%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP133^1 : TPTP v9.2.1. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.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 2.02s 2.26s % Output : Proof 2.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : ITP133^1 : TPTP v9.2.1. Released v7.5.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n017.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 04:14:01 EDT 2026 % 0.16/0.35 % CPUTime : % 0.39/0.57 %----Proving TH0 % 2.02/2.26 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 2.02/2.26 % SZS status Theorem % 2.02/2.26 % SZS output start Proof % 2.02/2.26 ( % 2.02/2.26 (declare-sort tptp.nat 0) % 2.02/2.26 (declare-sort tptp.set_set_nat 0) % 2.02/2.26 (declare-sort tptp.set_nat 0) % 2.02/2.26 (declare-const tptp.collect_nat (-> (-> tptp.nat Bool) tptp.set_nat)) % 2.02/2.26 (declare-const tptp.one_one_nat tptp.nat) % 2.02/2.26 (declare-const tptp.times_times_nat (-> tptp.nat tptp.nat tptp.nat)) % 2.02/2.26 (declare-const tptp.groups1842438620at_nat (-> (-> tptp.nat tptp.nat) tptp.set_nat tptp.nat)) % 2.02/2.26 (declare-const tptp.ord_less_eq_nat (-> tptp.nat tptp.nat Bool)) % 2.02/2.26 (declare-const tptp.zero_zero_nat tptp.nat) % 2.02/2.26 (declare-const tptp.member_nat (-> tptp.nat tptp.set_nat Bool)) % 2.02/2.26 (declare-const tptp.collect_set_nat (-> (-> tptp.set_nat Bool) tptp.set_set_nat)) % 2.02/2.26 (declare-const tptp.p (-> tptp.nat tptp.nat)) % 2.02/2.26 (declare-const tptp.member_set_nat (-> tptp.set_nat tptp.set_set_nat Bool)) % 2.02/2.26 (declare-const tptp.ord_le1613022364et_nat (-> tptp.set_set_nat tptp.set_set_nat Bool)) % 2.02/2.26 (declare-const tptp.ord_less_eq_nat_o (-> (-> tptp.nat Bool) (-> tptp.nat Bool) Bool)) % 2.02/2.26 (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))))))) % 2.02/2.26 (define tptp.number1551313001itions () (let ((_let_1 (@var "N2" tptp.nat))) (let ((_let_2 (@var "I2" tptp.nat))) (let ((_let_3 (@var "P2" (-> 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))))))))) % 2.02/2.26 (define tptp.ord_less_eq_set_nat () (let ((_let_1 (@var "B5" tptp.set_nat))) (let ((_let_2 (@var "T2" tptp.nat))) (let ((_let_3 (_ tptp.member_nat _let_2))) (let ((_let_4 (@var "A5" tptp.set_nat))) (lambda (@list _let_4 _let_1) (forall (@list _let_2) (=> (_ _let_3 _let_4) (_ _let_3 _let_1))))))))) % 2.02/2.26 (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))))))) % 2.02/2.26 (define tptp.ord_less_nat () (let ((_let_1 (@var "N2" tptp.nat))) (let ((_let_2 (@var "M4" tptp.nat))) (lambda (@list _let_2 _let_1) (and (_ (_ tptp.ord_less_eq_nat _let_2) _let_1) (not (= _let_2 _let_1))))))) % 2.02/2.26 (define tptp.ord_less_set_nat () (let ((_let_1 (@var "B5" tptp.set_nat))) (let ((_let_2 (@var "A5" tptp.set_nat))) (lambda (@list _let_2 _let_1) (and (_ (_ tptp.ord_less_eq_set_nat _let_2) _let_1) (not (= _let_2 _let_1))))))) % 2.02/2.26 (define @t1 () (@var "A" tptp.set_nat)) % 2.02/2.26 (define @t2 () (@list @t1)) % 2.02/2.26 (define @t3 () (@var "N" tptp.nat)) % 2.02/2.26 (define @t4 () (@var "I2" tptp.nat)) % 2.02/2.26 (define @t5 () (@var "P" (-> tptp.nat tptp.nat))) % 2.02/2.26 (define @t6 () (@list @t4)) % 2.02/2.26 (define @t7 () (= (_ (_ tptp.groups1842438620at_nat (lambda @t6 (_ (_ tptp.times_times_nat (_ @t5 @t4)) @t4))) (_ tptp.set_ord_atMost_nat @t3)) @t3)) % 2.02/2.26 (define @t8 () (@var "I" tptp.nat)) % 2.02/2.26 (define @t9 () (_ tptp.ord_less_eq_nat tptp.one_one_nat)) % 2.02/2.26 (define @t10 () (_ (_ tptp.number1551313001itions @t5) @t3)) % 2.02/2.26 (define @t11 () (@list @t5 @t3)) % 2.02/2.26 (define @t12 () (@var "I3" tptp.nat)) % 2.02/2.26 (define @t13 () (@list @t12)) % 2.02/2.26 (define @t14 () (= @t3 tptp.one_one_nat)) % 2.02/2.26 (define @t15 () (@var "M" tptp.nat)) % 2.02/2.26 (define @t16 () (and (= @t15 tptp.one_one_nat) @t14)) % 2.02/2.26 (define @t17 () (_ tptp.times_times_nat @t15)) % 2.02/2.26 (define @t18 () (_ @t17 @t3)) % 2.02/2.26 (define @t19 () (@list @t15 @t3)) % 2.02/2.26 (define @t20 () (@var "Y" tptp.set_nat)) % 2.02/2.26 (define @t21 () (@var "X" tptp.set_nat)) % 2.02/2.26 (define @t22 () (_ tptp.ord_less_eq_set_nat @t21)) % 2.02/2.26 (define @t23 () (_ @t22 @t20)) % 2.02/2.26 (define @t24 () (@list @t21 @t20)) % 2.02/2.26 (define @t25 () (@var "Y" tptp.nat)) % 2.02/2.26 (define @t26 () (@var "X" tptp.nat)) % 2.02/2.26 (define @t27 () (_ tptp.ord_less_eq_nat @t26)) % 2.02/2.26 (define @t28 () (_ @t27 @t25)) % 2.02/2.26 (define @t29 () (_ tptp.set_ord_atMost_nat @t25)) % 2.02/2.26 (define @t30 () (_ tptp.set_ord_atMost_nat @t26)) % 2.02/2.26 (define @t31 () (@list @t26 @t25)) % 2.02/2.26 (define @t32 () (@var "K" tptp.set_nat)) % 2.02/2.26 (define @t33 () (@var "I4" tptp.set_nat)) % 2.02/2.26 (define @t34 () (@var "K" tptp.nat)) % 2.02/2.26 (define @t35 () (@var "I4" tptp.nat)) % 2.02/2.26 (define @t36 () (_ tptp.ord_less_eq_nat @t35)) % 2.02/2.26 (define @t37 () (_ @t36 @t34)) % 2.02/2.26 (define @t38 () (= @t26 @t25)) % 2.02/2.26 (define @t39 () (@var "B" tptp.nat)) % 2.02/2.26 (define @t40 () (@var "A2" tptp.nat)) % 2.02/2.26 (define @t41 () (= @t40 @t39)) % 2.02/2.26 (define @t42 () (@var "C" tptp.nat)) % 2.02/2.26 (define @t43 () (= @t42 tptp.zero_zero_nat)) % 2.02/2.26 (define @t44 () (or @t43 @t41)) % 2.02/2.26 (define @t45 () (_ tptp.times_times_nat @t39)) % 2.02/2.26 (define @t46 () (_ @t45 @t42)) % 2.02/2.26 (define @t47 () (_ tptp.times_times_nat @t40)) % 2.02/2.26 (define @t48 () (_ @t47 @t42)) % 2.02/2.26 (define @t49 () (= @t48 @t46)) % 2.02/2.26 (define @t50 () (_ tptp.times_times_nat @t42)) % 2.02/2.26 (define @t51 () (_ @t50 @t39)) % 2.02/2.26 (define @t52 () (_ @t50 @t40)) % 2.02/2.26 (define @t53 () (= @t52 @t51)) % 2.02/2.26 (define @t54 () (@list @t42 @t40 @t39)) % 2.02/2.26 (define @t55 () (= @t39 tptp.zero_zero_nat)) % 2.02/2.26 (define @t56 () (= @t40 tptp.zero_zero_nat)) % 2.02/2.26 (define @t57 () (or @t56 @t55)) % 2.02/2.26 (define @t58 () (_ @t47 @t39)) % 2.02/2.26 (define @t59 () (= @t58 tptp.zero_zero_nat)) % 2.02/2.26 (define @t60 () (@list @t40 @t39)) % 2.02/2.26 (define @t61 () (@list @t40)) % 2.02/2.26 (define @t62 () (_ tptp.times_times_nat tptp.zero_zero_nat)) % 2.02/2.26 (define @t63 () (_ tptp.ord_less_eq_nat tptp.zero_zero_nat)) % 2.02/2.26 (define @t64 () (_ @t63 @t40)) % 2.02/2.26 (define @t65 () (@list @t3)) % 2.02/2.26 (define @t66 () (= @t34 tptp.zero_zero_nat)) % 2.02/2.26 (define @t67 () (= @t15 @t3)) % 2.02/2.26 (define @t68 () (or @t67 @t66)) % 2.02/2.26 (define @t69 () (_ tptp.times_times_nat @t3)) % 2.02/2.26 (define @t70 () (_ @t69 @t34)) % 2.02/2.26 (define @t71 () (_ @t17 @t34)) % 2.02/2.26 (define @t72 () (@list @t15 @t34 @t3)) % 2.02/2.26 (define @t73 () (_ tptp.times_times_nat @t34)) % 2.02/2.26 (define @t74 () (_ @t73 @t3)) % 2.02/2.26 (define @t75 () (_ @t73 @t15)) % 2.02/2.26 (define @t76 () (= @t75 @t74)) % 2.02/2.26 (define @t77 () (@list @t34 @t15 @t3)) % 2.02/2.26 (define @t78 () (@list @t15)) % 2.02/2.26 (define @t79 () (= @t3 tptp.zero_zero_nat)) % 2.02/2.26 (define @t80 () (= @t15 tptp.zero_zero_nat)) % 2.02/2.26 (define @t81 () (@var "M3" tptp.nat)) % 2.02/2.26 (define @t82 () (@var "X3" tptp.nat)) % 2.02/2.26 (define @t83 () (@var "P3" (-> tptp.nat Bool))) % 2.02/2.26 (define @t84 () (@list @t82)) % 2.02/2.26 (define @t85 () (@var "M2" tptp.nat)) % 2.02/2.26 (define @t86 () (@var "X2" tptp.nat)) % 2.02/2.26 (define @t87 () (_ tptp.ord_less_eq_nat @t86)) % 2.02/2.26 (define @t88 () (_ @t83 @t86)) % 2.02/2.26 (define @t89 () (@list @t86)) % 2.02/2.26 (define @t90 () (_ @t83 @t26)) % 2.02/2.26 (define @t91 () (@var "Y3" tptp.nat)) % 2.02/2.26 (define @t92 () (_ @t83 @t91)) % 2.02/2.26 (define @t93 () (@list @t91)) % 2.02/2.26 (define @t94 () (@var "Y2" tptp.nat)) % 2.02/2.26 (define @t95 () (@list @t94)) % 2.02/2.26 (define @t96 () (_ tptp.ord_less_eq_nat @t3)) % 2.02/2.26 (define @t97 () (_ @t96 @t15)) % 2.02/2.26 (define @t98 () (_ tptp.ord_less_eq_nat @t15)) % 2.02/2.26 (define @t99 () (_ @t98 @t3)) % 2.02/2.26 (define @t100 () (@var "J" tptp.nat)) % 2.02/2.26 (define @t101 () (_ (_ tptp.ord_less_eq_nat @t100) @t34)) % 2.02/2.26 (define @t102 () (=> @t101 @t37)) % 2.02/2.26 (define @t103 () (_ @t36 @t100)) % 2.02/2.26 (define @t104 () (@list @t35 @t100 @t34)) % 2.02/2.26 (define @t105 () (forall @t104 (=> @t103 @t102))) % 2.02/2.26 (define @t106 () (@var "T" tptp.set_nat)) % 2.02/2.26 (define @t107 () (@var "H" (-> tptp.nat tptp.nat))) % 2.02/2.26 (define @t108 () (_ tptp.groups1842438620at_nat @t107)) % 2.02/2.26 (define @t109 () (@var "S" tptp.set_nat)) % 2.02/2.26 (define @t110 () (@var "G" (-> tptp.nat tptp.nat))) % 2.02/2.26 (define @t111 () (_ tptp.groups1842438620at_nat @t110)) % 2.02/2.26 (define @t112 () (@var "A3" tptp.nat)) % 2.02/2.26 (define @t113 () (_ @t110 @t112)) % 2.02/2.26 (define @t114 () (@var "J" (-> tptp.nat tptp.nat))) % 2.02/2.26 (define @t115 () (_ @t114 @t112)) % 2.02/2.26 (define @t116 () (_ tptp.member_nat @t112)) % 2.02/2.26 (define @t117 () (_ @t116 @t109)) % 2.02/2.26 (define @t118 () (@list @t112)) % 2.02/2.26 (define @t119 () (@var "B2" tptp.nat)) % 2.02/2.26 (define @t120 () (@var "I4" (-> tptp.nat tptp.nat))) % 2.02/2.26 (define @t121 () (_ @t120 @t119)) % 2.02/2.26 (define @t122 () (_ (_ tptp.member_nat @t119) @t106)) % 2.02/2.26 (define @t123 () (@list @t119)) % 2.02/2.26 (define @t124 () (@var "B3" tptp.set_nat)) % 2.02/2.26 (define @t125 () (@var "Gamma" (-> tptp.nat tptp.nat))) % 2.02/2.26 (define @t126 () (@var "Phi" (-> tptp.nat tptp.nat))) % 2.02/2.26 (define @t127 () (= (_ (_ tptp.groups1842438620at_nat @t126) @t1) (_ (_ tptp.groups1842438620at_nat @t125) @t124))) % 2.02/2.26 (define @t128 () (_ @t107 @t86)) % 2.02/2.26 (define @t129 () (= (_ @t125 @t128) (_ @t126 @t86))) % 2.02/2.26 (define @t130 () (@var "K" (-> tptp.nat tptp.nat))) % 2.02/2.26 (define @t131 () (_ (_ tptp.member_nat @t128) @t124)) % 2.02/2.26 (define @t132 () (_ tptp.member_nat @t86)) % 2.02/2.26 (define @t133 () (_ @t132 @t1)) % 2.02/2.26 (define @t134 () (_ @t130 @t94)) % 2.02/2.26 (define @t135 () (_ (_ tptp.member_nat @t94) @t124)) % 2.02/2.26 (define @t136 () (@var "Ya" tptp.nat)) % 2.02/2.26 (define @t137 () (_ @t111 @t1)) % 2.02/2.26 (define @t138 () (_ @t110 @t86)) % 2.02/2.26 (define @t139 () (_ @t132 @t124)) % 2.02/2.26 (define @t140 () (= @t1 @t124)) % 2.02/2.26 (define @t141 () (@var "J2" tptp.nat)) % 2.02/2.26 (define @t142 () (@var "G" (-> tptp.nat tptp.nat tptp.nat))) % 2.02/2.26 (define @t143 () (_ @t142 @t4)) % 2.02/2.26 (define @t144 () (@list @t141)) % 2.02/2.26 (define @t145 () (not @t43)) % 2.02/2.26 (define @t146 () (not @t59)) % 2.02/2.26 (define @t147 () (not @t55)) % 2.02/2.26 (define @t148 () (not @t56)) % 2.02/2.26 (define @t149 () (_ @t116 @t1)) % 2.02/2.26 (define @t150 () (=> @t149 (= @t113 tptp.zero_zero_nat))) % 2.02/2.26 (define @t151 () (forall @t118 @t150)) % 2.02/2.26 (define @t152 () (not @t151)) % 2.02/2.26 (define @t153 () (= @t137 tptp.zero_zero_nat)) % 2.02/2.26 (define @t154 () (not @t153)) % 2.02/2.26 (define @t155 () (=> @t154 @t152)) % 2.02/2.26 (define @t156 () (@list @t110 @t1)) % 2.02/2.26 (define @t157 () (forall @t156 @t155)) % 2.02/2.26 (define @t158 () (_ @t83 @t40)) % 2.02/2.26 (define @t159 () (_ tptp.collect_nat @t83)) % 2.02/2.26 (define @t160 () (@var "X4" tptp.nat)) % 2.02/2.26 (define @t161 () (_ tptp.member_nat @t160)) % 2.02/2.26 (define @t162 () (_ @t161 @t1)) % 2.02/2.26 (define @t163 () (@list @t160)) % 2.02/2.26 (define @t164 () (@var "Q" (-> tptp.nat Bool))) % 2.02/2.26 (define @t165 () (_ tptp.collect_nat @t164)) % 2.02/2.26 (define @t166 () (_ @t164 @t86)) % 2.02/2.26 (define @t167 () (@list @t83 @t164)) % 2.02/2.26 (define @t168 () (_ tptp.ord_less_eq_nat @t40)) % 2.02/2.26 (define @t169 () (_ @t168 tptp.zero_zero_nat)) % 2.02/2.26 (define @t170 () (_ tptp.times_times_nat @t100)) % 2.02/2.26 (define @t171 () (_ tptp.ord_less_eq_nat (_ (_ tptp.times_times_nat @t35) @t34))) % 2.02/2.26 (define @t172 () (@var "L" tptp.nat)) % 2.02/2.26 (define @t173 () (_ @t17 @t15)) % 2.02/2.26 (define @t174 () (_ tptp.times_times_nat tptp.one_one_nat)) % 2.02/2.26 (define @t175 () (lambda (@list (@var "H2" tptp.nat)) tptp.zero_zero_nat)) % 2.02/2.26 (define @t176 () (@var "K2" tptp.set_nat)) % 2.02/2.26 (define @t177 () (@var "F" (-> tptp.nat tptp.nat))) % 2.02/2.26 (define @t178 () (_ tptp.groups1842438620at_nat @t177)) % 2.02/2.26 (define @t179 () (_ @t177 @t12)) % 2.02/2.26 (define @t180 () (@var "R" tptp.nat)) % 2.02/2.26 (define @t181 () (@var "N2" tptp.nat)) % 2.02/2.26 (define @t182 () (_ @t177 @t181)) % 2.02/2.26 (define @t183 () (@list @t181)) % 2.02/2.26 (define @t184 () (_ @t178 @t1)) % 2.02/2.26 (define @t185 () (_ tptp.times_times_nat @t184)) % 2.02/2.26 (define @t186 () (_ tptp.times_times_nat @t180)) % 2.02/2.26 (define @t187 () (_ @t63 @t42)) % 2.02/2.26 (define @t188 () (_ @t168 @t39)) % 2.02/2.26 (define @t189 () (@list @t40 @t39 @t42)) % 2.02/2.26 (define @t190 () (_ tptp.ord_less_eq_nat @t39)) % 2.02/2.26 (define @t191 () (_ @t190 tptp.zero_zero_nat)) % 2.02/2.26 (define @t192 () (_ tptp.ord_less_eq_nat @t58)) % 2.02/2.26 (define @t193 () (_ @t192 tptp.zero_zero_nat)) % 2.02/2.26 (define @t194 () (_ @t63 @t39)) % 2.02/2.26 (define @t195 () (_ tptp.ord_less_eq_nat @t48)) % 2.02/2.26 (define @t196 () (@var "D" tptp.nat)) % 2.02/2.26 (define @t197 () (=> @t187 (_ @t195 (_ @t45 @t196)))) % 2.02/2.26 (define @t198 () (_ tptp.ord_less_eq_nat @t42)) % 2.02/2.26 (define @t199 () (_ @t198 @t196)) % 2.02/2.26 (define @t200 () (@list @t40 @t39 @t42 @t196)) % 2.02/2.26 (define @t201 () (_ @t9 tptp.zero_zero_nat)) % 2.02/2.26 (define @t202 () (not @t201)) % 2.02/2.26 (define @t203 () (_ @t177 @t86)) % 2.02/2.26 (define @t204 () (_ tptp.ord_less_eq_nat @t203)) % 2.02/2.26 (define @t205 () (@list @t1 @t177)) % 2.02/2.26 (define @t206 () (_ tptp.ord_less_eq_set_nat @t1)) % 2.02/2.26 (define @t207 () (_ @t206 @t124)) % 2.02/2.26 (define @t208 () (@list @t1 @t124)) % 2.02/2.26 (define @t209 () (_ tptp.ord_less_eq_set_nat @t124)) % 2.02/2.26 (define @t210 () (_ @t209 @t1)) % 2.02/2.26 (define @t211 () (@list @t26)) % 2.02/2.26 (define @t212 () (@var "C" tptp.set_nat)) % 2.02/2.26 (define @t213 () (@var "F" (-> tptp.set_nat tptp.nat))) % 2.02/2.26 (define @t214 () (@var "Y2" tptp.set_nat)) % 2.02/2.26 (define @t215 () (@var "X2" tptp.set_nat)) % 2.02/2.26 (define @t216 () (_ (_ tptp.ord_less_eq_set_nat @t215) @t214)) % 2.02/2.26 (define @t217 () (@list @t215 @t214)) % 2.02/2.26 (define @t218 () (forall @t217 (=> @t216 (_ (_ tptp.ord_less_eq_nat (_ @t213 @t215)) (_ @t213 @t214))))) % 2.02/2.26 (define @t219 () (@var "B" tptp.set_nat)) % 2.02/2.26 (define @t220 () (_ tptp.ord_less_eq_set_nat @t219)) % 2.02/2.26 (define @t221 () (_ @t220 @t212)) % 2.02/2.26 (define @t222 () (=> @t221 (=> @t218 (_ @t168 (_ @t213 @t212))))) % 2.02/2.26 (define @t223 () (_ @t213 @t219)) % 2.02/2.26 (define @t224 () (@list @t40 @t213 @t219 @t212)) % 2.02/2.26 (define @t225 () (@var "F" (-> tptp.nat tptp.set_nat))) % 2.02/2.26 (define @t226 () (@var "A2" tptp.set_nat)) % 2.02/2.26 (define @t227 () (_ tptp.ord_less_eq_set_nat @t226)) % 2.02/2.26 (define @t228 () (_ @t87 @t94)) % 2.02/2.26 (define @t229 () (@list @t86 @t94)) % 2.02/2.26 (define @t230 () (forall @t229 (=> @t228 (_ (_ tptp.ord_less_eq_set_nat (_ @t225 @t86)) (_ @t225 @t94))))) % 2.02/2.26 (define @t231 () (_ @t190 @t42)) % 2.02/2.26 (define @t232 () (=> @t231 (=> @t230 (_ @t227 (_ @t225 @t42))))) % 2.02/2.26 (define @t233 () (_ @t225 @t39)) % 2.02/2.26 (define @t234 () (@list @t226 @t225 @t39 @t42)) % 2.02/2.26 (define @t235 () (@var "F" (-> tptp.set_nat tptp.set_nat))) % 2.02/2.26 (define @t236 () (forall @t217 (=> @t216 (_ (_ tptp.ord_less_eq_set_nat (_ @t235 @t215)) (_ @t235 @t214))))) % 2.02/2.26 (define @t237 () (=> @t221 (=> @t236 (_ @t227 (_ @t235 @t212))))) % 2.02/2.26 (define @t238 () (_ @t235 @t219)) % 2.02/2.26 (define @t239 () (@list @t226 @t235 @t219 @t212)) % 2.02/2.26 (define @t240 () (_ @t177 @t42)) % 2.02/2.26 (define @t241 () (_ @t177 @t94)) % 2.02/2.26 (define @t242 () (forall @t229 (=> @t228 (_ @t204 @t241)))) % 2.02/2.26 (define @t243 () (=> @t231 (=> @t242 (_ @t168 @t240)))) % 2.02/2.26 (define @t244 () (_ @t177 @t39)) % 2.02/2.26 (define @t245 () (@list @t40 @t177 @t39 @t42)) % 2.02/2.26 (define @t246 () (=> @t230 (_ (_ tptp.ord_less_eq_set_nat (_ @t225 @t40)) @t212))) % 2.02/2.26 (define @t247 () (@list @t40 @t39 @t225 @t212)) % 2.02/2.26 (define @t248 () (=> @t218 (_ (_ tptp.ord_less_eq_nat (_ @t213 @t226)) @t42))) % 2.02/2.26 (define @t249 () (_ @t227 @t219)) % 2.02/2.26 (define @t250 () (@list @t226 @t219 @t213 @t42)) % 2.02/2.26 (define @t251 () (=> @t236 (_ (_ tptp.ord_less_eq_set_nat (_ @t235 @t226)) @t212))) % 2.02/2.26 (define @t252 () (@list @t226 @t219 @t235 @t212)) % 2.02/2.26 (define @t253 () (_ @t177 @t40)) % 2.02/2.26 (define @t254 () (=> @t242 (_ (_ tptp.ord_less_eq_nat @t253) @t42))) % 2.02/2.26 (define @t255 () (@list @t40 @t39 @t177 @t42)) % 2.02/2.26 (define @t256 () (= @t40 @t244)) % 2.02/2.26 (define @t257 () (= @t244 @t42)) % 2.02/2.26 (define @t258 () (@var "X4" tptp.set_nat)) % 2.02/2.26 (define @t259 () (@var "Y5" tptp.set_nat)) % 2.02/2.26 (define @t260 () (_ tptp.ord_less_eq_set_nat @t258)) % 2.02/2.26 (define @t261 () (@var "Z" tptp.set_nat)) % 2.02/2.26 (define @t262 () (@var "Y4" tptp.set_nat)) % 2.02/2.26 (define @t263 () (lambda (@list @t262 @t261) (= @t262 @t261))) % 2.02/2.26 (define @t264 () (@var "Y5" tptp.nat)) % 2.02/2.26 (define @t265 () (_ tptp.ord_less_eq_nat @t160)) % 2.02/2.26 (define @t266 () (@var "Z" tptp.nat)) % 2.02/2.26 (define @t267 () (@var "Y4" tptp.nat)) % 2.02/2.26 (define @t268 () (lambda (@list @t267 @t266) (= @t267 @t266))) % 2.02/2.26 (define @t269 () (= @t21 @t20)) % 2.02/2.26 (define @t270 () (_ tptp.ord_less_eq_set_nat @t20)) % 2.02/2.26 (define @t271 () (_ @t270 @t21)) % 2.02/2.26 (define @t272 () (_ tptp.ord_less_eq_nat @t25)) % 2.02/2.26 (define @t273 () (_ @t272 @t26)) % 2.02/2.26 (define @t274 () (not @t28)) % 2.02/2.26 (define @t275 () (_ @t227 @t212)) % 2.02/2.26 (define @t276 () (=> @t221 @t275)) % 2.02/2.26 (define @t277 () (@list @t226 @t219 @t212)) % 2.02/2.26 (define @t278 () (_ @t168 @t42)) % 2.02/2.26 (define @t279 () (=> @t231 @t278)) % 2.02/2.26 (define @t280 () (@var "Z2" tptp.nat)) % 2.02/2.26 (define @t281 () (_ tptp.ord_less_eq_nat @t280)) % 2.02/2.26 (define @t282 () (_ @t281 @t26)) % 2.02/2.26 (define @t283 () (_ @t272 @t280)) % 2.02/2.26 (define @t284 () (_ @t281 @t25)) % 2.02/2.26 (define @t285 () (_ @t27 @t280)) % 2.02/2.26 (define @t286 () (@list @t26 @t25 @t280)) % 2.02/2.26 (define @t287 () (@list @t25 @t26)) % 2.02/2.26 (define @t288 () (@var "A4" tptp.set_nat)) % 2.02/2.26 (define @t289 () (@var "B4" tptp.set_nat)) % 2.02/2.26 (define @t290 () (_ (_ tptp.ord_less_eq_set_nat @t289) @t288)) % 2.02/2.26 (define @t291 () (_ (_ tptp.ord_less_eq_set_nat @t288) @t289)) % 2.02/2.26 (define @t292 () (@list @t288 @t289)) % 2.02/2.26 (define @t293 () (@var "A4" tptp.nat)) % 2.02/2.26 (define @t294 () (@var "B4" tptp.nat)) % 2.02/2.26 (define @t295 () (_ (_ tptp.ord_less_eq_nat @t294) @t293)) % 2.02/2.26 (define @t296 () (_ (_ tptp.ord_less_eq_nat @t293) @t294)) % 2.02/2.26 (define @t297 () (@list @t293 @t294)) % 2.02/2.26 (define @t298 () (= @t226 @t219)) % 2.02/2.26 (define @t299 () (= @t39 @t42)) % 2.02/2.26 (define @t300 () (_ @t220 @t226)) % 2.02/2.26 (define @t301 () (@list @t226 @t219)) % 2.02/2.26 (define @t302 () (_ @t190 @t40)) % 2.02/2.26 (define @t303 () (@var "Z2" tptp.set_nat)) % 2.02/2.26 (define @t304 () (@var "P3" (-> tptp.nat tptp.nat Bool))) % 2.02/2.26 (define @t305 () (_ @t304 @t112)) % 2.02/2.26 (define @t306 () (_ @t305 @t119)) % 2.02/2.26 (define @t307 () (@list @t112 @t119)) % 2.02/2.26 (define @t308 () (=> (forall @t307 (=> (_ (_ @t304 @t119) @t112) @t306)) (_ (_ @t304 @t40) @t39))) % 2.02/2.26 (define @t309 () (@list @t304 @t40 @t39)) % 2.02/2.26 (define @t310 () (_ tptp.ord_less_eq_set_nat @t212)) % 2.02/2.26 (define @t311 () (_ @t310 @t219)) % 2.02/2.26 (define @t312 () (@list @t219 @t226 @t212)) % 2.02/2.26 (define @t313 () (_ @t198 @t39)) % 2.02/2.26 (define @t314 () (@list @t39 @t40 @t42)) % 2.02/2.26 (define @t315 () (@list @t219 @t226)) % 2.02/2.26 (define @t316 () (@list @t39 @t40)) % 2.02/2.26 (define @t317 () (_ @t47 @t46)) % 2.02/2.26 (define @t318 () (_ @t164 @t160)) % 2.02/2.26 (define @t319 () (_ @t83 @t160)) % 2.02/2.26 (define @t320 () (_ (_ tptp.ord_less_eq_set_nat @t159) @t165)) % 2.02/2.26 (define @t321 () (@var "A5" tptp.set_nat)) % 2.02/2.26 (define @t322 () (@var "B5" tptp.set_nat)) % 2.02/2.26 (define @t323 () (_ (_ tptp.ord_less_eq_set_nat @t322) @t321)) % 2.02/2.26 (define @t324 () (_ (_ tptp.ord_less_eq_set_nat @t321) @t322)) % 2.02/2.26 (define @t325 () (@list @t321 @t322)) % 2.02/2.26 (define @t326 () (@var "C2" tptp.set_nat)) % 2.02/2.26 (define @t327 () (_ @t209 @t326)) % 2.02/2.26 (define @t328 () (@list @t1 @t124 @t326)) % 2.02/2.26 (define @t329 () (_ @t161 @t322)) % 2.02/2.26 (define @t330 () (_ @t161 @t321)) % 2.02/2.26 (define @t331 () (_ tptp.member_nat @t42)) % 2.02/2.26 (define @t332 () (_ tptp.member_nat @t26)) % 2.02/2.26 (define @t333 () (_ tptp.collect_nat (lambda @t163 (and @t162 @t319)))) % 2.02/2.26 (define @t334 () (_ @t161 @t124)) % 2.02/2.26 (define @t335 () (@var "X5" tptp.set_nat)) % 2.02/2.26 (define @t336 () (_ tptp.collect_nat (lambda @t163 (and (_ @t161 @t335) @t319)))) % 2.02/2.26 (define @t337 () (@var "Z3" tptp.set_nat)) % 2.02/2.26 (define @t338 () (@var "R2" tptp.set_nat)) % 2.02/2.26 (define @t339 () (_ tptp.ord_less_nat tptp.zero_zero_nat)) % 2.02/2.26 (define @t340 () (_ @t339 @t3)) % 2.02/2.26 (define @t341 () (not @t79)) % 2.02/2.26 (define @t342 () (_ tptp.ord_less_nat @t3)) % 2.02/2.26 (define @t343 () (_ tptp.ord_less_set_nat @t1)) % 2.02/2.26 (define @t344 () (_ @t343 @t124)) % 2.02/2.26 (define @t345 () (_ (_ tptp.ord_less_nat @t15) @t3)) % 2.02/2.26 (define @t346 () (_ @t339 @t34)) % 2.02/2.26 (define @t347 () (and @t346 @t345)) % 2.02/2.26 (define @t348 () (=> @t346 @t99)) % 2.02/2.26 (define @t349 () (not @t41)) % 2.02/2.26 (define @t350 () (_ tptp.ord_less_nat @t39)) % 2.02/2.26 (define @t351 () (_ @t350 @t40)) % 2.02/2.26 (define @t352 () (_ tptp.ord_less_nat @t40)) % 2.02/2.26 (define @t353 () (_ @t352 @t39)) % 2.02/2.26 (define @t354 () (_ tptp.ord_less_nat @t25)) % 2.02/2.26 (define @t355 () (_ @t354 @t26)) % 2.02/2.26 (define @t356 () (_ tptp.ord_less_nat @t26)) % 2.02/2.26 (define @t357 () (_ @t356 @t25)) % 2.02/2.26 (define @t358 () (not @t357)) % 2.02/2.26 (define @t359 () (_ tptp.ord_less_nat @t42)) % 2.02/2.26 (define @t360 () (_ @t359 @t40)) % 2.02/2.26 (define @t361 () (=> (_ @t359 @t39) @t360)) % 2.02/2.26 (define @t362 () (@var "M4" tptp.nat)) % 2.02/2.26 (define @t363 () (@var "P5" (-> tptp.nat Bool))) % 2.02/2.26 (define @t364 () (_ (_ tptp.ord_less_nat @t362) @t181)) % 2.02/2.26 (define @t365 () (@var "X6" tptp.nat)) % 2.02/2.26 (define @t366 () (@var "P4" (-> tptp.nat Bool))) % 2.02/2.26 (define @t367 () (not @t355)) % 2.02/2.26 (define @t368 () (_ @t352 @t42)) % 2.02/2.26 (define @t369 () (_ @t350 @t42)) % 2.02/2.26 (define @t370 () (=> @t369 @t368)) % 2.02/2.26 (define @t371 () (not @t38)) % 2.02/2.26 (define @t372 () (@var "P3" Bool)) % 2.02/2.26 (define @t373 () (@var "X_1" tptp.nat)) % 2.02/2.26 (define @t374 () (forall @t229 (=> (_ (_ tptp.ord_less_nat @t86) @t94) (_ (_ tptp.ord_less_nat @t203) @t241)))) % 2.02/2.26 (define @t375 () (=> @t374 (_ (_ tptp.ord_less_nat @t253) @t42))) % 2.02/2.26 (define @t376 () (=> @t369 (=> @t374 (_ @t352 @t240)))) % 2.02/2.26 (define @t377 () (= @t362 @t181)) % 2.02/2.26 (define @t378 () (@list @t362 @t181)) % 2.02/2.26 (define @t379 () (@var "J3" tptp.nat)) % 2.02/2.26 (define @t380 () (@var "M5" tptp.nat)) % 2.02/2.26 (define @t381 () (@var "N3" tptp.nat)) % 2.02/2.26 (define @t382 () (_ @t343 @t326)) % 2.02/2.26 (define @t383 () (= @t321 @t322)) % 2.02/2.26 (define @t384 () (_ tptp.ord_less_set_nat @t226)) % 2.02/2.26 (define @t385 () (_ @t384 @t219)) % 2.02/2.26 (define @t386 () (_ tptp.ord_less_set_nat @t219)) % 2.02/2.26 (define @t387 () (_ @t386 @t226)) % 2.02/2.26 (define @t388 () (= @t288 @t289)) % 2.02/2.26 (define @t389 () (not @t388)) % 2.02/2.26 (define @t390 () (@list @t289 @t288)) % 2.02/2.26 (define @t391 () (= @t293 @t294)) % 2.02/2.26 (define @t392 () (not @t391)) % 2.02/2.26 (define @t393 () (@list @t294 @t293)) % 2.02/2.26 (define @t394 () (_ tptp.ord_less_set_nat @t212)) % 2.02/2.26 (define @t395 () (_ @t394 @t226)) % 2.02/2.26 (define @t396 () (_ @t384 @t212)) % 2.02/2.26 (define @t397 () (lambda @t6 tptp.zero_zero_nat)) % 2.02/2.26 (define @t398 () (= tptp.p @t397)) % 2.02/2.26 (define @t399 () (_ tptp.p @t4)) % 2.02/2.26 (define @t400 () (_ (_ tptp.times_times_nat @t399) @t4)) % 2.02/2.26 (define @t401 () (lambda @t6 @t400)) % 2.02/2.26 (define @t402 () (_ tptp.groups1842438620at_nat @t401)) % 2.02/2.26 (define @t403 () (= (_ @t402 (_ tptp.set_ord_atMost_nat tptp.zero_zero_nat)) tptp.zero_zero_nat)) % 2.02/2.26 (define @t404 () (_ tptp.ord_less_eq_nat @t4)) % 2.02/2.26 (define @t405 () (_ @t404 tptp.zero_zero_nat)) % 2.02/2.26 (define @t406 () (_ @t9 @t4)) % 2.02/2.26 (define @t407 () (and @t406 @t405)) % 2.02/2.26 (define @t408 () (not (= @t399 tptp.zero_zero_nat))) % 2.02/2.26 (define @t409 () (=> @t408 @t407)) % 2.02/2.26 (define @t410 () (forall @t6 @t409)) % 2.02/2.26 (define @t411 () (and @t410 @t403)) % 2.02/2.26 (define @t412 () (= @t411 @t398)) % 2.02/2.26 (define @t413 () (not @t412)) % 2.02/2.26 (define @t414 () (@var "P2" (-> tptp.nat tptp.nat))) % 2.02/2.26 (define @t415 () (_ @t414 @t4)) % 2.02/2.26 (define @t416 () (lambda (@list @t414 @t181) (and (forall @t6 (=> (not (= @t415 tptp.zero_zero_nat)) (and @t406 (_ @t404 @t181)))) (= (_ (_ tptp.groups1842438620at_nat (lambda @t6 (_ (_ tptp.times_times_nat @t415) @t4))) (_ tptp.set_ord_atMost_nat @t181)) @t181)))) % 2.02/2.26 (define @t417 () (@var "U" tptp.set_nat)) % 2.02/2.26 (define @t418 () (lambda (@list @t417) (_ tptp.collect_set_nat (lambda (@list @t258) (_ @t260 @t417))))) % 2.02/2.26 (define @t419 () (@var "U" tptp.nat)) % 2.02/2.26 (define @t420 () (lambda (@list @t419) (_ tptp.collect_nat (lambda @t163 (_ @t265 @t419))))) % 2.02/2.26 (define @t421 () (@var "T2" tptp.nat)) % 2.02/2.26 (define @t422 () (_ tptp.member_nat @t421)) % 2.02/2.26 (define @t423 () (lambda @t325 (forall (@list @t421) (=> (_ @t422 @t321) (_ @t422 @t322))))) % 2.02/2.26 (define @t424 () (lambda @t378 (and (_ (_ tptp.ord_less_eq_nat @t362) @t181) (not @t377)))) % 2.02/2.26 (define @t425 () (lambda @t325 (and @t324 (not @t383)))) % 2.02/2.26 (define @t426 () (tptp.ord_less_eq_nat @t4 tptp.zero_zero_nat)) % 2.02/2.26 (define @t427 () (tptp.ord_less_eq_nat tptp.one_one_nat @t4)) % 2.02/2.26 (define @t428 () (tptp.p @t4)) % 2.02/2.26 (define @t429 () (forall @t6 (or (= tptp.zero_zero_nat @t428) (and @t427 @t426)))) % 2.02/2.26 (define @t430 () (@const 0 tptp.nat)) % 2.02/2.26 (define @t431 () (tptp.ord_less_eq_nat @t430 tptp.zero_zero_nat)) % 2.02/2.26 (define @t432 () (tptp.ord_less_eq_nat tptp.one_one_nat @t430)) % 2.02/2.26 (define @t433 () (and @t432 @t431)) % 2.02/2.26 (define @t434 () (tptp.p @t430)) % 2.02/2.26 (define @t435 () (= tptp.zero_zero_nat @t434)) % 2.02/2.26 (define @t436 () (or @t435 @t433)) % 2.02/2.26 (define @t437 () (not @t433)) % 2.02/2.26 (define @t438 () (tptp.ord_less_eq_nat tptp.one_one_nat tptp.zero_zero_nat)) % 2.02/2.26 (define @t439 () (tptp.ord_less_eq_nat @t35 @t34)) % 2.02/2.26 (define @t440 () (tptp.ord_less_eq_nat @t100 @t34)) % 2.02/2.26 (define @t441 () (not @t101)) % 2.02/2.26 (define @t442 () (tptp.ord_less_eq_nat @t35 @t100)) % 2.02/2.26 (define @t443 () (not @t103)) % 2.02/2.26 (define @t444 () (or @t443 @t441 @t37)) % 2.02/2.26 (define @t445 () (not @t431)) % 2.02/2.26 (define @t446 () (not @t432)) % 2.02/2.26 (define @t447 () (or @t446 @t445 @t438)) % 2.02/2.26 (define @t448 () (_ @t397 @t430)) % 2.02/2.26 (define @t449 () (@purify @t397)) % 2.02/2.26 (define @t450 () (_ @t449 @t430)) % 2.02/2.26 (define @t451 () (= @t434 @t450)) % 2.02/2.26 (define @t452 () (not @t451)) % 2.02/2.26 (define @t453 () (= tptp.p @t449)) % 2.02/2.26 (define @t454 () (or @t453 @t452)) % 2.02/2.26 (define @t455 () (lambda @t163 (_ @t265 tptp.zero_zero_nat))) % 2.02/2.26 (define @t456 () (@purify @t455)) % 2.02/2.26 (define @t457 () (tptp.collect_nat @t456)) % 2.02/2.26 (define @t458 () (@purify @t401)) % 2.02/2.26 (define @t459 () (tptp.groups1842438620at_nat @t458 @t457)) % 2.02/2.26 (define @t460 () (= tptp.zero_zero_nat @t459)) % 2.02/2.26 (define @t461 () (and @t429 @t460)) % 2.02/2.26 (define @t462 () (_ tptp.collect_nat @t456)) % 2.02/2.26 (define @t463 () (_ tptp.groups1842438620at_nat @t458)) % 2.02/2.26 (define @t464 () (_ tptp.collect_nat @t455)) % 2.02/2.26 (define @t465 () (_ @t402 @t464)) % 2.02/2.26 (define @t466 () (= tptp.zero_zero_nat @t465)) % 2.02/2.26 (define @t467 () (and @t429 @t466)) % 2.02/2.26 (define @t468 () (= @t398 @t467)) % 2.02/2.26 (define @t469 () (_ @t420 tptp.zero_zero_nat)) % 2.02/2.26 (define @t470 () (= (_ @t402 @t469) tptp.zero_zero_nat)) % 2.02/2.26 (define @t471 () (= tptp.zero_zero_nat @t399)) % 2.02/2.26 (define @t472 () (or @t471 @t407)) % 2.02/2.26 (define @t473 () (not @t471)) % 2.02/2.26 (define @t474 () (and @t410 @t470)) % 2.02/2.26 (define @t475 () (forall @t118 (or (not (tptp.member_nat @t112 @t457)) (= tptp.zero_zero_nat (_ @t458 @t112))))) % 2.02/2.26 (define @t476 () (@quantifiers_skolemize @t475 0)) % 2.02/2.26 (define @t477 () (tptp.p @t476)) % 2.02/2.26 (define @t478 () (=> @t453 (= @t477 tptp.zero_zero_nat))) % 2.02/2.26 (define @t479 () (_ @t110 @t112)) % 2.02/2.26 (define @t480 () (tptp.member_nat @t112 @t1)) % 2.02/2.26 (define @t481 () (not (forall @t118 (or (not @t480) (= tptp.zero_zero_nat @t479))))) % 2.02/2.26 (define @t482 () (tptp.groups1842438620at_nat @t110 @t1)) % 2.02/2.26 (define @t483 () (= tptp.zero_zero_nat @t137)) % 2.02/2.26 (define @t484 () (or @t483 @t481)) % 2.02/2.26 (define @t485 () (not @t483)) % 2.02/2.26 (define @t486 () (= tptp.zero_zero_nat @t113)) % 2.02/2.26 (define @t487 () (not @t149)) % 2.02/2.26 (define @t488 () (or @t487 @t486)) % 2.02/2.26 (define @t489 () (not @t475)) % 2.02/2.26 (define @t490 () (or @t460 @t489)) % 2.02/2.26 (define @t491 () (_ @t458 @t476)) % 2.02/2.26 (define @t492 () (= tptp.zero_zero_nat @t491)) % 2.02/2.26 (define @t493 () (or (not (tptp.member_nat @t476 @t457)) @t492)) % 2.02/2.26 (define @t494 () (not @t493)) % 2.02/2.26 (define @t495 () (tptp.times_times_nat @t428 @t4)) % 2.02/2.26 (define @t496 () (_ @t458 @t4)) % 2.02/2.26 (define @t497 () (= @t400 @t496)) % 2.02/2.26 (define @t498 () (_ @t401 @t4)) % 2.02/2.26 (define @t499 () (= @t496 @t498)) % 2.02/2.26 (define @t500 () (forall @t6 @t499)) % 2.02/2.26 (define @t501 () (tptp.times_times_nat @t477 @t476)) % 2.02/2.26 (define @t502 () (= tptp.zero_zero_nat @t501)) % 2.02/2.26 (define @t503 () (not @t502)) % 2.02/2.26 (define @t504 () (= @t491 @t501)) % 2.02/2.26 (define @t505 () (not @t504)) % 2.02/2.26 (define @t506 () (not @t492)) % 2.02/2.26 (define @t507 () (and @t506 @t504)) % 2.02/2.26 (define @t508 () (@purify @t175)) % 2.02/2.26 (define @t509 () (= @t62 @t508)) % 2.02/2.26 (define @t510 () (= tptp.zero_zero_nat @t477)) % 2.02/2.26 (define @t511 () (_ tptp.times_times_nat @t477)) % 2.02/2.26 (define @t512 () (= @t508 @t511)) % 2.02/2.26 (define @t513 () (and @t509 @t510)) % 2.02/2.26 (define @t514 () (_ tptp.p @t476)) % 2.02/2.26 (define @t515 () (_ @t511 @t476)) % 2.02/2.26 (define @t516 () (= tptp.zero_zero_nat @t515)) % 2.02/2.26 (define @t517 () (=> (= @t511 @t508) (= @t515 tptp.zero_zero_nat))) % 2.02/2.26 (define @t518 () (not @t429)) % 2.02/2.26 (define @t519 () (not @t461)) % 2.02/2.26 (define @t520 () (@list true)) % 2.02/2.26 (define @t521 () (@list @t429)) % 2.02/2.26 (define @t522 () (@quantifiers_skolemize @t429 0)) % 2.02/2.26 (define @t523 () (tptp.p @t522)) % 2.02/2.26 (define @t524 () (= tptp.zero_zero_nat @t523)) % 2.02/2.26 (define @t525 () (or @t524 (and (tptp.ord_less_eq_nat tptp.one_one_nat @t522) (tptp.ord_less_eq_nat @t522 tptp.zero_zero_nat)))) % 2.02/2.26 (define @t526 () (not @t525)) % 2.02/2.26 (define @t527 () (=> @t453 (= @t523 tptp.zero_zero_nat))) % 2.02/2.26 (assume @p1 (forall @t2 (= (_ (_ tptp.groups1842438620at_nat (lambda (@list (@var "Uu" tptp.nat)) tptp.zero_zero_nat)) @t1) tptp.zero_zero_nat))) % 2.02/2.26 (assume @p2 (forall @t11 (=> @t10 (not (=> (forall (@list @t8) (=> (not (= (_ @t5 @t8) tptp.zero_zero_nat)) (and (_ @t9 @t8) (_ (_ tptp.ord_less_eq_nat @t8) @t3)))) (not @t7)))))) % 2.02/2.26 (assume @p3 (forall @t11 (=> (forall @t13 (=> (not (= (_ @t5 @t12) tptp.zero_zero_nat)) (and (_ @t9 @t12) (_ (_ tptp.ord_less_eq_nat @t12) @t3)))) (=> @t7 @t10)))) % 2.02/2.26 (assume @p4 (forall @t19 (= (= tptp.one_one_nat @t18) @t16))) % 2.02/2.26 (assume @p5 (forall @t19 (= (= @t18 tptp.one_one_nat) @t16))) % 2.02/2.26 (assume @p6 (forall @t24 (= (_ (_ tptp.ord_le1613022364et_nat (_ tptp.set_or1086813439et_nat @t21)) (_ tptp.set_or1086813439et_nat @t20)) @t23))) % 2.02/2.26 (assume @p7 (forall @t31 (= (_ (_ tptp.ord_less_eq_set_nat @t30) @t29) @t28))) % 2.02/2.26 (assume @p8 (forall (@list @t33 @t32) (= (_ (_ tptp.member_set_nat @t33) (_ tptp.set_or1086813439et_nat @t32)) (_ (_ tptp.ord_less_eq_set_nat @t33) @t32)))) % 2.02/2.26 (assume @p9 (forall (@list @t35 @t34) (= (_ (_ tptp.member_nat @t35) (_ tptp.set_ord_atMost_nat @t34)) @t37))) % 2.02/2.26 (assume @p10 (forall @t31 (= (= @t30 @t29) @t38))) % 2.02/2.26 (assume @p11 (forall (@list @t40 @t42 @t39) (= @t49 @t44))) % 2.02/2.26 (assume @p12 (forall @t54 (= @t53 @t44))) % 2.02/2.26 (assume @p13 (forall @t60 (= @t59 @t57))) % 2.02/2.26 (assume @p14 (forall @t61 (= (_ @t47 tptp.zero_zero_nat) tptp.zero_zero_nat))) % 2.02/2.26 (assume @p15 (forall @t61 (= (_ @t62 @t40) tptp.zero_zero_nat))) % 2.02/2.26 (assume @p16 (forall @t61 @t64)) % 2.02/2.26 (assume @p17 (forall @t65 (_ @t63 @t3))) % 2.02/2.26 (assume @p18 (forall @t72 (= (= @t71 @t70) @t68))) % 2.02/2.26 (assume @p19 (forall @t77 (= @t76 @t68))) % 2.02/2.26 (assume @p20 (forall @t78 (= (_ @t17 tptp.zero_zero_nat) tptp.zero_zero_nat))) % 2.02/2.26 (assume @p21 (forall @t19 (= (= @t18 tptp.zero_zero_nat) (or @t80 @t79)))) % 2.02/2.26 (assume @p22 (forall (@list @t83 @t26 @t85) (=> @t90 (=> (forall @t89 (=> @t88 (_ @t87 @t85))) (not (forall (@list @t81) (=> (_ @t83 @t81) (not (forall @t84 (=> (_ @t83 @t82) (_ (_ tptp.ord_less_eq_nat @t82) @t81))))))))))) % 2.02/2.26 (assume @p23 (forall (@list @t83 @t34 @t39) (=> (_ @t83 @t34) (=> (forall @t95 (=> (_ @t83 @t94) (_ (_ tptp.ord_less_eq_nat @t94) @t39))) (exists @t89 (and @t88 (forall @t93 (=> @t92 (_ (_ tptp.ord_less_eq_nat @t91) @t86))))))))) % 2.02/2.26 (assume @p24 (forall @t19 (or @t99 @t97))) % 2.02/2.26 (assume @p25 (forall @t19 (=> @t99 (=> @t97 @t67)))) % 2.02/2.26 (assume @p26 (forall @t19 (=> @t67 @t99))) % 2.02/2.26 (assume @p27 @t105) % 2.02/2.26 (assume @p28 (forall @t65 (_ @t96 @t3))) % 2.02/2.26 (assume @p29 (forall (@list @t109 @t120 @t114 @t106 @t107 @t110) (=> (forall @t118 (=> @t117 (= (_ @t120 @t115) @t112))) (=> (forall @t118 (=> @t117 (_ (_ tptp.member_nat @t115) @t106))) (=> (forall @t123 (=> @t122 (= (_ @t114 @t121) @t119))) (=> (forall @t123 (=> @t122 (_ (_ tptp.member_nat @t121) @t109))) (=> (forall @t118 (=> @t117 (= (_ @t107 @t115) @t113))) (= (_ @t111 @t109) (_ @t108 @t106))))))))) % 2.02/2.26 (assume @p30 (forall (@list @t124 @t130 @t1 @t107 @t125 @t126) (=> (forall @t95 (=> @t135 (and (_ (_ tptp.member_nat @t134) @t1) (= (_ @t107 @t134) @t94)))) (=> (forall @t89 (=> @t133 (and @t131 (= (_ @t130 @t128) @t86) @t129))) @t127)))) % 2.02/2.26 (assume @p31 (forall (@list @t124 @t1 @t107 @t125 @t126) (=> (forall @t95 (=> @t135 (exists @t84 (and (_ (_ tptp.member_nat @t82) @t1) (= (_ @t107 @t82) @t94) (forall (@list @t136) (=> (and (_ (_ tptp.member_nat @t136) @t1) (= (_ @t107 @t136) @t94)) (= @t136 @t82))))))) (=> (forall @t89 (=> @t133 (and @t131 @t129))) @t127)))) % 2.02/2.26 (assume @p32 (forall (@list @t1 @t124 @t110 @t107) (=> @t140 (=> (forall @t89 (=> @t139 (= @t138 @t128))) (= @t137 (_ @t108 @t124)))))) % 2.02/2.26 (assume @p33 (forall (@list @t142 @t124 @t1) (= (_ (_ tptp.groups1842438620at_nat (lambda @t6 (_ (_ tptp.groups1842438620at_nat @t143) @t124))) @t1) (_ (_ tptp.groups1842438620at_nat (lambda @t144 (_ (_ tptp.groups1842438620at_nat (lambda @t6 (_ @t143 @t141))) @t1))) @t124)))) % 2.02/2.26 (assume @p34 (forall @t54 (=> @t145 (= @t49 @t41)))) % 2.02/2.26 (assume @p35 (forall @t54 (=> @t145 (= @t53 @t41)))) % 2.02/2.26 (assume @p36 (forall @t60 (=> @t148 (=> @t147 @t146)))) % 2.02/2.26 (assume @p37 (forall @t60 (=> @t59 @t57))) % 2.02/2.26 (assume @p38 (forall @t60 (=> @t146 (and @t148 @t147)))) % 2.02/2.26 (assume @p39 (not (= tptp.zero_zero_nat tptp.one_one_nat))) % 2.02/2.26 (assume @p40 @t157) % 2.02/2.26 (assume @p41 (forall (@list @t1 @t110) (=> (forall @t89 (=> @t133 (= @t138 tptp.zero_zero_nat))) @t153))) % 2.02/2.26 (assume @p42 (forall (@list @t40 @t83) (= (_ (_ tptp.member_nat @t40) @t159) @t158))) % 2.02/2.26 (assume @p43 (forall @t2 (= (_ tptp.collect_nat (lambda @t163 @t162)) @t1))) % 2.02/2.26 (assume @p44 (forall @t167 (=> (forall @t89 (= @t88 @t166)) (= @t159 @t165)))) % 2.02/2.26 (assume @p45 (forall @t61 (=> @t169 @t56))) % 2.02/2.26 (assume @p46 (forall @t61 (= @t169 @t56))) % 2.02/2.26 (assume @p47 (forall @t65 (= (_ @t96 tptp.zero_zero_nat) @t79))) % 2.02/2.26 (assume @p48 (forall @t65 (= (_ @t62 @t3) tptp.zero_zero_nat))) % 2.02/2.26 (assume @p49 (forall @t104 (=> @t103 (_ (_ tptp.ord_less_eq_nat (_ @t73 @t35)) (_ @t73 @t100))))) % 2.02/2.26 (assume @p50 (forall @t104 (=> @t103 (_ @t171 (_ @t170 @t34))))) % 2.02/2.26 (assume @p51 (forall (@list @t35 @t100 @t34 @t172) (=> @t103 (=> (_ (_ tptp.ord_less_eq_nat @t34) @t172) (_ @t171 (_ @t170 @t172)))))) % 2.02/2.26 (assume @p52 (forall @t78 (_ @t98 @t173))) % 2.02/2.26 (assume @p53 (forall @t78 (_ @t98 (_ @t17 @t173)))) % 2.02/2.26 (assume @p54 (forall @t65 (= (_ @t69 tptp.one_one_nat) @t3))) % 2.02/2.26 (assume @p55 (forall @t65 (= (_ @t174 @t3) @t3))) % 2.02/2.26 (assume @p56 (= @t175 @t62)) % 2.02/2.26 (assume @p57 (= (lambda @t163 @t160) @t174)) % 2.02/2.26 (assume @p58 (forall (@list @t176 @t177 @t110) (=> (forall @t13 (=> (_ (_ tptp.member_nat @t12) @t176) (_ (_ tptp.ord_less_eq_nat @t179) (_ @t110 @t12)))) (_ (_ tptp.ord_less_eq_nat (_ @t178 @t176)) (_ @t111 @t176))))) % 2.02/2.26 (assume @p59 (forall (@list @t177 @t1 @t180) (= (_ @t185 @t180) (_ (_ tptp.groups1842438620at_nat (lambda @t183 (_ (_ tptp.times_times_nat @t182) @t180))) @t1)))) % 2.02/2.26 (assume @p60 (forall (@list @t180 @t177 @t1) (= (_ @t186 @t184) (_ (_ tptp.groups1842438620at_nat (lambda @t183 (_ @t186 @t182))) @t1)))) % 2.02/2.26 (assume @p61 (forall (@list @t177 @t1 @t110 @t124) (= (_ @t185 (_ @t111 @t124)) (_ (_ tptp.groups1842438620at_nat (lambda @t6 (_ (_ tptp.groups1842438620at_nat (lambda @t144 (_ (_ tptp.times_times_nat (_ @t177 @t4)) (_ @t110 @t141)))) @t124))) @t1)))) % 2.02/2.26 (assume @p62 (forall @t189 (=> @t188 (=> @t187 (_ (_ tptp.ord_less_eq_nat @t52) @t51))))) % 2.02/2.26 (assume @p63 (forall @t60 (=> @t64 (=> @t191 (_ (_ tptp.ord_less_eq_nat (_ @t45 @t40)) tptp.zero_zero_nat))))) % 2.02/2.26 (assume @p64 (forall @t60 (=> @t169 (=> @t194 @t193)))) % 2.02/2.26 (assume @p65 (forall @t60 (=> @t64 (=> @t191 @t193)))) % 2.02/2.26 (assume @p66 (forall @t60 (=> @t64 (=> @t194 (_ @t63 @t58))))) % 2.02/2.26 (assume @p67 (forall @t60 (=> (or (and @t64 @t191) (and @t169 @t194)) @t193))) % 2.02/2.26 (assume @p68 (forall @t189 (=> @t188 (=> @t187 (_ @t195 @t46))))) % 2.02/2.26 (assume @p69 (forall @t200 (=> @t188 (=> @t199 (=> @t64 @t197))))) % 2.02/2.26 (assume @p70 (forall @t200 (=> @t188 (=> @t199 (=> @t194 @t197))))) % 2.02/2.26 (assume @p71 @t202) % 2.02/2.26 (assume @p72 (_ @t63 tptp.one_one_nat)) % 2.02/2.26 (assume @p73 (forall @t205 (=> (forall @t89 (=> @t133 (_ @t204 tptp.zero_zero_nat))) (_ (_ tptp.ord_less_eq_nat @t184) tptp.zero_zero_nat)))) % 2.02/2.26 (assume @p74 (forall @t205 (=> (forall @t89 (=> @t133 (_ @t63 @t203))) (_ @t63 @t184)))) % 2.02/2.26 (assume @p75 (forall @t19 (=> (= @t15 @t18) (or @t14 @t80)))) % 2.02/2.26 (assume @p76 (forall (@list @t42 @t40) (=> (_ @t198 tptp.one_one_nat) (=> @t64 (_ @t195 @t40))))) % 2.02/2.26 (assume @p77 (forall @t60 (=> (_ @t168 tptp.one_one_nat) (=> @t194 (=> (_ @t190 tptp.one_one_nat) (_ @t192 tptp.one_one_nat)))))) % 2.02/2.26 (assume @p78 (forall @t61 (= (_ @t47 tptp.one_one_nat) @t40))) % 2.02/2.26 (assume @p79 (forall @t61 (= (_ @t174 @t40) @t40))) % 2.02/2.26 (assume @p80 (forall @t208 (=> (forall @t89 (=> @t133 @t139)) @t207))) % 2.02/2.26 (assume @p81 (forall @t208 (=> @t207 (=> @t210 @t140)))) % 2.02/2.26 (assume @p82 (forall (@list @t21) (_ @t22 @t21))) % 2.02/2.26 (assume @p83 (forall @t211 (_ @t27 @t26))) % 2.02/2.26 (assume @p84 (forall @t77 (= @t76 (or @t66 @t67)))) % 2.02/2.26 (assume @p85 (forall @t224 (=> (_ @t168 @t223) @t222))) % 2.02/2.26 (assume @p86 (forall @t234 (=> (_ @t227 @t233) @t232))) % 2.02/2.26 (assume @p87 (forall @t239 (=> (_ @t227 @t238) @t237))) % 2.02/2.26 (assume @p88 (forall @t245 (=> (_ @t168 @t244) @t243))) % 2.02/2.26 (assume @p89 (forall @t247 (=> @t188 (=> (_ (_ tptp.ord_less_eq_set_nat @t233) @t212) @t246)))) % 2.02/2.26 (assume @p90 (forall @t250 (=> @t249 (=> (_ (_ tptp.ord_less_eq_nat @t223) @t42) @t248)))) % 2.02/2.26 (assume @p91 (forall @t252 (=> @t249 (=> (_ (_ tptp.ord_less_eq_set_nat @t238) @t212) @t251)))) % 2.02/2.26 (assume @p92 (forall @t255 (=> @t188 (=> (_ (_ tptp.ord_less_eq_nat @t244) @t42) @t254)))) % 2.02/2.26 (assume @p93 (forall @t234 (=> (= @t226 @t233) @t232))) % 2.02/2.26 (assume @p94 (forall @t224 (=> (= @t40 @t223) @t222))) % 2.02/2.26 (assume @p95 (forall @t239 (=> (= @t226 @t238) @t237))) % 2.02/2.26 (assume @p96 (forall @t245 (=> @t256 @t243))) % 2.02/2.26 (assume @p97 (forall @t247 (=> @t188 (=> (= @t233 @t212) @t246)))) % 2.02/2.26 (assume @p98 (forall @t250 (=> @t249 (=> (= @t223 @t42) @t248)))) % 2.02/2.26 (assume @p99 (forall @t252 (=> @t249 (=> (= @t238 @t212) @t251)))) % 2.02/2.26 (assume @p100 (forall @t255 (=> @t188 (=> @t257 @t254)))) % 2.02/2.26 (assume @p101 (= @t263 (lambda (@list @t258 @t259) (and (_ @t260 @t259) (_ (_ tptp.ord_less_eq_set_nat @t259) @t258))))) % 2.02/2.26 (assume @p102 (= @t268 (lambda (@list @t160 @t264) (and (_ @t265 @t264) (_ (_ tptp.ord_less_eq_nat @t264) @t160))))) % 2.02/2.26 (assume @p103 (forall @t24 (=> @t23 (=> @t271 @t269)))) % 2.02/2.26 (assume @p104 (forall @t31 (=> @t28 (=> @t273 @t38)))) % 2.02/2.26 (assume @p105 (forall @t31 (or @t28 @t273))) % 2.02/2.26 (assume @p106 (forall @t24 (=> @t269 @t23))) % 2.02/2.26 (assume @p107 (forall @t31 (=> @t38 @t28))) % 2.02/2.26 (assume @p108 (forall @t31 (=> @t274 @t273))) % 2.02/2.26 (assume @p109 (forall @t277 (=> @t249 @t276))) % 2.02/2.26 (assume @p110 (forall @t189 (=> @t188 @t279))) % 2.02/2.26 (assume @p111 (forall @t286 (=> (=> @t28 (not @t283)) (=> (=> @t273 (not @t285)) (=> (=> @t285 (not @t284)) (=> (=> @t284 (not @t273)) (=> (=> @t283 (not @t282)) (not (=> @t282 @t274))))))))) % 2.02/2.26 (assume @p112 (forall (@list @t20 @t21) (=> @t271 (= @t23 @t269)))) % 2.02/2.26 (assume @p113 (forall @t287 (=> @t273 (= @t28 @t38)))) % 2.02/2.26 (assume @p114 (= @t263 (lambda @t292 (and @t291 @t290)))) % 2.02/2.26 (assume @p115 (= @t268 (lambda @t297 (and @t296 @t295)))) % 2.02/2.26 (assume @p116 (forall @t277 (=> @t298 @t276))) % 2.02/2.26 (assume @p117 (forall @t189 (=> @t41 @t279))) % 2.02/2.26 (assume @p118 (forall @t277 (=> @t249 (=> (= @t219 @t212) @t275)))) % 2.02/2.26 (assume @p119 (forall @t189 (=> @t188 (=> @t299 @t278)))) % 2.02/2.26 (assume @p120 (forall @t301 (=> @t249 (=> @t300 @t298)))) % 2.02/2.26 (assume @p121 (forall @t60 (=> @t188 (=> @t302 @t41)))) % 2.02/2.26 (assume @p122 (forall (@list @t21 @t20 @t303) (=> @t23 (=> (_ @t270 @t303) (_ @t22 @t303))))) % 2.02/2.26 (assume @p123 (forall @t286 (=> @t28 (=> @t283 @t285)))) % 2.02/2.26 (assume @p124 (forall (@list @t226) (_ @t227 @t226))) % 2.02/2.26 (assume @p125 (forall @t61 (_ @t168 @t40))) % 2.02/2.26 (assume @p126 (forall @t309 (=> (forall @t307 (=> (_ (_ tptp.ord_less_eq_nat @t112) @t119) @t306)) @t308))) % 2.02/2.26 (assume @p127 (forall @t312 (=> @t300 (=> @t311 (_ @t310 @t226))))) % 2.02/2.26 (assume @p128 (forall @t314 (=> @t302 (=> @t313 (_ @t198 @t40))))) % 2.02/2.26 (assume @p129 (= @t263 (lambda @t292 (and @t290 @t291)))) % 2.02/2.26 (assume @p130 (= @t268 (lambda @t297 (and @t295 @t296)))) % 2.02/2.26 (assume @p131 (forall @t315 (=> @t300 (=> @t249 @t298)))) % 2.02/2.26 (assume @p132 (forall @t316 (=> @t302 (=> @t188 @t41)))) % 2.02/2.26 (assume @p133 (forall @t211 (= (= tptp.zero_zero_nat @t26) (= @t26 tptp.zero_zero_nat)))) % 2.02/2.26 (assume @p134 (forall @t189 (= (_ (_ tptp.times_times_nat @t58) @t42) @t317))) % 2.02/2.26 (assume @p135 (= tptp.times_times_nat (lambda @t297 (_ (_ tptp.times_times_nat @t294) @t293)))) % 2.02/2.26 (assume @p136 (forall @t314 (= (_ @t45 @t48) @t317))) % 2.02/2.26 (assume @p137 (forall @t211 (= (= tptp.one_one_nat @t26) (= @t26 tptp.one_one_nat)))) % 2.02/2.26 (assume @p138 (forall @t167 (= @t320 (forall @t163 (=> @t319 @t318))))) % 2.02/2.26 (assume @p139 (= @t263 (lambda @t325 (and @t324 @t323)))) % 2.02/2.26 (assume @p140 (forall @t328 (=> @t207 (=> @t327 (_ @t206 @t326))))) % 2.02/2.26 (assume @p141 (forall @t167 (=> (forall @t89 (=> @t88 @t166)) @t320))) % 2.02/2.26 (assume @p142 (forall @t2 (_ @t206 @t1))) % 2.02/2.26 (assume @p143 (forall @t208 (=> @t140 @t210))) % 2.02/2.26 (assume @p144 (forall @t208 (=> @t140 @t207))) % 2.02/2.26 (assume @p145 (= tptp.ord_less_eq_set_nat (lambda @t325 (forall @t163 (=> @t330 @t329))))) % 2.02/2.26 (assume @p146 (forall @t208 (=> @t140 (not (=> @t207 (not @t210)))))) % 2.02/2.26 (assume @p147 (forall (@list @t1 @t124 @t42) (=> @t207 (=> (_ @t331 @t1) (_ @t331 @t124))))) % 2.02/2.26 (assume @p148 (forall (@list @t1 @t124 @t26) (=> @t207 (=> (_ @t332 @t1) (_ @t332 @t124))))) % 2.02/2.26 (assume @p149 (= tptp.ord_less_eq_set_nat (lambda @t325 (_ (_ tptp.ord_less_eq_nat_o (lambda @t163 @t330)) (lambda @t163 @t329))))) % 2.02/2.26 (assume @p150 (forall (@list @t1 @t83) (_ (_ tptp.ord_less_eq_set_nat @t333) @t1))) % 2.02/2.26 (assume @p151 (forall @t211 (_ @t63 @t26))) % 2.02/2.26 (assume @p152 (_ @t9 tptp.one_one_nat)) % 2.02/2.26 (assume @p153 (_ @t63 tptp.zero_zero_nat)) % 2.02/2.26 (assume @p154 (forall (@list @t124 @t1 @t83) (=> @t210 (= (_ @t209 @t333) (forall @t163 (=> @t334 @t319)))))) % 2.02/2.26 (assume @p155 (forall (@list @t124 @t1 @t164 @t83) (=> @t210 (=> (forall @t89 (=> @t139 (=> @t166 @t88))) (_ (_ tptp.ord_less_eq_set_nat (_ tptp.collect_nat (lambda @t163 (and @t334 @t318)))) @t333))))) % 2.02/2.26 (assume @p156 (forall (@list @t335 @t83) (_ (_ tptp.ord_less_eq_set_nat @t336) @t335))) % 2.02/2.26 (assume @p157 (forall (@list @t26 @t337 @t335 @t83) (=> (_ @t332 @t337) (=> (_ (_ tptp.ord_less_eq_set_nat @t337) @t336) @t90)))) % 2.02/2.26 (assume @p158 (forall (@list @t338 @t109) (= (_ (_ tptp.ord_less_eq_nat_o (lambda @t163 (_ @t161 @t338))) (lambda @t163 (_ @t161 @t109))) (_ (_ tptp.ord_less_eq_set_nat @t338) @t109)))) % 2.02/2.26 (assume @p159 (forall (@list @t1 @t83 @t164) (= (_ @t206 (_ tptp.collect_nat (lambda @t163 (and @t319 @t318)))) (and (_ @t206 @t159) (_ @t206 @t165))))) % 2.02/2.26 (assume @p160 (forall @t65 (= @t341 @t340))) % 2.02/2.26 (assume @p161 (forall @t65 (not (_ @t342 tptp.zero_zero_nat)))) % 2.02/2.26 (assume @p162 (forall @t61 (= @t148 (_ @t339 @t40)))) % 2.02/2.26 (assume @p163 (forall @t208 (=> @t207 (=> (not @t140) @t344)))) % 2.02/2.26 (assume @p164 (forall @t65 (= (not @t340) @t79))) % 2.02/2.26 (assume @p165 (forall @t19 (= (_ @t339 @t18) (and (_ @t339 @t15) @t340)))) % 2.02/2.26 (assume @p166 (forall @t72 (= (_ (_ tptp.ord_less_nat @t71) @t70) @t347))) % 2.02/2.26 (assume @p167 (forall @t77 (= (_ (_ tptp.ord_less_nat @t75) @t74) @t347))) % 2.02/2.26 (assume @p168 (forall @t65 (= (_ @t342 tptp.one_one_nat) @t79))) % 2.02/2.26 (assume @p169 (forall @t72 (= (_ (_ tptp.ord_less_eq_nat @t71) @t70) @t348))) % 2.02/2.26 (assume @p170 (forall @t77 (= (_ (_ tptp.ord_less_eq_nat @t75) @t74) @t348))) % 2.02/2.26 (assume @p171 (forall @t316 (=> @t351 @t349))) % 2.02/2.26 (assume @p172 (forall @t60 (=> @t353 @t349))) % 2.02/2.26 (assume @p173 (forall @t31 (= @t358 (or @t355 @t38)))) % 2.02/2.26 (assume @p174 (forall @t314 (=> @t351 @t361))) % 2.02/2.26 (assume @p175 (forall @t309 (=> (forall @t307 (=> (_ (_ tptp.ord_less_nat @t112) @t119) @t306)) (=> (forall @t118 (_ @t305 @t112)) @t308)))) % 2.02/2.26 (assume @p176 (= (lambda (@list @t366) (exists (@list @t365) (_ @t366 @t365))) (lambda (@list @t363) (exists @t183 (and (_ @t363 @t181) (forall (@list @t362) (=> @t364 (not (_ @t363 @t362))))))))) % 2.02/2.26 (assume @p177 (forall @t31 (=> @t357 @t367))) % 2.02/2.26 (assume @p178 (forall @t189 (=> @t353 @t370))) % 2.02/2.26 (assume @p179 (forall @t61 (not (_ @t352 @t40)))) % 2.02/2.26 (assume @p180 (forall @t31 (=> @t358 (=> @t371 @t355)))) % 2.02/2.26 (assume @p181 (forall (@list @t26 @t25 @t372) (=> @t357 (=> @t355 @t372)))) % 2.02/2.26 (assume @p182 (forall @t31 (=> @t357 (not (= @t25 @t26))))) % 2.02/2.26 (assume @p183 (forall @t287 (=> @t367 (= @t358 @t38)))) % 2.02/2.26 (assume @p184 (forall (@list @t83 @t40) (=> (forall @t89 (=> (forall @t93 (=> (_ (_ tptp.ord_less_nat @t91) @t86) @t92)) @t88)) @t158))) % 2.02/2.26 (assume @p185 (forall @t31 (=> @t357 @t371))) % 2.02/2.26 (assume @p186 (forall @t316 (=> @t351 (not @t353)))) % 2.02/2.26 (assume @p187 (forall @t189 (=> @t353 (=> @t299 @t368)))) % 2.02/2.26 (assume @p188 (forall @t189 (=> @t41 @t370))) % 2.02/2.26 (assume @p189 (forall @t211 (not (_ @t356 @t26)))) % 2.02/2.26 (assume @p190 (forall @t31 (or @t357 @t38 @t355))) % 2.02/2.26 (assume @p191 (forall @t286 (=> @t357 (=> (_ @t354 @t280) (_ @t356 @t280))))) % 2.02/2.26 (assume @p192 (forall @t60 (=> @t353 (not @t351)))) % 2.02/2.26 (assume @p193 (forall @t31 (= @t371 (or @t357 @t355)))) % 2.02/2.26 (assume @p194 (forall @t31 (=> @t371 (=> @t358 @t355)))) % 2.02/2.26 (assume @p195 (forall @t211 (exists (@list @t373) (_ @t356 @t373)))) % 2.02/2.26 (assume @p196 (forall @t255 (=> @t353 (=> (_ (_ tptp.ord_less_nat @t244) @t42) @t375)))) % 2.02/2.26 (assume @p197 (forall @t245 (=> (_ @t352 @t244) @t376))) % 2.02/2.26 (assume @p198 (forall @t255 (=> @t353 (=> @t257 @t375)))) % 2.02/2.26 (assume @p199 (forall @t245 (=> @t256 @t376))) % 2.02/2.26 (assume @p200 (forall @t65 (=> @t341 @t340))) % 2.02/2.26 (assume @p201 (forall @t19 (=> @t345 @t341))) % 2.02/2.26 (assume @p202 (forall @t65 (= @t340 @t341))) % 2.02/2.26 (assume @p203 (forall @t19 (=> @t345 @t99))) % 2.02/2.26 (assume @p204 (= tptp.ord_less_eq_nat (lambda @t378 (or @t364 @t377)))) % 2.02/2.26 (assume @p205 (forall @t19 (=> (or @t345 @t67) @t99))) % 2.02/2.26 (assume @p206 (forall @t19 (=> @t99 (=> (not @t67) @t345)))) % 2.02/2.26 (assume @p207 (forall (@list @t177 @t35 @t100) (=> (forall (@list @t12 @t379) (=> (_ (_ tptp.ord_less_nat @t12) @t379) (_ (_ tptp.ord_less_nat @t179) (_ @t177 @t379)))) (=> @t103 (_ (_ tptp.ord_less_eq_nat (_ @t177 @t35)) (_ @t177 @t100)))))) % 2.02/2.26 (assume @p208 (forall (@list @t83 @t3) (=> (_ @t83 tptp.zero_zero_nat) (=> (forall (@list @t381) (=> (_ @t339 @t381) (=> (not (_ @t83 @t381)) (exists (@list @t380) (and (_ (_ tptp.ord_less_nat @t380) @t381) (not (_ @t83 @t380))))))) (_ @t83 @t3))))) % 2.02/2.26 (assume @p209 (forall @t61 (not (_ @t352 tptp.zero_zero_nat)))) % 2.02/2.26 (assume @p210 (forall @t208 (=> @t344 (not (=> @t207 @t210))))) % 2.02/2.26 (assume @p211 (forall @t208 (=> @t344 @t207))) % 2.02/2.26 (assume @p212 (forall @t328 (=> @t344 (=> @t327 @t382)))) % 2.02/2.26 (assume @p213 (= tptp.ord_less_set_nat (lambda @t325 (and @t324 (not @t323))))) % 2.02/2.26 (assume @p214 (forall @t328 (=> @t207 (=> (_ (_ tptp.ord_less_set_nat @t124) @t326) @t382)))) % 2.02/2.26 (assume @p215 (= tptp.ord_less_eq_set_nat (lambda @t325 (or (_ (_ tptp.ord_less_set_nat @t321) @t322) @t383)))) % 2.02/2.26 (assume @p216 (not (_ (_ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat))) % 2.02/2.26 (assume @p217 (not (_ @t339 tptp.zero_zero_nat))) % 2.02/2.26 (assume @p218 (forall @t301 (=> (not @t298) (=> @t249 @t385)))) % 2.02/2.26 (assume @p219 (forall @t60 (=> @t349 (=> @t188 @t353)))) % 2.02/2.26 (assume @p220 (forall @t315 (=> @t387 @t300))) % 2.02/2.26 (assume @p221 (forall @t316 (=> @t351 @t302))) % 2.02/2.26 (assume @p222 (= tptp.ord_less_set_nat (lambda @t390 (and @t290 @t389)))) % 2.02/2.26 (assume @p223 (= tptp.ord_less_nat (lambda @t393 (and @t295 @t392)))) % 2.02/2.26 (assume @p224 (= tptp.ord_less_eq_set_nat (lambda @t390 (or (_ (_ tptp.ord_less_set_nat @t289) @t288) @t388)))) % 2.02/2.26 (assume @p225 (= tptp.ord_less_eq_nat (lambda @t393 (or (_ (_ tptp.ord_less_nat @t294) @t293) @t391)))) % 2.02/2.26 (assume @p226 (forall @t301 (=> @t385 @t249))) % 2.02/2.26 (assume @p227 (forall @t60 (=> @t353 @t188))) % 2.02/2.26 (assume @p228 (forall @t312 (=> @t387 (=> @t311 @t395)))) % 2.02/2.26 (assume @p229 (forall @t314 (=> @t351 (=> @t313 @t360)))) % 2.02/2.26 (assume @p230 (forall @t312 (=> @t300 (=> (_ @t394 @t219) @t395)))) % 2.02/2.26 (assume @p231 (forall @t314 (=> @t302 @t361))) % 2.02/2.26 (assume @p232 (= tptp.ord_less_set_nat (lambda @t292 (and @t291 @t389)))) % 2.02/2.26 (assume @p233 (= tptp.ord_less_nat (lambda @t297 (and @t296 @t392)))) % 2.02/2.26 (assume @p234 (= tptp.ord_less_eq_set_nat (lambda @t292 (or (_ (_ tptp.ord_less_set_nat @t288) @t289) @t388)))) % 2.02/2.26 (assume @p235 (= tptp.ord_less_eq_nat (lambda @t297 (or (_ (_ tptp.ord_less_nat @t293) @t294) @t391)))) % 2.02/2.26 (assume @p236 (forall @t277 (=> @t385 (=> @t221 @t396)))) % 2.02/2.26 (assume @p237 (forall @t189 (=> @t353 (=> @t231 @t368)))) % 2.02/2.26 (assume @p238 (forall @t277 (=> @t249 (=> (_ @t386 @t212) @t396)))) % 2.02/2.26 (assume @p239 (forall @t189 (=> @t188 @t370))) % 2.02/2.26 (assume @p240 @t413) % 2.02/2.26 (assume @p241 true) % 2.02/2.26 (step @p242 (= tptp.number1551313001itions @t416) :rule refl :args (@t416)) % 2.02/2.26 (step @p243 (= tptp.set_or1086813439et_nat @t418) :rule refl :args (@t418)) % 2.02/2.26 (step @p244 (= tptp.set_ord_atMost_nat @t420) :rule refl :args (@t420)) % 2.02/2.26 (step @p245 (= tptp.ord_less_eq_set_nat @t423) :rule refl :args (@t423)) % 2.02/2.26 (step @p246 (= tptp.ord_less_nat @t424) :rule refl :args (@t424)) % 2.02/2.26 (step @p247 (= tptp.ord_less_set_nat @t425) :rule refl :args (@t425)) % 2.02/2.26 (assume-push @p628 @t429) % 2.02/2.26 (step @p249 :rule instantiate :premises (@p628) :args ((@list @t430))) % 2.02/2.26 (step-pop @p629 :rule scope :premises (@p249)) % 2.02/2.26 (step @p250 :rule process_scope :premises (@p629) :args (@t436)) % 2.02/2.26 (step @p252 :rule implies_elim :premises (@p250)) % 2.02/2.26 (step @p253 :rule cnf_and_pos :args (@t433 0)) % 2.02/2.26 (step @p254 :rule reordering :premises (@p253) :args ((or @t432 @t437))) % 2.02/2.26 (step @p255 :rule cnf_and_pos :args (@t433 1)) % 2.02/2.26 (step @p256 :rule reordering :premises (@p255) :args ((or @t431 @t437))) % 2.02/2.26 (step @p257 :rule refl :args (@t438)) % 2.02/2.26 (step @p258 :rule refl :args (@t201)) % 2.02/2.26 (step @p259 :rule cong :premises (@p258 @p257) :args ((= @t201 @t438))) % 2.02/2.26 (step @p260 :rule symm :premises (@p259)) % 2.02/2.26 (step @p261 :rule eq_resolve :premises (@p258 @p260)) % 2.02/2.26 (step @p262 :rule cong :premises (@p261) :args (@t202)) % 2.02/2.26 (step @p263 :rule eq_resolve :premises (@p71 @p262)) % 2.02/2.26 (step @p264 :rule refl :args (@t439)) % 2.02/2.26 (step @p265 :rule refl :args (@t37)) % 2.02/2.26 (step @p266 :rule cong :premises (@p265 @p264) :args ((= @t37 @t439))) % 2.02/2.26 (step @p267 :rule symm :premises (@p266)) % 2.02/2.26 (step @p268 :rule eq_resolve :premises (@p265 @p267)) % 2.02/2.26 (step @p269 :rule refl :args (@t440)) % 2.02/2.26 (step @p270 :rule refl :args (@t101)) % 2.02/2.26 (step @p271 :rule cong :premises (@p270 @p269) :args ((= @t101 @t440))) % 2.02/2.26 (step @p272 :rule symm :premises (@p271)) % 2.02/2.26 (step @p273 :rule eq_resolve :premises (@p270 @p272)) % 2.02/2.26 (step @p274 :rule cong :premises (@p273) :args (@t441)) % 2.02/2.26 (step @p275 :rule refl :args (@t442)) % 2.02/2.26 (step @p276 :rule refl :args (@t103)) % 2.02/2.26 (step @p277 :rule cong :premises (@p276 @p275) :args ((= @t103 @t442))) % 2.02/2.26 (step @p278 :rule symm :premises (@p277)) % 2.02/2.26 (step @p279 :rule eq_resolve :premises (@p276 @p278)) % 2.02/2.26 (step @p280 :rule cong :premises (@p279) :args (@t443)) % 2.02/2.26 (step @p281 :rule nary_cong :premises (@p280 @p274 @p268) :args (@t444)) % 2.02/2.26 (step @p282 :rule cong :premises (@p281) :args ((forall @t104 @t444))) % 2.02/2.26 (step @p283 :rule aci_norm :args ((= (or @t443 (or @t441 @t37)) @t444))) % 2.02/2.26 (step @p284 :rule bool-impl-elim :args (@t101 @t37)) % 2.02/2.26 (step @p285 :rule refl :args (@t443)) % 2.02/2.26 (step @p286 :rule nary_cong :premises (@p285 @p284) :args ((or @t443 @t102))) % 2.02/2.26 (step @p287 :rule trans :premises (@p286 @p283)) % 2.02/2.26 (step @p288 :rule bool-impl-elim :args (@t103 @t102)) % 2.02/2.26 (step @p289 :rule trans :premises (@p288 @p287)) % 2.02/2.26 (step @p290 :rule cong :premises (@p289) :args (@t105)) % 2.02/2.26 (step @p291 :rule trans :premises (@p290 @p282)) % 2.02/2.26 (step @p292 :rule eq_resolve :premises (@p27 @p291)) % 2.02/2.26 (step @p293 :rule instantiate :premises (@p292) :args ((@list tptp.one_one_nat @t430 tptp.zero_zero_nat))) % 2.02/2.26 (step @p294 :rule cnf_or_pos :args (@t447)) % 2.02/2.26 (step @p295 :rule reordering :premises (@p294) :args ((or @t438 @t446 @t445 (not @t447)))) % 2.02/2.26 (step @p296 :rule chain_m_resolution :premises (@p295 @p293 @p263 @p256 @p254) :args (@t437 (@list false true false false) (@list @t447 @t438 @t431 @t432))) % 2.02/2.26 (step @p297 :rule cnf_or_pos :args (@t436)) % 2.02/2.26 (step @p298 :rule reordering :premises (@p297) :args ((or @t435 @t433 (not @t436)))) % 2.02/2.26 (step @p299 :rule eq-symm :args (@t434 tptp.zero_zero_nat)) % 2.02/2.26 (step @p300 :rule eq-refl :args (tptp.zero_zero_nat)) % 2.02/2.26 (step @p301 :rule beta-reduce :args ((= @t448 tptp.zero_zero_nat))) % 2.02/2.26 (step @p302 :rule refl :args (tptp.zero_zero_nat)) % 2.02/2.26 (step @p303 :rule cong :premises (@p302 @p301) :args ((= tptp.zero_zero_nat @t448))) % 2.02/2.26 (step @p304 :rule trans :premises (@p303 @p300)) % 2.02/2.26 (step @p305 :rule refl :args (@t430)) % 2.02/2.26 (step @p306 :rule skolem_intro :args (@t449)) % 2.02/2.26 (step @p307 :rule ho_cong :premises (@p306 @p305)) % 2.02/2.26 (step @p308 :rule cong :premises (@p302 @p307) :args ((= tptp.zero_zero_nat @t450))) % 2.02/2.26 (step @p309 :rule eq-symm :args (@t450 tptp.zero_zero_nat)) % 2.02/2.26 (step @p310 :rule trans :premises (@p309 @p308 @p304)) % 2.02/2.26 (step @p311 :rule true_elim :premises (@p310)) % 2.02/2.26 (step @p312 :rule refl :args (@t434)) % 2.02/2.26 (step @p313 :rule cong :premises (@p312 @p311) :args (@t451)) % 2.02/2.26 (step @p314 :rule trans :premises (@p313 @p299)) % 2.02/2.26 (step @p315 :rule cong :premises (@p314) :args (@t452)) % 2.02/2.26 (step @p316 :rule refl :args (@t453)) % 2.02/2.26 (step @p317 :rule nary_cong :premises (@p316 @p315) :args (@t454)) % 2.02/2.26 ; WARNING: add trust step for TRUST % 2.02/2.26 ; trust TRUST THEORY_LEMMA % 2.02/2.26 (step @p318 :rule trust :premises () :args (@t454)) % 2.02/2.26 (step @p319 :rule eq_resolve :premises (@p318 @p317)) % 2.02/2.26 (step @p320 :rule eq-symm :args (@t453 @t461)) % 2.02/2.26 (step @p321 :rule refl :args ((tptp.groups1842438620at_nat @t458 @t462))) % 2.02/2.26 (step @p322 :rule refl :args (@t457)) % 2.02/2.26 (step @p323 :rule refl :args (@t458)) % 2.02/2.26 (step @p324 :rule cong :premises (@p323 @p322) :args (@t459)) % 2.02/2.26 (step @p325 :rule trans :premises (@p324 @p321)) % 2.02/2.26 (step @p326 :rule refl :args (@t463)) % 2.02/2.26 (step @p327 :rule ho_cong :premises (@p326 @p322)) % 2.02/2.26 (step @p328 :rule cong :premises (@p327 @p325) :args ((= (_ @t463 @t457) @t459))) % 2.02/2.26 (step @p329 :rule symm :premises (@p328)) % 2.02/2.26 (step @p330 :rule refl :args ((_ @t463 @t462))) % 2.02/2.26 (step @p331 :rule eq_resolve :premises (@p330 @p329)) % 2.02/2.26 (step @p332 :rule refl :args (@t462)) % 2.02/2.26 (step @p333 :rule cong :premises (@p332 @p322) :args ((= @t462 @t457))) % 2.02/2.26 (step @p334 :rule symm :premises (@p333)) % 2.02/2.26 (step @p335 :rule eq_resolve :premises (@p332 @p334)) % 2.02/2.26 (step @p336 :rule eq-refl :args (@t455)) % 2.02/2.26 (step @p337 :rule skolem_intro :args (@t456)) % 2.02/2.26 (step @p338 :rule refl :args (@t455)) % 2.02/2.26 (step @p339 :rule cong :premises (@p338 @p337) :args ((= @t455 @t456))) % 2.02/2.26 (step @p340 :rule trans :premises (@p339 @p336)) % 2.02/2.26 (step @p341 :rule true_elim :premises (@p340)) % 2.02/2.26 (step @p342 :rule refl :args (tptp.collect_nat)) % 2.02/2.26 (step @p343 :rule ho_cong :premises (@p342 @p341)) % 2.02/2.26 (step @p344 :rule trans :premises (@p343 @p335)) % 2.02/2.26 (step @p345 :rule eq-refl :args (@t401)) % 2.02/2.26 (step @p346 :rule skolem_intro :args (@t458)) % 2.02/2.26 (step @p347 :rule refl :args (@t401)) % 2.02/2.26 (step @p348 :rule cong :premises (@p347 @p346) :args ((= @t401 @t458))) % 2.02/2.26 (step @p349 :rule trans :premises (@p348 @p345)) % 2.02/2.26 (step @p350 :rule true_elim :premises (@p349)) % 2.02/2.26 (step @p351 :rule refl :args (tptp.groups1842438620at_nat)) % 2.02/2.26 (step @p352 :rule ho_cong :premises (@p351 @p350)) % 2.02/2.26 (step @p353 :rule ho_cong :premises (@p352 @p344)) % 2.02/2.26 (step @p354 :rule trans :premises (@p353 @p331)) % 2.02/2.26 (step @p355 :rule cong :premises (@p302 @p354) :args (@t466)) % 2.02/2.26 (step @p356 :rule refl :args (@t429)) % 2.02/2.26 (step @p357 :rule nary_cong :premises (@p356 @p355) :args (@t467)) % 2.02/2.26 (step @p358 :rule eq-refl :args (@t397)) % 2.02/2.26 (step @p359 :rule refl :args (@t397)) % 2.02/2.26 (step @p360 :rule cong :premises (@p359 @p306) :args ((= @t397 @t449))) % 2.02/2.26 (step @p361 :rule trans :premises (@p360 @p358)) % 2.02/2.26 (step @p362 :rule true_elim :premises (@p361)) % 2.02/2.26 (step @p363 :rule refl :args (tptp.p)) % 2.02/2.26 (step @p364 :rule cong :premises (@p363 @p362) :args (@t398)) % 2.02/2.26 (step @p365 :rule cong :premises (@p364 @p357) :args (@t468)) % 2.02/2.26 (step @p366 :rule trans :premises (@p365 @p320)) % 2.02/2.26 (step @p367 :rule cong :premises (@p366) :args ((not @t468))) % 2.02/2.26 (step @p368 :rule eq-symm :args (@t465 tptp.zero_zero_nat)) % 2.02/2.26 (step @p369 :rule beta-reduce :args ((= @t469 @t464))) % 2.02/2.26 (step @p370 :rule refl :args (@t402)) % 2.02/2.26 (step @p371 :rule ho_cong :premises (@p370 @p369)) % 2.02/2.26 (step @p372 :rule cong :premises (@p371 @p302) :args (@t470)) % 2.02/2.26 (step @p373 :rule trans :premises (@p372 @p368)) % 2.02/2.26 (step @p374 :rule refl :args (@t426)) % 2.02/2.26 (step @p375 :rule refl :args (@t405)) % 2.02/2.26 (step @p376 :rule cong :premises (@p375 @p374) :args ((= @t405 @t426))) % 2.02/2.26 (step @p377 :rule symm :premises (@p376)) % 2.02/2.26 (step @p378 :rule eq_resolve :premises (@p375 @p377)) % 2.02/2.26 (step @p379 :rule refl :args (@t427)) % 2.02/2.26 (step @p380 :rule refl :args (@t406)) % 2.02/2.26 (step @p381 :rule cong :premises (@p380 @p379) :args ((= @t406 @t427))) % 2.02/2.26 (step @p382 :rule symm :premises (@p381)) % 2.02/2.26 (step @p383 :rule eq_resolve :premises (@p380 @p382)) % 2.02/2.26 (step @p384 :rule nary_cong :premises (@p383 @p378) :args (@t407)) % 2.02/2.26 (step @p385 :rule refl :args (@t428)) % 2.02/2.26 (step @p386 :rule refl :args (@t399)) % 2.02/2.26 (step @p387 :rule cong :premises (@p386 @p385) :args ((= @t399 @t428))) % 2.02/2.26 (step @p388 :rule symm :premises (@p387)) % 2.02/2.26 (step @p389 :rule eq_resolve :premises (@p386 @p388)) % 2.02/2.26 (step @p390 :rule refl :args (tptp.zero_zero_nat)) % 2.02/2.26 (step @p391 :rule cong :premises (@p390 @p389) :args (@t471)) % 2.02/2.26 (step @p392 :rule nary_cong :premises (@p391 @p384) :args (@t472)) % 2.02/2.26 (step @p393 :rule cong :premises (@p392) :args ((forall @t6 @t472))) % 2.02/2.26 (step @p394 :rule refl :args (@t407)) % 2.02/2.26 (step @p395 :rule bool-double-not-elim :args (@t471)) % 2.02/2.26 (step @p396 :rule nary_cong :premises (@p395 @p394) :args ((or (not @t473) @t407))) % 2.02/2.26 (step @p397 :rule bool-impl-elim :args (@t473 @t407)) % 2.02/2.26 (step @p398 :rule trans :premises (@p397 @p396)) % 2.02/2.26 (step @p399 :rule cong :premises (@p398) :args ((forall @t6 (=> @t473 @t407)))) % 2.02/2.26 (step @p400 :rule trans :premises (@p399 @p393)) % 2.02/2.26 (step @p401 :rule refl :args (@t407)) % 2.02/2.26 (step @p402 :rule eq-symm :args (@t399 tptp.zero_zero_nat)) % 2.02/2.26 (step @p403 :rule cong :premises (@p402) :args (@t408)) % 2.02/2.26 (step @p404 :rule cong :premises (@p403 @p401) :args (@t409)) % 2.02/2.26 (step @p405 :rule cong :premises (@p404) :args (@t410)) % 2.02/2.26 (step @p406 :rule trans :premises (@p405 @p400)) % 2.02/2.26 (step @p407 :rule nary_cong :premises (@p406 @p373) :args (@t474)) % 2.02/2.26 (step @p408 :rule refl :args (@t398)) % 2.02/2.26 (step @p409 :rule cong :premises (@p408 @p407) :args ((= @t398 @t474))) % 2.02/2.26 (step @p410 :rule eq-symm :args (@t474 @t398)) % 2.02/2.26 (step @p411 :rule trans :premises (@p410 @p409)) % 2.02/2.26 (step @p412 :rule cong :premises (@p411) :args ((not (= @t474 @t398)))) % 2.02/2.26 (step @p413 :rule ho_cong :premises (@p244 @p302)) % 2.02/2.26 (step @p414 :rule ho_cong :premises (@p370 @p413)) % 2.02/2.26 (step @p415 :rule cong :premises (@p414 @p302) :args (@t403)) % 2.02/2.26 (step @p416 :rule refl :args (@t410)) % 2.02/2.26 (step @p417 :rule nary_cong :premises (@p416 @p415) :args (@t411)) % 2.02/2.26 (step @p418 :rule cong :premises (@p417 @p408) :args (@t412)) % 2.02/2.26 (step @p419 :rule cong :premises (@p418) :args (@t413)) % 2.02/2.26 (step @p420 :rule trans :premises (@p419 @p412)) % 2.02/2.26 (step @p421 :rule trans :premises (@p420 @p367)) % 2.02/2.26 (step @p422 :rule eq_resolve :premises (@p240 @p421)) % 2.02/2.26 (step @p423 :rule not_equiv_elim2 :premises (@p422)) % 2.02/2.26 (step @p424 :rule eq-symm :args (@t477 tptp.zero_zero_nat)) % 2.02/2.26 (step @p425 :rule cong :premises (@p316 @p424) :args (@t478)) % 2.02/2.26 ; trust TRUST THEORY_LEMMA % 2.02/2.26 (step @p426 :rule trust :premises () :args (@t478)) % 2.02/2.26 (step @p427 :rule eq_resolve :premises (@p426 @p425)) % 2.02/2.26 (step @p428 :rule implies_elim :premises (@p427)) % 2.02/2.26 (step @p429 :rule cnf_and_neg :args (@t461)) % 2.02/2.26 (step @p430 :rule refl :args (@t481)) % 2.02/2.26 (step @p431 :rule refl :args (@t482)) % 2.02/2.26 (step @p432 :rule refl :args (@t137)) % 2.02/2.26 (step @p433 :rule cong :premises (@p432 @p431) :args ((= @t137 @t482))) % 2.02/2.26 (step @p434 :rule symm :premises (@p433)) % 2.02/2.26 (step @p435 :rule eq_resolve :premises (@p432 @p434)) % 2.02/2.26 (step @p436 :rule cong :premises (@p390 @p435) :args (@t483)) % 2.02/2.26 (step @p437 :rule nary_cong :premises (@p436 @p430) :args (@t484)) % 2.02/2.26 (step @p438 :rule cong :premises (@p437) :args ((forall @t156 @t484))) % 2.02/2.26 (step @p439 :rule bool-double-not-elim :args (@t483)) % 2.02/2.26 (step @p440 :rule nary_cong :premises (@p439 @p430) :args ((or (not @t485) @t481))) % 2.02/2.26 (step @p441 :rule bool-impl-elim :args (@t485 @t481)) % 2.02/2.26 (step @p442 :rule trans :premises (@p441 @p440)) % 2.02/2.26 (step @p443 :rule cong :premises (@p442) :args ((forall @t156 (=> @t485 @t481)))) % 2.02/2.26 (step @p444 :rule trans :premises (@p443 @p438)) % 2.02/2.26 (step @p445 :rule refl :args (@t479)) % 2.02/2.26 (step @p446 :rule refl :args (@t113)) % 2.02/2.26 (step @p447 :rule cong :premises (@p446 @p445) :args ((= @t113 @t479))) % 2.02/2.26 (step @p448 :rule symm :premises (@p447)) % 2.02/2.26 (step @p449 :rule eq_resolve :premises (@p446 @p448)) % 2.02/2.26 (step @p450 :rule cong :premises (@p390 @p449) :args (@t486)) % 2.02/2.26 (step @p451 :rule refl :args (@t480)) % 2.02/2.26 (step @p452 :rule refl :args (@t149)) % 2.02/2.26 (step @p453 :rule cong :premises (@p452 @p451) :args ((= @t149 @t480))) % 2.02/2.26 (step @p454 :rule symm :premises (@p453)) % 2.02/2.26 (step @p455 :rule eq_resolve :premises (@p452 @p454)) % 2.02/2.26 (step @p456 :rule cong :premises (@p455) :args (@t487)) % 2.02/2.26 (step @p457 :rule nary_cong :premises (@p456 @p450) :args (@t488)) % 2.02/2.26 (step @p458 :rule cong :premises (@p457) :args ((forall @t118 @t488))) % 2.02/2.26 (step @p459 :rule bool-impl-elim :args (@t149 @t486)) % 2.02/2.26 (step @p460 :rule cong :premises (@p459) :args ((forall @t118 (=> @t149 @t486)))) % 2.02/2.26 (step @p461 :rule trans :premises (@p460 @p458)) % 2.02/2.26 (step @p462 :rule eq-symm :args (@t113 tptp.zero_zero_nat)) % 2.02/2.26 (step @p463 :rule refl :args (@t149)) % 2.02/2.26 (step @p464 :rule cong :premises (@p463 @p462) :args (@t150)) % 2.02/2.26 (step @p465 :rule cong :premises (@p464) :args (@t151)) % 2.02/2.26 (step @p466 :rule trans :premises (@p465 @p461)) % 2.02/2.26 (step @p467 :rule cong :premises (@p466) :args (@t152)) % 2.02/2.26 (step @p468 :rule eq-symm :args (@t137 tptp.zero_zero_nat)) % 2.02/2.26 (step @p469 :rule cong :premises (@p468) :args (@t154)) % 2.02/2.26 (step @p470 :rule cong :premises (@p469 @p467) :args (@t155)) % 2.02/2.26 (step @p471 :rule cong :premises (@p470) :args (@t157)) % 2.02/2.26 (step @p472 :rule trans :premises (@p471 @p444)) % 2.02/2.26 (step @p473 :rule eq_resolve :premises (@p40 @p472)) % 2.02/2.26 (step @p474 :rule instantiate :premises (@p473) :args ((@list @t458 @t457))) % 2.02/2.26 (step @p475 :rule cnf_or_pos :args (@t490)) % 2.02/2.26 (step @p476 :rule reordering :premises (@p475) :args ((or @t460 @t489 (not @t490)))) % 2.02/2.26 (step @p477 :rule refl :args (@t494)) % 2.02/2.26 (step @p478 :rule bool-double-not-elim :args (@t475)) % 2.02/2.26 (step @p479 :rule nary_cong :premises (@p478 @p477) :args ((or (not @t489) @t494))) % 2.02/2.26 (assume-push @p630 @t489) % 2.02/2.26 (step @p481 :rule skolemize :premises (@p630)) % 2.02/2.26 (step-pop @p631 :rule scope :premises (@p481)) % 2.02/2.26 (step @p482 :rule process_scope :premises (@p631) :args (@t494)) % 2.02/2.26 (step @p484 :rule implies_elim :premises (@p482)) % 2.02/2.26 (step @p485 :rule eq_resolve :premises (@p484 @p479)) % 2.02/2.26 (step @p486 :rule cnf_or_neg :args (@t493 1)) % 2.02/2.26 (step @p487 :rule eq-symm :args (@t495 @t496)) % 2.02/2.26 (step @p488 :rule cong :premises (@p487) :args ((forall @t6 (= @t495 @t496)))) % 2.02/2.26 (step @p489 :rule refl :args (@t496)) % 2.02/2.26 (step @p490 :rule refl :args ((tptp.times_times_nat @t399 @t4))) % 2.02/2.26 (step @p491 :rule refl :args (@t4)) % 2.02/2.26 (step @p492 :rule cong :premises (@p385 @p491) :args (@t495)) % 2.02/2.26 (step @p493 :rule trans :premises (@p492 @p490)) % 2.02/2.26 (step @p494 :rule refl :args (tptp.times_times_nat)) % 2.02/2.26 (step @p495 :rule ho_cong :premises (@p494 @p385)) % 2.02/2.26 (step @p496 :rule ho_cong :premises (@p495 @p491)) % 2.02/2.26 (step @p497 :rule cong :premises (@p496 @p493) :args ((= (_ (_ tptp.times_times_nat @t428) @t4) @t495))) % 2.02/2.26 (step @p498 :rule symm :premises (@p497)) % 2.02/2.26 (step @p499 :rule refl :args (@t400)) % 2.02/2.26 (step @p500 :rule eq_resolve :premises (@p499 @p498)) % 2.02/2.26 (step @p501 :rule ho_cong :premises (@p494 @p389)) % 2.02/2.26 (step @p502 :rule ho_cong :premises (@p501 @p491)) % 2.02/2.26 (step @p503 :rule trans :premises (@p502 @p500)) % 2.02/2.26 (step @p504 :rule cong :premises (@p503 @p489) :args (@t497)) % 2.02/2.26 (step @p505 :rule cong :premises (@p504) :args ((forall @t6 @t497))) % 2.02/2.26 (step @p506 :rule trans :premises (@p505 @p488)) % 2.02/2.26 (step @p507 :rule eq-symm :args (@t496 @t400)) % 2.02/2.26 (step @p508 :rule beta-reduce :args ((= @t498 @t400))) % 2.02/2.26 (step @p509 :rule refl :args (@t496)) % 2.02/2.26 (step @p510 :rule cong :premises (@p509 @p508) :args (@t499)) % 2.02/2.26 (step @p511 :rule trans :premises (@p510 @p507)) % 2.02/2.26 (step @p512 :rule cong :premises (@p511) :args (@t500)) % 2.02/2.26 (step @p513 :rule trans :premises (@p512 @p506)) % 2.02/2.26 (step @p514 :rule quant-unused-vars :args ((= (forall @t6 true) true))) % 2.02/2.26 (step @p515 :rule eq-refl :args (@t498)) % 2.02/2.26 (step @p516 :rule cong :premises (@p515) :args ((forall @t6 (= @t498 @t498)))) % 2.02/2.26 (step @p517 :rule trans :premises (@p516 @p514)) % 2.02/2.26 (step @p518 :rule refl :args (@t498)) % 2.02/2.26 (step @p519 :rule refl :args (@t4)) % 2.02/2.26 (step @p520 :rule ho_cong :premises (@p346 @p519)) % 2.02/2.26 (step @p521 :rule cong :premises (@p520 @p518) :args (@t499)) % 2.02/2.26 (step @p522 :rule cong :premises (@p521) :args (@t500)) % 2.02/2.26 (step @p523 :rule trans :premises (@p522 @p517)) % 2.02/2.26 (step @p524 :rule true_elim :premises (@p523)) % 2.02/2.26 (step @p525 :rule eq_resolve :premises (@p524 @p513)) % 2.02/2.26 (step @p526 :rule instantiate :premises (@p525) :args ((@list @t476))) % 2.02/2.26 (step @p527 :rule refl :args (@t503)) % 2.02/2.26 (step @p528 :rule refl :args (@t505)) % 2.02/2.26 (step @p529 :rule bool-double-not-elim :args (@t492)) % 2.02/2.26 (step @p530 :rule nary_cong :premises (@p529 @p528 @p527) :args ((or (not @t506) @t505 @t503))) % 2.02/2.26 (assume-push @p632 @t506) % 2.02/2.26 (assume-push @p633 @t504) % 2.02/2.26 (assume-push @p634 @t506) % 2.02/2.26 (assume-push @p635 @t504) % 2.02/2.26 (step @p535 :rule false_intro :premises (@p632)) % 2.02/2.26 (step @p536 :rule symm :premises (@p526)) % 2.02/2.26 (step @p537 :rule cong :premises (@p302 @p536) :args (@t502)) % 2.02/2.26 (step @p538 :rule trans :premises (@p537 @p535)) % 2.02/2.26 (step @p539 :rule false_elim :premises (@p538)) % 2.02/2.26 (step-pop @p636 :rule scope :premises (@p539)) % 2.02/2.26 (step-pop @p637 :rule scope :premises (@p636)) % 2.02/2.26 (step @p540 :rule process_scope :premises (@p637) :args (@t503)) % 2.02/2.26 (step @p543 :rule and_intro :premises (@p632 @p526)) % 2.02/2.26 (step @p544 :rule modus_ponens :premises (@p543 @p540)) % 2.02/2.26 (step-pop @p638 :rule scope :premises (@p544)) % 2.02/2.26 (step-pop @p639 :rule scope :premises (@p638)) % 2.02/2.26 (step @p545 :rule process_scope :premises (@p639) :args (@t503)) % 2.02/2.26 (step @p548 :rule implies_elim :premises (@p545)) % 2.02/2.26 (step @p549 :rule cnf_and_neg :args (@t507)) % 2.02/2.26 (step @p550 :rule resolution :premises (@p549 @p548) :args (true @t507)) % 2.02/2.26 (step @p551 :rule eq_resolve :premises (@p550 @p530)) % 2.02/2.26 (step @p552 :rule eq-refl :args (@t175)) % 2.02/2.26 (step @p553 :rule skolem_intro :args (@t508)) % 2.02/2.26 (step @p554 :rule refl :args (@t175)) % 2.02/2.26 (step @p555 :rule cong :premises (@p554 @p553) :args ((= @t175 @t508))) % 2.02/2.26 (step @p556 :rule trans :premises (@p555 @p552)) % 2.02/2.26 (step @p557 :rule true_elim :premises (@p556)) % 2.02/2.26 (step @p558 :rule refl :args (@t62)) % 2.02/2.26 (step @p559 :rule cong :premises (@p558 @p557) :args ((= @t62 @t175))) % 2.02/2.26 (step @p560 :rule eq-symm :args (@t175 @t62)) % 2.02/2.26 (step @p561 :rule trans :premises (@p560 @p559)) % 2.02/2.26 (step @p562 :rule eq_resolve :premises (@p56 @p561)) % 2.02/2.26 (assume-push @p640 @t509) % 2.02/2.26 (assume-push @p641 @t510) % 2.02/2.26 (assume-push @p642 @t510) % 2.02/2.26 (assume-push @p643 @t509) % 2.02/2.26 (step @p567 :rule refl :args (tptp.times_times_nat)) % 2.02/2.26 (step @p568 :rule ho_cong :premises (@p567 @p641)) % 2.02/2.26 (step @p569 :rule symm :premises (@p562)) % 2.02/2.26 (step @p570 :rule trans :premises (@p569 @p568)) % 2.02/2.26 (step-pop @p644 :rule scope :premises (@p570)) % 2.02/2.26 (step-pop @p645 :rule scope :premises (@p644)) % 2.02/2.26 (step @p571 :rule process_scope :premises (@p645) :args (@t512)) % 2.02/2.26 (step @p574 :rule and_intro :premises (@p641 @p562)) % 2.02/2.26 (step @p575 :rule modus_ponens :premises (@p574 @p571)) % 2.02/2.26 (step-pop @p646 :rule scope :premises (@p575)) % 2.02/2.26 (step-pop @p647 :rule scope :premises (@p646)) % 2.02/2.26 (step @p576 :rule process_scope :premises (@p647) :args (@t512)) % 2.02/2.26 (step @p579 :rule implies_elim :premises (@p576)) % 2.02/2.26 (step @p580 :rule cnf_and_neg :args (@t513)) % 2.02/2.26 (step @p581 :rule resolution :premises (@p580 @p579) :args (true @t513)) % 2.02/2.26 (step @p582 :rule refl :args ((tptp.times_times_nat @t514 @t476))) % 2.02/2.26 (step @p583 :rule refl :args (@t476)) % 2.02/2.26 (step @p584 :rule refl :args (@t477)) % 2.02/2.26 (step @p585 :rule cong :premises (@p584 @p583) :args (@t501)) % 2.02/2.26 (step @p586 :rule trans :premises (@p585 @p582)) % 2.02/2.26 (step @p587 :rule ho_cong :premises (@p494 @p584)) % 2.02/2.26 (step @p588 :rule ho_cong :premises (@p587 @p583)) % 2.02/2.26 (step @p589 :rule cong :premises (@p588 @p586) :args ((= @t515 @t501))) % 2.02/2.26 (step @p590 :rule symm :premises (@p589)) % 2.02/2.26 (step @p591 :rule refl :args ((_ (_ tptp.times_times_nat @t514) @t476))) % 2.02/2.26 (step @p592 :rule eq_resolve :premises (@p591 @p590)) % 2.02/2.26 (step @p593 :rule cong :premises (@p302 @p592) :args (@t516)) % 2.02/2.26 (step @p594 :rule refl :args (@t512)) % 2.02/2.26 (step @p595 :rule cong :premises (@p594 @p593) :args ((=> @t512 @t516))) % 2.02/2.26 (step @p596 :rule eq-symm :args (@t515 tptp.zero_zero_nat)) % 2.02/2.26 (step @p597 :rule eq-symm :args (@t511 @t508)) % 2.02/2.26 (step @p598 :rule cong :premises (@p597 @p596) :args (@t517)) % 2.02/2.26 (step @p599 :rule trans :premises (@p598 @p595)) % 2.02/2.26 ; trust TRUST THEORY_LEMMA % 2.02/2.26 (step @p600 :rule trust :premises () :args (@t517)) % 2.02/2.26 (step @p601 :rule eq_resolve :premises (@p600 @p599)) % 2.02/2.26 (step @p602 :rule implies_elim :premises (@p601)) % 2.02/2.26 (step @p603 :rule reordering :premises (@p602) :args ((or @t502 (not @t512)))) % 2.02/2.26 (step @p604 :rule chain_m_resolution :premises (@p603 @p581 @p562 @p551 @p526 @p486 @p485 @p476 @p474 @p429 @p428 @p423 @p319 @p298 @p296 @p252) :args (@t518 (@list false false true false true true true false true false true false false true false) (@list @t512 @t509 @t502 @t504 @t492 @t493 @t475 @t490 @t460 @t510 @t461 @t453 @t435 @t433 @t436))) % 2.02/2.26 (step @p605 :rule cnf_and_pos :args (@t461 0)) % 2.02/2.26 (step @p606 :rule reordering :premises (@p605) :args ((or @t429 @t519))) % 2.02/2.26 (step @p607 :rule chain_m_resolution :premises (@p606 @p604) :args (@t519 @t520 @t521)) % 2.02/2.26 (step @p608 :rule not_equiv_elim1 :premises (@p422)) % 2.02/2.26 (step @p609 :rule chain_m_resolution :premises (@p608 @p607) :args (@t453 @t520 (@list @t461))) % 2.02/2.26 (step @p610 :rule refl :args (@t526)) % 2.02/2.26 (step @p611 :rule bool-double-not-elim :args (@t429)) % 2.02/2.26 (step @p612 :rule nary_cong :premises (@p611 @p610) :args ((or (not @t518) @t526))) % 2.02/2.26 (assume-push @p648 @t518) % 2.02/2.26 (step @p614 :rule skolemize :premises (@p648)) % 2.02/2.26 (step-pop @p649 :rule scope :premises (@p614)) % 2.02/2.26 (step @p615 :rule process_scope :premises (@p649) :args (@t526)) % 2.02/2.26 (step @p617 :rule implies_elim :premises (@p615)) % 2.02/2.26 (step @p618 :rule eq_resolve :premises (@p617 @p612)) % 2.02/2.26 (step @p619 :rule chain_m_resolution :premises (@p618 @p604) :args (@t526 @t520 @t521)) % 2.02/2.26 (step @p620 :rule cnf_or_neg :args (@t525 0)) % 2.02/2.26 (step @p621 :rule chain_m_resolution :premises (@p620 @p619) :args ((not @t524) @t520 (@list @t525))) % 2.02/2.26 (step @p622 :rule eq-symm :args (@t523 tptp.zero_zero_nat)) % 2.02/2.26 (step @p623 :rule cong :premises (@p316 @p622) :args (@t527)) % 2.02/2.26 ; trust TRUST THEORY_LEMMA % 2.02/2.26 (step @p624 :rule trust :premises () :args (@t527)) % 2.02/2.26 (step @p625 :rule eq_resolve :premises (@p624 @p623)) % 2.02/2.26 (step @p626 :rule implies_elim :premises (@p625)) % 2.02/2.26 (step @p627 false :rule chain_m_resolution :premises (@p626 @p621 @p609) :args (false (@list true false) (@list @t524 @t453))) % 2.02/2.26 ) % 2.02/2.26 % SZS output end Proof % 2.02/2.27 % cvc5 exiting %------------------------------------------------------------------------------