%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP132^1 : 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 : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:25:09 AM UTC 2026 % Result : Theorem 0.40s 0.74s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP132^1 : TPTP v9.2.1. Released v7.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n011.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 04:15:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.40/0.56 %----Proving TH0 % 0.40/0.74 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.74 % SZS status Theorem % 0.40/0.74 % SZS output start Proof % 0.40/0.74 ( % 0.40/0.74 (declare-sort tptp.set_nat 0) % 0.40/0.74 (declare-sort tptp.nat 0) % 0.40/0.74 (declare-sort tptp.set_set_nat 0) % 0.40/0.74 (declare-const tptp.ord_less_eq_set_nat (-> tptp.set_nat tptp.set_nat Bool)) % 0.40/0.74 (declare-const tptp.collect_set_nat (-> (-> tptp.set_nat Bool) tptp.set_set_nat)) % 0.40/0.74 (declare-const tptp.ord_less_eq_nat (-> tptp.nat tptp.nat Bool)) % 0.40/0.74 (declare-const tptp.collect_nat (-> (-> tptp.nat Bool) tptp.set_nat)) % 0.40/0.74 (declare-const tptp.if_nat (-> Bool tptp.nat tptp.nat tptp.nat)) % 0.40/0.74 (declare-const tptp.times_times_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.40/0.74 (declare-const tptp.groups1842438620at_nat (-> (-> tptp.nat tptp.nat) tptp.set_nat tptp.nat)) % 0.40/0.74 (declare-const tptp.one_one_nat tptp.nat) % 0.40/0.74 (declare-const tptp.zero_zero_nat tptp.nat) % 0.40/0.74 (declare-const tptp.member_nat (-> tptp.nat tptp.set_nat Bool)) % 0.40/0.74 (declare-const tptp.member_set_nat (-> tptp.set_nat tptp.set_set_nat Bool)) % 0.40/0.74 (declare-const tptp.ord_le1613022364et_nat (-> tptp.set_set_nat tptp.set_set_nat Bool)) % 0.40/0.74 (declare-const tptp.ord_less_nat (-> tptp.nat tptp.nat Bool)) % 0.40/0.74 (declare-const tptp.minus_minus_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.40/0.74 (declare-const tptp.k tptp.nat) % 0.40/0.74 (declare-const tptp.p (-> tptp.nat tptp.nat)) % 0.40/0.74 (declare-const tptp.n tptp.nat) % 0.40/0.74 (define tptp.set_or1086813439et_nat () (let ((_let_1 (@var "U" tptp.set_nat))) (let ((_let_2 (@var "X4" tptp.set_nat))) (lambda (@list _let_1) (_ tptp.collect_set_nat (lambda (@list _let_2) (_ (_ tptp.ord_less_eq_set_nat _let_2) _let_1))))))) % 0.40/0.74 (define tptp.set_ord_atMost_nat () (let ((_let_1 (@var "U" tptp.nat))) (let ((_let_2 (@var "X4" tptp.nat))) (lambda (@list _let_1) (_ tptp.collect_nat (lambda (@list _let_2) (_ (_ tptp.ord_less_eq_nat _let_2) _let_1))))))) % 0.40/0.74 (define tptp.fun_upd_nat_nat () (let ((_let_1 (@var "Z2" tptp.nat))) (let ((_let_2 (@var "F2" (-> tptp.nat tptp.nat)))) (let ((_let_3 (@var "Y4" tptp.nat))) (let ((_let_4 (@var "X4" tptp.nat))) (lambda (@list _let_2 _let_4 _let_3 _let_1) (_ (_ (_ tptp.if_nat (= _let_1 _let_4)) _let_3) (_ _let_2 _let_1)))))))) % 0.40/0.74 (define tptp.number1551313001itions () (let ((_let_1 (@var "N" tptp.nat))) (let ((_let_2 (@var "I" tptp.nat))) (let ((_let_3 (@var "P3" (-> tptp.nat tptp.nat)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@list _let_2))) (lambda (@list _let_3 _let_1) (and (forall _let_5 (=> (not (= _let_4 tptp.zero_zero_nat)) (and (_ (_ tptp.ord_less_eq_nat tptp.one_one_nat) _let_2) (_ (_ tptp.ord_less_eq_nat _let_2) _let_1)))) (= (_ (_ tptp.groups1842438620at_nat (lambda _let_5 (_ (_ tptp.times_times_nat _let_4) _let_2))) (_ tptp.set_ord_atMost_nat _let_1)) _let_1))))))))) % 0.40/0.74 (define @t1 () (@var "Y" tptp.nat)) % 0.40/0.74 (define @t2 () (@var "X" tptp.nat)) % 0.40/0.74 (define @t3 () (= @t2 @t1)) % 0.40/0.74 (define @t4 () (_ tptp.set_ord_atMost_nat @t1)) % 0.40/0.74 (define @t5 () (_ tptp.set_ord_atMost_nat @t2)) % 0.40/0.74 (define @t6 () (@list @t2 @t1)) % 0.40/0.74 (define @t7 () (_ tptp.set_ord_atMost_nat tptp.n)) % 0.40/0.74 (define @t8 () (@var "I" tptp.nat)) % 0.40/0.74 (define @t9 () (_ tptp.p tptp.k)) % 0.40/0.74 (define @t10 () (@list @t8)) % 0.40/0.74 (define @t11 () (_ tptp.groups1842438620at_nat (lambda @t10 (_ (_ tptp.times_times_nat (_ (_ (_ (_ tptp.fun_upd_nat_nat tptp.p) tptp.k) (_ (_ tptp.minus_minus_nat @t9) tptp.one_one_nat)) @t8)) @t8)))) % 0.40/0.74 (define @t12 () (_ (_ tptp.minus_minus_nat tptp.n) tptp.k)) % 0.40/0.74 (define @t13 () (_ @t11 (_ tptp.set_ord_atMost_nat @t12))) % 0.40/0.74 (define @t14 () (lambda @t10 (_ (_ tptp.times_times_nat (_ tptp.p @t8)) @t8))) % 0.40/0.74 (define @t15 () (_ tptp.groups1842438620at_nat @t14)) % 0.40/0.74 (define @t16 () (_ (_ tptp.minus_minus_nat (_ @t15 @t7)) tptp.k)) % 0.40/0.74 (define @t17 () (@var "A" tptp.set_nat)) % 0.40/0.74 (define @t18 () (@var "B" tptp.set_nat)) % 0.40/0.74 (define @t19 () (@var "J" tptp.nat)) % 0.40/0.74 (define @t20 () (@var "G" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t21 () (@var "F" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t22 () (@list @t19)) % 0.40/0.74 (define @t23 () (_ tptp.groups1842438620at_nat @t20)) % 0.40/0.74 (define @t24 () (_ tptp.groups1842438620at_nat @t21)) % 0.40/0.74 (define @t25 () (_ @t24 @t17)) % 0.40/0.74 (define @t26 () (_ tptp.times_times_nat @t25)) % 0.40/0.74 (define @t27 () (@var "N" tptp.nat)) % 0.40/0.74 (define @t28 () (_ @t21 @t27)) % 0.40/0.74 (define @t29 () (@var "R" tptp.nat)) % 0.40/0.74 (define @t30 () (_ tptp.times_times_nat @t29)) % 0.40/0.74 (define @t31 () (@list @t27)) % 0.40/0.74 (define @t32 () (@var "K" tptp.nat)) % 0.40/0.74 (define @t33 () (@var "N2" tptp.nat)) % 0.40/0.74 (define @t34 () (_ tptp.times_times_nat @t33)) % 0.40/0.74 (define @t35 () (_ @t34 @t32)) % 0.40/0.74 (define @t36 () (@var "M" tptp.nat)) % 0.40/0.74 (define @t37 () (_ tptp.times_times_nat @t36)) % 0.40/0.74 (define @t38 () (_ @t37 @t32)) % 0.40/0.74 (define @t39 () (_ tptp.minus_minus_nat @t36)) % 0.40/0.74 (define @t40 () (_ @t39 @t33)) % 0.40/0.74 (define @t41 () (_ tptp.times_times_nat @t32)) % 0.40/0.74 (define @t42 () (_ @t41 @t33)) % 0.40/0.74 (define @t43 () (_ @t41 @t36)) % 0.40/0.74 (define @t44 () (@list @t32 @t36 @t33)) % 0.40/0.74 (define @t45 () (@var "Y" tptp.set_nat)) % 0.40/0.74 (define @t46 () (@var "X" tptp.set_nat)) % 0.40/0.74 (define @t47 () (_ tptp.ord_less_eq_set_nat @t46)) % 0.40/0.74 (define @t48 () (_ @t47 @t45)) % 0.40/0.74 (define @t49 () (@list @t46 @t45)) % 0.40/0.74 (define @t50 () (_ tptp.ord_less_eq_nat @t2)) % 0.40/0.74 (define @t51 () (_ @t50 @t1)) % 0.40/0.74 (define @t52 () (@var "K" tptp.set_nat)) % 0.40/0.74 (define @t53 () (@var "I2" tptp.set_nat)) % 0.40/0.74 (define @t54 () (@var "I2" tptp.nat)) % 0.40/0.74 (define @t55 () (_ tptp.ord_less_eq_nat @t54)) % 0.40/0.74 (define @t56 () (_ @t55 @t32)) % 0.40/0.74 (define @t57 () (_ tptp.minus_minus_nat @t33)) % 0.40/0.74 (define @t58 () (= @t33 tptp.one_one_nat)) % 0.40/0.74 (define @t59 () (and (= @t36 tptp.one_one_nat) @t58)) % 0.40/0.74 (define @t60 () (_ @t37 @t33)) % 0.40/0.74 (define @t61 () (@list @t36 @t33)) % 0.40/0.74 (define @t62 () (_ tptp.ord_less_eq_nat @t33)) % 0.40/0.74 (define @t63 () (@list @t33)) % 0.40/0.74 (define @t64 () (@var "J2" tptp.nat)) % 0.40/0.74 (define @t65 () (_ @t55 @t64)) % 0.40/0.74 (define @t66 () (@list @t54 @t64 @t32)) % 0.40/0.74 (define @t67 () (_ tptp.ord_less_eq_nat @t36)) % 0.40/0.74 (define @t68 () (_ @t67 @t33)) % 0.40/0.74 (define @t69 () (= @t36 @t33)) % 0.40/0.74 (define @t70 () (_ @t62 @t36)) % 0.40/0.74 (define @t71 () (@var "X2" tptp.nat)) % 0.40/0.74 (define @t72 () (@var "Y3" tptp.nat)) % 0.40/0.74 (define @t73 () (@var "P" (-> tptp.nat Bool))) % 0.40/0.74 (define @t74 () (_ @t73 @t72)) % 0.40/0.74 (define @t75 () (@list @t72)) % 0.40/0.74 (define @t76 () (_ @t73 @t71)) % 0.40/0.74 (define @t77 () (@list @t71)) % 0.40/0.74 (define @t78 () (@var "B2" tptp.nat)) % 0.40/0.74 (define @t79 () (@var "Y2" tptp.nat)) % 0.40/0.74 (define @t80 () (@list @t79)) % 0.40/0.74 (define @t81 () (@var "M3" tptp.nat)) % 0.40/0.74 (define @t82 () (@var "X3" tptp.nat)) % 0.40/0.74 (define @t83 () (@list @t82)) % 0.40/0.74 (define @t84 () (@var "M2" tptp.nat)) % 0.40/0.74 (define @t85 () (_ tptp.ord_less_eq_nat @t71)) % 0.40/0.74 (define @t86 () (@var "P2" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t87 () (_ tptp.number1551313001itions @t86)) % 0.40/0.74 (define @t88 () (_ @t87 @t33)) % 0.40/0.74 (define @t89 () (@var "L" tptp.nat)) % 0.40/0.74 (define @t90 () (_ tptp.minus_minus_nat @t89)) % 0.40/0.74 (define @t91 () (@list @t36 @t33 @t89)) % 0.40/0.74 (define @t92 () (@var "A2" tptp.nat)) % 0.40/0.74 (define @t93 () (_ tptp.ord_less_eq_nat @t78)) % 0.40/0.74 (define @t94 () (_ @t93 @t92)) % 0.40/0.74 (define @t95 () (@var "C" tptp.nat)) % 0.40/0.74 (define @t96 () (_ tptp.minus_minus_nat @t95)) % 0.40/0.74 (define @t97 () (_ @t93 @t95)) % 0.40/0.74 (define @t98 () (_ tptp.ord_less_eq_nat @t92)) % 0.40/0.74 (define @t99 () (_ @t98 @t95)) % 0.40/0.74 (define @t100 () (@list @t92 @t95 @t78)) % 0.40/0.74 (define @t101 () (_ @t57 @t32)) % 0.40/0.74 (define @t102 () (_ @t39 @t32)) % 0.40/0.74 (define @t103 () (_ tptp.ord_less_eq_nat @t32)) % 0.40/0.74 (define @t104 () (_ @t103 @t33)) % 0.40/0.74 (define @t105 () (_ @t103 @t36)) % 0.40/0.74 (define @t106 () (_ tptp.times_times_nat @t64)) % 0.40/0.74 (define @t107 () (_ tptp.ord_less_eq_nat (_ (_ tptp.times_times_nat @t54) @t32))) % 0.40/0.74 (define @t108 () (_ @t37 @t36)) % 0.40/0.74 (define @t109 () (@list @t36)) % 0.40/0.74 (define @t110 () (_ tptp.times_times_nat tptp.one_one_nat)) % 0.40/0.74 (define @t111 () (@var "K2" tptp.set_nat)) % 0.40/0.74 (define @t112 () (@var "I3" tptp.nat)) % 0.40/0.74 (define @t113 () (@list @t112)) % 0.40/0.74 (define @t114 () (_ @t23 @t17)) % 0.40/0.74 (define @t115 () (@var "X4" tptp.nat)) % 0.40/0.74 (define @t116 () (@list @t115)) % 0.40/0.74 (define @t117 () (_ @t21 @t71)) % 0.40/0.74 (define @t118 () (_ @t20 @t71)) % 0.40/0.74 (define @t119 () (_ tptp.member_nat @t71)) % 0.40/0.74 (define @t120 () (_ @t119 @t17)) % 0.40/0.74 (define @t121 () (_ tptp.set_ord_atMost_nat @t33)) % 0.40/0.74 (define @t122 () (@list @t86 @t33)) % 0.40/0.74 (define @t123 () (_ @t73 @t92)) % 0.40/0.74 (define @t124 () (_ tptp.collect_nat @t73)) % 0.40/0.74 (define @t125 () (@list @t17)) % 0.40/0.74 (define @t126 () (@var "Q" (-> tptp.nat Bool))) % 0.40/0.74 (define @t127 () (@var "T" tptp.set_nat)) % 0.40/0.74 (define @t128 () (@var "H" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t129 () (_ tptp.groups1842438620at_nat @t128)) % 0.40/0.74 (define @t130 () (@var "S" tptp.set_nat)) % 0.40/0.74 (define @t131 () (@var "A3" tptp.nat)) % 0.40/0.74 (define @t132 () (_ @t20 @t131)) % 0.40/0.74 (define @t133 () (@var "J2" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t134 () (_ @t133 @t131)) % 0.40/0.74 (define @t135 () (_ tptp.member_nat @t131)) % 0.40/0.74 (define @t136 () (_ @t135 @t130)) % 0.40/0.74 (define @t137 () (@list @t131)) % 0.40/0.74 (define @t138 () (@var "B3" tptp.nat)) % 0.40/0.74 (define @t139 () (@var "I2" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t140 () (_ @t139 @t138)) % 0.40/0.74 (define @t141 () (_ (_ tptp.member_nat @t138) @t127)) % 0.40/0.74 (define @t142 () (@list @t138)) % 0.40/0.74 (define @t143 () (@var "Gamma" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t144 () (@var "Phi" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t145 () (= (_ (_ tptp.groups1842438620at_nat @t144) @t17) (_ (_ tptp.groups1842438620at_nat @t143) @t18))) % 0.40/0.74 (define @t146 () (_ @t128 @t71)) % 0.40/0.74 (define @t147 () (= (_ @t143 @t146) (_ @t144 @t71))) % 0.40/0.74 (define @t148 () (@var "K" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t149 () (_ (_ tptp.member_nat @t146) @t18)) % 0.40/0.74 (define @t150 () (_ @t148 @t79)) % 0.40/0.74 (define @t151 () (_ (_ tptp.member_nat @t79) @t18)) % 0.40/0.74 (define @t152 () (@var "Ya" tptp.nat)) % 0.40/0.74 (define @t153 () (_ @t119 @t18)) % 0.40/0.74 (define @t154 () (= @t17 @t18)) % 0.40/0.74 (define @t155 () (_ tptp.minus_minus_nat @t54)) % 0.40/0.74 (define @t156 () (@var "G" (-> tptp.nat tptp.nat tptp.nat))) % 0.40/0.74 (define @t157 () (_ @t156 @t8)) % 0.40/0.74 (define @t158 () (_ tptp.times_times_nat @t92)) % 0.40/0.74 (define @t159 () (@list @t92)) % 0.40/0.74 (define @t160 () (@var "Z" tptp.nat)) % 0.40/0.74 (define @t161 () (_ (_ tptp.fun_upd_nat_nat @t21) @t2)) % 0.40/0.74 (define @t162 () (_ @t161 @t1)) % 0.40/0.74 (define @t163 () (_ @t21 @t2)) % 0.40/0.74 (define @t164 () (@list @t2)) % 0.40/0.74 (define @t165 () (= (_ (_ tptp.groups1842438620at_nat (lambda @t10 (_ (_ tptp.times_times_nat (_ @t86 @t8)) @t8))) @t121) @t33)) % 0.40/0.74 (define @t166 () (_ tptp.ord_less_eq_nat tptp.one_one_nat)) % 0.40/0.74 (define @t167 () (@var "I4" tptp.nat)) % 0.40/0.74 (define @t168 () (= @t33 tptp.zero_zero_nat)) % 0.40/0.74 (define @t169 () (_ tptp.times_times_nat tptp.zero_zero_nat)) % 0.40/0.74 (define @t170 () (= @t78 tptp.zero_zero_nat)) % 0.40/0.74 (define @t171 () (= @t92 tptp.zero_zero_nat)) % 0.40/0.74 (define @t172 () (or @t171 @t170)) % 0.40/0.74 (define @t173 () (_ @t158 @t78)) % 0.40/0.74 (define @t174 () (= @t173 tptp.zero_zero_nat)) % 0.40/0.74 (define @t175 () (@list @t92 @t78)) % 0.40/0.74 (define @t176 () (= @t92 @t78)) % 0.40/0.74 (define @t177 () (= @t95 tptp.zero_zero_nat)) % 0.40/0.74 (define @t178 () (or @t177 @t176)) % 0.40/0.74 (define @t179 () (_ tptp.times_times_nat @t95)) % 0.40/0.74 (define @t180 () (_ @t179 @t78)) % 0.40/0.74 (define @t181 () (_ @t179 @t92)) % 0.40/0.74 (define @t182 () (= @t181 @t180)) % 0.40/0.74 (define @t183 () (@list @t95 @t92 @t78)) % 0.40/0.74 (define @t184 () (_ tptp.times_times_nat @t78)) % 0.40/0.74 (define @t185 () (_ @t184 @t95)) % 0.40/0.74 (define @t186 () (_ @t158 @t95)) % 0.40/0.74 (define @t187 () (= @t186 @t185)) % 0.40/0.74 (define @t188 () (_ tptp.minus_minus_nat tptp.zero_zero_nat)) % 0.40/0.74 (define @t189 () (_ tptp.minus_minus_nat @t92)) % 0.40/0.74 (define @t190 () (_ tptp.ord_less_eq_nat tptp.zero_zero_nat)) % 0.40/0.74 (define @t191 () (_ @t190 @t92)) % 0.40/0.74 (define @t192 () (= @t36 tptp.zero_zero_nat)) % 0.40/0.74 (define @t193 () (= @t32 tptp.zero_zero_nat)) % 0.40/0.74 (define @t194 () (or @t69 @t193)) % 0.40/0.74 (define @t195 () (= @t43 @t42)) % 0.40/0.74 (define @t196 () (@list @t36 @t32 @t33)) % 0.40/0.74 (define @t197 () (= @t40 tptp.zero_zero_nat)) % 0.40/0.74 (define @t198 () (_ tptp.ord_less_nat tptp.zero_zero_nat)) % 0.40/0.74 (define @t199 () (not @t170)) % 0.40/0.74 (define @t200 () (not @t171)) % 0.40/0.74 (define @t201 () (not @t174)) % 0.40/0.74 (define @t202 () (not @t177)) % 0.40/0.74 (define @t203 () (= @t114 tptp.zero_zero_nat)) % 0.40/0.74 (define @t204 () (_ @t98 tptp.zero_zero_nat)) % 0.40/0.74 (define @t205 () (_ @t57 @t36)) % 0.40/0.74 (define @t206 () (_ @t190 @t95)) % 0.40/0.74 (define @t207 () (_ @t98 @t78)) % 0.40/0.74 (define @t208 () (@list @t92 @t78 @t95)) % 0.40/0.74 (define @t209 () (_ @t184 @t92)) % 0.40/0.74 (define @t210 () (_ @t93 tptp.zero_zero_nat)) % 0.40/0.74 (define @t211 () (_ tptp.ord_less_eq_nat @t173)) % 0.40/0.74 (define @t212 () (_ @t211 tptp.zero_zero_nat)) % 0.40/0.74 (define @t213 () (_ @t190 @t78)) % 0.40/0.74 (define @t214 () (_ tptp.ord_less_eq_nat @t186)) % 0.40/0.74 (define @t215 () (@var "D" tptp.nat)) % 0.40/0.74 (define @t216 () (=> @t206 (_ @t214 (_ @t184 @t215)))) % 0.40/0.74 (define @t217 () (_ tptp.ord_less_eq_nat @t95)) % 0.40/0.74 (define @t218 () (_ @t217 @t215)) % 0.40/0.74 (define @t219 () (@list @t92 @t78 @t95 @t215)) % 0.40/0.74 (define @t220 () (_ tptp.ord_less_eq_nat @t117)) % 0.40/0.74 (define @t221 () (@list @t17 @t21)) % 0.40/0.74 (define @t222 () (@var "B2" tptp.set_nat)) % 0.40/0.74 (define @t223 () (@var "A2" tptp.set_nat)) % 0.40/0.74 (define @t224 () (= @t223 @t222)) % 0.40/0.74 (define @t225 () (_ tptp.ord_less_eq_set_nat @t223)) % 0.40/0.74 (define @t226 () (_ @t225 @t222)) % 0.40/0.74 (define @t227 () (_ tptp.ord_less_eq_set_nat @t222)) % 0.40/0.74 (define @t228 () (_ @t227 @t223)) % 0.40/0.74 (define @t229 () (@list @t78 @t92)) % 0.40/0.74 (define @t230 () (@var "B4" tptp.set_nat)) % 0.40/0.74 (define @t231 () (@var "A4" tptp.set_nat)) % 0.40/0.74 (define @t232 () (_ (_ tptp.ord_less_eq_set_nat @t231) @t230)) % 0.40/0.74 (define @t233 () (_ (_ tptp.ord_less_eq_set_nat @t230) @t231)) % 0.40/0.74 (define @t234 () (@list @t231 @t230)) % 0.40/0.74 (define @t235 () (@var "Z3" tptp.set_nat)) % 0.40/0.74 (define @t236 () (@var "Y5" tptp.set_nat)) % 0.40/0.74 (define @t237 () (lambda (@list @t236 @t235) (= @t236 @t235))) % 0.40/0.74 (define @t238 () (@var "B4" tptp.nat)) % 0.40/0.74 (define @t239 () (@var "A4" tptp.nat)) % 0.40/0.74 (define @t240 () (_ (_ tptp.ord_less_eq_nat @t239) @t238)) % 0.40/0.74 (define @t241 () (_ (_ tptp.ord_less_eq_nat @t238) @t239)) % 0.40/0.74 (define @t242 () (@list @t239 @t238)) % 0.40/0.74 (define @t243 () (@var "Z3" tptp.nat)) % 0.40/0.74 (define @t244 () (@var "Y5" tptp.nat)) % 0.40/0.74 (define @t245 () (lambda (@list @t244 @t243) (= @t244 @t243))) % 0.40/0.74 (define @t246 () (@var "C" tptp.set_nat)) % 0.40/0.74 (define @t247 () (_ tptp.ord_less_eq_set_nat @t246)) % 0.40/0.74 (define @t248 () (@list @t78 @t92 @t95)) % 0.40/0.74 (define @t249 () (@var "P" (-> tptp.nat tptp.nat Bool))) % 0.40/0.74 (define @t250 () (_ @t249 @t131)) % 0.40/0.74 (define @t251 () (_ @t250 @t138)) % 0.40/0.74 (define @t252 () (@list @t131 @t138)) % 0.40/0.74 (define @t253 () (=> (forall @t252 (=> (_ (_ @t249 @t138) @t131) @t251)) (_ (_ @t249 @t92) @t78))) % 0.40/0.74 (define @t254 () (@list @t249 @t92 @t78)) % 0.40/0.74 (define @t255 () (@var "Z" tptp.set_nat)) % 0.40/0.74 (define @t256 () (_ tptp.ord_less_eq_set_nat @t45)) % 0.40/0.74 (define @t257 () (_ @t50 @t160)) % 0.40/0.74 (define @t258 () (_ tptp.ord_less_eq_nat @t1)) % 0.40/0.74 (define @t259 () (_ @t258 @t160)) % 0.40/0.74 (define @t260 () (@list @t2 @t1 @t160)) % 0.40/0.74 (define @t261 () (_ @t225 @t246)) % 0.40/0.74 (define @t262 () (@list @t223 @t222 @t246)) % 0.40/0.74 (define @t263 () (= @t78 @t95)) % 0.40/0.74 (define @t264 () (_ @t227 @t246)) % 0.40/0.74 (define @t265 () (=> @t264 @t261)) % 0.40/0.74 (define @t266 () (=> @t97 @t99)) % 0.40/0.74 (define @t267 () (= @t46 @t45)) % 0.40/0.74 (define @t268 () (_ @t256 @t46)) % 0.40/0.74 (define @t269 () (_ @t258 @t2)) % 0.40/0.74 (define @t270 () (@list @t1 @t2)) % 0.40/0.74 (define @t271 () (not @t51)) % 0.40/0.74 (define @t272 () (_ tptp.ord_less_eq_nat @t160)) % 0.40/0.74 (define @t273 () (_ @t272 @t2)) % 0.40/0.74 (define @t274 () (_ @t272 @t1)) % 0.40/0.74 (define @t275 () (@var "X4" tptp.set_nat)) % 0.40/0.74 (define @t276 () (@var "Y4" tptp.set_nat)) % 0.40/0.74 (define @t277 () (_ tptp.ord_less_eq_set_nat @t275)) % 0.40/0.74 (define @t278 () (@var "Y4" tptp.nat)) % 0.40/0.74 (define @t279 () (_ tptp.ord_less_eq_nat @t115)) % 0.40/0.74 (define @t280 () (@var "F" (-> tptp.nat tptp.set_nat))) % 0.40/0.74 (define @t281 () (_ @t85 @t79)) % 0.40/0.74 (define @t282 () (@list @t71 @t79)) % 0.40/0.74 (define @t283 () (forall @t282 (=> @t281 (_ (_ tptp.ord_less_eq_set_nat (_ @t280 @t71)) (_ @t280 @t79))))) % 0.40/0.74 (define @t284 () (=> @t283 (_ (_ tptp.ord_less_eq_set_nat (_ @t280 @t92)) @t246))) % 0.40/0.74 (define @t285 () (_ @t280 @t78)) % 0.40/0.74 (define @t286 () (@list @t92 @t78 @t280 @t246)) % 0.40/0.74 (define @t287 () (@var "F" (-> tptp.set_nat tptp.nat))) % 0.40/0.74 (define @t288 () (@var "Y2" tptp.set_nat)) % 0.40/0.74 (define @t289 () (@var "X2" tptp.set_nat)) % 0.40/0.74 (define @t290 () (_ (_ tptp.ord_less_eq_set_nat @t289) @t288)) % 0.40/0.74 (define @t291 () (@list @t289 @t288)) % 0.40/0.74 (define @t292 () (forall @t291 (=> @t290 (_ (_ tptp.ord_less_eq_nat (_ @t287 @t289)) (_ @t287 @t288))))) % 0.40/0.74 (define @t293 () (=> @t292 (_ (_ tptp.ord_less_eq_nat (_ @t287 @t223)) @t95))) % 0.40/0.74 (define @t294 () (_ @t287 @t222)) % 0.40/0.74 (define @t295 () (@list @t223 @t222 @t287 @t95)) % 0.40/0.74 (define @t296 () (@var "F" (-> tptp.set_nat tptp.set_nat))) % 0.40/0.74 (define @t297 () (forall @t291 (=> @t290 (_ (_ tptp.ord_less_eq_set_nat (_ @t296 @t289)) (_ @t296 @t288))))) % 0.40/0.74 (define @t298 () (=> @t297 (_ (_ tptp.ord_less_eq_set_nat (_ @t296 @t223)) @t246))) % 0.40/0.74 (define @t299 () (_ @t296 @t222)) % 0.40/0.74 (define @t300 () (@list @t223 @t222 @t296 @t246)) % 0.40/0.74 (define @t301 () (_ @t21 @t92)) % 0.40/0.74 (define @t302 () (_ @t21 @t79)) % 0.40/0.74 (define @t303 () (forall @t282 (=> @t281 (_ @t220 @t302)))) % 0.40/0.74 (define @t304 () (=> @t303 (_ (_ tptp.ord_less_eq_nat @t301) @t95))) % 0.40/0.74 (define @t305 () (_ @t21 @t78)) % 0.40/0.74 (define @t306 () (= @t305 @t95)) % 0.40/0.74 (define @t307 () (@list @t92 @t78 @t21 @t95)) % 0.40/0.74 (define @t308 () (=> @t97 (=> @t283 (_ @t225 (_ @t280 @t95))))) % 0.40/0.74 (define @t309 () (@list @t223 @t280 @t78 @t95)) % 0.40/0.74 (define @t310 () (=> @t264 (=> @t292 (_ @t98 (_ @t287 @t246))))) % 0.40/0.74 (define @t311 () (@list @t92 @t287 @t222 @t246)) % 0.40/0.74 (define @t312 () (=> @t264 (=> @t297 (_ @t225 (_ @t296 @t246))))) % 0.40/0.74 (define @t313 () (@list @t223 @t296 @t222 @t246)) % 0.40/0.74 (define @t314 () (_ @t21 @t95)) % 0.40/0.74 (define @t315 () (=> @t97 (=> @t303 (_ @t98 @t314)))) % 0.40/0.74 (define @t316 () (= @t92 @t305)) % 0.40/0.74 (define @t317 () (@list @t92 @t21 @t78 @t95)) % 0.40/0.74 (define @t318 () (_ @t158 @t185)) % 0.40/0.74 (define @t319 () (= @t163 @t1)) % 0.40/0.74 (define @t320 () (= @t162 @t21)) % 0.40/0.74 (define @t321 () (@list @t21 @t2 @t1)) % 0.40/0.74 (define @t322 () (@var "M" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t323 () (_ tptp.fun_upd_nat_nat @t322)) % 0.40/0.74 (define @t324 () (@var "F2" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t325 () (_ (_ tptp.minus_minus_nat @t78) @t95)) % 0.40/0.74 (define @t326 () (_ (_ tptp.ord_less_eq_set_nat @t17) @t18)) % 0.40/0.74 (define @t327 () (@list @t17 @t18)) % 0.40/0.74 (define @t328 () (_ @t86 @t32)) % 0.40/0.74 (define @t329 () (_ @t198 @t33)) % 0.40/0.74 (define @t330 () (_ tptp.ord_less_nat @t33)) % 0.40/0.74 (define @t331 () (_ (_ tptp.ord_less_nat @t36) @t33)) % 0.40/0.74 (define @t332 () (_ @t198 @t32)) % 0.40/0.74 (define @t333 () (and @t332 @t331)) % 0.40/0.74 (define @t334 () (=> @t332 @t68)) % 0.40/0.74 (define @t335 () (not @t176)) % 0.40/0.74 (define @t336 () (_ tptp.ord_less_nat @t78)) % 0.40/0.74 (define @t337 () (_ @t336 @t92)) % 0.40/0.74 (define @t338 () (_ tptp.ord_less_nat @t92)) % 0.40/0.74 (define @t339 () (_ @t338 @t78)) % 0.40/0.74 (define @t340 () (_ tptp.ord_less_nat @t1)) % 0.40/0.74 (define @t341 () (_ @t340 @t2)) % 0.40/0.74 (define @t342 () (_ tptp.ord_less_nat @t2)) % 0.40/0.74 (define @t343 () (_ @t342 @t1)) % 0.40/0.74 (define @t344 () (not @t343)) % 0.40/0.74 (define @t345 () (_ tptp.ord_less_nat @t95)) % 0.40/0.74 (define @t346 () (@var "M4" tptp.nat)) % 0.40/0.74 (define @t347 () (@var "P5" (-> tptp.nat Bool))) % 0.40/0.74 (define @t348 () (@var "X5" tptp.nat)) % 0.40/0.74 (define @t349 () (@var "P4" (-> tptp.nat Bool))) % 0.40/0.74 (define @t350 () (not @t341)) % 0.40/0.74 (define @t351 () (_ @t338 @t95)) % 0.40/0.74 (define @t352 () (_ @t336 @t95)) % 0.40/0.74 (define @t353 () (=> @t352 @t351)) % 0.40/0.74 (define @t354 () (not @t3)) % 0.40/0.74 (define @t355 () (@var "P" Bool)) % 0.40/0.74 (define @t356 () (@var "X_1" tptp.nat)) % 0.40/0.74 (define @t357 () (forall @t282 (=> (_ (_ tptp.ord_less_nat @t71) @t79) (_ (_ tptp.ord_less_nat @t117) @t302)))) % 0.40/0.74 (define @t358 () (=> @t357 (_ (_ tptp.ord_less_nat @t301) @t95))) % 0.40/0.74 (define @t359 () (=> @t352 (=> @t357 (_ @t338 @t314)))) % 0.40/0.74 (define @t360 () (_ @t73 @t33)) % 0.40/0.74 (define @t361 () (@var "M5" tptp.nat)) % 0.40/0.74 (define @t362 () (_ @t73 @t361)) % 0.40/0.74 (define @t363 () (@var "N3" tptp.nat)) % 0.40/0.74 (define @t364 () (_ (_ tptp.ord_less_nat @t361) @t363)) % 0.40/0.74 (define @t365 () (@list @t361)) % 0.40/0.74 (define @t366 () (_ @t73 @t363)) % 0.40/0.74 (define @t367 () (@list @t363)) % 0.40/0.74 (define @t368 () (@list @t73 @t33)) % 0.40/0.74 (define @t369 () (= @t16 @t12)) % 0.40/0.74 (define @t370 () (not @t369)) % 0.40/0.74 (define @t371 () (@var "U" tptp.set_nat)) % 0.40/0.74 (define @t372 () (lambda (@list @t371) (_ tptp.collect_set_nat (lambda (@list @t275) (_ @t277 @t371))))) % 0.40/0.74 (define @t373 () (@var "U" tptp.nat)) % 0.40/0.74 (define @t374 () (lambda (@list @t373) (_ tptp.collect_nat (lambda @t116 (_ @t279 @t373))))) % 0.40/0.74 (define @t375 () (@var "Z2" tptp.nat)) % 0.40/0.74 (define @t376 () (lambda (@list @t324 @t115 @t278 @t375) (_ (_ (_ tptp.if_nat (= @t375 @t115)) @t278) (_ @t324 @t375)))) % 0.40/0.74 (define @t377 () (@var "P3" (-> tptp.nat tptp.nat))) % 0.40/0.74 (define @t378 () (_ @t377 @t8)) % 0.40/0.74 (define @t379 () (_ tptp.groups1842438620at_nat (lambda @t10 (_ (_ tptp.times_times_nat @t378) @t8)))) % 0.40/0.74 (define @t380 () (= (_ @t379 (_ tptp.set_ord_atMost_nat @t27)) @t27)) % 0.40/0.74 (define @t381 () (_ (_ tptp.ord_less_eq_nat @t8) @t27)) % 0.40/0.74 (define @t382 () (_ @t166 @t8)) % 0.40/0.74 (define @t383 () (and @t382 @t381)) % 0.40/0.74 (define @t384 () (not (= @t378 tptp.zero_zero_nat))) % 0.40/0.74 (define @t385 () (=> @t384 @t383)) % 0.40/0.74 (define @t386 () (forall @t10 @t385)) % 0.40/0.74 (define @t387 () (and @t386 @t380)) % 0.40/0.74 (define @t388 () (@list @t377 @t27)) % 0.40/0.74 (define @t389 () (lambda @t388 @t387)) % 0.40/0.74 (define @t390 () (lambda @t116 (_ @t279 tptp.n))) % 0.40/0.74 (define @t391 () (@purify @t390)) % 0.40/0.74 (define @t392 () (_ tptp.collect_nat @t391)) % 0.40/0.74 (define @t393 () (@purify @t14)) % 0.40/0.74 (define @t394 () (tptp.collect_nat @t391)) % 0.40/0.74 (define @t395 () (tptp.groups1842438620at_nat @t393 @t394)) % 0.40/0.74 (define @t396 () (_ tptp.groups1842438620at_nat @t393)) % 0.40/0.74 (define @t397 () (_ @t396 @t392)) % 0.40/0.74 (define @t398 () (_ tptp.collect_nat @t390)) % 0.40/0.74 (define @t399 () (_ @t15 @t398)) % 0.40/0.74 (define @t400 () (= tptp.n @t399)) % 0.40/0.74 (define @t401 () (tptp.ord_less_eq_nat tptp.one_one_nat @t8)) % 0.40/0.74 (define @t402 () (= tptp.zero_zero_nat (tptp.p @t8))) % 0.40/0.74 (define @t403 () (forall @t10 (or @t402 (and @t401 (tptp.ord_less_eq_nat @t8 tptp.n))))) % 0.40/0.74 (define @t404 () (and @t403 @t400)) % 0.40/0.74 (define @t405 () (_ tptp.collect_nat (lambda @t116 (_ @t279 @t27)))) % 0.40/0.74 (define @t406 () (tptp.ord_less_eq_nat @t8 @t27)) % 0.40/0.74 (define @t407 () (and @t401 @t406)) % 0.40/0.74 (define @t408 () (lambda @t31 (and (forall @t10 (or @t402 @t407)) (= @t27 (_ @t15 @t405))))) % 0.40/0.74 (define @t409 () (_ @t379 @t405)) % 0.40/0.74 (define @t410 () (_ @t377 @t8)) % 0.40/0.74 (define @t411 () (_ @t374 @t27)) % 0.40/0.74 (define @t412 () (= (_ @t379 @t411) @t27)) % 0.40/0.74 (define @t413 () (= tptp.zero_zero_nat @t378)) % 0.40/0.74 (define @t414 () (or @t413 @t383)) % 0.40/0.74 (define @t415 () (not @t413)) % 0.40/0.74 (define @t416 () (tptp.minus_minus_nat @t395 tptp.k)) % 0.40/0.74 (define @t417 () (tptp.minus_minus_nat tptp.n tptp.k)) % 0.40/0.74 (define @t418 () (_ (_ tptp.minus_minus_nat @t399) tptp.k)) % 0.40/0.74 (define @t419 () (= @t12 @t418)) % 0.40/0.74 (define @t420 () (_ @t374 tptp.n)) % 0.40/0.74 (define @t421 () (= (_ (_ tptp.minus_minus_nat (_ @t15 @t420)) tptp.k) @t12)) % 0.40/0.74 (define @t422 () (= tptp.n @t395)) % 0.40/0.74 (define @t423 () (= @t417 @t416)) % 0.40/0.74 (assume @p1 (_ (_ tptp.number1551313001itions tptp.p) tptp.n)) % 0.40/0.74 (assume @p2 (_ (_ tptp.ord_less_eq_nat tptp.k) tptp.n)) % 0.40/0.74 (assume @p3 (forall @t6 (= (= @t5 @t4) @t3))) % 0.40/0.74 (assume @p4 (= @t13 (_ @t11 @t7))) % 0.40/0.74 (assume @p5 (= @t13 @t16)) % 0.40/0.74 (assume @p6 (forall (@list @t21 @t17 @t20 @t18) (= (_ @t26 (_ @t23 @t18)) (_ (_ tptp.groups1842438620at_nat (lambda @t10 (_ (_ tptp.groups1842438620at_nat (lambda @t22 (_ (_ tptp.times_times_nat (_ @t21 @t8)) (_ @t20 @t19)))) @t18))) @t17)))) % 0.40/0.74 (assume @p7 (forall (@list @t29 @t21 @t17) (= (_ @t30 @t25) (_ (_ tptp.groups1842438620at_nat (lambda @t31 (_ @t30 @t28))) @t17)))) % 0.40/0.74 (assume @p8 (forall (@list @t21 @t17 @t29) (= (_ @t26 @t29) (_ (_ tptp.groups1842438620at_nat (lambda @t31 (_ (_ tptp.times_times_nat @t28) @t29))) @t17)))) % 0.40/0.74 (assume @p9 (forall (@list @t36 @t33 @t32) (= (_ (_ tptp.times_times_nat @t40) @t32) (_ (_ tptp.minus_minus_nat @t38) @t35)))) % 0.40/0.74 (assume @p10 (forall @t44 (= (_ @t41 @t40) (_ (_ tptp.minus_minus_nat @t43) @t42)))) % 0.40/0.74 (assume @p11 (forall @t49 (= (_ (_ tptp.ord_le1613022364et_nat (_ tptp.set_or1086813439et_nat @t46)) (_ tptp.set_or1086813439et_nat @t45)) @t48))) % 0.40/0.74 (assume @p12 (forall @t6 (= (_ (_ tptp.ord_less_eq_set_nat @t5) @t4) @t51))) % 0.40/0.74 (assume @p13 (forall (@list @t53 @t52) (= (_ (_ tptp.member_set_nat @t53) (_ tptp.set_or1086813439et_nat @t52)) (_ (_ tptp.ord_less_eq_set_nat @t53) @t52)))) % 0.40/0.74 (assume @p14 (forall (@list @t54 @t32) (= (_ (_ tptp.member_nat @t54) (_ tptp.set_ord_atMost_nat @t32)) @t56))) % 0.40/0.74 (assume @p15 (forall (@list @t54 @t33) (=> (_ @t55 @t33) (= (_ @t57 (_ @t57 @t54)) @t54)))) % 0.40/0.74 (assume @p16 (forall @t61 (= (= @t60 tptp.one_one_nat) @t59))) % 0.40/0.74 (assume @p17 (forall @t61 (= (= tptp.one_one_nat @t60) @t59))) % 0.40/0.74 (assume @p18 (forall @t63 (_ @t62 @t33))) % 0.40/0.74 (assume @p19 (forall @t66 (=> @t65 (=> (_ (_ tptp.ord_less_eq_nat @t64) @t32) @t56)))) % 0.40/0.74 (assume @p20 (forall @t61 (=> @t69 @t68))) % 0.40/0.74 (assume @p21 (forall @t61 (=> @t68 (=> @t70 @t69)))) % 0.40/0.74 (assume @p22 (forall @t61 (or @t68 @t70))) % 0.40/0.74 (assume @p23 (forall (@list @t73 @t32 @t78) (=> (_ @t73 @t32) (=> (forall @t80 (=> (_ @t73 @t79) (_ (_ tptp.ord_less_eq_nat @t79) @t78))) (exists @t77 (and @t76 (forall @t75 (=> @t74 (_ (_ tptp.ord_less_eq_nat @t72) @t71))))))))) % 0.40/0.74 (assume @p24 (forall (@list @t73 @t2 @t84) (=> (_ @t73 @t2) (=> (forall @t77 (=> @t76 (_ @t85 @t84))) (not (forall (@list @t81) (=> (_ @t73 @t81) (not (forall @t83 (=> (_ @t73 @t82) (_ (_ tptp.ord_less_eq_nat @t82) @t81))))))))))) % 0.40/0.74 (assume @p25 (forall (@list @t86 @t33 @t54) (=> @t88 (_ (_ tptp.ord_less_eq_nat (_ @t86 @t54)) @t33)))) % 0.40/0.74 (assume @p26 (forall @t91 (=> @t68 (_ (_ tptp.ord_less_eq_nat (_ @t90 @t33)) (_ @t90 @t36))))) % 0.40/0.74 (assume @p27 (forall @t100 (=> @t99 (=> @t97 (= (_ (_ tptp.ord_less_eq_nat (_ @t96 @t92)) (_ @t96 @t78)) @t94))))) % 0.40/0.74 (assume @p28 (forall @t61 (_ (_ tptp.ord_less_eq_nat @t40) @t36))) % 0.40/0.74 (assume @p29 (forall @t91 (=> @t68 (_ (_ tptp.ord_less_eq_nat (_ @t39 @t89)) (_ @t57 @t89))))) % 0.40/0.74 (assume @p30 (forall @t44 (=> @t105 (=> @t104 (= (_ (_ tptp.minus_minus_nat @t102) @t101) @t40))))) % 0.40/0.74 (assume @p31 (forall @t44 (=> @t105 (=> @t104 (= (_ (_ tptp.ord_less_eq_nat @t102) @t101) @t68))))) % 0.40/0.74 (assume @p32 (forall @t44 (=> @t105 (=> @t104 (= (= @t102 @t101) @t69))))) % 0.40/0.74 (assume @p33 (forall @t66 (=> @t65 (_ (_ tptp.ord_less_eq_nat (_ @t41 @t54)) (_ @t41 @t64))))) % 0.40/0.74 (assume @p34 (forall @t66 (=> @t65 (_ @t107 (_ @t106 @t32))))) % 0.40/0.74 (assume @p35 (forall (@list @t54 @t64 @t32 @t89) (=> @t65 (=> (_ @t103 @t89) (_ @t107 (_ @t106 @t89)))))) % 0.40/0.74 (assume @p36 (forall @t109 (_ @t67 @t108))) % 0.40/0.74 (assume @p37 (forall @t109 (_ @t67 (_ @t37 @t108)))) % 0.40/0.74 (assume @p38 (forall @t63 (= (_ @t34 tptp.one_one_nat) @t33))) % 0.40/0.74 (assume @p39 (forall @t63 (= (_ @t110 @t33) @t33))) % 0.40/0.74 (assume @p40 (forall (@list @t111 @t21 @t20) (=> (forall @t113 (=> (_ (_ tptp.member_nat @t112) @t111) (_ (_ tptp.ord_less_eq_nat (_ @t21 @t112)) (_ @t20 @t112)))) (_ (_ tptp.ord_less_eq_nat (_ @t24 @t111)) (_ @t23 @t111))))) % 0.40/0.74 (assume @p41 (forall (@list @t17 @t20 @t21) (=> (forall @t77 (=> @t120 (_ (_ tptp.ord_less_eq_nat @t118) @t117))) (= (_ (_ tptp.groups1842438620at_nat (lambda @t116 (_ (_ tptp.minus_minus_nat (_ @t21 @t115)) (_ @t20 @t115)))) @t17) (_ (_ tptp.minus_minus_nat @t25) @t114))))) % 0.40/0.74 (assume @p42 (forall @t122 (=> @t88 (_ (_ tptp.ord_less_eq_nat (_ (_ tptp.groups1842438620at_nat @t86) @t121)) @t33)))) % 0.40/0.74 (assume @p43 (forall (@list @t92 @t73) (= (_ (_ tptp.member_nat @t92) @t124) @t123))) % 0.40/0.74 (assume @p44 (forall @t125 (= (_ tptp.collect_nat (lambda @t116 (_ (_ tptp.member_nat @t115) @t17))) @t17))) % 0.40/0.74 (assume @p45 (forall (@list @t73 @t126) (=> (forall @t77 (= @t76 (_ @t126 @t71))) (= @t124 (_ tptp.collect_nat @t126))))) % 0.40/0.74 (assume @p46 (forall (@list @t130 @t139 @t133 @t127 @t128 @t20) (=> (forall @t137 (=> @t136 (= (_ @t139 @t134) @t131))) (=> (forall @t137 (=> @t136 (_ (_ tptp.member_nat @t134) @t127))) (=> (forall @t142 (=> @t141 (= (_ @t133 @t140) @t138))) (=> (forall @t142 (=> @t141 (_ (_ tptp.member_nat @t140) @t130))) (=> (forall @t137 (=> @t136 (= (_ @t128 @t134) @t132))) (= (_ @t23 @t130) (_ @t129 @t127))))))))) % 0.40/0.74 (assume @p47 (forall (@list @t18 @t148 @t17 @t128 @t143 @t144) (=> (forall @t80 (=> @t151 (and (_ (_ tptp.member_nat @t150) @t17) (= (_ @t128 @t150) @t79)))) (=> (forall @t77 (=> @t120 (and @t149 (= (_ @t148 @t146) @t71) @t147))) @t145)))) % 0.40/0.74 (assume @p48 (forall (@list @t18 @t17 @t128 @t143 @t144) (=> (forall @t80 (=> @t151 (exists @t83 (and (_ (_ tptp.member_nat @t82) @t17) (= (_ @t128 @t82) @t79) (forall (@list @t152) (=> (and (_ (_ tptp.member_nat @t152) @t17) (= (_ @t128 @t152) @t79)) (= @t152 @t82))))))) (=> (forall @t77 (=> @t120 (and @t149 @t147))) @t145)))) % 0.40/0.74 (assume @p49 (forall (@list @t17 @t18 @t20 @t128) (=> @t154 (=> (forall @t77 (=> @t153 (= @t118 @t146))) (= @t114 (_ @t129 @t18)))))) % 0.40/0.74 (assume @p50 (forall @t66 (= (_ (_ tptp.minus_minus_nat (_ @t155 @t64)) @t32) (_ (_ tptp.minus_minus_nat (_ @t155 @t32)) @t64)))) % 0.40/0.74 (assume @p51 (forall (@list @t156 @t18 @t17) (= (_ (_ tptp.groups1842438620at_nat (lambda @t10 (_ (_ tptp.groups1842438620at_nat @t157) @t18))) @t17) (_ (_ tptp.groups1842438620at_nat (lambda @t22 (_ (_ tptp.groups1842438620at_nat (lambda @t10 (_ @t157 @t19))) @t17))) @t18)))) % 0.40/0.74 (assume @p52 (forall @t159 (= (_ @t158 tptp.one_one_nat) @t92))) % 0.40/0.74 (assume @p53 (forall @t159 (= (_ @t110 @t92) @t92))) % 0.40/0.74 (assume @p54 (forall (@list @t21 @t2 @t1 @t160) (= (_ (_ (_ tptp.fun_upd_nat_nat @t162) @t2) @t160) (_ @t161 @t160)))) % 0.40/0.74 (assume @p55 (forall (@list @t21 @t2) (= (_ @t161 @t163) @t21))) % 0.40/0.74 (assume @p56 (forall (@list @t46) (_ @t47 @t46))) % 0.40/0.74 (assume @p57 (forall @t164 (_ @t50 @t2))) % 0.40/0.74 (assume @p58 (= (lambda @t116 @t115) @t110)) % 0.40/0.74 (assume @p59 (forall @t122 (=> (forall @t113 (=> (not (= (_ @t86 @t112) tptp.zero_zero_nat)) (and (_ @t166 @t112) (_ (_ tptp.ord_less_eq_nat @t112) @t33)))) (=> @t165 @t88)))) % 0.40/0.74 (assume @p60 (forall @t122 (=> @t88 (not (=> (forall (@list @t167) (=> (not (= (_ @t86 @t167) tptp.zero_zero_nat)) (and (_ @t166 @t167) (_ (_ tptp.ord_less_eq_nat @t167) @t33)))) (not @t165)))))) % 0.40/0.74 (assume @p61 (forall @t63 (= (_ @t62 tptp.zero_zero_nat) @t168))) % 0.40/0.74 (assume @p62 (forall @t159 (= (_ @t169 @t92) tptp.zero_zero_nat))) % 0.40/0.74 (assume @p63 (forall @t159 (= (_ @t158 tptp.zero_zero_nat) tptp.zero_zero_nat))) % 0.40/0.74 (assume @p64 (forall @t175 (= @t174 @t172))) % 0.40/0.74 (assume @p65 (forall @t183 (= @t182 @t178))) % 0.40/0.74 (assume @p66 (forall @t100 (= @t187 @t178))) % 0.40/0.74 (assume @p67 (forall @t159 (= (_ @t188 @t92) tptp.zero_zero_nat))) % 0.40/0.74 (assume @p68 (forall @t159 (= (_ @t189 tptp.zero_zero_nat) @t92))) % 0.40/0.74 (assume @p69 (forall @t159 (= (_ @t189 @t92) tptp.zero_zero_nat))) % 0.40/0.74 (assume @p70 (forall @t159 @t191)) % 0.40/0.74 (assume @p71 (forall @t63 (_ @t190 @t33))) % 0.40/0.74 (assume @p72 (forall @t63 (= (_ @t188 @t33) tptp.zero_zero_nat))) % 0.40/0.74 (assume @p73 (forall @t109 (= (_ @t39 @t36) tptp.zero_zero_nat))) % 0.40/0.74 (assume @p74 (forall @t61 (= (= @t60 tptp.zero_zero_nat) (or @t192 @t168)))) % 0.40/0.74 (assume @p75 (forall @t109 (= (_ @t37 tptp.zero_zero_nat) tptp.zero_zero_nat))) % 0.40/0.74 (assume @p76 (forall @t44 (= @t195 @t194))) % 0.40/0.74 (assume @p77 (forall @t196 (= (= @t38 @t35) @t194))) % 0.40/0.74 (assume @p78 (forall @t125 (= (_ (_ tptp.groups1842438620at_nat (lambda (@list (@var "Uu" tptp.nat)) tptp.zero_zero_nat)) @t17) tptp.zero_zero_nat))) % 0.40/0.74 (assume @p79 (forall @t61 (=> @t68 @t197))) % 0.40/0.74 (assume @p80 (forall @t61 (= @t197 @t68))) % 0.40/0.74 (assume @p81 (_ @t198 @t9)) % 0.40/0.74 (assume @p82 (forall @t164 (= (= tptp.zero_zero_nat @t2) (= @t2 tptp.zero_zero_nat)))) % 0.40/0.74 (assume @p83 (forall @t164 (_ @t190 @t2))) % 0.40/0.74 (assume @p84 (forall @t175 (=> @t201 (and @t200 @t199)))) % 0.40/0.74 (assume @p85 (forall @t175 (=> @t174 @t172))) % 0.40/0.74 (assume @p86 (forall @t175 (=> @t200 (=> @t199 @t201)))) % 0.40/0.74 (assume @p87 (forall @t183 (=> @t202 (= @t182 @t176)))) % 0.40/0.74 (assume @p88 (forall @t183 (=> @t202 (= @t187 @t176)))) % 0.40/0.74 (assume @p89 (not (= tptp.zero_zero_nat tptp.one_one_nat))) % 0.40/0.74 (assume @p90 (= (lambda (@list (@var "H2" tptp.nat)) tptp.zero_zero_nat) @t169)) % 0.40/0.74 (assume @p91 (forall (@list @t17 @t20) (=> (forall @t77 (=> @t120 (= @t118 tptp.zero_zero_nat))) @t203))) % 0.40/0.74 (assume @p92 (forall (@list @t20 @t17) (=> (not @t203) (not (forall @t137 (=> (_ @t135 @t17) (= @t132 tptp.zero_zero_nat))))))) % 0.40/0.74 (assume @p93 (forall @t159 (=> @t204 @t171))) % 0.40/0.74 (assume @p94 (forall @t159 (= @t204 @t171))) % 0.40/0.74 (assume @p95 (forall @t61 (=> @t197 (=> (= @t205 tptp.zero_zero_nat) @t69)))) % 0.40/0.74 (assume @p96 (forall @t109 (= (_ @t39 tptp.zero_zero_nat) @t36))) % 0.40/0.74 (assume @p97 (forall @t63 (= (_ @t169 @t33) tptp.zero_zero_nat))) % 0.40/0.74 (assume @p98 (forall @t208 (=> @t207 (=> @t206 (_ (_ tptp.ord_less_eq_nat @t181) @t180))))) % 0.40/0.74 (assume @p99 (forall @t175 (=> @t191 (=> @t210 (_ (_ tptp.ord_less_eq_nat @t209) tptp.zero_zero_nat))))) % 0.40/0.74 (assume @p100 (forall @t175 (=> @t204 (=> @t213 @t212)))) % 0.40/0.74 (assume @p101 (forall @t175 (=> @t191 (=> @t210 @t212)))) % 0.40/0.74 (assume @p102 (forall @t175 (=> @t191 (=> @t213 (_ @t190 @t173))))) % 0.40/0.74 (assume @p103 (forall @t175 (=> (or (and @t191 @t210) (and @t204 @t213)) @t212))) % 0.40/0.74 (assume @p104 (forall @t208 (=> @t207 (=> @t206 (_ @t214 @t185))))) % 0.40/0.74 (assume @p105 (forall @t219 (=> @t207 (=> @t218 (=> @t191 @t216))))) % 0.40/0.74 (assume @p106 (forall @t219 (=> @t207 (=> @t218 (=> @t213 @t216))))) % 0.40/0.74 (assume @p107 (not (_ @t166 tptp.zero_zero_nat))) % 0.40/0.74 (assume @p108 (_ @t190 tptp.one_one_nat)) % 0.40/0.74 (assume @p109 (forall (@list @t86) (= (_ @t87 tptp.zero_zero_nat) (= @t86 (lambda @t10 tptp.zero_zero_nat))))) % 0.40/0.74 (assume @p110 (forall (@list @t95 @t92) (=> (_ @t217 tptp.one_one_nat) (=> @t191 (_ @t214 @t92))))) % 0.40/0.74 (assume @p111 (forall @t175 (=> (_ @t98 tptp.one_one_nat) (=> @t213 (=> (_ @t93 tptp.one_one_nat) (_ @t211 tptp.one_one_nat)))))) % 0.40/0.74 (assume @p112 (forall @t221 (=> (forall @t77 (=> @t120 (_ @t220 tptp.zero_zero_nat))) (_ (_ tptp.ord_less_eq_nat @t25) tptp.zero_zero_nat)))) % 0.40/0.74 (assume @p113 (forall @t221 (=> (forall @t77 (=> @t120 (_ @t190 @t117))) (_ @t190 @t25)))) % 0.40/0.74 (assume @p114 (forall @t61 (=> (= @t36 @t60) (or @t58 @t192)))) % 0.40/0.74 (assume @p115 (forall (@list @t222 @t223) (=> @t228 (=> @t226 @t224)))) % 0.40/0.74 (assume @p116 (forall @t229 (=> @t94 (=> @t207 @t176)))) % 0.40/0.74 (assume @p117 (= @t237 (lambda @t234 (and @t233 @t232)))) % 0.40/0.74 (assume @p118 (= @t245 (lambda @t242 (and @t241 @t240)))) % 0.40/0.74 (assume @p119 (forall (@list @t222 @t223 @t246) (=> @t228 (=> (_ @t247 @t222) (_ @t247 @t223))))) % 0.40/0.74 (assume @p120 (forall @t248 (=> @t94 (=> (_ @t217 @t78) (_ @t217 @t92))))) % 0.40/0.74 (assume @p121 (forall @t254 (=> (forall @t252 (=> (_ (_ tptp.ord_less_eq_nat @t131) @t138) @t251)) @t253))) % 0.40/0.74 (assume @p122 (forall (@list @t223) (_ @t225 @t223))) % 0.40/0.74 (assume @p123 (forall @t159 (_ @t98 @t92))) % 0.40/0.74 (assume @p124 (forall (@list @t46 @t45 @t255) (=> @t48 (=> (_ @t256 @t255) (_ @t47 @t255))))) % 0.40/0.74 (assume @p125 (forall @t260 (=> @t51 (=> @t259 @t257)))) % 0.40/0.74 (assume @p126 (forall (@list @t223 @t222) (=> @t226 (=> @t228 @t224)))) % 0.40/0.74 (assume @p127 (forall @t175 (=> @t207 (=> @t94 @t176)))) % 0.40/0.74 (assume @p128 (forall @t262 (=> @t226 (=> (= @t222 @t246) @t261)))) % 0.40/0.74 (assume @p129 (forall @t208 (=> @t207 (=> @t263 @t99)))) % 0.40/0.74 (assume @p130 (forall @t262 (=> @t224 @t265))) % 0.40/0.74 (assume @p131 (forall @t208 (=> @t176 @t266))) % 0.40/0.74 (assume @p132 (= @t237 (lambda @t234 (and @t232 @t233)))) % 0.40/0.74 (assume @p133 (= @t245 (lambda @t242 (and @t240 @t241)))) % 0.40/0.74 (assume @p134 (forall (@list @t45 @t46) (=> @t268 (= @t48 @t267)))) % 0.40/0.74 (assume @p135 (forall @t270 (=> @t269 (= @t51 @t3)))) % 0.40/0.74 (assume @p136 (forall @t260 (=> (=> @t51 (not @t259)) (=> (=> @t269 (not @t257)) (=> (=> @t257 (not @t274)) (=> (=> @t274 (not @t269)) (=> (=> @t259 (not @t273)) (not (=> @t273 @t271))))))))) % 0.40/0.74 (assume @p137 (forall @t262 (=> @t226 @t265))) % 0.40/0.74 (assume @p138 (forall @t208 (=> @t207 @t266))) % 0.40/0.74 (assume @p139 (forall @t6 (=> @t271 @t269))) % 0.40/0.74 (assume @p140 (forall @t49 (=> @t267 @t48))) % 0.40/0.74 (assume @p141 (forall @t6 (=> @t3 @t51))) % 0.40/0.74 (assume @p142 (forall @t6 (or @t51 @t269))) % 0.40/0.74 (assume @p143 (forall @t49 (=> @t48 (=> @t268 @t267)))) % 0.40/0.74 (assume @p144 (forall @t6 (=> @t51 (=> @t269 @t3)))) % 0.40/0.74 (assume @p145 (= @t237 (lambda (@list @t275 @t276) (and (_ @t277 @t276) (_ (_ tptp.ord_less_eq_set_nat @t276) @t275))))) % 0.40/0.74 (assume @p146 (= @t245 (lambda (@list @t115 @t278) (and (_ @t279 @t278) (_ (_ tptp.ord_less_eq_nat @t278) @t115))))) % 0.40/0.74 (assume @p147 (forall @t286 (=> @t207 (=> (= @t285 @t246) @t284)))) % 0.40/0.74 (assume @p148 (forall @t295 (=> @t226 (=> (= @t294 @t95) @t293)))) % 0.40/0.74 (assume @p149 (forall @t300 (=> @t226 (=> (= @t299 @t246) @t298)))) % 0.40/0.74 (assume @p150 (forall @t307 (=> @t207 (=> @t306 @t304)))) % 0.40/0.74 (assume @p151 (forall @t309 (=> (= @t223 @t285) @t308))) % 0.40/0.74 (assume @p152 (forall @t311 (=> (= @t92 @t294) @t310))) % 0.40/0.74 (assume @p153 (forall @t313 (=> (= @t223 @t299) @t312))) % 0.40/0.74 (assume @p154 (forall @t317 (=> @t316 @t315))) % 0.40/0.74 (assume @p155 (forall @t286 (=> @t207 (=> (_ (_ tptp.ord_less_eq_set_nat @t285) @t246) @t284)))) % 0.40/0.74 (assume @p156 (forall @t295 (=> @t226 (=> (_ (_ tptp.ord_less_eq_nat @t294) @t95) @t293)))) % 0.40/0.74 (assume @p157 (forall @t300 (=> @t226 (=> (_ (_ tptp.ord_less_eq_set_nat @t299) @t246) @t298)))) % 0.40/0.74 (assume @p158 (forall @t307 (=> @t207 (=> (_ (_ tptp.ord_less_eq_nat @t305) @t95) @t304)))) % 0.40/0.74 (assume @p159 (forall @t311 (=> (_ @t98 @t294) @t310))) % 0.40/0.74 (assume @p160 (forall @t309 (=> (_ @t225 @t285) @t308))) % 0.40/0.74 (assume @p161 (forall @t313 (=> (_ @t225 @t299) @t312))) % 0.40/0.74 (assume @p162 (forall @t317 (=> (_ @t98 @t305) @t315))) % 0.40/0.74 (assume @p163 (forall @t208 (= (_ (_ tptp.times_times_nat @t173) @t95) @t318))) % 0.40/0.74 (assume @p164 (= tptp.times_times_nat (lambda @t242 (_ (_ tptp.times_times_nat @t238) @t239)))) % 0.40/0.74 (assume @p165 (forall @t248 (= (_ @t184 @t186) @t318))) % 0.40/0.74 (assume @p166 (forall @t100 (= (_ (_ tptp.minus_minus_nat (_ @t189 @t95)) @t78) (_ (_ tptp.minus_minus_nat (_ @t189 @t78)) @t95)))) % 0.40/0.74 (assume @p167 (forall @t164 (= (= tptp.one_one_nat @t2) (= @t2 tptp.one_one_nat)))) % 0.40/0.74 (assume @p168 (forall @t321 (= @t320 @t319))) % 0.40/0.74 (assume @p169 (forall (@list @t92 @t95 @t322 @t78 @t215) (=> (not (= @t92 @t95)) (= (_ (_ (_ tptp.fun_upd_nat_nat (_ (_ @t323 @t92) @t78)) @t95) @t215) (_ (_ (_ tptp.fun_upd_nat_nat (_ (_ @t323 @t95) @t215)) @t92) @t78))))) % 0.40/0.74 (assume @p170 (forall (@list @t160 @t2 @t21 @t1) (=> (not (= @t160 @t2)) (= (_ @t162 @t160) (_ @t21 @t160))))) % 0.40/0.74 (assume @p171 (forall @t321 (= (_ @t162 @t2) @t1))) % 0.40/0.74 (assume @p172 (forall @t321 (=> @t319 @t320))) % 0.40/0.74 (assume @p173 (forall (@list @t21 @t2 @t1 @t20 @t160) (=> (= @t162 (_ (_ (_ tptp.fun_upd_nat_nat @t20) @t2) @t160)) (= @t1 @t160)))) % 0.40/0.74 (assume @p174 (= tptp.fun_upd_nat_nat (lambda (@list @t324 @t239 @t238 @t115) (_ (_ (_ tptp.if_nat (= @t115 @t239)) @t238) (_ @t324 @t115))))) % 0.40/0.74 (assume @p175 (forall (@list @t78 @t95 @t92) (= (_ (_ tptp.times_times_nat @t325) @t92) (_ (_ tptp.minus_minus_nat @t209) @t181)))) % 0.40/0.74 (assume @p176 (forall @t208 (= (_ @t158 @t325) (_ (_ tptp.minus_minus_nat @t173) @t186)))) % 0.40/0.74 (assume @p177 (forall @t327 (=> (forall @t77 (=> @t120 @t153)) @t326))) % 0.40/0.74 (assume @p178 (forall @t327 (=> @t326 (=> (_ (_ tptp.ord_less_eq_set_nat @t18) @t17) @t154)))) % 0.40/0.74 (assume @p179 (forall (@list @t86 @t33 @t32 @t54) (=> @t88 (=> (_ @t198 @t328) (=> (not (= (_ (_ (_ (_ tptp.fun_upd_nat_nat @t86) @t32) (_ (_ tptp.minus_minus_nat @t328) tptp.one_one_nat)) @t54) tptp.zero_zero_nat)) (and (_ @t166 @t54) (_ @t55 @t101))))))) % 0.40/0.74 (assume @p180 (forall @t44 (= @t195 (or @t193 @t69)))) % 0.40/0.74 (assume @p181 (_ @t166 tptp.one_one_nat)) % 0.40/0.74 (assume @p182 (_ @t190 tptp.zero_zero_nat)) % 0.40/0.74 (assume @p183 (forall @t63 (= (not @t329) @t168))) % 0.40/0.74 (assume @p184 (forall @t159 (= @t200 (_ @t198 @t92)))) % 0.40/0.74 (assume @p185 (forall @t63 (not (_ @t330 tptp.zero_zero_nat)))) % 0.40/0.74 (assume @p186 (forall @t63 (= (not @t168) @t329))) % 0.40/0.74 (assume @p187 (forall (@list @t33 @t36) (= (_ @t198 @t205) @t331))) % 0.40/0.74 (assume @p188 (forall @t44 (= (_ (_ tptp.ord_less_nat @t43) @t42) @t333))) % 0.40/0.74 (assume @p189 (forall @t196 (= (_ (_ tptp.ord_less_nat @t38) @t35) @t333))) % 0.40/0.74 (assume @p190 (forall @t61 (= (_ @t198 @t60) (and (_ @t198 @t36) @t329)))) % 0.40/0.74 (assume @p191 (forall @t63 (= (_ @t330 tptp.one_one_nat) @t168))) % 0.40/0.74 (assume @p192 (forall @t44 (= (_ (_ tptp.ord_less_eq_nat @t43) @t42) @t334))) % 0.40/0.74 (assume @p193 (forall @t196 (= (_ (_ tptp.ord_less_eq_nat @t38) @t35) @t334))) % 0.40/0.74 (assume @p194 (forall @t229 (=> @t337 @t335))) % 0.40/0.74 (assume @p195 (forall @t175 (=> @t339 @t335))) % 0.40/0.74 (assume @p196 (forall @t6 (= @t344 (or @t341 @t3)))) % 0.40/0.74 (assume @p197 (forall @t248 (=> @t337 (=> (_ @t345 @t78) (_ @t345 @t92))))) % 0.40/0.74 (assume @p198 (forall @t254 (=> (forall @t252 (=> (_ (_ tptp.ord_less_nat @t131) @t138) @t251)) (=> (forall @t137 (_ @t250 @t131)) @t253)))) % 0.40/0.74 (assume @p199 (= (lambda (@list @t349) (exists (@list @t348) (_ @t349 @t348))) (lambda (@list @t347) (exists @t31 (and (_ @t347 @t27) (forall (@list @t346) (=> (_ (_ tptp.ord_less_nat @t346) @t27) (not (_ @t347 @t346))))))))) % 0.40/0.74 (assume @p200 (forall @t6 (=> @t343 @t350))) % 0.40/0.74 (assume @p201 (forall @t208 (=> @t339 @t353))) % 0.40/0.74 (assume @p202 (forall @t159 (not (_ @t338 @t92)))) % 0.40/0.74 (assume @p203 (forall @t6 (=> @t344 (=> @t354 @t341)))) % 0.40/0.74 (assume @p204 (forall (@list @t2 @t1 @t355) (=> @t343 (=> @t341 @t355)))) % 0.40/0.74 (assume @p205 (forall @t6 (=> @t343 (not (= @t1 @t2))))) % 0.40/0.74 (assume @p206 (forall @t270 (=> @t350 (= @t344 @t3)))) % 0.40/0.74 (assume @p207 (forall (@list @t73 @t92) (=> (forall @t77 (=> (forall @t75 (=> (_ (_ tptp.ord_less_nat @t72) @t71) @t74)) @t76)) @t123))) % 0.40/0.74 (assume @p208 (forall @t6 (=> @t343 @t354))) % 0.40/0.74 (assume @p209 (forall @t229 (=> @t337 (not @t339)))) % 0.40/0.74 (assume @p210 (forall @t208 (=> @t339 (=> @t263 @t351)))) % 0.40/0.74 (assume @p211 (forall @t208 (=> @t176 @t353))) % 0.40/0.74 (assume @p212 (forall @t164 (not (_ @t342 @t2)))) % 0.40/0.74 (assume @p213 (forall @t6 (or @t343 @t3 @t341))) % 0.40/0.74 (assume @p214 (forall @t260 (=> @t343 (=> (_ @t340 @t160) (_ @t342 @t160))))) % 0.40/0.74 (assume @p215 (forall @t175 (=> @t339 (not @t337)))) % 0.40/0.74 (assume @p216 (forall @t6 (= @t354 (or @t343 @t341)))) % 0.40/0.74 (assume @p217 (forall @t6 (=> @t354 (=> @t344 @t341)))) % 0.40/0.74 (assume @p218 (forall @t164 (exists (@list @t356) (_ @t342 @t356)))) % 0.40/0.74 (assume @p219 (forall @t307 (=> @t339 (=> (_ (_ tptp.ord_less_nat @t305) @t95) @t358)))) % 0.40/0.74 (assume @p220 (forall @t317 (=> (_ @t338 @t305) @t359))) % 0.40/0.74 (assume @p221 (forall @t307 (=> @t339 (=> @t306 @t358)))) % 0.40/0.74 (assume @p222 (forall @t317 (=> @t316 @t359))) % 0.40/0.74 (assume @p223 (not (_ @t198 tptp.zero_zero_nat))) % 0.40/0.74 (assume @p224 (not (_ (_ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat))) % 0.40/0.74 (assume @p225 (forall @t368 (=> (forall @t367 (=> (not @t366) (exists @t365 (and @t364 (not @t362))))) @t360))) % 0.40/0.74 (assume @p226 (forall @t368 (=> (forall @t367 (=> (forall @t365 (=> @t364 @t362)) @t366)) @t360))) % 0.40/0.74 (assume @p227 (forall (@list @t355) (or (= @t355 true) (= @t355 false)))) % 0.40/0.74 (assume @p228 (forall @t6 (= (_ (_ (_ tptp.if_nat false) @t2) @t1) @t1))) % 0.40/0.74 (assume @p229 (forall @t6 (= (_ (_ (_ tptp.if_nat true) @t2) @t1) @t2))) % 0.40/0.74 (assume @p230 @t370) % 0.40/0.74 (assume @p231 true) % 0.40/0.74 (step @p232 (= tptp.set_or1086813439et_nat @t372) :rule refl :args (@t372)) % 0.40/0.74 (step @p233 (= tptp.set_ord_atMost_nat @t374) :rule refl :args (@t374)) % 0.40/0.74 (step @p234 (= tptp.fun_upd_nat_nat @t376) :rule refl :args (@t376)) % 0.40/0.74 (step @p235 (= tptp.number1551313001itions @t389) :rule refl :args (@t389)) % 0.40/0.74 (step @p236 :rule refl :args ((tptp.groups1842438620at_nat @t393 @t392))) % 0.40/0.74 (step @p237 :rule refl :args (@t394)) % 0.40/0.74 (step @p238 :rule refl :args (@t393)) % 0.40/0.74 (step @p239 :rule cong :premises (@p238 @p237) :args (@t395)) % 0.40/0.74 (step @p240 :rule trans :premises (@p239 @p236)) % 0.40/0.74 (step @p241 :rule refl :args (@t396)) % 0.40/0.74 (step @p242 :rule ho_cong :premises (@p241 @p237)) % 0.40/0.74 (step @p243 :rule cong :premises (@p242 @p240) :args ((= (_ @t396 @t394) @t395))) % 0.40/0.74 (step @p244 :rule symm :premises (@p243)) % 0.40/0.74 (step @p245 :rule refl :args (@t397)) % 0.40/0.74 (step @p246 :rule eq_resolve :premises (@p245 @p244)) % 0.40/0.74 (step @p247 :rule refl :args (@t392)) % 0.40/0.74 (step @p248 :rule cong :premises (@p247 @p237) :args ((= @t392 @t394))) % 0.40/0.74 (step @p249 :rule symm :premises (@p248)) % 0.40/0.74 (step @p250 :rule eq_resolve :premises (@p247 @p249)) % 0.40/0.74 (step @p251 :rule eq-refl :args (@t390)) % 0.40/0.74 (step @p252 :rule skolem_intro :args (@t391)) % 0.40/0.74 (step @p253 :rule refl :args (@t390)) % 0.40/0.74 (step @p254 :rule cong :premises (@p253 @p252) :args ((= @t390 @t391))) % 0.40/0.74 (step @p255 :rule trans :premises (@p254 @p251)) % 0.40/0.74 (step @p256 :rule true_elim :premises (@p255)) % 0.40/0.74 (step @p257 :rule refl :args (tptp.collect_nat)) % 0.40/0.74 (step @p258 :rule ho_cong :premises (@p257 @p256)) % 0.40/0.74 (step @p259 :rule trans :premises (@p258 @p250)) % 0.40/0.74 (step @p260 :rule eq-refl :args (@t14)) % 0.40/0.74 (step @p261 :rule skolem_intro :args (@t393)) % 0.40/0.74 (step @p262 :rule refl :args (@t14)) % 0.40/0.74 (step @p263 :rule cong :premises (@p262 @p261) :args ((= @t14 @t393))) % 0.40/0.74 (step @p264 :rule trans :premises (@p263 @p260)) % 0.40/0.74 (step @p265 :rule true_elim :premises (@p264)) % 0.40/0.74 (step @p266 :rule refl :args (tptp.groups1842438620at_nat)) % 0.40/0.74 (step @p267 :rule ho_cong :premises (@p266 @p265)) % 0.40/0.74 (step @p268 :rule ho_cong :premises (@p267 @p259)) % 0.40/0.74 (step @p269 :rule trans :premises (@p268 @p246)) % 0.40/0.74 (step @p270 :rule refl :args (tptp.n)) % 0.40/0.74 (step @p271 :rule cong :premises (@p270 @p269) :args (@t400)) % 0.40/0.74 (step @p272 :rule refl :args (@t403)) % 0.40/0.74 (step @p273 :rule nary_cong :premises (@p272 @p271) :args (@t404)) % 0.40/0.74 (step @p274 :rule beta-reduce :args ((= (_ @t408 tptp.n) @t404))) % 0.40/0.74 (step @p275 :rule beta-reduce :args ((= (_ (lambda @t388 (and (forall @t10 (or (= tptp.zero_zero_nat @t410) @t407)) (= @t27 @t409))) tptp.p) @t408))) % 0.40/0.74 (step @p276 :rule ho_cong :premises (@p275 @p270)) % 0.40/0.74 (step @p277 :rule trans :premises (@p276 @p274)) % 0.40/0.74 (step @p278 :rule refl :args (tptp.p)) % 0.40/0.74 (step @p279 :rule eq-symm :args (@t409 @t27)) % 0.40/0.74 (step @p280 :rule refl :args (@t27)) % 0.40/0.74 (step @p281 :rule beta-reduce :args ((= @t411 @t405))) % 0.40/0.74 (step @p282 :rule refl :args (@t379)) % 0.40/0.74 (step @p283 :rule ho_cong :premises (@p282 @p281)) % 0.40/0.74 (step @p284 :rule cong :premises (@p283 @p280) :args (@t412)) % 0.40/0.74 (step @p285 :rule trans :premises (@p284 @p279)) % 0.40/0.74 (step @p286 :rule refl :args (@t406)) % 0.40/0.74 (step @p287 :rule refl :args (@t381)) % 0.40/0.74 (step @p288 :rule cong :premises (@p287 @p286) :args ((= @t381 @t406))) % 0.40/0.74 (step @p289 :rule symm :premises (@p288)) % 0.40/0.74 (step @p290 :rule eq_resolve :premises (@p287 @p289)) % 0.40/0.74 (step @p291 :rule refl :args (@t401)) % 0.40/0.74 (step @p292 :rule refl :args (@t382)) % 0.40/0.74 (step @p293 :rule cong :premises (@p292 @p291) :args ((= @t382 @t401))) % 0.40/0.74 (step @p294 :rule symm :premises (@p293)) % 0.40/0.74 (step @p295 :rule eq_resolve :premises (@p292 @p294)) % 0.40/0.74 (step @p296 :rule nary_cong :premises (@p295 @p290) :args (@t383)) % 0.40/0.74 (step @p297 :rule refl :args (@t410)) % 0.40/0.74 (step @p298 :rule refl :args (@t378)) % 0.40/0.74 (step @p299 :rule cong :premises (@p298 @p297) :args ((= @t378 @t410))) % 0.40/0.74 (step @p300 :rule symm :premises (@p299)) % 0.40/0.74 (step @p301 :rule eq_resolve :premises (@p298 @p300)) % 0.40/0.74 (step @p302 :rule refl :args (tptp.zero_zero_nat)) % 0.40/0.74 (step @p303 :rule cong :premises (@p302 @p301) :args (@t413)) % 0.40/0.74 (step @p304 :rule nary_cong :premises (@p303 @p296) :args (@t414)) % 0.40/0.74 (step @p305 :rule cong :premises (@p304) :args ((forall @t10 @t414))) % 0.40/0.74 (step @p306 :rule refl :args (@t383)) % 0.40/0.74 (step @p307 :rule bool-double-not-elim :args (@t413)) % 0.40/0.74 (step @p308 :rule nary_cong :premises (@p307 @p306) :args ((or (not @t415) @t383))) % 0.40/0.74 (step @p309 :rule bool-impl-elim :args (@t415 @t383)) % 0.40/0.74 (step @p310 :rule trans :premises (@p309 @p308)) % 0.40/0.74 (step @p311 :rule cong :premises (@p310) :args ((forall @t10 (=> @t415 @t383)))) % 0.40/0.74 (step @p312 :rule trans :premises (@p311 @p305)) % 0.40/0.74 (step @p313 :rule refl :args (@t383)) % 0.40/0.74 (step @p314 :rule eq-symm :args (@t378 tptp.zero_zero_nat)) % 0.40/0.74 (step @p315 :rule cong :premises (@p314) :args (@t384)) % 0.40/0.74 (step @p316 :rule cong :premises (@p315 @p313) :args (@t385)) % 0.40/0.74 (step @p317 :rule cong :premises (@p316) :args (@t386)) % 0.40/0.74 (step @p318 :rule trans :premises (@p317 @p312)) % 0.40/0.74 (step @p319 :rule nary_cong :premises (@p318 @p285) :args ((and @t386 @t412))) % 0.40/0.74 (step @p320 :rule ho_cong :premises (@p233 @p280)) % 0.40/0.74 (step @p321 :rule ho_cong :premises (@p282 @p320)) % 0.40/0.74 (step @p322 :rule cong :premises (@p321 @p280) :args (@t380)) % 0.40/0.74 (step @p323 :rule refl :args (@t386)) % 0.40/0.74 (step @p324 :rule nary_cong :premises (@p323 @p322) :args (@t387)) % 0.40/0.74 (step @p325 :rule trans :premises (@p324 @p319)) % 0.40/0.74 (step @p326 :rule cong :premises (@p325) :args (@t389)) % 0.40/0.74 (step @p327 :rule trans :premises (@p235 @p326)) % 0.40/0.74 (step @p328 :rule ho_cong :premises (@p327 @p278)) % 0.40/0.74 (step @p329 :rule ho_cong :premises (@p328 @p270)) % 0.40/0.74 (step @p330 :rule trans :premises (@p329 @p277)) % 0.40/0.74 (step @p331 :rule trans :premises (@p330 @p273)) % 0.40/0.74 (step @p332 :rule eq_resolve :premises (@p1 @p331)) % 0.40/0.74 (step @p333 :rule and_elim :premises (@p332) :args (1)) % 0.40/0.74 (step @p334 :rule refl :args ((tptp.minus_minus_nat @t397 tptp.k))) % 0.40/0.74 (step @p335 :rule refl :args (tptp.k)) % 0.40/0.74 (step @p336 :rule cong :premises (@p240 @p335) :args (@t416)) % 0.40/0.74 (step @p337 :rule trans :premises (@p336 @p334)) % 0.40/0.74 (step @p338 :rule refl :args (tptp.minus_minus_nat)) % 0.40/0.74 (step @p339 :rule ho_cong :premises (@p338 @p240)) % 0.40/0.74 (step @p340 :rule ho_cong :premises (@p339 @p335)) % 0.40/0.74 (step @p341 :rule cong :premises (@p340 @p337) :args ((= (_ (_ tptp.minus_minus_nat @t395) tptp.k) @t416))) % 0.40/0.74 (step @p342 :rule symm :premises (@p341)) % 0.40/0.74 (step @p343 :rule refl :args ((_ (_ tptp.minus_minus_nat @t397) tptp.k))) % 0.40/0.74 (step @p344 :rule eq_resolve :premises (@p343 @p342)) % 0.40/0.74 (step @p345 :rule refl :args (tptp.k)) % 0.40/0.74 (step @p346 :rule refl :args (tptp.minus_minus_nat)) % 0.40/0.74 (step @p347 :rule ho_cong :premises (@p346 @p269)) % 0.40/0.74 (step @p348 :rule ho_cong :premises (@p347 @p345)) % 0.40/0.74 (step @p349 :rule trans :premises (@p348 @p344)) % 0.40/0.74 (step @p350 :rule refl :args (@t417)) % 0.40/0.74 (step @p351 :rule refl :args (@t12)) % 0.40/0.74 (step @p352 :rule cong :premises (@p351 @p350) :args ((= @t12 @t417))) % 0.40/0.74 (step @p353 :rule symm :premises (@p352)) % 0.40/0.74 (step @p354 :rule eq_resolve :premises (@p351 @p353)) % 0.40/0.74 (step @p355 :rule cong :premises (@p354 @p349) :args (@t419)) % 0.40/0.74 (step @p356 :rule cong :premises (@p355) :args ((not @t419))) % 0.40/0.74 (step @p357 :rule eq-symm :args (@t418 @t12)) % 0.40/0.74 (step @p358 :rule refl :args (@t12)) % 0.40/0.74 (step @p359 :rule beta-reduce :args ((= @t420 @t398))) % 0.40/0.74 (step @p360 :rule refl :args (@t15)) % 0.40/0.74 (step @p361 :rule ho_cong :premises (@p360 @p359)) % 0.40/0.74 (step @p362 :rule ho_cong :premises (@p346 @p361)) % 0.40/0.74 (step @p363 :rule ho_cong :premises (@p362 @p345)) % 0.40/0.74 (step @p364 :rule cong :premises (@p363 @p358) :args (@t421)) % 0.40/0.74 (step @p365 :rule trans :premises (@p364 @p357)) % 0.40/0.74 (step @p366 :rule cong :premises (@p365) :args ((not @t421))) % 0.40/0.74 (step @p367 :rule ho_cong :premises (@p233 @p270)) % 0.40/0.74 (step @p368 :rule ho_cong :premises (@p360 @p367)) % 0.40/0.74 (step @p369 :rule ho_cong :premises (@p346 @p368)) % 0.40/0.74 (step @p370 :rule ho_cong :premises (@p369 @p345)) % 0.40/0.74 (step @p371 :rule cong :premises (@p370 @p358) :args (@t369)) % 0.40/0.74 (step @p372 :rule cong :premises (@p371) :args (@t370)) % 0.40/0.74 (step @p373 :rule trans :premises (@p372 @p366)) % 0.40/0.74 (step @p374 :rule trans :premises (@p373 @p356)) % 0.40/0.74 (step @p375 :rule eq_resolve :premises (@p230 @p374)) % 0.40/0.74 (assume-push @p383 @t422) % 0.40/0.74 (step @p377 :rule cong :premises (@p333 @p345) :args (@t417)) % 0.40/0.74 (step-pop @p384 :rule scope :premises (@p377)) % 0.40/0.74 (step @p378 :rule process_scope :premises (@p384) :args (@t423)) % 0.40/0.74 (step @p380 :rule implies_elim :premises (@p378)) % 0.40/0.74 (step @p381 :rule reordering :premises (@p380) :args ((or @t423 (not @t422)))) % 0.40/0.74 (step @p382 false :rule chain_m_resolution :premises (@p381 @p375 @p333) :args (false (@list true false) (@list @t423 @t422))) % 0.40/0.74 ) % 0.40/0.74 % SZS output end Proof % 0.40/0.74 % cvc5 exiting %------------------------------------------------------------------------------