (true @t723)) % 151.05/151.86 (step @p857 :rule not_and :premises (@p856)) % 151.05/151.86 (step @p858 :rule eq_resolve :premises (@p857 @p823)) % 151.05/151.86 (step @p859 false :rule chain_m_resolution :premises (@p858 @p817 @p723 @p549 @p474 @p361) :args (false (@list true false false false false) (@list @t717 @t678 @t583 @t551 @t720))) % 151.05/151.86 ) % 151.05/151.86 % SZS output end Proof % 151.05/151.86 % cvc5 exiting %------------------------------------------------------------------------------