%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP131^1 : 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 : n020.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 08:25:08 AM UTC 2026 % Result : Theorem 0.40s 0.73s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP131^1 : 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 % 0.15/0.34 % Computer : n020.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 04:15:25 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.54 %----Proving TH0 % 0.40/0.73 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.73 % SZS status Theorem % 0.40/0.73 % SZS output start Proof % 0.40/0.73 ( % 0.40/0.73 (declare-sort tptp.nat 0) % 0.40/0.73 (declare-const tptp.plus_plus_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.40/0.73 (declare-const tptp.zero_zero_nat tptp.nat) % 0.40/0.73 (declare-const tptp.times_times_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.40/0.73 (declare-const tptp.k tptp.nat) % 0.40/0.73 (declare-const tptp.number1551313001itions (-> (-> tptp.nat tptp.nat) tptp.nat Bool)) % 0.40/0.73 (declare-const tptp.minus_minus_nat (-> tptp.nat tptp.nat tptp.nat)) % 0.40/0.73 (declare-const tptp.p (-> tptp.nat tptp.nat)) % 0.40/0.73 (declare-const tptp.i tptp.nat) % 0.40/0.73 (declare-const tptp.n tptp.nat) % 0.40/0.73 (define tptp.ord_less_eq_nat () (let ((_let_1 (@var "C2" tptp.nat))) (let ((_let_2 (@var "A2" tptp.nat))) (let ((_let_3 (@var "B2" tptp.nat))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (= _let_3 (_ (_ tptp.plus_plus_nat _let_2) _let_1)))))))) % 0.40/0.73 (define tptp.ord_less_nat () (let ((_let_1 (@var "N3" tptp.nat))) (let ((_let_2 (@var "M3" tptp.nat))) (lambda (@list _let_2 _let_1) (and (_ (_ tptp.ord_less_eq_nat _let_2) _let_1) (not (= _let_2 _let_1))))))) % 0.40/0.73 (define @t1 () (_ tptp.p tptp.k)) % 0.40/0.73 (define @t2 () (_ (_ tptp.times_times_nat @t1) tptp.k)) % 0.40/0.73 (define @t3 () (_ tptp.p tptp.i)) % 0.40/0.73 (define @t4 () (_ (_ tptp.times_times_nat @t3) tptp.i)) % 0.40/0.73 (define @t5 () (_ (_ tptp.plus_plus_nat @t4) @t2)) % 0.40/0.73 (define @t6 () (_ tptp.ord_less_nat tptp.zero_zero_nat)) % 0.40/0.73 (define @t7 () (@var "P" (-> tptp.nat tptp.nat))) % 0.40/0.73 (define @t8 () (_ tptp.number1551313001itions @t7)) % 0.40/0.73 (define @t9 () (@var "N" tptp.nat)) % 0.40/0.73 (define @t10 () (@var "I2" tptp.nat)) % 0.40/0.73 (define @t11 () (@var "M" tptp.nat)) % 0.40/0.73 (define @t12 () (_ tptp.ord_less_eq_nat @t11)) % 0.40/0.73 (define @t13 () (_ @t12 @t9)) % 0.40/0.73 (define @t14 () (@var "K" tptp.nat)) % 0.40/0.73 (define @t15 () (_ @t6 @t14)) % 0.40/0.73 (define @t16 () (=> @t15 @t13)) % 0.40/0.73 (define @t17 () (_ (_ tptp.times_times_nat @t9) @t14)) % 0.40/0.73 (define @t18 () (_ tptp.times_times_nat @t11)) % 0.40/0.73 (define @t19 () (_ @t18 @t14)) % 0.40/0.73 (define @t20 () (@list @t11 @t14 @t9)) % 0.40/0.73 (define @t21 () (_ tptp.times_times_nat @t14)) % 0.40/0.73 (define @t22 () (_ @t21 @t9)) % 0.40/0.73 (define @t23 () (_ @t21 @t11)) % 0.40/0.73 (define @t24 () (@list @t14 @t11 @t9)) % 0.40/0.73 (define @t25 () (_ tptp.ord_less_nat @t11)) % 0.40/0.73 (define @t26 () (_ @t25 @t9)) % 0.40/0.73 (define @t27 () (and @t15 @t26)) % 0.40/0.73 (define @t28 () (_ @t6 @t9)) % 0.40/0.73 (define @t29 () (_ @t6 @t11)) % 0.40/0.73 (define @t30 () (_ @t18 @t9)) % 0.40/0.73 (define @t31 () (@list @t11 @t9)) % 0.40/0.73 (define @t32 () (_ tptp.plus_plus_nat @t11)) % 0.40/0.73 (define @t33 () (_ @t32 @t9)) % 0.40/0.73 (define @t34 () (@var "A" tptp.nat)) % 0.40/0.73 (define @t35 () (_ tptp.ord_less_nat @t34)) % 0.40/0.73 (define @t36 () (_ @t35 tptp.zero_zero_nat)) % 0.40/0.73 (define @t37 () (@var "B" tptp.nat)) % 0.40/0.73 (define @t38 () (_ tptp.plus_plus_nat @t37)) % 0.40/0.73 (define @t39 () (_ @t38 @t34)) % 0.40/0.73 (define @t40 () (@list @t37 @t34)) % 0.40/0.73 (define @t41 () (_ tptp.plus_plus_nat @t34)) % 0.40/0.73 (define @t42 () (_ @t41 @t37)) % 0.40/0.73 (define @t43 () (@list @t34 @t37)) % 0.40/0.73 (define @t44 () (_ @t6 @t37)) % 0.40/0.73 (define @t45 () (@var "C" tptp.nat)) % 0.40/0.73 (define @t46 () (= @t37 @t45)) % 0.40/0.73 (define @t47 () (_ tptp.plus_plus_nat @t45)) % 0.40/0.73 (define @t48 () (_ @t47 @t34)) % 0.40/0.73 (define @t49 () (= @t39 @t48)) % 0.40/0.73 (define @t50 () (@list @t37 @t34 @t45)) % 0.40/0.73 (define @t51 () (_ @t41 @t45)) % 0.40/0.73 (define @t52 () (= @t42 @t51)) % 0.40/0.73 (define @t53 () (@list @t34 @t37 @t45)) % 0.40/0.73 (define @t54 () (= @t9 tptp.zero_zero_nat)) % 0.40/0.73 (define @t55 () (_ tptp.ord_less_eq_nat @t9)) % 0.40/0.73 (define @t56 () (@list @t9)) % 0.40/0.73 (define @t57 () (_ tptp.ord_less_eq_nat @t34)) % 0.40/0.73 (define @t58 () (_ @t57 @t37)) % 0.40/0.73 (define @t59 () (_ @t38 @t45)) % 0.40/0.73 (define @t60 () (_ tptp.ord_less_eq_nat @t51)) % 0.40/0.73 (define @t61 () (_ @t60 @t59)) % 0.40/0.73 (define @t62 () (@list @t34 @t45 @t37)) % 0.40/0.73 (define @t63 () (_ @t47 @t37)) % 0.40/0.73 (define @t64 () (_ tptp.ord_less_eq_nat @t48)) % 0.40/0.73 (define @t65 () (_ @t64 @t63)) % 0.40/0.73 (define @t66 () (@list @t45 @t34 @t37)) % 0.40/0.73 (define @t67 () (@var "Y" tptp.nat)) % 0.40/0.73 (define @t68 () (@var "X" tptp.nat)) % 0.40/0.73 (define @t69 () (= @t68 tptp.zero_zero_nat)) % 0.40/0.73 (define @t70 () (and @t69 (= @t67 tptp.zero_zero_nat))) % 0.40/0.73 (define @t71 () (_ (_ tptp.plus_plus_nat @t68) @t67)) % 0.40/0.73 (define @t72 () (@list @t68 @t67)) % 0.40/0.73 (define @t73 () (= @t37 tptp.zero_zero_nat)) % 0.40/0.73 (define @t74 () (@list @t34)) % 0.40/0.73 (define @t75 () (_ tptp.plus_plus_nat tptp.zero_zero_nat)) % 0.40/0.73 (define @t76 () (_ tptp.minus_minus_nat @t34)) % 0.40/0.73 (define @t77 () (_ tptp.minus_minus_nat tptp.zero_zero_nat)) % 0.40/0.73 (define @t78 () (_ @t35 @t37)) % 0.40/0.73 (define @t79 () (_ tptp.ord_less_nat @t51)) % 0.40/0.73 (define @t80 () (_ @t79 @t59)) % 0.40/0.73 (define @t81 () (_ (_ tptp.ord_less_nat @t48) @t63)) % 0.40/0.73 (define @t82 () (_ tptp.minus_minus_nat @t42)) % 0.40/0.73 (define @t83 () (_ @t76 @t37)) % 0.40/0.73 (define @t84 () (_ tptp.minus_minus_nat @t48)) % 0.40/0.73 (define @t85 () (= @t34 tptp.zero_zero_nat)) % 0.40/0.73 (define @t86 () (_ tptp.ord_less_nat @t9)) % 0.40/0.73 (define @t87 () (not @t54)) % 0.40/0.73 (define @t88 () (_ tptp.ord_less_eq_nat tptp.zero_zero_nat)) % 0.40/0.73 (define @t89 () (@list @t11)) % 0.40/0.73 (define @t90 () (= @t11 tptp.zero_zero_nat)) % 0.40/0.73 (define @t91 () (_ tptp.plus_plus_nat @t14)) % 0.40/0.73 (define @t92 () (_ @t91 @t9)) % 0.40/0.73 (define @t93 () (_ @t91 @t11)) % 0.40/0.73 (define @t94 () (_ tptp.minus_minus_nat @t11)) % 0.40/0.73 (define @t95 () (= @t14 tptp.zero_zero_nat)) % 0.40/0.73 (define @t96 () (= @t11 @t9)) % 0.40/0.73 (define @t97 () (or @t96 @t95)) % 0.40/0.73 (define @t98 () (= @t23 @t22)) % 0.40/0.73 (define @t99 () (_ tptp.minus_minus_nat @t9)) % 0.40/0.73 (define @t100 () (_ tptp.ord_less_eq_nat @t10)) % 0.40/0.73 (define @t101 () (@var "J" tptp.nat)) % 0.40/0.73 (define @t102 () (_ tptp.plus_plus_nat @t101)) % 0.40/0.73 (define @t103 () (_ @t102 @t14)) % 0.40/0.73 (define @t104 () (_ tptp.minus_minus_nat @t10)) % 0.40/0.73 (define @t105 () (_ @t104 @t101)) % 0.40/0.73 (define @t106 () (_ (_ tptp.minus_minus_nat @t105) @t14)) % 0.40/0.73 (define @t107 () (@list @t10 @t101 @t14)) % 0.40/0.73 (define @t108 () (_ @t88 @t37)) % 0.40/0.73 (define @t109 () (_ @t57 tptp.zero_zero_nat)) % 0.40/0.73 (define @t110 () (_ @t99 @t11)) % 0.40/0.73 (define @t111 () (@list @t9 @t11)) % 0.40/0.73 (define @t112 () (_ @t94 @t9)) % 0.40/0.73 (define @t113 () (= @t112 tptp.zero_zero_nat)) % 0.40/0.73 (define @t114 () (_ tptp.plus_plus_nat @t10)) % 0.40/0.73 (define @t115 () (_ @t114 @t14)) % 0.40/0.73 (define @t116 () (_ tptp.minus_minus_nat @t101)) % 0.40/0.73 (define @t117 () (_ @t116 @t14)) % 0.40/0.73 (define @t118 () (_ tptp.ord_less_eq_nat @t14)) % 0.40/0.73 (define @t119 () (_ @t118 @t101)) % 0.40/0.73 (define @t120 () (@list @t14 @t101 @t10)) % 0.40/0.73 (define @t121 () (_ @t102 @t10)) % 0.40/0.73 (define @t122 () (_ (_ tptp.minus_minus_nat @t121) @t14)) % 0.40/0.73 (define @t123 () (_ (_ tptp.plus_plus_nat @t117) @t10)) % 0.40/0.73 (define @t124 () (_ @t114 @t101)) % 0.40/0.73 (define @t125 () (_ (_ tptp.minus_minus_nat @t124) @t14)) % 0.40/0.73 (define @t126 () (_ @t114 @t117)) % 0.40/0.73 (define @t127 () (_ (_ tptp.minus_minus_nat @t83) @t45)) % 0.40/0.73 (define @t128 () (_ @t76 @t45)) % 0.40/0.73 (define @t129 () (_ tptp.ord_less_nat @t101)) % 0.40/0.73 (define @t130 () (@var "L" tptp.nat)) % 0.40/0.73 (define @t131 () (_ tptp.minus_minus_nat @t130)) % 0.40/0.73 (define @t132 () (_ @t131 @t11)) % 0.40/0.73 (define @t133 () (_ @t131 @t9)) % 0.40/0.73 (define @t134 () (@list @t11 @t9 @t130)) % 0.40/0.73 (define @t135 () (_ tptp.ord_less_eq_nat @t37)) % 0.40/0.73 (define @t136 () (_ tptp.minus_minus_nat @t45)) % 0.40/0.73 (define @t137 () (_ @t99 @t14)) % 0.40/0.73 (define @t138 () (_ @t94 @t14)) % 0.40/0.73 (define @t139 () (_ @t118 @t9)) % 0.40/0.73 (define @t140 () (_ @t118 @t11)) % 0.40/0.73 (define @t141 () (_ tptp.plus_plus_nat @t9)) % 0.40/0.73 (define @t142 () (_ @t141 @t11)) % 0.40/0.73 (define @t143 () (_ tptp.minus_minus_nat @t37)) % 0.40/0.73 (define @t144 () (_ @t143 @t34)) % 0.40/0.73 (define @t145 () (_ tptp.plus_plus_nat @t144)) % 0.40/0.73 (define @t146 () (_ @t145 @t45)) % 0.40/0.73 (define @t147 () (_ (_ tptp.minus_minus_nat @t59) @t34)) % 0.40/0.73 (define @t148 () (_ @t47 @t144)) % 0.40/0.73 (define @t149 () (_ (_ tptp.minus_minus_nat @t63) @t34)) % 0.40/0.73 (define @t150 () (_ tptp.ord_less_eq_nat @t45)) % 0.40/0.73 (define @t151 () (_ tptp.ord_less_nat @t115)) % 0.40/0.73 (define @t152 () (_ tptp.ord_less_nat @t10)) % 0.40/0.73 (define @t153 () (_ @t116 @t10)) % 0.40/0.73 (define @t154 () (_ @t100 @t101)) % 0.40/0.73 (define @t155 () (_ tptp.ord_less_eq_nat @t115)) % 0.40/0.73 (define @t156 () (_ tptp.ord_less_eq_nat @t101)) % 0.40/0.73 (define @t157 () (@var "D" tptp.nat)) % 0.40/0.73 (define @t158 () (@var "P2" (-> tptp.nat Bool))) % 0.40/0.73 (define @t159 () (_ @t158 @t157)) % 0.40/0.73 (define @t160 () (= @t34 (_ @t38 @t157))) % 0.40/0.73 (define @t161 () (@list @t157)) % 0.40/0.73 (define @t162 () (_ @t158 tptp.zero_zero_nat)) % 0.40/0.73 (define @t163 () (_ @t158 @t83)) % 0.40/0.73 (define @t164 () (@list @t158 @t34 @t37)) % 0.40/0.73 (define @t165 () (@var "U" tptp.nat)) % 0.40/0.73 (define @t166 () (_ (_ tptp.plus_plus_nat (_ (_ tptp.times_times_nat @t153) @t165)) @t9)) % 0.40/0.73 (define @t167 () (_ (_ tptp.plus_plus_nat (_ (_ tptp.times_times_nat @t101) @t165)) @t9)) % 0.40/0.73 (define @t168 () (_ (_ tptp.plus_plus_nat (_ (_ tptp.times_times_nat @t10) @t165)) @t11)) % 0.40/0.73 (define @t169 () (_ (_ tptp.minus_minus_nat @t168) @t167)) % 0.40/0.73 (define @t170 () (@list @t10 @t101 @t165 @t11 @t9)) % 0.40/0.73 (define @t171 () (_ (_ tptp.plus_plus_nat (_ (_ tptp.times_times_nat @t105) @t165)) @t11)) % 0.40/0.73 (define @t172 () (_ @t156 @t10)) % 0.40/0.73 (define @t173 () (@list @t101 @t10 @t165 @t11 @t9)) % 0.40/0.73 (define @t174 () (_ (_ tptp.ord_less_eq_nat @t168) @t167)) % 0.40/0.73 (define @t175 () (= @t168 @t167)) % 0.40/0.73 (define @t176 () (_ (_ tptp.ord_less_nat @t168) @t167)) % 0.40/0.73 (define @t177 () (@list @t68)) % 0.40/0.73 (define @t178 () (_ @t41 @t59)) % 0.40/0.73 (define @t179 () (@var "A2" tptp.nat)) % 0.40/0.73 (define @t180 () (@var "B2" tptp.nat)) % 0.40/0.73 (define @t181 () (@list @t179 @t180)) % 0.40/0.73 (define @t182 () (_ @t91 @t42)) % 0.40/0.73 (define @t183 () (@var "B3" tptp.nat)) % 0.40/0.73 (define @t184 () (@var "A3" tptp.nat)) % 0.40/0.73 (define @t185 () (_ @t102 @t130)) % 0.40/0.73 (define @t186 () (= @t14 @t130)) % 0.40/0.73 (define @t187 () (= @t10 @t101)) % 0.40/0.73 (define @t188 () (@list @t10 @t101 @t14 @t130)) % 0.40/0.73 (define @t189 () (_ tptp.times_times_nat @t37)) % 0.40/0.73 (define @t190 () (_ tptp.times_times_nat @t34)) % 0.40/0.73 (define @t191 () (_ @t190 (_ @t189 @t45))) % 0.40/0.73 (define @t192 () (_ @t158 @t9)) % 0.40/0.73 (define @t193 () (@var "M2" tptp.nat)) % 0.40/0.73 (define @t194 () (_ @t158 @t193)) % 0.40/0.73 (define @t195 () (@var "N2" tptp.nat)) % 0.40/0.73 (define @t196 () (_ (_ tptp.ord_less_nat @t193) @t195)) % 0.40/0.73 (define @t197 () (@list @t193)) % 0.40/0.73 (define @t198 () (_ @t158 @t195)) % 0.40/0.73 (define @t199 () (=> (not @t198) (exists @t197 (and @t196 (not @t194))))) % 0.40/0.73 (define @t200 () (@list @t195)) % 0.40/0.73 (define @t201 () (@list @t158 @t9)) % 0.40/0.73 (define @t202 () (@var "T" tptp.nat)) % 0.40/0.73 (define @t203 () (@var "S" tptp.nat)) % 0.40/0.73 (define @t204 () (not @t96)) % 0.40/0.73 (define @t205 () (_ @t86 @t11)) % 0.40/0.73 (define @t206 () (@var "X2" tptp.nat)) % 0.40/0.73 (define @t207 () (@var "Y3" tptp.nat)) % 0.40/0.73 (define @t208 () (@var "Y2" tptp.nat)) % 0.40/0.73 (define @t209 () (_ @t55 @t11)) % 0.40/0.73 (define @t210 () (=> @t209 @t96)) % 0.40/0.73 (define @t211 () (=> @t13 @t210)) % 0.40/0.73 (define @t212 () (forall @t31 @t211)) % 0.40/0.73 (define @t213 () (@var "C3" tptp.nat)) % 0.40/0.73 (define @t214 () (@var "D2" tptp.nat)) % 0.40/0.73 (define @t215 () (_ @t38 @t214)) % 0.40/0.73 (define @t216 () (@list @t34 @t37 @t45 @t214)) % 0.40/0.73 (define @t217 () (_ @t155 @t185)) % 0.40/0.73 (define @t218 () (_ @t118 @t130)) % 0.40/0.73 (define @t219 () (_ @t151 @t185)) % 0.40/0.73 (define @t220 () (_ @t152 @t101)) % 0.40/0.73 (define @t221 () (_ (_ tptp.ord_less_nat @t14) @t130)) % 0.40/0.73 (define @t222 () (@var "F" (-> tptp.nat tptp.nat))) % 0.40/0.73 (define @t223 () (@var "J2" tptp.nat)) % 0.40/0.73 (define @t224 () (@var "I3" tptp.nat)) % 0.40/0.73 (define @t225 () (@var "N3" tptp.nat)) % 0.40/0.73 (define @t226 () (@var "M3" tptp.nat)) % 0.40/0.73 (define @t227 () (= @t226 @t225)) % 0.40/0.73 (define @t228 () (@list @t226 @t225)) % 0.40/0.73 (define @t229 () (_ @t32 @t101)) % 0.40/0.73 (define @t230 () (@list @t10 @t101 @t11)) % 0.40/0.73 (define @t231 () (_ @t102 @t11)) % 0.40/0.73 (define @t232 () (_ tptp.ord_less_nat @t124)) % 0.40/0.73 (define @t233 () (@var "K2" tptp.nat)) % 0.40/0.73 (define @t234 () (@var "C2" tptp.nat)) % 0.40/0.73 (define @t235 () (_ (_ tptp.plus_plus_nat @t179) @t234)) % 0.40/0.73 (define @t236 () (= @t180 @t235)) % 0.40/0.73 (define @t237 () (@list @t234)) % 0.40/0.73 (define @t238 () (exists @t237 @t236)) % 0.40/0.73 (define @t239 () (lambda @t181 @t238)) % 0.40/0.73 (define @t240 () (not @t227)) % 0.40/0.73 (define @t241 () (and (_ (_ tptp.ord_less_eq_nat @t226) @t225) @t240)) % 0.40/0.73 (define @t242 () (lambda @t228 @t241)) % 0.40/0.73 (define @t243 () (@var "BOUND_VARIABLE_12627" tptp.nat)) % 0.40/0.73 (define @t244 () (tptp.plus_plus_nat @t11 @t243)) % 0.40/0.73 (define @t245 () (= @t11 @t244)) % 0.40/0.73 (define @t246 () (@var "BOUND_VARIABLE_12632" tptp.nat)) % 0.40/0.73 (define @t247 () (not (= @t11 (tptp.plus_plus_nat @t244 @t246)))) % 0.40/0.73 (define @t248 () (or @t247 @t245)) % 0.40/0.73 (define @t249 () (not (= @t244 @t244))) % 0.40/0.73 (define @t250 () (or @t249 @t247 (= @t244 @t11))) % 0.40/0.73 (define @t251 () (@list @t11 @t243 @t246)) % 0.40/0.73 (define @t252 () (= @t9 @t11)) % 0.40/0.73 (define @t253 () (not (= @t11 (tptp.plus_plus_nat @t9 @t246)))) % 0.40/0.73 (define @t254 () (not (= @t9 @t244))) % 0.40/0.73 (define @t255 () (or @t254 @t254 @t253 @t252)) % 0.40/0.73 (define @t256 () (or @t254 @t253 @t252)) % 0.40/0.73 (define @t257 () (forall @t56 @t256)) % 0.40/0.73 (define @t258 () (forall @t251 @t257)) % 0.40/0.73 (define @t259 () (forall (@list @t11 @t243 @t246 @t9) @t256)) % 0.40/0.73 (define @t260 () (forall (@list @t11 @t9 @t243 @t246) @t256)) % 0.40/0.73 (define @t261 () (forall (@list @t243 @t246) @t256)) % 0.40/0.73 (define @t262 () (forall (@list @t246) @t253)) % 0.40/0.73 (define @t263 () (@list @t234)) % 0.40/0.73 (define @t264 () (forall (@list @t243) @t254)) % 0.40/0.73 (define @t265 () (or @t264 @t262 @t252)) % 0.40/0.73 (define @t266 () (tptp.plus_plus_nat @t9 @t234)) % 0.40/0.73 (define @t267 () (forall @t237 (not (= @t11 @t266)))) % 0.40/0.73 (define @t268 () (tptp.plus_plus_nat @t11 @t234)) % 0.40/0.73 (define @t269 () (forall @t237 (not (= @t9 @t268)))) % 0.40/0.73 (define @t270 () (or @t269 @t267 @t252)) % 0.40/0.73 (define @t271 () (not @t267)) % 0.40/0.73 (define @t272 () (=> @t271 @t252)) % 0.40/0.73 (define @t273 () (not @t269)) % 0.40/0.73 (define @t274 () (@list @t180)) % 0.40/0.73 (define @t275 () (lambda @t274 (not (forall @t237 (not (= @t180 @t266)))))) % 0.40/0.73 (define @t276 () (tptp.plus_plus_nat @t179 @t234)) % 0.40/0.73 (define @t277 () (lambda @t181 (not (forall @t237 (not (= @t180 @t276)))))) % 0.40/0.73 (define @t278 () (_ @t277 @t9)) % 0.40/0.73 (define @t279 () (=> (_ @t278 @t11) @t96)) % 0.40/0.73 (define @t280 () (lambda @t274 (not (forall @t237 (not (= @t180 @t268)))))) % 0.40/0.73 (define @t281 () (_ @t277 @t11)) % 0.40/0.73 (define @t282 () (=> (_ @t281 @t9) @t279)) % 0.40/0.73 (define @t283 () (not @t236)) % 0.40/0.73 (define @t284 () (forall @t237 @t283)) % 0.40/0.73 (define @t285 () (not @t284)) % 0.40/0.73 (define @t286 () (tptp.p tptp.k)) % 0.40/0.73 (define @t287 () (tptp.times_times_nat @t286 tptp.k)) % 0.40/0.73 (define @t288 () (tptp.p tptp.i)) % 0.40/0.73 (define @t289 () (tptp.times_times_nat @t288 tptp.i)) % 0.40/0.73 (define @t290 () (tptp.plus_plus_nat @t289 @t287)) % 0.40/0.73 (define @t291 () (tptp.plus_plus_nat @t290 @t234)) % 0.40/0.73 (define @t292 () (forall @t237 (not (= tptp.n @t291)))) % 0.40/0.73 (define @t293 () (@quantifiers_skolemize @t292 0)) % 0.40/0.73 (define @t294 () (tptp.plus_plus_nat @t290 @t293)) % 0.40/0.73 (define @t295 () (= @t290 @t294)) % 0.40/0.73 (define @t296 () (= @t294 @t290)) % 0.40/0.73 (define @t297 () (= tptp.n @t5)) % 0.40/0.73 (define @t298 () (not @t297)) % 0.40/0.73 (define @t299 () (tptp.plus_plus_nat tptp.n @t234)) % 0.40/0.73 (define @t300 () (forall @t237 (not (= @t290 @t299)))) % 0.40/0.73 (define @t301 () (not @t300)) % 0.40/0.73 (define @t302 () (= @t5 @t299)) % 0.40/0.73 (define @t303 () (not @t302)) % 0.40/0.73 (define @t304 () (forall @t237 @t303)) % 0.40/0.73 (define @t305 () (not @t304)) % 0.40/0.73 (define @t306 () (and @t305 @t298)) % 0.40/0.73 (define @t307 () (lambda (@list @t225) (and (not (forall @t237 (not (= @t225 @t299)))) (not (= tptp.n @t225))))) % 0.40/0.73 (define @t308 () (tptp.plus_plus_nat @t226 @t234)) % 0.40/0.73 (define @t309 () (not (forall @t237 (not (= @t225 @t308))))) % 0.40/0.73 (define @t310 () (lambda @t274 (not (forall @t237 (not (= @t180 @t308)))))) % 0.40/0.73 (define @t311 () (_ @t277 @t226)) % 0.40/0.73 (define @t312 () (not @t292)) % 0.40/0.73 (define @t313 () (tptp.plus_plus_nat @t5 @t234)) % 0.40/0.73 (define @t314 () (= @t180 @t313)) % 0.40/0.73 (define @t315 () (not @t314)) % 0.40/0.73 (define @t316 () (forall @t237 @t315)) % 0.40/0.73 (define @t317 () (not @t316)) % 0.40/0.73 (define @t318 () (lambda @t274 @t317)) % 0.40/0.73 (define @t319 () (= tptp.n @t294)) % 0.40/0.73 (define @t320 () (not (not @t319))) % 0.40/0.73 (define @t321 () (@list true)) % 0.40/0.73 (define @t322 () (@quantifiers_skolemize @t300 0)) % 0.40/0.73 (define @t323 () (tptp.plus_plus_nat tptp.n @t322)) % 0.40/0.73 (define @t324 () (= @t290 @t323)) % 0.40/0.73 (define @t325 () (not (not @t324))) % 0.40/0.73 (define @t326 () (= @t290 (tptp.plus_plus_nat @t294 @t322))) % 0.40/0.73 (define @t327 () (not @t326)) % 0.40/0.73 (define @t328 () (or @t327 @t295)) % 0.40/0.73 (define @t329 () (not @t328)) % 0.40/0.73 (define @t330 () (forall @t251 @t248)) % 0.40/0.73 (assume @p1 (_ (_ tptp.ord_less_eq_nat tptp.i) tptp.n)) % 0.40/0.73 (assume @p2 (_ (_ tptp.number1551313001itions tptp.p) tptp.n)) % 0.40/0.73 (assume @p3 (_ (_ tptp.ord_less_eq_nat @t5) tptp.n)) % 0.40/0.73 (assume @p4 (_ (_ tptp.ord_less_nat tptp.n) @t5)) % 0.40/0.73 (assume @p5 (_ (_ tptp.ord_less_eq_nat tptp.k) tptp.n)) % 0.40/0.73 (assume @p6 (not (= @t3 tptp.zero_zero_nat))) % 0.40/0.73 (assume @p7 (_ @t6 @t1)) % 0.40/0.73 (assume @p8 (not (= tptp.i tptp.k))) % 0.40/0.73 (assume @p9 (_ (_ tptp.ord_less_nat (_ (_ tptp.minus_minus_nat tptp.n) tptp.k)) tptp.i)) % 0.40/0.73 (assume @p10 (forall (@list @t7) (= (_ @t8 tptp.zero_zero_nat) (= @t7 (lambda (@list (@var "I" tptp.nat)) tptp.zero_zero_nat))))) % 0.40/0.73 (assume @p11 (forall (@list @t7 @t9 @t10) (=> (_ @t8 @t9) (_ (_ tptp.ord_less_eq_nat (_ @t7 @t10)) @t9)))) % 0.40/0.73 (assume @p12 (forall @t20 (= (_ (_ tptp.ord_less_eq_nat @t19) @t17) @t16))) % 0.40/0.73 (assume @p13 (forall @t24 (= (_ (_ tptp.ord_less_eq_nat @t23) @t22) @t16))) % 0.40/0.73 (assume @p14 (forall @t20 (= (_ (_ tptp.ord_less_nat @t19) @t17) @t27))) % 0.40/0.73 (assume @p15 (forall @t31 (= (_ @t6 @t30) (and @t29 @t28)))) % 0.40/0.73 (assume @p16 (forall @t24 (= (_ (_ tptp.ord_less_nat @t23) @t22) @t27))) % 0.40/0.73 (assume @p17 (forall @t31 (= (_ @t6 @t33) (or @t29 @t28)))) % 0.40/0.73 (assume @p18 (forall @t40 (= (_ (_ tptp.ord_less_nat @t39) @t37) @t36))) % 0.40/0.73 (assume @p19 (forall @t43 (= (_ (_ tptp.ord_less_nat @t42) @t37) @t36))) % 0.40/0.73 (assume @p20 (forall @t43 (= (_ @t35 @t42) @t44))) % 0.40/0.73 (assume @p21 (forall @t43 (= (_ @t35 @t39) @t44))) % 0.40/0.73 (assume @p22 (forall @t50 (= @t49 @t46))) % 0.40/0.73 (assume @p23 (forall @t53 (= @t52 @t46))) % 0.40/0.73 (assume @p24 (forall @t56 (= (_ @t55 tptp.zero_zero_nat) @t54))) % 0.40/0.73 (assume @p25 (forall @t56 (= (not @t28) @t54))) % 0.40/0.73 (assume @p26 (forall @t62 (= @t61 @t58))) % 0.40/0.73 (assume @p27 (forall @t66 (= @t65 @t58))) % 0.40/0.73 (assume @p28 (forall @t72 (= (= tptp.zero_zero_nat @t71) @t70))) % 0.40/0.73 (assume @p29 (forall @t72 (= (= @t71 tptp.zero_zero_nat) @t70))) % 0.40/0.73 (assume @p30 (forall @t43 (= (= @t34 @t42) @t73))) % 0.40/0.73 (assume @p31 (forall @t43 (= (= @t34 @t39) @t73))) % 0.40/0.73 (assume @p32 (forall @t43 (= (= @t42 @t34) @t73))) % 0.40/0.73 (assume @p33 (forall @t40 (= (= @t39 @t34) @t73))) % 0.40/0.73 (assume @p34 (forall @t74 (= (_ @t41 tptp.zero_zero_nat) @t34))) % 0.40/0.73 (assume @p35 (forall @t74 (= (_ @t75 @t34) @t34))) % 0.40/0.73 (assume @p36 (forall @t74 (= (_ @t76 @t34) tptp.zero_zero_nat))) % 0.40/0.73 (assume @p37 (forall @t74 (= (_ @t76 tptp.zero_zero_nat) @t34))) % 0.40/0.73 (assume @p38 (forall @t74 (= (_ @t77 @t34) tptp.zero_zero_nat))) % 0.40/0.73 (assume @p39 (forall @t62 (= @t80 @t78))) % 0.40/0.73 (assume @p40 (forall @t66 (= @t81 @t78))) % 0.40/0.73 (assume @p41 (forall @t43 (= (_ @t82 @t37) @t34))) % 0.40/0.73 (assume @p42 (forall @t62 (= (_ (_ tptp.minus_minus_nat @t51) @t59) @t83))) % 0.40/0.73 (assume @p43 (forall @t43 (= (_ @t82 @t34) @t37))) % 0.40/0.73 (assume @p44 (forall @t66 (= (_ @t84 @t63) @t83))) % 0.40/0.73 (assume @p45 (forall @t74 (= (not @t85) (_ @t6 @t34)))) % 0.40/0.73 (assume @p46 (forall @t56 (not (_ @t86 tptp.zero_zero_nat)))) % 0.40/0.73 (assume @p47 (forall @t56 (= @t87 @t28))) % 0.40/0.73 (assume @p48 (forall @t74 (_ @t88 @t34))) % 0.40/0.73 (assume @p49 (forall @t56 (_ @t88 @t9))) % 0.40/0.73 (assume @p50 (forall @t89 (= (_ @t32 tptp.zero_zero_nat) @t11))) % 0.40/0.73 (assume @p51 (forall @t31 (= (= @t33 tptp.zero_zero_nat) (and @t90 @t54)))) % 0.40/0.73 (assume @p52 (forall @t24 (= (_ (_ tptp.ord_less_nat @t93) @t92) @t26))) % 0.40/0.73 (assume @p53 (forall @t89 (= (_ @t94 @t11) tptp.zero_zero_nat))) % 0.40/0.73 (assume @p54 (forall @t56 (= (_ @t77 @t9) tptp.zero_zero_nat))) % 0.40/0.73 (assume @p55 (forall @t20 (= (= @t19 @t17) @t97))) % 0.40/0.73 (assume @p56 (forall @t24 (= @t98 @t97))) % 0.40/0.73 (assume @p57 (forall @t89 (= (_ @t18 tptp.zero_zero_nat) tptp.zero_zero_nat))) % 0.40/0.73 (assume @p58 (forall @t31 (= (= @t30 tptp.zero_zero_nat) (or @t90 @t54)))) % 0.40/0.73 (assume @p59 (forall @t24 (= (_ (_ tptp.ord_less_eq_nat @t93) @t92) @t13))) % 0.40/0.73 (assume @p60 (forall (@list @t10 @t9) (=> (_ @t100 @t9) (= (_ @t99 (_ @t99 @t10)) @t10)))) % 0.40/0.73 (assume @p61 (forall @t107 (= @t106 (_ @t104 @t103)))) % 0.40/0.73 (assume @p62 (forall @t43 (= (_ @t57 @t39) @t108))) % 0.40/0.73 (assume @p63 (forall @t43 (= (_ @t57 @t42) @t108))) % 0.40/0.73 (assume @p64 (forall @t43 (= (_ (_ tptp.ord_less_eq_nat @t42) @t37) @t109))) % 0.40/0.73 (assume @p65 (forall @t40 (= (_ (_ tptp.ord_less_eq_nat @t39) @t37) @t109))) % 0.40/0.73 (assume @p66 (forall @t43 (= (_ @t76 @t42) tptp.zero_zero_nat))) % 0.40/0.73 (assume @p67 (forall @t111 (= (_ @t6 @t110) @t26))) % 0.40/0.73 (assume @p68 (forall @t31 (=> @t13 @t113))) % 0.40/0.73 (assume @p69 (forall @t31 (= @t113 @t13))) % 0.40/0.73 (assume @p70 (forall @t120 (=> @t119 (= (_ @t104 @t117) (_ (_ tptp.minus_minus_nat @t115) @t101))))) % 0.40/0.73 (assume @p71 (forall @t120 (=> @t119 (= @t123 @t122)))) % 0.40/0.73 (assume @p72 (forall @t120 (=> @t119 (= @t126 @t125)))) % 0.40/0.73 (assume @p73 (forall @t62 (= (_ (_ tptp.minus_minus_nat @t128) @t37) @t127))) % 0.40/0.73 (assume @p74 (forall @t107 (= @t106 (_ (_ tptp.minus_minus_nat (_ @t104 @t14)) @t101)))) % 0.40/0.73 (assume @p75 (forall (@list @t45 @t37 @t34) (=> (= @t63 @t34) (= @t45 @t83)))) % 0.40/0.73 (assume @p76 (forall @t53 (= @t127 (_ @t76 @t59)))) % 0.40/0.73 (assume @p77 (forall @t89 (= (_ @t94 tptp.zero_zero_nat) @t11))) % 0.40/0.73 (assume @p78 (forall @t31 (=> @t113 (=> (= @t110 tptp.zero_zero_nat) @t96)))) % 0.40/0.73 (assume @p79 (forall (@list @t101 @t14 @t9) (=> (_ @t129 @t14) (_ (_ tptp.ord_less_nat (_ @t116 @t9)) @t14)))) % 0.40/0.73 (assume @p80 (forall @t134 (=> @t26 (=> (_ @t25 @t130) (_ (_ tptp.ord_less_nat @t133) @t132))))) % 0.40/0.73 (assume @p81 (forall @t134 (=> @t13 (_ (_ tptp.ord_less_eq_nat @t133) @t132)))) % 0.40/0.73 (assume @p82 (forall @t62 (=> (_ @t57 @t45) (=> (_ @t135 @t45) (= (_ (_ tptp.ord_less_eq_nat (_ @t136 @t34)) (_ @t136 @t37)) (_ @t135 @t34)))))) % 0.40/0.73 (assume @p83 (forall @t31 (_ (_ tptp.ord_less_eq_nat @t112) @t11))) % 0.40/0.73 (assume @p84 (forall @t134 (=> @t13 (_ (_ tptp.ord_less_eq_nat (_ @t94 @t130)) (_ @t99 @t130))))) % 0.40/0.73 (assume @p85 (forall @t24 (=> @t140 (=> @t139 (= (_ (_ tptp.minus_minus_nat @t138) @t137) @t112))))) % 0.40/0.73 (assume @p86 (forall @t24 (=> @t140 (=> @t139 (= (_ (_ tptp.ord_less_eq_nat @t138) @t137) @t13))))) % 0.40/0.73 (assume @p87 (forall @t24 (=> @t140 (=> @t139 (= (= @t138 @t137) @t96))))) % 0.40/0.73 (assume @p88 (forall @t31 (= (_ (_ tptp.minus_minus_nat @t33) @t9) @t11))) % 0.40/0.73 (assume @p89 (forall @t111 (= (_ (_ tptp.minus_minus_nat @t142) @t9) @t11))) % 0.40/0.73 (assume @p90 (forall @t20 (= (_ (_ tptp.minus_minus_nat (_ @t32 @t14)) (_ @t141 @t14)) @t112))) % 0.40/0.73 (assume @p91 (forall @t24 (= (_ (_ tptp.minus_minus_nat @t93) @t92) @t112))) % 0.40/0.73 (assume @p92 (forall @t24 (= (_ @t21 @t112) (_ (_ tptp.minus_minus_nat @t23) @t22)))) % 0.40/0.73 (assume @p93 (forall (@list @t11 @t9 @t14) (= (_ (_ tptp.times_times_nat @t112) @t14) (_ (_ tptp.minus_minus_nat @t19) @t17)))) % 0.40/0.73 (assume @p94 (forall @t53 (=> @t58 (=> @t58 (= (= @t144 @t45) (= @t37 @t48)))))) % 0.40/0.73 (assume @p95 (forall @t43 (=> @t58 (= (_ @t41 @t144) @t37)))) % 0.40/0.73 (assume @p96 (forall @t53 (=> @t58 (= (_ @t136 @t144) (_ @t84 @t37))))) % 0.40/0.73 (assume @p97 (forall @t53 (=> @t58 (= @t147 @t146)))) % 0.40/0.73 (assume @p98 (forall @t53 (=> @t58 (= @t146 @t147)))) % 0.40/0.73 (assume @p99 (forall @t53 (=> @t58 (= @t149 @t148)))) % 0.40/0.73 (assume @p100 (forall @t53 (=> @t58 (= @t148 @t149)))) % 0.40/0.73 (assume @p101 (forall @t53 (=> @t58 (= (_ @t150 @t144) (_ @t64 @t37))))) % 0.40/0.73 (assume @p102 (forall @t53 (=> @t58 (_ @t150 @t147)))) % 0.40/0.73 (assume @p103 (forall @t43 (=> @t58 (= (_ @t145 @t34) @t37)))) % 0.40/0.73 (assume @p104 (forall @t111 (=> @t28 (=> @t29 (_ (_ tptp.ord_less_nat @t112) @t11))))) % 0.40/0.73 (assume @p105 (forall @t111 (= (_ @t99 @t142) tptp.zero_zero_nat))) % 0.40/0.73 (assume @p106 (forall @t53 (=> @t78 (=> (_ @t150 @t34) (_ (_ tptp.ord_less_nat @t128) (_ @t143 @t45)))))) % 0.40/0.73 (assume @p107 (forall @t24 (=> @t140 (=> @t139 (= (_ (_ tptp.ord_less_nat @t138) @t137) @t26))))) % 0.40/0.73 (assume @p108 (forall @t31 (=> (not @t26) (= (_ @t141 @t112) @t11)))) % 0.40/0.73 (assume @p109 (forall @t107 (= (_ @t152 @t117) (_ @t151 @t101)))) % 0.40/0.73 (assume @p110 (forall @t107 (=> @t154 (= (= @t153 @t14) (= @t101 (_ @t91 @t10)))))) % 0.40/0.73 (assume @p111 (forall @t120 (=> @t119 (= @t122 @t123)))) % 0.40/0.73 (assume @p112 (forall @t120 (=> @t119 (= @t125 @t126)))) % 0.40/0.73 (assume @p113 (forall @t120 (=> @t119 (= (_ @t100 @t117) (_ @t155 @t101))))) % 0.40/0.73 (assume @p114 (forall (@list @t101 @t14 @t10) (= (_ (_ tptp.ord_less_eq_nat @t117) @t10) (_ @t156 @t115)))) % 0.40/0.73 (assume @p115 (forall @t164 (= @t163 (not (or (and @t78 (not @t162)) (exists @t161 (and @t160 (not @t159)))))))) % 0.40/0.73 (assume @p116 (forall @t164 (= @t163 (and (=> @t78 @t162) (forall @t161 (=> @t160 @t159)))))) % 0.40/0.73 (assume @p117 (forall @t120 (=> @t119 (= (_ (_ tptp.ord_less_nat @t117) @t10) (_ @t129 @t115))))) % 0.40/0.73 (assume @p118 (forall @t170 (=> @t154 (= @t169 (_ @t94 @t166))))) % 0.40/0.73 (assume @p119 (forall @t173 (=> @t172 (= @t169 (_ (_ tptp.minus_minus_nat @t171) @t9))))) % 0.40/0.73 (assume @p120 (forall @t170 (=> @t154 (= @t174 (_ @t12 @t166))))) % 0.40/0.73 (assume @p121 (forall @t173 (=> @t172 (= @t174 (_ (_ tptp.ord_less_eq_nat @t171) @t9))))) % 0.40/0.73 (assume @p122 (forall @t170 (=> @t154 (= @t175 (= @t11 @t166))))) % 0.40/0.73 (assume @p123 (forall @t173 (=> @t172 (= @t175 (= @t171 @t9))))) % 0.40/0.73 (assume @p124 (forall @t170 (=> @t154 (= @t176 (_ @t25 @t166))))) % 0.40/0.73 (assume @p125 (forall @t173 (=> @t172 (= @t176 (_ (_ tptp.ord_less_nat @t171) @t9))))) % 0.40/0.73 (assume @p126 (forall @t177 (= (= tptp.zero_zero_nat @t68) @t69))) % 0.40/0.73 (assume @p127 (forall @t50 (=> @t49 @t46))) % 0.40/0.73 (assume @p128 (forall @t53 (=> @t52 @t46))) % 0.40/0.73 (assume @p129 (forall @t50 (= (_ @t38 @t51) @t178))) % 0.40/0.73 (assume @p130 (= tptp.plus_plus_nat (lambda @t181 (_ (_ tptp.plus_plus_nat @t180) @t179)))) % 0.40/0.73 (assume @p131 (forall @t53 (= (_ (_ tptp.plus_plus_nat @t42) @t45) @t178))) % 0.40/0.73 (assume @p132 (forall (@list @t183 @t14 @t37 @t34) (=> (= @t183 (_ @t91 @t37)) (= (_ @t41 @t183) @t182)))) % 0.40/0.73 (assume @p133 (forall (@list @t184 @t14 @t34 @t37) (=> (= @t184 (_ @t91 @t34)) (= (_ (_ tptp.plus_plus_nat @t184) @t37) @t182)))) % 0.40/0.73 (assume @p134 (forall @t188 (=> (and @t187 @t186) (= @t115 @t185)))) % 0.40/0.73 (assume @p135 (forall @t50 (= (_ @t189 (_ @t190 @t45)) @t191))) % 0.40/0.73 (assume @p136 (= tptp.times_times_nat (lambda @t181 (_ (_ tptp.times_times_nat @t180) @t179)))) % 0.40/0.73 (assume @p137 (forall @t53 (= (_ (_ tptp.times_times_nat (_ @t190 @t37)) @t45) @t191))) % 0.40/0.73 (assume @p138 (forall @t72 (=> (not (= @t68 @t67)) (=> (not (_ (_ tptp.ord_less_nat @t68) @t67)) (_ (_ tptp.ord_less_nat @t67) @t68))))) % 0.40/0.73 (assume @p139 (forall @t201 (=> (forall @t200 @t199) @t192))) % 0.40/0.73 (assume @p140 (forall @t201 (=> (forall @t200 (=> (forall @t197 (=> @t196 @t194)) @t198)) @t192))) % 0.40/0.73 (assume @p141 (forall @t56 (not (_ @t86 @t9)))) % 0.40/0.73 (assume @p142 (forall (@list @t203 @t202) (=> (_ (_ tptp.ord_less_nat @t203) @t202) (not (= @t203 @t202))))) % 0.40/0.73 (assume @p143 (forall @t111 (=> @t205 @t204))) % 0.40/0.73 (assume @p144 (forall @t31 (= @t204 (or @t26 @t205)))) % 0.40/0.73 (assume @p145 (forall (@list @t158 @t14 @t37) (=> (_ @t158 @t14) (=> (forall (@list @t208) (=> (_ @t158 @t208) (_ (_ tptp.ord_less_eq_nat @t208) @t37))) (exists (@list @t206) (and (_ @t158 @t206) (forall (@list @t207) (=> (_ @t158 @t207) (_ (_ tptp.ord_less_eq_nat @t207) @t206))))))))) % 0.40/0.73 (assume @p146 (forall @t31 (or @t13 @t209))) % 0.40/0.73 (assume @p147 @t212) % 0.40/0.73 (assume @p148 (forall @t31 (=> @t96 @t13))) % 0.40/0.73 (assume @p149 (forall @t107 (=> @t154 (=> (_ @t156 @t14) (_ @t100 @t14))))) % 0.40/0.73 (assume @p150 (forall @t56 (_ @t55 @t9))) % 0.40/0.73 (assume @p151 (forall @t177 (_ @t88 @t68))) % 0.40/0.73 (assume @p152 (forall @t56 (= @t28 @t87))) % 0.40/0.73 (assume @p153 (forall @t31 (=> @t26 @t87))) % 0.40/0.73 (assume @p154 (forall @t56 (=> @t87 @t28))) % 0.40/0.73 (assume @p155 (forall @t62 (=> @t61 @t58))) % 0.40/0.73 (assume @p156 (forall @t66 (=> @t65 @t58))) % 0.40/0.73 (assume @p157 (forall @t53 (=> @t58 @t61))) % 0.40/0.73 (assume @p158 (forall @t43 (=> @t58 (not (forall (@list @t213) (not (= @t37 (_ @t41 @t213)))))))) % 0.40/0.73 (assume @p159 (forall @t53 (=> @t58 @t65))) % 0.40/0.73 (assume @p160 (forall @t216 (=> @t58 (=> (_ @t150 @t214) (_ @t60 @t215))))) % 0.40/0.73 (assume @p161 (forall @t188 (=> (and @t154 @t218) @t217))) % 0.40/0.73 (assume @p162 (forall @t188 (=> (and @t187 @t218) @t217))) % 0.40/0.73 (assume @p163 (forall @t188 (=> (and @t154 @t186) @t217))) % 0.40/0.73 (assume @p164 (forall @t62 (=> @t80 @t78))) % 0.40/0.73 (assume @p165 (forall @t66 (=> @t81 @t78))) % 0.40/0.73 (assume @p166 (forall @t53 (=> @t78 @t80))) % 0.40/0.73 (assume @p167 (forall @t53 (=> @t78 @t81))) % 0.40/0.73 (assume @p168 (forall @t216 (=> @t78 (=> (_ (_ tptp.ord_less_nat @t45) @t214) (_ @t79 @t215))))) % 0.40/0.73 (assume @p169 (forall @t188 (=> (and @t220 @t186) @t219))) % 0.40/0.73 (assume @p170 (forall @t188 (=> (and @t187 @t221) @t219))) % 0.40/0.73 (assume @p171 (forall @t188 (=> (and @t220 @t221) @t219))) % 0.40/0.73 (assume @p172 (forall @t74 (not @t36))) % 0.40/0.73 (assume @p173 (forall @t201 (=> @t162 (=> (forall @t200 (=> (_ @t6 @t195) @t199)) @t192)))) % 0.40/0.73 (assume @p174 (forall @t74 (=> @t109 @t85))) % 0.40/0.73 (assume @p175 (forall @t74 (= @t109 @t85))) % 0.40/0.73 (assume @p176 (forall @t31 (=> (= @t33 @t11) @t54))) % 0.40/0.73 (assume @p177 (forall @t56 (= (_ @t75 @t9) @t9))) % 0.40/0.73 (assume @p178 (forall (@list @t222 @t10 @t101) (=> (forall (@list @t224 @t223) (=> (_ (_ tptp.ord_less_nat @t224) @t223) (_ (_ tptp.ord_less_nat (_ @t222 @t224)) (_ @t222 @t223)))) (=> @t154 (_ (_ tptp.ord_less_eq_nat (_ @t222 @t10)) (_ @t222 @t101)))))) % 0.40/0.73 (assume @p179 (forall @t31 (=> @t13 (=> @t204 @t26)))) % 0.40/0.73 (assume @p180 (forall @t31 (=> (or @t26 @t96) @t13))) % 0.40/0.73 (assume @p181 (= tptp.ord_less_eq_nat (lambda @t228 (or (_ (_ tptp.ord_less_nat @t226) @t225) @t227)))) % 0.40/0.73 (assume @p182 (forall @t31 (=> @t26 @t13))) % 0.40/0.73 (assume @p183 (forall (@list @t14 @t130 @t11 @t9) (=> @t221 (=> (= (_ @t32 @t130) @t92) @t26)))) % 0.40/0.73 (assume @p184 (forall @t230 (=> @t220 (_ @t152 @t229)))) % 0.40/0.73 (assume @p185 (forall @t230 (=> @t220 (_ @t152 @t231)))) % 0.40/0.73 (assume @p186 (forall @t107 (=> @t220 (_ @t151 @t103)))) % 0.40/0.73 (assume @p187 (forall (@list @t101 @t10) (not (_ (_ tptp.ord_less_nat @t121) @t10)))) % 0.40/0.73 (assume @p188 (forall (@list @t10 @t101) (not (_ @t232 @t10)))) % 0.40/0.73 (assume @p189 (forall @t188 (=> @t220 (=> @t221 @t219)))) % 0.40/0.73 (assume @p190 (forall @t107 (=> (_ @t232 @t14) (_ @t152 @t14)))) % 0.40/0.73 (assume @p191 (forall @t24 (= @t98 (or @t95 @t96)))) % 0.40/0.73 (assume @p192 (forall @t56 (= (_ (_ tptp.times_times_nat tptp.zero_zero_nat) @t9) tptp.zero_zero_nat))) % 0.40/0.73 (assume @p193 (= tptp.ord_less_eq_nat (lambda @t228 (exists (@list @t233) (= @t225 (_ (_ tptp.plus_plus_nat @t226) @t233)))))) % 0.40/0.73 (assume @p194 (forall @t230 (=> @t154 (_ @t100 @t229)))) % 0.40/0.73 (assume @p195 (forall @t230 (=> @t154 (_ @t100 @t231)))) % 0.40/0.73 (assume @p196 (forall @t107 (=> @t154 (_ @t155 @t103)))) % 0.40/0.73 (assume @p197 (forall @t188 (=> @t154 (=> @t218 @t217)))) % 0.40/0.73 (assume @p198 (not false)) % 0.40/0.73 (assume @p199 true) % 0.40/0.73 (step @p200 (= tptp.ord_less_eq_nat @t239) :rule refl :args (@t239)) % 0.40/0.73 (step @p201 (= tptp.ord_less_nat @t242) :rule refl :args (@t242)) % 0.40/0.73 (step @p202 :rule aci_norm :args ((= (or false @t247 @t245) @t248))) % 0.40/0.73 (step @p203 :rule eq-symm :args (@t244 @t11)) % 0.40/0.73 (step @p204 :rule refl :args (@t247)) % 0.40/0.73 (step @p205 :rule evaluate :args ((not true))) % 0.40/0.73 (step @p206 :rule eq-refl :args (@t244)) % 0.40/0.73 (step @p207 :rule cong :premises (@p206) :args (@t249)) % 0.40/0.73 (step @p208 :rule trans :premises (@p207 @p205)) % 0.40/0.73 (step @p209 :rule nary_cong :premises (@p208 @p204 @p203) :args (@t250)) % 0.40/0.73 (step @p210 :rule trans :premises (@p209 @p202)) % 0.40/0.73 (step @p211 :rule cong :premises (@p210) :args ((forall @t251 @t250))) % 0.40/0.73 (step @p212 :rule quant-var-elim-eq :args ((= (forall @t56 @t255) @t250))) % 0.40/0.73 (step @p213 :rule aci_norm :args ((= @t256 @t255))) % 0.40/0.73 (step @p214 :rule cong :premises (@p213) :args (@t257)) % 0.40/0.73 (step @p215 :rule trans :premises (@p214 @p212)) % 0.40/0.73 (step @p216 :rule cong :premises (@p215) :args (@t258)) % 0.40/0.73 (step @p217 :rule quant-merge-prenex :args ((= @t258 @t259))) % 0.40/0.73 (step @p218 :rule symm :premises (@p217)) % 0.40/0.73 (step @p219 :rule quant_var_reordering :args ((= @t260 @t259))) % 0.40/0.73 (step @p220 :rule trans :premises (@p219 @p218 @p216)) % 0.40/0.73 (step @p221 :rule trans :premises (@p220 @p211)) % 0.40/0.73 (step @p222 :rule quant-merge-prenex :args ((= (forall @t31 @t261) @t260))) % 0.40/0.73 (step @p223 :rule refl :args (@t252)) % 0.40/0.73 (step @p224 :rule alpha_equiv :args (@t262 (@list @t246) @t263)) % 0.40/0.73 (step @p225 :rule alpha_equiv :args (@t264 (@list @t243) @t263)) % 0.40/0.73 (step @p226 :rule nary_cong :premises (@p225 @p224 @p223) :args (@t265)) % 0.40/0.73 (step @p227 :rule quant-miniscope-or :args ((= @t261 @t265))) % 0.40/0.73 (step @p228 :rule trans :premises (@p227 @p226)) % 0.40/0.73 (step @p229 :rule symm :premises (@p228)) % 0.40/0.73 (step @p230 :rule cong :premises (@p229) :args ((forall @t31 @t270))) % 0.40/0.73 (step @p231 :rule trans :premises (@p230 @p222)) % 0.40/0.73 (step @p232 :rule trans :premises (@p231 @p221)) % 0.40/0.73 (step @p233 :rule aci_norm :args ((= (or @t269 (or @t267 @t252)) @t270))) % 0.40/0.73 (step @p234 :rule bool-double-not-elim :args (@t267)) % 0.40/0.73 (step @p235 :rule nary_cong :premises (@p234 @p223) :args ((or (not @t271) @t252))) % 0.40/0.73 (step @p236 :rule bool-impl-elim :args (@t271 @t252)) % 0.40/0.73 (step @p237 :rule trans :premises (@p236 @p235)) % 0.40/0.73 (step @p238 :rule refl :args (@t269)) % 0.40/0.73 (step @p239 :rule nary_cong :premises (@p238 @p237) :args ((or @t269 @t272))) % 0.40/0.73 (step @p240 :rule trans :premises (@p239 @p233)) % 0.40/0.73 (step @p241 :rule refl :args (@t272)) % 0.40/0.73 (step @p242 :rule bool-double-not-elim :args (@t269)) % 0.40/0.73 (step @p243 :rule nary_cong :premises (@p242 @p241) :args ((or (not @t273) @t272))) % 0.40/0.73 (step @p244 :rule bool-impl-elim :args (@t273 @t272)) % 0.40/0.73 (step @p245 :rule trans :premises (@p244 @p243)) % 0.40/0.73 (step @p246 :rule trans :premises (@p245 @p240)) % 0.40/0.73 (step @p247 :rule cong :premises (@p246) :args ((forall @t31 (=> @t273 @t272)))) % 0.40/0.73 (step @p248 :rule trans :premises (@p247 @p232)) % 0.40/0.73 (step @p249 :rule eq-symm :args (@t11 @t9)) % 0.40/0.73 (step @p250 :rule beta-reduce :args ((= (_ @t275 @t11) @t271))) % 0.40/0.73 (step @p251 :rule refl :args (@t11)) % 0.40/0.73 (step @p252 :rule beta-reduce :args ((= @t278 @t275))) % 0.40/0.73 (step @p253 :rule ho_cong :premises (@p252 @p251)) % 0.40/0.73 (step @p254 :rule trans :premises (@p253 @p250)) % 0.40/0.73 (step @p255 :rule cong :premises (@p254 @p249) :args (@t279)) % 0.40/0.73 (step @p256 :rule beta-reduce :args ((= (_ @t280 @t9) @t273))) % 0.40/0.73 (step @p257 :rule refl :args (@t9)) % 0.40/0.73 (step @p258 :rule beta-reduce :args ((= @t281 @t280))) % 0.40/0.73 (step @p259 :rule ho_cong :premises (@p258 @p257)) % 0.40/0.73 (step @p260 :rule trans :premises (@p259 @p256)) % 0.40/0.73 (step @p261 :rule cong :premises (@p260 @p255) :args (@t282)) % 0.40/0.73 (step @p262 :rule cong :premises (@p261) :args ((forall @t31 @t282))) % 0.40/0.73 (step @p263 :rule trans :premises (@p262 @p248)) % 0.40/0.73 (step @p264 :rule refl :args (@t96)) % 0.40/0.73 (step @p265 :rule refl :args (@t276)) % 0.40/0.73 (step @p266 :rule refl :args (@t235)) % 0.40/0.73 (step @p267 :rule cong :premises (@p266 @p265) :args ((= @t235 @t276))) % 0.40/0.73 (step @p268 :rule symm :premises (@p267)) % 0.40/0.73 (step @p269 :rule eq_resolve :premises (@p266 @p268)) % 0.40/0.73 (step @p270 :rule refl :args (@t180)) % 0.40/0.73 (step @p271 :rule cong :premises (@p270 @p269) :args (@t236)) % 0.40/0.73 (step @p272 :rule cong :premises (@p271) :args (@t283)) % 0.40/0.73 (step @p273 :rule cong :premises (@p272) :args (@t284)) % 0.40/0.73 (step @p274 :rule cong :premises (@p273) :args (@t285)) % 0.40/0.73 (step @p275 :rule exists-elim :args ((= @t238 @t285))) % 0.40/0.73 (step @p276 :rule trans :premises (@p275 @p274)) % 0.40/0.73 (step @p277 :rule cong :premises (@p276) :args (@t239)) % 0.40/0.73 (step @p278 :rule trans :premises (@p200 @p277)) % 0.40/0.73 (step @p279 :rule ho_cong :premises (@p278 @p257)) % 0.40/0.73 (step @p280 :rule ho_cong :premises (@p279 @p251)) % 0.40/0.73 (step @p281 :rule cong :premises (@p280 @p264) :args (@t210)) % 0.40/0.73 (step @p282 :rule ho_cong :premises (@p278 @p251)) % 0.40/0.73 (step @p283 :rule ho_cong :premises (@p282 @p257)) % 0.40/0.73 (step @p284 :rule cong :premises (@p283 @p281) :args (@t211)) % 0.40/0.73 (step @p285 :rule cong :premises (@p284) :args (@t212)) % 0.40/0.73 (step @p286 :rule trans :premises (@p285 @p263)) % 0.40/0.73 (step @p287 :rule eq_resolve :premises (@p147 @p286)) % 0.40/0.73 (step @p288 :rule bool-eq-false :args (@t295)) % 0.40/0.73 (step @p289 :rule symm :premises (@p288)) % 0.40/0.73 (step @p290 :rule eq-symm :args (@t294 @t290)) % 0.40/0.73 (step @p291 :rule cong :premises (@p290) :args ((not @t296))) % 0.40/0.73 (step @p292 :rule bool-eq-false :args (@t296)) % 0.40/0.73 (step @p293 :rule trans :premises (@p292 @p291)) % 0.40/0.73 (step @p294 :rule trans :premises (@p293 @p289)) % 0.40/0.73 (step @p295 :rule refl :args ((tptp.plus_plus_nat @t4 @t2))) % 0.40/0.73 (step @p296 :rule refl :args ((tptp.times_times_nat @t1 tptp.k))) % 0.40/0.73 (step @p297 :rule refl :args (tptp.k)) % 0.40/0.73 (step @p298 :rule refl :args (@t286)) % 0.40/0.73 (step @p299 :rule cong :premises (@p298 @p297) :args (@t287)) % 0.40/0.73 (step @p300 :rule trans :premises (@p299 @p296)) % 0.40/0.73 (step @p301 :rule refl :args ((tptp.times_times_nat @t3 tptp.i))) % 0.40/0.73 (step @p302 :rule refl :args (tptp.i)) % 0.40/0.73 (step @p303 :rule refl :args (@t288)) % 0.40/0.73 (step @p304 :rule cong :premises (@p303 @p302) :args (@t289)) % 0.40/0.73 (step @p305 :rule trans :premises (@p304 @p301)) % 0.40/0.73 (step @p306 :rule cong :premises (@p305 @p300) :args (@t290)) % 0.40/0.73 (step @p307 :rule trans :premises (@p306 @p295)) % 0.40/0.73 (step @p308 :rule refl :args (tptp.plus_plus_nat)) % 0.40/0.73 (step @p309 :rule ho_cong :premises (@p308 @p305)) % 0.40/0.73 (step @p310 :rule ho_cong :premises (@p309 @p300)) % 0.40/0.73 (step @p311 :rule cong :premises (@p310 @p307) :args ((= (_ (_ tptp.plus_plus_nat @t289) @t287) @t290))) % 0.40/0.73 (step @p312 :rule symm :premises (@p311)) % 0.40/0.73 (step @p313 :rule refl :args (@t5)) % 0.40/0.73 (step @p314 :rule eq_resolve :premises (@p313 @p312)) % 0.40/0.73 (step @p315 :rule refl :args (tptp.times_times_nat)) % 0.40/0.73 (step @p316 :rule ho_cong :premises (@p315 @p298)) % 0.40/0.73 (step @p317 :rule ho_cong :premises (@p316 @p297)) % 0.40/0.73 (step @p318 :rule cong :premises (@p317 @p300) :args ((= (_ (_ tptp.times_times_nat @t286) tptp.k) @t287))) % 0.40/0.73 (step @p319 :rule symm :premises (@p318)) % 0.40/0.73 (step @p320 :rule refl :args (@t2)) % 0.40/0.73 (step @p321 :rule eq_resolve :premises (@p320 @p319)) % 0.40/0.73 (step @p322 :rule refl :args (tptp.k)) % 0.40/0.73 (step @p323 :rule refl :args (@t1)) % 0.40/0.73 (step @p324 :rule cong :premises (@p323 @p298) :args ((= @t1 @t286))) % 0.40/0.73 (step @p325 :rule symm :premises (@p324)) % 0.40/0.73 (step @p326 :rule eq_resolve :premises (@p323 @p325)) % 0.40/0.73 (step @p327 :rule refl :args (tptp.times_times_nat)) % 0.40/0.73 (step @p328 :rule ho_cong :premises (@p327 @p326)) % 0.40/0.73 (step @p329 :rule ho_cong :premises (@p328 @p322)) % 0.40/0.73 (step @p330 :rule trans :premises (@p329 @p321)) % 0.40/0.73 (step @p331 :rule ho_cong :premises (@p315 @p303)) % 0.40/0.73 (step @p332 :rule ho_cong :premises (@p331 @p302)) % 0.40/0.73 (step @p333 :rule cong :premises (@p332 @p305) :args ((= (_ (_ tptp.times_times_nat @t288) tptp.i) @t289))) % 0.40/0.73 (step @p334 :rule symm :premises (@p333)) % 0.40/0.73 (step @p335 :rule refl :args (@t4)) % 0.40/0.73 (step @p336 :rule eq_resolve :premises (@p335 @p334)) % 0.40/0.73 (step @p337 :rule refl :args (tptp.i)) % 0.40/0.73 (step @p338 :rule refl :args (@t3)) % 0.40/0.73 (step @p339 :rule cong :premises (@p338 @p303) :args ((= @t3 @t288))) % 0.40/0.73 (step @p340 :rule symm :premises (@p339)) % 0.40/0.73 (step @p341 :rule eq_resolve :premises (@p338 @p340)) % 0.40/0.73 (step @p342 :rule ho_cong :premises (@p327 @p341)) % 0.40/0.73 (step @p343 :rule ho_cong :premises (@p342 @p337)) % 0.40/0.73 (step @p344 :rule trans :premises (@p343 @p336)) % 0.40/0.73 (step @p345 :rule refl :args (tptp.plus_plus_nat)) % 0.40/0.73 (step @p346 :rule ho_cong :premises (@p345 @p344)) % 0.40/0.73 (step @p347 :rule ho_cong :premises (@p346 @p330)) % 0.40/0.73 (step @p348 :rule trans :premises (@p347 @p314)) % 0.40/0.73 (step @p349 :rule refl :args (tptp.n)) % 0.40/0.73 (step @p350 :rule cong :premises (@p349 @p348) :args (@t297)) % 0.40/0.73 (step @p351 :rule cong :premises (@p350) :args (@t298)) % 0.40/0.73 (step @p352 :rule refl :args (@t301)) % 0.40/0.73 (step @p353 :rule nary_cong :premises (@p352 @p351) :args ((and @t301 @t298))) % 0.40/0.73 (step @p354 :rule refl :args (@t298)) % 0.40/0.73 (step @p355 :rule refl :args (@t299)) % 0.40/0.73 (step @p356 :rule eq_resolve :premises (@p313 @p312)) % 0.40/0.73 (step @p357 :rule eq_resolve :premises (@p320 @p319)) % 0.40/0.73 (step @p358 :rule eq_resolve :premises (@p323 @p325)) % 0.40/0.73 (step @p359 :rule ho_cong :premises (@p315 @p358)) % 0.40/0.73 (step @p360 :rule ho_cong :premises (@p359 @p297)) % 0.40/0.73 (step @p361 :rule trans :premises (@p360 @p357)) % 0.40/0.73 (step @p362 :rule eq_resolve :premises (@p335 @p334)) % 0.40/0.73 (step @p363 :rule eq_resolve :premises (@p338 @p340)) % 0.40/0.73 (step @p364 :rule ho_cong :premises (@p315 @p363)) % 0.40/0.73 (step @p365 :rule ho_cong :premises (@p364 @p302)) % 0.40/0.73 (step @p366 :rule trans :premises (@p365 @p362)) % 0.40/0.73 (step @p367 :rule ho_cong :premises (@p308 @p366)) % 0.40/0.73 (step @p368 :rule ho_cong :premises (@p367 @p361)) % 0.40/0.73 (step @p369 :rule trans :premises (@p368 @p356)) % 0.40/0.73 (step @p370 :rule cong :premises (@p369 @p355) :args (@t302)) % 0.40/0.73 (step @p371 :rule cong :premises (@p370) :args (@t303)) % 0.40/0.73 (step @p372 :rule cong :premises (@p371) :args (@t304)) % 0.40/0.73 (step @p373 :rule cong :premises (@p372) :args (@t305)) % 0.40/0.73 (step @p374 :rule nary_cong :premises (@p373 @p354) :args (@t306)) % 0.40/0.73 (step @p375 :rule beta-reduce :args ((= (_ @t307 @t5) @t306))) % 0.40/0.73 (step @p376 :rule trans :premises (@p375 @p374)) % 0.40/0.73 (step @p377 :rule refl :args (@t5)) % 0.40/0.73 (step @p378 :rule beta-reduce :args ((= (_ (lambda @t228 (and @t309 @t240)) tptp.n) @t307))) % 0.40/0.73 (step @p379 :rule ho_cong :premises (@p378 @p377)) % 0.40/0.73 (step @p380 :rule trans :premises (@p379 @p376)) % 0.40/0.73 (step @p381 :rule refl :args (@t240)) % 0.40/0.73 (step @p382 :rule beta-reduce :args ((= (_ @t310 @t225) @t309))) % 0.40/0.73 (step @p383 :rule refl :args (@t225)) % 0.40/0.73 (step @p384 :rule beta-reduce :args ((= @t311 @t310))) % 0.40/0.73 (step @p385 :rule ho_cong :premises (@p384 @p383)) % 0.40/0.73 (step @p386 :rule trans :premises (@p385 @p382)) % 0.40/0.73 (step @p387 :rule nary_cong :premises (@p386 @p381) :args ((and (_ @t311 @t225) @t240))) % 0.40/0.73 (step @p388 :rule refl :args (@t226)) % 0.40/0.73 (step @p389 :rule ho_cong :premises (@p278 @p388)) % 0.40/0.73 (step @p390 :rule ho_cong :premises (@p389 @p383)) % 0.40/0.73 (step @p391 :rule nary_cong :premises (@p390 @p381) :args (@t241)) % 0.40/0.73 (step @p392 :rule trans :premises (@p391 @p387)) % 0.40/0.73 (step @p393 :rule cong :premises (@p392) :args (@t242)) % 0.40/0.73 (step @p394 :rule trans :premises (@p201 @p393)) % 0.40/0.73 (step @p395 :rule ho_cong :premises (@p394 @p349)) % 0.40/0.73 (step @p396 :rule ho_cong :premises (@p395 @p377)) % 0.40/0.73 (step @p397 :rule trans :premises (@p396 @p380)) % 0.40/0.73 (step @p398 :rule trans :premises (@p397 @p353)) % 0.40/0.73 (step @p399 :rule eq_resolve :premises (@p4 @p398)) % 0.40/0.73 (step @p400 :rule and_elim :premises (@p399) :args (1)) % 0.40/0.73 (step @p401 :rule false_intro :premises (@p400)) % 0.40/0.73 (step @p402 :rule refl :args (@t290)) % 0.40/0.73 (step @p403 :rule beta-reduce :args ((= (_ (lambda @t274 (not (forall @t237 (not (= @t180 @t291))))) tptp.n) @t312))) % 0.40/0.73 (step @p404 :rule refl :args (@t234)) % 0.40/0.73 (step @p405 :rule cong :premises (@p369 @p404) :args (@t313)) % 0.40/0.73 (step @p406 :rule cong :premises (@p270 @p405) :args (@t314)) % 0.40/0.73 (step @p407 :rule cong :premises (@p406) :args (@t315)) % 0.40/0.73 (step @p408 :rule cong :premises (@p407) :args (@t316)) % 0.40/0.73 (step @p409 :rule cong :premises (@p408) :args (@t317)) % 0.40/0.73 (step @p410 :rule cong :premises (@p409) :args (@t318)) % 0.40/0.73 (step @p411 :rule beta-reduce :args ((= (_ @t277 @t5) @t318))) % 0.40/0.73 (step @p412 :rule trans :premises (@p411 @p410)) % 0.40/0.73 (step @p413 :rule ho_cong :premises (@p412 @p349)) % 0.40/0.73 (step @p414 :rule trans :premises (@p413 @p403)) % 0.40/0.73 (step @p415 :rule ho_cong :premises (@p278 @p377)) % 0.40/0.73 (step @p416 :rule ho_cong :premises (@p415 @p349)) % 0.40/0.73 (step @p417 :rule trans :premises (@p416 @p414)) % 0.40/0.73 (step @p418 :rule eq_resolve :premises (@p3 @p417)) % 0.40/0.73 (step @p419 :rule refl :args (@t319)) % 0.40/0.73 (step @p420 :rule bool-double-not-elim :args (@t292)) % 0.40/0.73 (step @p421 :rule nary_cong :premises (@p420 @p419) :args ((or (not @t312) @t319))) % 0.40/0.73 (step @p422 :rule bool-double-not-elim :args (@t319)) % 0.40/0.73 (step @p423 :rule refl :args (@t312)) % 0.40/0.73 (step @p424 :rule cong :premises (@p423 @p422) :args ((=> @t312 @t320))) % 0.40/0.73 (assume-push @p464 @t312) % 0.40/0.73 (step @p426 :rule skolemize :premises (@p418)) % 0.40/0.73 (step-pop @p465 :rule scope :premises (@p426)) % 0.40/0.73 (step @p427 :rule process_scope :premises (@p465) :args (@t320)) % 0.40/0.73 (step @p429 :rule eq_resolve :premises (@p427 @p424)) % 0.40/0.73 (step @p430 :rule implies_elim :premises (@p429)) % 0.40/0.73 (step @p431 :rule eq_resolve :premises (@p430 @p421)) % 0.40/0.73 (step @p432 :rule chain_m_resolution :premises (@p431 @p418) :args (@t319 @t321 (@list @t292))) % 0.40/0.73 (step @p433 :rule symm :premises (@p432)) % 0.40/0.73 (step @p434 :rule cong :premises (@p433 @p402) :args (@t296)) % 0.40/0.73 (step @p435 :rule trans :premises (@p434 @p401)) % 0.40/0.73 (step @p436 :rule eq_resolve :premises (@p435 @p294)) % 0.40/0.73 (step @p437 :rule false_elim :premises (@p436)) % 0.40/0.73 (step @p438 :rule refl :args (@t322)) % 0.40/0.73 (step @p439 :rule cong :premises (@p432 @p438) :args (@t323)) % 0.40/0.73 (step @p440 :rule and_elim :premises (@p399) :args (0)) % 0.40/0.73 (step @p441 :rule refl :args (@t324)) % 0.40/0.73 (step @p442 :rule bool-double-not-elim :args (@t300)) % 0.40/0.73 (step @p443 :rule nary_cong :premises (@p442 @p441) :args ((or (not @t301) @t324))) % 0.40/0.73 (step @p444 :rule bool-double-not-elim :args (@t324)) % 0.40/0.73 (step @p445 :rule cong :premises (@p352 @p444) :args ((=> @t301 @t325))) % 0.40/0.73 (assume-push @p466 @t301) % 0.40/0.73 (step @p447 :rule skolemize :premises (@p440)) % 0.40/0.73 (step-pop @p467 :rule scope :premises (@p447)) % 0.40/0.73 (step @p448 :rule process_scope :premises (@p467) :args (@t325)) % 0.40/0.73 (step @p450 :rule eq_resolve :premises (@p448 @p445)) % 0.40/0.73 (step @p451 :rule implies_elim :premises (@p450)) % 0.40/0.73 (step @p452 :rule eq_resolve :premises (@p451 @p443)) % 0.40/0.73 (step @p453 :rule chain_m_resolution :premises (@p452 @p440) :args (@t324 @t321 (@list @t300))) % 0.40/0.73 (step @p454 :rule trans :premises (@p453 @p439)) % 0.40/0.73 (step @p455 :rule cnf_or_pos :args (@t328)) % 0.40/0.73 (step @p456 :rule reordering :premises (@p455) :args ((or @t327 @t295 @t329))) % 0.40/0.73 (step @p457 :rule chain_m_resolution :premises (@p456 @p454 @p437) :args (@t329 (@list false true) (@list @t326 @t295))) % 0.40/0.73 (assume-push @p468 @t330) % 0.40/0.73 (step @p459 :rule instantiate :premises (@p287) :args ((@list @t290 @t293 @t322))) % 0.40/0.73 (step-pop @p469 :rule scope :premises (@p459)) % 0.40/0.73 (step @p460 :rule process_scope :premises (@p469) :args (@t328)) % 0.40/0.73 (step @p462 :rule implies_elim :premises (@p460)) % 0.40/0.73 (step @p463 false :rule chain_m_resolution :premises (@p462 @p457 @p287) :args (false (@list true false) (@list @t328 @t330))) % 0.40/0.73 ) % 0.40/0.73 % SZS output end Proof % 0.40/0.73 % cvc5 exiting %------------------------------------------------------------------------------