%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV028^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n009.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 08:55:20 AM UTC 2026 % Result : Theorem 152.51s 152.82s % Output : Proof 152.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV028^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n009.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 18:08:44 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.49 %----Proving TH0 % 152.51/152.82 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 152.51/152.82 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 152.51/152.82 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 152.51/152.82 --- Run --ho-elim --full-saturate-quant at 18s... % 152.51/152.82 % SZS status Theorem % 152.51/152.82 % SZS output start Proof % 152.51/152.82 ( % 152.51/152.82 (declare-sort tptp.a 0) % 152.51/152.82 (declare-const tptp.cQ (-> tptp.a tptp.a Bool)) % 152.51/152.82 (define @t1 () (@var "Xz" tptp.a)) % 152.51/152.82 (define @t2 () (@var "Xx" tptp.a)) % 152.51/152.82 (define @t3 () (_ tptp.cQ @t2)) % 152.51/152.82 (define @t4 () (_ @t3 @t1)) % 152.51/152.82 (define @t5 () (@var "Xy" tptp.a)) % 152.51/152.82 (define @t6 () (_ tptp.cQ @t5)) % 152.51/152.82 (define @t7 () (_ @t6 @t1)) % 152.51/152.82 (define @t8 () (_ @t3 @t5)) % 152.51/152.82 (define @t9 () (and @t8 @t7)) % 152.51/152.82 (define @t10 () (@list @t2 @t5 @t1)) % 152.51/152.82 (define @t11 () (forall @t10 (=> @t9 @t4))) % 152.51/152.82 (define @t12 () (_ @t6 @t2)) % 152.51/152.82 (define @t13 () (@list @t2 @t5)) % 152.51/152.82 (define @t14 () (forall @t13 (=> @t8 @t12))) % 152.51/152.82 (define @t15 () (_ @t3 @t2)) % 152.51/152.82 (define @t16 () (@list @t2)) % 152.51/152.82 (define @t17 () (forall @t16 @t15)) % 152.51/152.82 (define @t18 () (and @t17 @t14 @t11)) % 152.51/152.82 (define @t19 () (@var "Xp" (-> tptp.a Bool))) % 152.51/152.82 (define @t20 () (@var "Xq" (-> tptp.a Bool))) % 152.51/152.82 (define @t21 () (_ @t20 @t2)) % 152.51/152.82 (define @t22 () (@var "Xx0" tptp.a)) % 152.51/152.82 (define @t23 () (_ (_ tptp.cQ @t22) @t5)) % 152.51/152.82 (define @t24 () (_ @t20 @t5)) % 152.51/152.82 (define @t25 () (@list @t5)) % 152.51/152.82 (define @t26 () (forall @t25 (= @t24 @t23))) % 152.51/152.82 (define @t27 () (_ @t20 @t22)) % 152.51/152.82 (define @t28 () (=> @t27 @t26)) % 152.51/152.82 (define @t29 () (@list @t22)) % 152.51/152.82 (define @t30 () (forall @t29 @t28)) % 152.51/152.82 (define @t31 () (_ @t20 @t1)) % 152.51/152.82 (define @t32 () (@list @t1)) % 152.51/152.82 (define @t33 () (exists @t32 @t31)) % 152.51/152.82 (define @t34 () (and @t33 @t30 @t21)) % 152.51/152.82 (define @t35 () (=> @t34 (= @t20 @t19))) % 152.51/152.82 (define @t36 () (@list @t20)) % 152.51/152.82 (define @t37 () (forall @t36 @t35)) % 152.51/152.82 (define @t38 () (_ @t19 @t2)) % 152.51/152.82 (define @t39 () (_ @t19 @t5)) % 152.51/152.82 (define @t40 () (= @t39 @t23)) % 152.51/152.82 (define @t41 () (forall @t25 @t40)) % 152.51/152.82 (define @t42 () (_ @t19 @t22)) % 152.51/152.82 (define @t43 () (=> @t42 @t41)) % 152.51/152.82 (define @t44 () (forall @t29 @t43)) % 152.51/152.82 (define @t45 () (_ @t19 @t1)) % 152.51/152.82 (define @t46 () (exists @t32 @t45)) % 152.51/152.82 (define @t47 () (and @t46 @t44 @t38 @t37)) % 152.51/152.82 (define @t48 () (@list @t19)) % 152.51/152.82 (define @t49 () (exists @t48 @t47)) % 152.51/152.82 (define @t50 () (forall @t16 @t49)) % 152.51/152.82 (define @t51 () (= @t39 @t8)) % 152.51/152.82 (define @t52 () (forall @t25 @t51)) % 152.51/152.82 (define @t53 () (=> @t38 @t52)) % 152.51/152.82 (define @t54 () (forall @t16 @t53)) % 152.51/152.82 (define @t55 () (and @t46 @t54)) % 152.51/152.82 (define @t56 () (=> @t55 @t46)) % 152.51/152.82 (define @t57 () (forall @t48 @t56)) % 152.51/152.82 (define @t58 () (and @t57 @t50)) % 152.51/152.82 (define @t59 () (=> @t58 @t18)) % 152.51/152.82 (define @t60 () (not @t59)) % 152.51/152.82 (define @t61 () (@const 0 (@ho-elim-sort (-> tptp.a tptp.a Bool)))) % 152.51/152.82 (define @t62 () (@const 1 (-> (@ho-elim-sort (-> tptp.a tptp.a Bool)) tptp.a (@ho-elim-sort (-> tptp.a Bool))))) % 152.51/152.82 (define @t63 () (_ @t62 @t61 @t2)) % 152.51/152.82 (define @t64 () (@const 2 (-> (@ho-elim-sort (-> tptp.a Bool)) tptp.a Bool))) % 152.51/152.82 (define @t65 () (_ @t62 @t61 @t5)) % 152.51/152.82 (define @t66 () (not (_ @t64 @t63 @t5))) % 152.51/152.82 (define @t67 () (forall @t10 (or @t66 (not (_ @t64 @t65 @t1)) (_ @t64 @t63 @t1)))) % 152.51/152.82 (define @t68 () (forall @t13 (or @t66 (_ @t64 @t65 @t2)))) % 152.51/152.82 (define @t69 () (forall @t16 (_ @t64 @t63 @t2))) % 152.51/152.82 (define @t70 () (and @t69 @t68 @t67)) % 152.51/152.82 (define @t71 () (@var "BOUND_VARIABLE_7652" (@ho-elim-sort (-> tptp.a Bool)))) % 152.51/152.82 (define @t72 () (@var "BOUND_VARIABLE_7651" (@ho-elim-sort (-> tptp.a Bool)))) % 152.51/152.82 (define @t73 () (not (_ @t64 @t72 @t2))) % 152.51/152.82 (define @t74 () (@var "BOUND_VARIABLE_7552" tptp.a)) % 152.51/152.82 (define @t75 () (_ @t62 @t61 @t22)) % 152.51/152.82 (define @t76 () (_ @t64 @t75 @t74)) % 152.51/152.82 (define @t77 () (_ @t64 @t72 @t74)) % 152.51/152.82 (define @t78 () (not (_ @t64 @t72 @t22))) % 152.51/152.82 (define @t79 () (or @t78 (= @t76 @t77))) % 152.51/152.82 (define @t80 () (@list @t22 @t74)) % 152.51/152.82 (define @t81 () (forall @t80 @t79)) % 152.51/152.82 (define @t82 () (not @t81)) % 152.51/152.82 (define @t83 () (@var "BOUND_VARIABLE_7574" tptp.a)) % 152.51/152.82 (define @t84 () (not (_ @t64 @t72 @t83))) % 152.51/152.82 (define @t85 () (or @t84 @t82 @t73 (= @t71 @t72))) % 152.51/152.82 (define @t86 () (@list @t72 @t83)) % 152.51/152.82 (define @t87 () (forall @t86 @t85)) % 152.51/152.82 (define @t88 () (not @t87)) % 152.51/152.82 (define @t89 () (not (_ @t64 @t71 @t2))) % 152.51/152.82 (define @t90 () (@var "BOUND_VARIABLE_7523" tptp.a)) % 152.51/152.82 (define @t91 () (_ @t64 @t71 @t90)) % 152.51/152.82 (define @t92 () (_ @t64 @t75 @t90)) % 152.51/152.82 (define @t93 () (not (_ @t64 @t71 @t22))) % 152.51/152.82 (define @t94 () (or @t93 (= @t91 @t92))) % 152.51/152.82 (define @t95 () (@list @t22 @t90)) % 152.51/152.82 (define @t96 () (forall @t95 @t94)) % 152.51/152.82 (define @t97 () (not @t96)) % 152.51/152.82 (define @t98 () (@var "BOUND_VARIABLE_7592" tptp.a)) % 152.51/152.82 (define @t99 () (not (_ @t64 @t71 @t98))) % 152.51/152.82 (define @t100 () (or @t99 @t97 @t89 @t88)) % 152.51/152.82 (define @t101 () (@list @t71 @t98)) % 152.51/152.82 (define @t102 () (forall @t101 @t100)) % 152.51/152.82 (define @t103 () (not @t102)) % 152.51/152.82 (define @t104 () (forall @t16 @t103)) % 152.51/152.82 (define @t105 () (=> @t104 @t70)) % 152.51/152.82 (define @t106 () (not @t105)) % 152.51/152.82 (define @t107 () (tptp.cQ @t2 @t1)) % 152.51/152.82 (define @t108 () (tptp.cQ @t5 @t1)) % 152.51/152.82 (define @t109 () (tptp.cQ @t2 @t5)) % 152.51/152.82 (define @t110 () (not @t109)) % 152.51/152.82 (define @t111 () (tptp.cQ @t5 @t2)) % 152.51/152.82 (define @t112 () (tptp.cQ @t2 @t2)) % 152.51/152.82 (define @t113 () (= @t19 @t20)) % 152.51/152.82 (define @t114 () (_ @t20 @t2)) % 152.51/152.82 (define @t115 () (not @t114)) % 152.51/152.82 (define @t116 () (= (tptp.cQ @t22 @t74) (_ @t20 @t74))) % 152.51/152.82 (define @t117 () (_ @t20 @t22)) % 152.51/152.82 (define @t118 () (not @t117)) % 152.51/152.82 (define @t119 () (or @t118 @t116)) % 152.51/152.82 (define @t120 () (forall @t80 @t119)) % 152.51/152.82 (define @t121 () (not @t120)) % 152.51/152.82 (define @t122 () (not (_ @t20 @t83))) % 152.51/152.82 (define @t123 () (or @t122 @t121 @t115 @t113)) % 152.51/152.82 (define @t124 () (forall (@list @t20 @t83) @t123)) % 152.51/152.82 (define @t125 () (not @t124)) % 152.51/152.82 (define @t126 () (_ @t19 @t2)) % 152.51/152.82 (define @t127 () (not @t126)) % 152.51/152.82 (define @t128 () (= (_ @t19 @t90) (tptp.cQ @t22 @t90))) % 152.51/152.82 (define @t129 () (_ @t19 @t22)) % 152.51/152.82 (define @t130 () (not @t129)) % 152.51/152.82 (define @t131 () (or @t130 @t128)) % 152.51/152.82 (define @t132 () (forall @t95 @t131)) % 152.51/152.82 (define @t133 () (not @t132)) % 152.51/152.82 (define @t134 () (not (_ @t19 @t98))) % 152.51/152.82 (define @t135 () (or @t134 @t133 @t127 @t125)) % 152.51/152.82 (define @t136 () (forall (@list @t19 @t98) @t135)) % 152.51/152.82 (define @t137 () (forall @t16 (not @t136))) % 152.51/152.82 (define @t138 () (not @t7)) % 152.51/152.82 (define @t139 () (not @t8)) % 152.51/152.82 (define @t140 () (or @t139 @t138 @t4)) % 152.51/152.82 (define @t141 () (or @t139 @t12)) % 152.51/152.82 (define @t142 () (@list @t98)) % 152.51/152.82 (define @t143 () (forall @t142 @t135)) % 152.51/152.82 (define @t144 () (forall @t142 @t134)) % 152.51/152.82 (define @t145 () (@list @t1)) % 152.51/152.82 (define @t146 () (or @t144 @t133 @t127 @t125)) % 152.51/152.82 (define @t147 () (_ @t19 @t1)) % 152.51/152.82 (define @t148 () (forall @t32 (not @t147))) % 152.51/152.82 (define @t149 () (not @t38)) % 152.51/152.82 (define @t150 () (or @t148 @t133 @t149 @t125)) % 152.51/152.82 (define @t151 () (not @t148)) % 152.51/152.82 (define @t152 () (not @t151)) % 152.51/152.82 (define @t153 () (or @t152 @t133 @t149 @t125)) % 152.51/152.82 (define @t154 () (and @t151 @t132 @t38 @t124)) % 152.51/152.82 (define @t155 () (forall @t48 (not @t154))) % 152.51/152.82 (define @t156 () (not @t155)) % 152.51/152.82 (define @t157 () (@list @t83)) % 152.51/152.82 (define @t158 () (forall @t157 @t123)) % 152.51/152.82 (define @t159 () (forall @t157 @t122)) % 152.51/152.82 (define @t160 () (or @t159 @t121 @t115 @t113)) % 152.51/152.82 (define @t161 () (_ @t20 @t1)) % 152.51/152.82 (define @t162 () (forall @t32 (not @t161))) % 152.51/152.82 (define @t163 () (not @t21)) % 152.51/152.82 (define @t164 () (or @t162 @t121 @t163 @t113)) % 152.51/152.82 (define @t165 () (not @t162)) % 152.51/152.82 (define @t166 () (not @t165)) % 152.51/152.82 (define @t167 () (or @t166 @t121 @t163)) % 152.51/152.82 (define @t168 () (and @t165 @t120 @t21)) % 152.51/152.82 (define @t169 () (@list @t74)) % 152.51/152.82 (define @t170 () (forall @t169 @t119)) % 152.51/152.82 (define @t171 () (forall @t169 @t116)) % 152.51/152.82 (define @t172 () (@list @t5)) % 152.51/152.82 (define @t173 () (or @t118 @t171)) % 152.51/152.82 (define @t174 () (_ @t20 @t5)) % 152.51/152.82 (define @t175 () (tptp.cQ @t22 @t5)) % 152.51/152.82 (define @t176 () (forall @t25 (= @t175 @t174))) % 152.51/152.82 (define @t177 () (not @t27)) % 152.51/152.82 (define @t178 () (or @t177 @t176)) % 152.51/152.82 (define @t179 () (= @t23 @t24)) % 152.51/152.82 (define @t180 () (not @t31)) % 152.51/152.82 (define @t181 () (forall @t32 @t180)) % 152.51/152.82 (define @t182 () (not @t181)) % 152.51/152.82 (define @t183 () (@list @t90)) % 152.51/152.82 (define @t184 () (forall @t183 @t131)) % 152.51/152.82 (define @t185 () (forall @t183 @t128)) % 152.51/152.82 (define @t186 () (or @t130 @t185)) % 152.51/152.82 (define @t187 () (_ @t19 @t5)) % 152.51/152.82 (define @t188 () (forall @t25 (= @t187 @t175))) % 152.51/152.82 (define @t189 () (not @t42)) % 152.51/152.82 (define @t190 () (or @t189 @t188)) % 152.51/152.82 (define @t191 () (not @t45)) % 152.51/152.82 (define @t192 () (forall @t32 @t191)) % 152.51/152.82 (define @t193 () (not @t192)) % 152.51/152.82 (define @t194 () (@var "BOUND_VARIABLE_7496" tptp.a)) % 152.51/152.82 (define @t195 () (= (_ @t19 @t194) (tptp.cQ @t2 @t194))) % 152.51/152.82 (define @t196 () (or @t127 @t195)) % 152.51/152.82 (define @t197 () (forall (@list @t2 @t194) @t196)) % 152.51/152.82 (define @t198 () (not @t197)) % 152.51/152.82 (define @t199 () (and @t151 @t197)) % 152.51/152.82 (define @t200 () (@list @t194)) % 152.51/152.82 (define @t201 () (forall @t200 @t196)) % 152.51/152.82 (define @t202 () (forall @t200 @t195)) % 152.51/152.82 (define @t203 () (or @t127 @t202)) % 152.51/152.82 (define @t204 () (forall @t25 (= @t187 @t109))) % 152.51/152.82 (define @t205 () (or @t149 @t204)) % 152.51/152.82 (define @t206 () (@quantifiers_skolemize @t67 1)) % 152.51/152.82 (define @t207 () (= @t72 @t71)) % 152.51/152.82 (define @t208 () (not (_ @t64 @t72 @t206))) % 152.51/152.82 (define @t209 () (not (forall @t80 (or @t78 (= @t77 @t76))))) % 152.51/152.82 (define @t210 () (not (forall @t95 (or @t93 (= @t92 @t91))))) % 152.51/152.82 (define @t211 () (forall @t101 (or @t99 @t210 (not (_ @t64 @t71 @t206)) (not (forall @t86 (or @t84 @t209 @t208 @t207)))))) % 152.51/152.82 (define @t212 () (@quantifiers_skolemize @t211 0)) % 152.51/152.82 (define @t213 () (forall @t95 (or (not (_ @t64 @t212 @t22)) (= @t92 (_ @t64 @t212 @t90))))) % 152.51/152.82 (define @t214 () (_ @t64 @t212 @t206)) % 152.51/152.82 (define @t215 () (not @t214)) % 152.51/152.82 (define @t216 () (not @t213)) % 152.51/152.82 (define @t217 () (or (not (_ @t64 @t212 (@quantifiers_skolemize @t211 1))) @t216 @t215 (not (forall @t86 (or @t84 @t209 @t208 (= @t72 @t212)))))) % 152.51/152.82 (define @t218 () (@list true)) % 152.51/152.82 (define @t219 () (@list @t217)) % 152.51/152.82 (define @t220 () (@quantifiers_skolemize @t67 2)) % 152.51/152.82 (define @t221 () (@quantifiers_skolemize @t67 0)) % 152.51/152.82 (define @t222 () (_ @t64 @t212 @t221)) % 152.51/152.82 (define @t223 () (_ @t62 @t61 @t206)) % 152.51/152.82 (define @t224 () (_ @t64 @t223 @t221)) % 152.51/152.82 (define @t225 () (= @t224 @t222)) % 152.51/152.82 (define @t226 () (or @t215 @t225)) % 152.51/152.82 (define @t227 () (@list false false)) % 152.51/152.82 (define @t228 () (@quantifiers_skolemize @t68 1)) % 152.51/152.82 (define @t229 () (@quantifiers_skolemize @t68 0)) % 152.51/152.82 (define @t230 () (_ @t64 (_ @t62 @t61 @t229) @t228)) % 152.51/152.82 (define @t231 () (_ @t64 (_ @t62 @t61 @t228) @t229)) % 152.51/152.82 (define @t232 () (not @t230)) % 152.51/152.82 (define @t233 () (or @t232 @t231)) % 152.51/152.82 (define @t234 () (not (_ @t64 @t72 @t229))) % 152.51/152.82 (define @t235 () (forall @t101 (or @t99 @t210 (not (_ @t64 @t71 @t229)) (not (forall @t86 (or @t84 @t209 @t234 @t207)))))) % 152.51/152.82 (define @t236 () (@quantifiers_skolemize @t235 0)) % 152.51/152.82 (define @t237 () (forall @t95 (or (not (_ @t64 @t236 @t22)) (= @t92 (_ @t64 @t236 @t90))))) % 152.51/152.82 (define @t238 () (_ @t64 @t236 @t229)) % 152.51/152.82 (define @t239 () (not @t238)) % 152.51/152.82 (define @t240 () (not @t237)) % 152.51/152.82 (define @t241 () (or (not (_ @t64 @t236 (@quantifiers_skolemize @t235 1))) @t240 @t239 (not (forall @t86 (or @t84 @t209 @t234 (= @t72 @t236)))))) % 152.51/152.82 (define @t242 () (@list @t241)) % 152.51/152.82 (define @t243 () (_ @t64 @t236 @t228)) % 152.51/152.82 (define @t244 () (= @t230 @t243)) % 152.51/152.82 (define @t245 () (or @t239 @t244)) % 152.51/152.82 (define @t246 () (= @t231 @t238)) % 152.51/152.82 (define @t247 () (not @t243)) % 152.51/152.82 (define @t248 () (or @t247 @t246)) % 152.51/152.82 (define @t249 () (not @t233)) % 152.51/152.82 (define @t250 () (not @t68)) % 152.51/152.82 (define @t251 () (@list false)) % 152.51/152.82 (define @t252 () (_ @t62 @t61 @t221)) % 152.51/152.82 (define @t253 () (_ @t64 @t252 @t206)) % 152.51/152.82 (define @t254 () (not @t253)) % 152.51/152.82 (define @t255 () (or @t254 @t224)) % 152.51/152.82 (define @t256 () (@quantifiers_skolemize @t69 0)) % 152.51/152.82 (define @t257 () (not (_ @t64 @t72 @t256))) % 152.51/152.82 (define @t258 () (forall @t101 (or @t99 @t210 (not (_ @t64 @t71 @t256)) (not (forall @t86 (or @t84 @t209 @t257 @t207)))))) % 152.51/152.82 (define @t259 () (@quantifiers_skolemize @t258 0)) % 152.51/152.82 (define @t260 () (forall @t95 (or (not (_ @t64 @t259 @t22)) (= @t92 (_ @t64 @t259 @t90))))) % 152.51/152.82 (define @t261 () (_ @t64 @t259 @t256)) % 152.51/152.82 (define @t262 () (not @t261)) % 152.51/152.82 (define @t263 () (not @t260)) % 152.51/152.82 (define @t264 () (or (not (_ @t64 @t259 (@quantifiers_skolemize @t258 1))) @t263 @t262 (not (forall @t86 (or @t84 @t209 @t257 (= @t72 @t259)))))) % 152.51/152.82 (define @t265 () (@list @t264)) % 152.51/152.82 (define @t266 () (_ @t64 (_ @t62 @t61 @t256) @t256)) % 152.51/152.82 (define @t267 () (= @t266 @t261)) % 152.51/152.82 (define @t268 () (or @t262 @t267)) % 152.51/152.82 (define @t269 () (not @t266)) % 152.51/152.82 (define @t270 () (not @t69)) % 152.51/152.82 (define @t271 () (not @t67)) % 152.51/152.82 (define @t272 () (_ @t64 @t252 @t220)) % 152.51/152.82 (define @t273 () (_ @t64 @t223 @t220)) % 152.51/152.82 (define @t274 () (not @t273)) % 152.51/152.82 (define @t275 () (or @t254 @t274 @t272)) % 152.51/152.82 (define @t276 () (not @t275)) % 152.51/152.82 (define @t277 () (@list @t275)) % 152.51/152.82 (define @t278 () (_ @t64 @t212 @t220)) % 152.51/152.82 (define @t279 () (= @t273 @t278)) % 152.51/152.82 (define @t280 () (or @t215 @t279)) % 152.51/152.82 (define @t281 () (= @t272 @t278)) % 152.51/152.82 (define @t282 () (not @t281)) % 152.51/152.82 (define @t283 () (not @t222)) % 152.51/152.82 (define @t284 () (or @t283 @t281)) % 152.51/152.82 (assume @p1 @t60) % 152.51/152.82 (assume @p2 true) % 152.51/152.82 (step @p3 :rule refl :args (@t70)) % 152.51/152.82 (step @p4 :rule eq-symm :args (@t71 @t72)) % 152.51/152.82 (step @p5 :rule refl :args (@t73)) % 152.51/152.82 (step @p6 :rule eq-symm :args (@t76 @t77)) % 152.51/152.82 (step @p7 :rule refl :args (@t78)) % 152.51/152.82 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t79)) % 152.51/152.82 (step @p9 :rule cong :premises (@p8) :args (@t81)) % 152.51/152.82 (step @p10 :rule cong :premises (@p9) :args (@t82)) % 152.51/152.82 (step @p11 :rule refl :args (@t84)) % 152.51/152.82 (step @p12 :rule nary_cong :premises (@p11 @p10 @p5 @p4) :args (@t85)) % 152.51/152.82 (step @p13 :rule cong :premises (@p12) :args (@t87)) % 152.51/152.82 (step @p14 :rule cong :premises (@p13) :args (@t88)) % 152.51/152.82 (step @p15 :rule refl :args (@t89)) % 152.51/152.82 (step @p16 :rule eq-symm :args (@t91 @t92)) % 152.51/152.82 (step @p17 :rule refl :args (@t93)) % 152.51/152.82 (step @p18 :rule nary_cong :premises (@p17 @p16) :args (@t94)) % 152.51/152.82 (step @p19 :rule cong :premises (@p18) :args (@t96)) % 152.51/152.82 (step @p20 :rule cong :premises (@p19) :args (@t97)) % 152.51/152.82 (step @p21 :rule refl :args (@t99)) % 152.51/152.82 (step @p22 :rule nary_cong :premises (@p21 @p20 @p15 @p14) :args (@t100)) % 152.51/152.82 (step @p23 :rule cong :premises (@p22) :args (@t102)) % 152.51/152.82 (step @p24 :rule cong :premises (@p23) :args (@t103)) % 152.51/152.82 (step @p25 :rule cong :premises (@p24) :args (@t104)) % 152.51/152.82 (step @p26 :rule cong :premises (@p25 @p3) :args (@t105)) % 152.51/152.82 (step @p27 :rule cong :premises (@p26) :args (@t106)) % 152.51/152.82 ; WARNING: add trust step for TRUST % 152.51/152.82 ; trust TRUST PREPROCESS_HO_ELIM % 152.51/152.82 (step @p28 :rule trust :premises () :args ((= (not (=> @t137 (and (forall @t16 @t112) (forall @t13 (or @t110 @t111)) (forall @t10 (or @t110 (not @t108) @t107))))) @t106))) % 152.51/152.82 (step @p29 :rule refl :args (@t107)) % 152.51/152.82 (step @p30 :rule refl :args (@t4)) % 152.51/152.82 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t4 @t107))) % 152.51/152.82 (step @p32 :rule symm :premises (@p31)) % 152.51/152.82 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 152.51/152.82 (step @p34 :rule refl :args (@t108)) % 152.51/152.82 (step @p35 :rule refl :args (@t7)) % 152.51/152.82 (step @p36 :rule cong :premises (@p35 @p34) :args ((= @t7 @t108))) % 152.51/152.82 (step @p37 :rule symm :premises (@p36)) % 152.51/152.82 (step @p38 :rule eq_resolve :premises (@p35 @p37)) % 152.51/152.82 (step @p39 :rule cong :premises (@p38) :args (@t138)) % 152.51/152.82 (step @p40 :rule refl :args (@t109)) % 152.51/152.82 (step @p41 :rule refl :args (@t8)) % 152.51/152.82 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t8 @t109))) % 152.51/152.82 (step @p43 :rule symm :premises (@p42)) % 152.51/152.82 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 152.51/152.82 (step @p45 :rule cong :premises (@p44) :args (@t139)) % 152.51/152.82 (step @p46 :rule nary_cong :premises (@p45 @p39 @p33) :args (@t140)) % 152.51/152.82 (step @p47 :rule cong :premises (@p46) :args ((forall @t10 @t140))) % 152.51/152.82 (step @p48 :rule aci_norm :args ((= (or (or @t139 @t138) @t4) @t140))) % 152.51/152.82 (step @p49 :rule bool-and-de-morgan :args (@t8 @t7 true)) % 152.51/152.82 (step @p50 :rule nary_cong :premises (@p49 @p30) :args ((or (not @t9) @t4))) % 152.51/152.82 (step @p51 :rule trans :premises (@p50 @p48)) % 152.51/152.82 (step @p52 :rule bool-impl-elim :args (@t9 @t4)) % 152.51/152.82 (step @p53 :rule trans :premises (@p52 @p51)) % 152.51/152.82 (step @p54 :rule cong :premises (@p53) :args (@t11)) % 152.51/152.82 (step @p55 :rule trans :premises (@p54 @p47)) % 152.51/152.82 (step @p56 :rule refl :args (@t111)) % 152.51/152.82 (step @p57 :rule refl :args (@t12)) % 152.51/152.82 (step @p58 :rule cong :premises (@p57 @p56) :args ((= @t12 @t111))) % 152.51/152.82 (step @p59 :rule symm :premises (@p58)) % 152.51/152.82 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 152.51/152.82 (step @p61 :rule nary_cong :premises (@p45 @p60) :args (@t141)) % 152.51/152.82 (step @p62 :rule cong :premises (@p61) :args ((forall @t13 @t141))) % 152.51/152.82 (step @p63 :rule bool-impl-elim :args (@t8 @t12)) % 152.51/152.82 (step @p64 :rule cong :premises (@p63) :args (@t14)) % 152.51/152.82 (step @p65 :rule trans :premises (@p64 @p62)) % 152.51/152.82 (step @p66 :rule refl :args (@t112)) % 152.51/152.82 (step @p67 :rule refl :args (@t15)) % 152.51/152.82 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t15 @t112))) % 152.51/152.82 (step @p69 :rule symm :premises (@p68)) % 152.51/152.82 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 152.51/152.82 (step @p71 :rule cong :premises (@p70) :args (@t17)) % 152.51/152.82 (step @p72 :rule nary_cong :premises (@p71 @p65 @p55) :args (@t18)) % 152.51/152.82 (step @p73 :rule aci_norm :args ((= (and true @t137) @t137))) % 152.51/152.82 (step @p74 :rule quant-merge-prenex :args ((= (forall @t48 @t143) @t136))) % 152.51/152.82 (step @p75 :rule refl :args (@t125)) % 152.51/152.82 (step @p76 :rule refl :args (@t127)) % 152.51/152.82 (step @p77 :rule refl :args (@t133)) % 152.51/152.82 (step @p78 :rule alpha_equiv :args (@t144 (@list @t98) @t145)) % 152.51/152.82 (step @p79 :rule nary_cong :premises (@p78 @p77 @p76 @p75) :args (@t146)) % 152.51/152.82 (step @p80 :rule quant-miniscope-or :args ((= @t143 @t146))) % 152.51/152.82 (step @p81 :rule trans :premises (@p80 @p79)) % 152.51/152.82 (step @p82 :rule symm :premises (@p81)) % 152.51/152.82 (step @p83 :rule cong :premises (@p82) :args ((forall @t48 (or @t148 @t133 @t127 @t125)))) % 152.51/152.82 (step @p84 :rule trans :premises (@p83 @p74)) % 152.51/152.82 (step @p85 :rule refl :args (@t126)) % 152.51/152.82 (step @p86 :rule refl :args (@t38)) % 152.51/152.82 (step @p87 :rule cong :premises (@p86 @p85) :args ((= @t38 @t126))) % 152.51/152.82 (step @p88 :rule symm :premises (@p87)) % 152.51/152.82 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 152.51/152.82 (step @p90 :rule cong :premises (@p89) :args (@t149)) % 152.51/152.82 (step @p91 :rule refl :args (@t148)) % 152.51/152.82 (step @p92 :rule nary_cong :premises (@p91 @p77 @p90 @p75) :args (@t150)) % 152.51/152.82 (step @p93 :rule cong :premises (@p92) :args ((forall @t48 @t150))) % 152.51/152.82 (step @p94 :rule trans :premises (@p93 @p84)) % 152.51/152.82 (step @p95 :rule refl :args (@t149)) % 152.51/152.82 (step @p96 :rule bool-double-not-elim :args (@t148)) % 152.51/152.82 (step @p97 :rule nary_cong :premises (@p96 @p77 @p95 @p75) :args (@t153)) % 152.51/152.82 (step @p98 :rule aci_norm :args ((= (or @t152 (or @t133 (or @t149 @t125))) @t153))) % 152.51/152.82 (step @p99 :rule trans :premises (@p98 @p97)) % 152.51/152.82 (step @p100 :rule bool-and-de-morgan :args (@t38 @t124 true)) % 152.51/152.82 (step @p101 :rule nary_cong :premises (@p77 @p100) :args ((or @t133 (not (and @t38 @t124))))) % 152.51/152.82 (step @p102 :rule bool-and-de-morgan :args (@t132 @t38 (and @t124))) % 152.51/152.82 (step @p103 :rule trans :premises (@p102 @p101)) % 152.51/152.82 (step @p104 :rule refl :args (@t152)) % 152.51/152.82 (step @p105 :rule nary_cong :premises (@p104 @p103) :args ((or @t152 (not (and @t132 @t38 @t124))))) % 152.51/152.82 (step @p106 :rule bool-and-de-morgan :args (@t151 @t132 (and @t38 @t124))) % 152.51/152.82 (step @p107 :rule trans :premises (@p106 @p105)) % 152.51/152.82 (step @p108 :rule trans :premises (@p107 @p99)) % 152.51/152.82 (step @p109 :rule cong :premises (@p108) :args (@t155)) % 152.51/152.82 (step @p110 :rule trans :premises (@p109 @p94)) % 152.51/152.82 (step @p111 :rule cong :premises (@p110) :args (@t156)) % 152.51/152.82 (step @p112 :rule exists-elim :args ((= (exists @t48 @t154) @t156))) % 152.51/152.82 (step @p113 :rule trans :premises (@p112 @p111)) % 152.51/152.82 (step @p114 :rule quant-merge-prenex :args ((= (forall @t36 @t158) @t124))) % 152.51/152.82 (step @p115 :rule refl :args (@t113)) % 152.51/152.82 (step @p116 :rule refl :args (@t115)) % 152.51/152.82 (step @p117 :rule refl :args (@t121)) % 152.51/152.82 (step @p118 :rule alpha_equiv :args (@t159 (@list @t83) @t145)) % 152.51/152.82 (step @p119 :rule nary_cong :premises (@p118 @p117 @p116 @p115) :args (@t160)) % 152.51/152.82 (step @p120 :rule quant-miniscope-or :args ((= @t158 @t160))) % 152.51/152.82 (step @p121 :rule trans :premises (@p120 @p119)) % 152.51/152.82 (step @p122 :rule symm :premises (@p121)) % 152.51/152.82 (step @p123 :rule cong :premises (@p122) :args ((forall @t36 (or @t162 @t121 @t115 @t113)))) % 152.51/152.82 (step @p124 :rule trans :premises (@p123 @p114)) % 152.51/152.82 (step @p125 :rule refl :args (@t114)) % 152.51/152.82 (step @p126 :rule refl :args (@t21)) % 152.51/152.82 (step @p127 :rule cong :premises (@p126 @p125) :args ((= @t21 @t114))) % 152.51/152.82 (step @p128 :rule symm :premises (@p127)) % 152.51/152.82 (step @p129 :rule eq_resolve :premises (@p126 @p128)) % 152.51/152.82 (step @p130 :rule cong :premises (@p129) :args (@t163)) % 152.51/152.82 (step @p131 :rule refl :args (@t162)) % 152.51/152.82 (step @p132 :rule nary_cong :premises (@p131 @p117 @p130 @p115) :args (@t164)) % 152.51/152.82 (step @p133 :rule cong :premises (@p132) :args ((forall @t36 @t164))) % 152.51/152.82 (step @p134 :rule trans :premises (@p133 @p124)) % 152.51/152.82 (step @p135 :rule aci_norm :args ((= (or (or @t162 @t121 @t163) @t113) @t164))) % 152.51/152.82 (step @p136 :rule refl :args (@t163)) % 152.51/152.82 (step @p137 :rule bool-double-not-elim :args (@t162)) % 152.51/152.82 (step @p138 :rule nary_cong :premises (@p137 @p117 @p136) :args (@t167)) % 152.51/152.82 (step @p139 :rule aci_norm :args ((= (or @t166 (or @t121 @t163)) @t167))) % 152.51/152.82 (step @p140 :rule trans :premises (@p139 @p138)) % 152.51/152.82 (step @p141 :rule bool-and-de-morgan :args (@t120 @t21 true)) % 152.51/152.82 (step @p142 :rule refl :args (@t166)) % 152.51/152.82 (step @p143 :rule nary_cong :premises (@p142 @p141) :args ((or @t166 (not (and @t120 @t21))))) % 152.51/152.82 (step @p144 :rule bool-and-de-morgan :args (@t165 @t120 (and @t21))) % 152.51/152.82 (step @p145 :rule trans :premises (@p144 @p143)) % 152.51/152.82 (step @p146 :rule trans :premises (@p145 @p140)) % 152.51/152.82 (step @p147 :rule nary_cong :premises (@p146 @p115) :args ((or (not @t168) @t113))) % 152.51/152.82 (step @p148 :rule trans :premises (@p147 @p135)) % 152.51/152.82 (step @p149 :rule bool-impl-elim :args (@t168 @t113)) % 152.51/152.82 (step @p150 :rule trans :premises (@p149 @p148)) % 152.51/152.82 (step @p151 :rule cong :premises (@p150) :args ((forall @t36 (=> @t168 @t113)))) % 152.51/152.82 (step @p152 :rule trans :premises (@p151 @p134)) % 152.51/152.82 (step @p153 :rule eq-symm :args (@t20 @t19)) % 152.51/152.82 (step @p154 :rule refl :args (@t21)) % 152.51/152.82 (step @p155 :rule quant-merge-prenex :args ((= (forall @t29 @t170) @t120))) % 152.51/152.82 (step @p156 :rule alpha_equiv :args (@t171 (@list @t74) @t172)) % 152.51/152.82 (step @p157 :rule refl :args (@t118)) % 152.51/152.82 (step @p158 :rule nary_cong :premises (@p157 @p156) :args (@t173)) % 152.51/152.82 (step @p159 :rule quant-miniscope-or :args ((= @t170 @t173))) % 152.51/152.82 (step @p160 :rule trans :premises (@p159 @p158)) % 152.51/152.82 (step @p161 :rule symm :premises (@p160)) % 152.51/152.82 (step @p162 :rule cong :premises (@p161) :args ((forall @t29 (or @t118 @t176)))) % 152.51/152.82 (step @p163 :rule trans :premises (@p162 @p155)) % 152.51/152.82 (step @p164 :rule refl :args (@t176)) % 152.51/152.82 (step @p165 :rule refl :args (@t117)) % 152.51/152.82 (step @p166 :rule refl :args (@t27)) % 152.51/152.82 (step @p167 :rule cong :premises (@p166 @p165) :args ((= @t27 @t117))) % 152.51/152.82 (step @p168 :rule symm :premises (@p167)) % 152.51/152.82 (step @p169 :rule eq_resolve :premises (@p166 @p168)) % 152.51/152.82 (step @p170 :rule cong :premises (@p169) :args (@t177)) % 152.51/152.82 (step @p171 :rule nary_cong :premises (@p170 @p164) :args (@t178)) % 152.51/152.82 (step @p172 :rule cong :premises (@p171) :args ((forall @t29 @t178))) % 152.51/152.82 (step @p173 :rule trans :premises (@p172 @p163)) % 152.51/152.82 (step @p174 :rule bool-impl-elim :args (@t27 @t176)) % 152.51/152.82 (step @p175 :rule cong :premises (@p174) :args ((forall @t29 (=> @t27 @t176)))) % 152.51/152.82 (step @p176 :rule trans :premises (@p175 @p173)) % 152.51/152.82 (step @p177 :rule refl :args (@t174)) % 152.51/152.82 (step @p178 :rule refl :args (@t24)) % 152.51/152.82 (step @p179 :rule cong :premises (@p178 @p177) :args ((= @t24 @t174))) % 152.51/152.82 (step @p180 :rule symm :premises (@p179)) % 152.51/152.82 (step @p181 :rule eq_resolve :premises (@p178 @p180)) % 152.51/152.82 (step @p182 :rule refl :args (@t175)) % 152.51/152.82 (step @p183 :rule refl :args (@t23)) % 152.51/152.82 (step @p184 :rule cong :premises (@p183 @p182) :args ((= @t23 @t175))) % 152.51/152.82 (step @p185 :rule symm :premises (@p184)) % 152.51/152.82 (step @p186 :rule eq_resolve :premises (@p183 @p185)) % 152.51/152.82 (step @p187 :rule cong :premises (@p186 @p181) :args (@t179)) % 152.51/152.82 (step @p188 :rule cong :premises (@p187) :args ((forall @t25 @t179))) % 152.51/152.82 (step @p189 :rule eq-symm :args (@t24 @t23)) % 152.51/152.82 (step @p190 :rule cong :premises (@p189) :args (@t26)) % 152.51/152.82 (step @p191 :rule trans :premises (@p190 @p188)) % 152.51/152.82 (step @p192 :rule refl :args (@t27)) % 152.51/152.82 (step @p193 :rule cong :premises (@p192 @p191) :args (@t28)) % 152.51/152.82 (step @p194 :rule cong :premises (@p193) :args (@t30)) % 152.51/152.82 (step @p195 :rule trans :premises (@p194 @p176)) % 152.51/152.82 (step @p196 :rule refl :args (@t161)) % 152.51/152.82 (step @p197 :rule refl :args (@t31)) % 152.51/152.82 (step @p198 :rule cong :premises (@p197 @p196) :args ((= @t31 @t161))) % 152.51/152.82 (step @p199 :rule symm :premises (@p198)) % 152.51/152.82 (step @p200 :rule eq_resolve :premises (@p197 @p199)) % 152.51/152.82 (step @p201 :rule cong :premises (@p200) :args (@t180)) % 152.51/152.82 (step @p202 :rule cong :premises (@p201) :args (@t181)) % 152.51/152.82 (step @p203 :rule cong :premises (@p202) :args (@t182)) % 152.51/152.82 (step @p204 :rule exists-elim :args ((= @t33 @t182))) % 152.51/152.82 (step @p205 :rule trans :premises (@p204 @p203)) % 152.51/152.82 (step @p206 :rule nary_cong :premises (@p205 @p195 @p154) :args (@t34)) % 152.51/152.82 (step @p207 :rule cong :premises (@p206 @p153) :args (@t35)) % 152.51/152.82 (step @p208 :rule cong :premises (@p207) :args (@t37)) % 152.51/152.82 (step @p209 :rule trans :premises (@p208 @p152)) % 152.51/152.82 (step @p210 :rule refl :args (@t38)) % 152.51/152.82 (step @p211 :rule quant-merge-prenex :args ((= (forall @t29 @t184) @t132))) % 152.51/152.82 (step @p212 :rule alpha_equiv :args (@t185 (@list @t90) @t172)) % 152.51/152.82 (step @p213 :rule refl :args (@t130)) % 152.51/152.82 (step @p214 :rule nary_cong :premises (@p213 @p212) :args (@t186)) % 152.51/152.82 (step @p215 :rule quant-miniscope-or :args ((= @t184 @t186))) % 152.51/152.82 (step @p216 :rule trans :premises (@p215 @p214)) % 152.51/152.82 (step @p217 :rule symm :premises (@p216)) % 152.51/152.82 (step @p218 :rule cong :premises (@p217) :args ((forall @t29 (or @t130 @t188)))) % 152.51/152.82 (step @p219 :rule trans :premises (@p218 @p211)) % 152.51/152.82 (step @p220 :rule refl :args (@t188)) % 152.51/152.82 (step @p221 :rule refl :args (@t129)) % 152.51/152.82 (step @p222 :rule refl :args (@t42)) % 152.51/152.82 (step @p223 :rule cong :premises (@p222 @p221) :args ((= @t42 @t129))) % 152.51/152.82 (step @p224 :rule symm :premises (@p223)) % 152.51/152.82 (step @p225 :rule eq_resolve :premises (@p222 @p224)) % 152.51/152.82 (step @p226 :rule cong :premises (@p225) :args (@t189)) % 152.51/152.82 (step @p227 :rule nary_cong :premises (@p226 @p220) :args (@t190)) % 152.51/152.82 (step @p228 :rule cong :premises (@p227) :args ((forall @t29 @t190))) % 152.51/152.82 (step @p229 :rule trans :premises (@p228 @p219)) % 152.51/152.82 (step @p230 :rule bool-impl-elim :args (@t42 @t188)) % 152.51/152.82 (step @p231 :rule cong :premises (@p230) :args ((forall @t29 (=> @t42 @t188)))) % 152.51/152.82 (step @p232 :rule trans :premises (@p231 @p229)) % 152.51/152.82 (step @p233 :rule refl :args (@t187)) % 152.51/152.82 (step @p234 :rule refl :args (@t39)) % 152.51/152.82 (step @p235 :rule cong :premises (@p234 @p233) :args ((= @t39 @t187))) % 152.51/152.82 (step @p236 :rule symm :premises (@p235)) % 152.51/152.82 (step @p237 :rule eq_resolve :premises (@p234 @p236)) % 152.51/152.82 (step @p238 :rule cong :premises (@p237 @p186) :args (@t40)) % 152.51/152.82 (step @p239 :rule cong :premises (@p238) :args (@t41)) % 152.51/152.82 (step @p240 :rule refl :args (@t42)) % 152.51/152.82 (step @p241 :rule cong :premises (@p240 @p239) :args (@t43)) % 152.51/152.82 (step @p242 :rule cong :premises (@p241) :args (@t44)) % 152.51/152.82 (step @p243 :rule trans :premises (@p242 @p232)) % 152.51/152.82 (step @p244 :rule refl :args (@t147)) % 152.51/152.82 (step @p245 :rule refl :args (@t45)) % 152.51/152.82 (step @p246 :rule cong :premises (@p245 @p244) :args ((= @t45 @t147))) % 152.51/152.82 (step @p247 :rule symm :premises (@p246)) % 152.51/152.82 (step @p248 :rule eq_resolve :premises (@p245 @p247)) % 152.51/152.82 (step @p249 :rule cong :premises (@p248) :args (@t191)) % 152.51/152.82 (step @p250 :rule cong :premises (@p249) :args (@t192)) % 152.51/152.82 (step @p251 :rule cong :premises (@p250) :args (@t193)) % 152.51/152.82 (step @p252 :rule exists-elim :args ((= @t46 @t193))) % 152.51/152.82 (step @p253 :rule trans :premises (@p252 @p251)) % 152.51/152.82 (step @p254 :rule nary_cong :premises (@p253 @p243 @p210 @p209) :args (@t47)) % 152.51/152.82 (step @p255 :rule cong :premises (@p254) :args (@t49)) % 152.51/152.82 (step @p256 :rule trans :premises (@p255 @p113)) % 152.51/152.82 (step @p257 :rule cong :premises (@p256) :args (@t50)) % 152.51/152.82 (step @p258 :rule quant-unused-vars :args ((= (forall @t48 true) true))) % 152.51/152.82 (step @p259 :rule bool-or-taut :args (false @t148 (or @t198) false)) % 152.51/152.82 (step @p260 :rule aci_norm :args ((= (or (or @t148 @t198) @t151) (or @t148 @t198 @t151)))) % 152.51/152.82 (step @p261 :rule trans :premises (@p260 @p259)) % 152.51/152.82 (step @p262 :rule refl :args (@t151)) % 152.51/152.82 (step @p263 :rule refl :args (@t198)) % 152.51/152.82 (step @p264 :rule nary_cong :premises (@p96 @p263) :args ((or @t152 @t198))) % 152.51/152.82 (step @p265 :rule bool-and-de-morgan :args (@t151 @t197 true)) % 152.51/152.82 (step @p266 :rule trans :premises (@p265 @p264)) % 152.51/152.82 (step @p267 :rule nary_cong :premises (@p266 @p262) :args ((or (not @t199) @t151))) % 152.51/152.82 (step @p268 :rule trans :premises (@p267 @p261)) % 152.51/152.82 (step @p269 :rule bool-impl-elim :args (@t199 @t151)) % 152.51/152.82 (step @p270 :rule trans :premises (@p269 @p268)) % 152.51/152.82 (step @p271 :rule cong :premises (@p270) :args ((forall @t48 (=> @t199 @t151)))) % 152.51/152.82 (step @p272 :rule trans :premises (@p271 @p258)) % 152.51/152.82 (step @p273 :rule quant-merge-prenex :args ((= (forall @t16 @t201) @t197))) % 152.51/152.82 (step @p274 :rule alpha_equiv :args (@t202 (@list @t194) @t172)) % 152.51/152.82 (step @p275 :rule nary_cong :premises (@p76 @p274) :args (@t203)) % 152.51/152.82 (step @p276 :rule quant-miniscope-or :args ((= @t201 @t203))) % 152.51/152.82 (step @p277 :rule trans :premises (@p276 @p275)) % 152.51/152.82 (step @p278 :rule symm :premises (@p277)) % 152.51/152.82 (step @p279 :rule cong :premises (@p278) :args ((forall @t16 (or @t127 @t204)))) % 152.51/152.82 (step @p280 :rule trans :premises (@p279 @p273)) % 152.51/152.82 (step @p281 :rule refl :args (@t204)) % 152.51/152.82 (step @p282 :rule nary_cong :premises (@p90 @p281) :args (@t205)) % 152.51/152.82 (step @p283 :rule cong :premises (@p282) :args ((forall @t16 @t205))) % 152.51/152.82 (step @p284 :rule trans :premises (@p283 @p280)) % 152.51/152.82 (step @p285 :rule bool-impl-elim :args (@t38 @t204)) % 152.51/152.82 (step @p286 :rule cong :premises (@p285) :args ((forall @t16 (=> @t38 @t204)))) % 152.51/152.82 (step @p287 :rule trans :premises (@p286 @p284)) % 152.51/152.82 (step @p288 :rule cong :premises (@p237 @p44) :args (@t51)) % 152.51/152.82 (step @p289 :rule cong :premises (@p288) :args (@t52)) % 152.51/152.82 (step @p290 :rule cong :premises (@p210 @p289) :args (@t53)) % 152.51/152.82 (step @p291 :rule cong :premises (@p290) :args (@t54)) % 152.51/152.82 (step @p292 :rule trans :premises (@p291 @p287)) % 152.51/152.82 (step @p293 :rule nary_cong :premises (@p253 @p292) :args (@t55)) % 152.51/152.82 (step @p294 :rule cong :premises (@p293 @p253) :args (@t56)) % 152.51/152.82 (step @p295 :rule cong :premises (@p294) :args (@t57)) % 152.51/152.82 (step @p296 :rule trans :premises (@p295 @p272)) % 152.51/152.82 (step @p297 :rule nary_cong :premises (@p296 @p257) :args (@t58)) % 152.51/152.82 (step @p298 :rule trans :premises (@p297 @p73)) % 152.51/152.82 (step @p299 :rule cong :premises (@p298 @p72) :args (@t59)) % 152.51/152.82 (step @p300 :rule cong :premises (@p299) :args (@t60)) % 152.51/152.82 (step @p301 :rule trans :premises (@p300 @p28 @p27)) % 152.51/152.82 (step @p302 :rule eq_resolve :premises (@p1 @p301)) % 152.51/152.82 (step @p303 :rule not_implies_elim1 :premises (@p302)) % 152.51/152.82 (step @p304 :rule instantiate :premises (@p303) :args ((@list @t206))) % 152.51/152.82 (step @p305 :rule skolemize :premises (@p304)) % 152.51/152.82 (step @p306 :rule bool-double-not-elim :args (@t213)) % 152.51/152.82 (step @p307 :rule refl :args (@t217)) % 152.51/152.82 (step @p308 :rule nary_cong :premises (@p307 @p306) :args ((or @t217 (not @t216)))) % 152.51/152.82 (step @p309 :rule cnf_or_neg :args (@t217 1)) % 152.51/152.82 (step @p310 :rule eq_resolve :premises (@p309 @p308)) % 152.51/152.82 (step @p311 :rule reordering :premises (@p310) :args ((or @t213 @t217))) % 152.51/152.82 (step @p312 :rule chain_m_resolution :premises (@p311 @p305) :args (@t213 @t218 @t219)) % 152.51/152.82 (step @p313 :rule instantiate :premises (@p312) :args ((@list @t221 @t220))) % 152.51/152.82 (step @p314 :rule instantiate :premises (@p312) :args ((@list @t206 @t221))) % 152.51/152.82 (step @p315 :rule bool-double-not-elim :args (@t214)) % 152.51/152.82 (step @p316 :rule nary_cong :premises (@p307 @p315) :args ((or @t217 (not @t215)))) % 152.51/152.82 (step @p317 :rule cnf_or_neg :args (@t217 2)) % 152.51/152.82 (step @p318 :rule eq_resolve :premises (@p317 @p316)) % 152.51/152.82 (step @p319 :rule reordering :premises (@p318) :args ((or @t214 @t217))) % 152.51/152.82 (step @p320 :rule chain_m_resolution :premises (@p319 @p305) :args (@t214 @t218 @t219)) % 152.51/152.82 (step @p321 :rule cnf_or_pos :args (@t226)) % 152.51/152.82 (step @p322 :rule reordering :premises (@p321) :args ((or @t215 @t225 (not @t226)))) % 152.51/152.82 (step @p323 :rule chain_m_resolution :premises (@p322 @p320 @p314) :args (@t225 @t227 (@list @t214 @t226))) % 152.51/152.82 (step @p324 :rule bool-double-not-elim :args (@t230)) % 152.51/152.82 (step @p325 :rule refl :args (@t233)) % 152.51/152.82 (step @p326 :rule nary_cong :premises (@p325 @p324) :args ((or @t233 (not @t232)))) % 152.51/152.82 (step @p327 :rule cnf_or_neg :args (@t233 0)) % 152.51/152.82 (step @p328 :rule eq_resolve :premises (@p327 @p326)) % 152.51/152.82 (step @p329 :rule reordering :premises (@p328) :args ((or @t230 @t233))) % 152.51/152.82 (step @p330 :rule cnf_or_neg :args (@t233 1)) % 152.51/152.82 (step @p331 :rule instantiate :premises (@p303) :args ((@list @t229))) % 152.51/152.82 (step @p332 :rule skolemize :premises (@p331)) % 152.51/152.82 (step @p333 :rule bool-double-not-elim :args (@t237)) % 152.51/152.82 (step @p334 :rule refl :args (@t241)) % 152.51/152.82 (step @p335 :rule nary_cong :premises (@p334 @p333) :args ((or @t241 (not @t240)))) % 152.51/152.82 (step @p336 :rule cnf_or_neg :args (@t241 1)) % 152.51/152.82 (step @p337 :rule eq_resolve :premises (@p336 @p335)) % 152.51/152.82 (step @p338 :rule reordering :premises (@p337) :args ((or @t237 @t241))) % 152.51/152.82 (step @p339 :rule chain_m_resolution :premises (@p338 @p332) :args (@t237 @t218 @t242)) % 152.51/152.82 (step @p340 :rule instantiate :premises (@p339) :args ((@list @t229 @t228))) % 152.51/152.82 (step @p341 :rule bool-double-not-elim :args (@t238)) % 152.51/152.82 (step @p342 :rule nary_cong :premises (@p334 @p341) :args ((or @t241 (not @t239)))) % 152.51/152.82 (step @p343 :rule cnf_or_neg :args (@t241 2)) % 152.51/152.82 (step @p344 :rule eq_resolve :premises (@p343 @p342)) % 152.51/152.82 (step @p345 :rule reordering :premises (@p344) :args ((or @t238 @t241))) % 152.51/152.82 (step @p346 :rule chain_m_resolution :premises (@p345 @p332) :args (@t238 @t218 @t242)) % 152.51/152.82 (step @p347 :rule cnf_or_pos :args (@t245)) % 152.51/152.82 (step @p348 :rule reordering :premises (@p347) :args ((or @t239 @t244 (not @t245)))) % 152.51/152.82 (step @p349 :rule chain_m_resolution :premises (@p348 @p346 @p340) :args (@t244 @t227 (@list @t238 @t245))) % 152.51/152.82 (step @p350 :rule cnf_equiv_pos1 :args (@t244)) % 152.51/152.82 (step @p351 :rule reordering :premises (@p350) :args ((or @t232 @t243 (not @t244)))) % 152.51/152.82 (step @p352 :rule cnf_equiv_pos2 :args (@t246)) % 152.51/152.82 (step @p353 :rule reordering :premises (@p352) :args ((or @t231 @t239 (not @t246)))) % 152.51/152.82 (step @p354 :rule instantiate :premises (@p339) :args ((@list @t228 @t229))) % 152.51/152.82 (step @p355 :rule cnf_or_pos :args (@t248)) % 152.51/152.82 (step @p356 :rule reordering :premises (@p355) :args ((or @t247 @t246 (not @t248)))) % 152.51/152.82 (step @p357 :rule chain_m_resolution :premises (@p356 @p354 @p353 @p346 @p351 @p349 @p330 @p329) :args (@t233 (@list false true false false false true false) (@list @t248 @t246 @t238 @t243 @t244 @t231 @t230))) % 152.51/152.82 (step @p358 :rule refl :args (@t249)) % 152.51/152.82 (step @p359 :rule bool-double-not-elim :args (@t68)) % 152.51/152.82 (step @p360 :rule nary_cong :premises (@p359 @p358) :args ((or (not @t250) @t249))) % 152.51/152.82 (assume-push @p453 @t250) % 152.51/152.82 (step @p362 :rule skolemize :premises (@p453)) % 152.51/152.82 (step-pop @p454 :rule scope :premises (@p362)) % 152.51/152.82 (step @p363 :rule process_scope :premises (@p454) :args (@t249)) % 152.51/152.82 (step @p365 :rule implies_elim :premises (@p363)) % 152.51/152.82 (step @p366 :rule eq_resolve :premises (@p365 @p360)) % 152.51/152.82 (step @p367 :rule chain_m_resolution :premises (@p366 @p357) :args (@t68 @t251 (@list @t233))) % 152.51/152.82 (assume-push @p455 @t68) % 152.51/152.82 (step @p369 :rule instantiate :premises (@p455) :args ((@list @t221 @t206))) % 152.51/152.82 (step-pop @p456 :rule scope :premises (@p369)) % 152.51/152.82 (step @p370 :rule process_scope :premises (@p456) :args (@t255)) % 152.51/152.82 (step @p372 :rule implies_elim :premises (@p370)) % 152.51/152.82 (step @p373 :rule chain_m_resolution :premises (@p372 @p367) :args (@t255 @t251 (@list @t68))) % 152.51/152.82 (step @p374 :rule instantiate :premises (@p303) :args ((@list @t256))) % 152.51/152.82 (step @p375 :rule skolemize :premises (@p374)) % 152.51/152.82 (step @p376 :rule bool-double-not-elim :args (@t260)) % 152.51/152.82 (step @p377 :rule refl :args (@t264)) % 152.51/152.82 (step @p378 :rule nary_cong :premises (@p377 @p376) :args ((or @t264 (not @t263)))) % 152.51/152.82 (step @p379 :rule cnf_or_neg :args (@t264 1)) % 152.51/152.82 (step @p380 :rule eq_resolve :premises (@p379 @p378)) % 152.51/152.82 (step @p381 :rule reordering :premises (@p380) :args ((or @t260 @t264))) % 152.51/152.82 (step @p382 :rule chain_m_resolution :premises (@p381 @p375) :args (@t260 @t218 @t265)) % 152.51/152.82 (step @p383 :rule instantiate :premises (@p382) :args ((@list @t256 @t256))) % 152.51/152.82 (step @p384 :rule bool-double-not-elim :args (@t261)) % 152.51/152.82 (step @p385 :rule nary_cong :premises (@p377 @p384) :args ((or @t264 (not @t262)))) % 152.51/152.82 (step @p386 :rule cnf_or_neg :args (@t264 2)) % 152.51/152.82 (step @p387 :rule eq_resolve :premises (@p386 @p385)) % 152.51/152.82 (step @p388 :rule reordering :premises (@p387) :args ((or @t261 @t264))) % 152.51/152.82 (step @p389 :rule chain_m_resolution :premises (@p388 @p375) :args (@t261 @t218 @t265)) % 152.51/152.82 (step @p390 :rule cnf_or_pos :args (@t268)) % 152.51/152.82 (step @p391 :rule reordering :premises (@p390) :args ((or @t262 @t267 (not @t268)))) % 152.51/152.82 (step @p392 :rule chain_m_resolution :premises (@p391 @p389 @p383) :args (@t267 @t227 (@list @t261 @t268))) % 152.51/152.82 (step @p393 :rule cnf_equiv_pos2 :args (@t267)) % 152.51/152.82 (step @p394 :rule reordering :premises (@p393) :args ((or @t266 @t262 (not @t267)))) % 152.51/152.82 (step @p395 :rule chain_m_resolution :premises (@p394 @p389 @p392) :args (@t266 @t227 (@list @t261 @t267))) % 152.51/152.82 (step @p396 :rule refl :args (@t269)) % 152.51/152.82 (step @p397 :rule bool-double-not-elim :args (@t69)) % 152.51/152.82 (step @p398 :rule nary_cong :premises (@p397 @p396) :args ((or (not @t270) @t269))) % 152.51/152.82 (assume-push @p457 @t270) % 152.51/152.82 (step @p400 :rule skolemize :premises (@p457)) % 152.51/152.82 (step-pop @p458 :rule scope :premises (@p400)) % 152.51/152.82 (step @p401 :rule process_scope :premises (@p458) :args (@t269)) % 152.51/152.82 (step @p403 :rule implies_elim :premises (@p401)) % 152.51/152.82 (step @p404 :rule eq_resolve :premises (@p403 @p398)) % 152.51/152.82 (step @p405 :rule chain_m_resolution :premises (@p404 @p395) :args (@t69 @t251 (@list @t266))) % 152.51/152.82 (step @p406 :rule not_implies_elim2 :premises (@p302)) % 152.51/152.82 (step @p407 :rule not_and :premises (@p406)) % 152.51/152.82 (step @p408 :rule chain_m_resolution :premises (@p407 @p405 @p367) :args (@t271 @t227 (@list @t69 @t68))) % 152.51/152.82 (step @p409 :rule refl :args (@t276)) % 152.51/152.82 (step @p410 :rule bool-double-not-elim :args (@t67)) % 152.51/152.82 (step @p411 :rule nary_cong :premises (@p410 @p409) :args ((or (not @t271) @t276))) % 152.51/152.82 (assume-push @p459 @t271) % 152.51/152.82 (step @p413 :rule skolemize :premises (@p459)) % 152.51/152.82 (step-pop @p460 :rule scope :premises (@p413)) % 152.51/152.82 (step @p414 :rule process_scope :premises (@p460) :args (@t276)) % 152.51/152.82 (step @p416 :rule implies_elim :premises (@p414)) % 152.51/152.82 (step @p417 :rule eq_resolve :premises (@p416 @p411)) % 152.51/152.82 (step @p418 :rule chain_m_resolution :premises (@p417 @p408) :args (@t276 @t218 (@list @t67))) % 152.51/152.82 (step @p419 :rule bool-double-not-elim :args (@t253)) % 152.51/152.82 (step @p420 :rule refl :args (@t275)) % 152.51/152.82 (step @p421 :rule nary_cong :premises (@p420 @p419) :args ((or @t275 (not @t254)))) % 152.51/152.82 (step @p422 :rule cnf_or_neg :args (@t275 0)) % 152.51/152.82 (step @p423 :rule eq_resolve :premises (@p422 @p421)) % 152.51/152.82 (step @p424 :rule reordering :premises (@p423) :args ((or @t253 @t275))) % 152.51/152.82 (step @p425 :rule chain_m_resolution :premises (@p424 @p418) :args (@t253 @t218 @t277)) % 152.51/152.82 (step @p426 :rule cnf_or_pos :args (@t255)) % 152.51/152.82 (step @p427 :rule reordering :premises (@p426) :args ((or @t254 @t224 (not @t255)))) % 152.51/152.82 (step @p428 :rule chain_m_resolution :premises (@p427 @p425 @p373) :args (@t224 @t227 (@list @t253 @t255))) % 152.51/152.82 (step @p429 :rule cnf_equiv_pos1 :args (@t225)) % 152.51/152.82 (step @p430 :rule reordering :premises (@p429) :args ((or (not @t224) @t222 (not @t225)))) % 152.51/152.82 (step @p431 :rule chain_m_resolution :premises (@p430 @p428 @p323) :args (@t222 @t227 (@list @t224 @t225))) % 152.51/152.82 (step @p432 :rule instantiate :premises (@p312) :args ((@list @t206 @t220))) % 152.51/152.82 (step @p433 :rule cnf_or_pos :args (@t280)) % 152.51/152.82 (step @p434 :rule reordering :premises (@p433) :args ((or @t215 @t279 (not @t280)))) % 152.51/152.82 (step @p435 :rule chain_m_resolution :premises (@p434 @p320 @p432) :args (@t279 @t227 (@list @t214 @t280))) % 152.51/152.82 (step @p436 :rule bool-double-not-elim :args (@t273)) % 152.51/152.82 (step @p437 :rule nary_cong :premises (@p420 @p436) :args ((or @t275 (not @t274)))) % 152.51/152.82 (step @p438 :rule cnf_or_neg :args (@t275 1)) % 152.51/152.82 (step @p439 :rule eq_resolve :premises (@p438 @p437)) % 152.51/152.82 (step @p440 :rule reordering :premises (@p439) :args ((or @t273 @t275))) % 152.51/152.82 (step @p441 :rule chain_m_resolution :premises (@p440 @p418) :args (@t273 @t218 @t277)) % 152.51/152.82 (step @p442 :rule cnf_equiv_pos1 :args (@t279)) % 152.51/152.82 (step @p443 :rule reordering :premises (@p442) :args ((or @t274 @t278 (not @t279)))) % 152.51/152.82 (step @p444 :rule chain_m_resolution :premises (@p443 @p441 @p435) :args (@t278 @t227 (@list @t273 @t279))) % 152.51/152.82 (step @p445 :rule cnf_or_neg :args (@t275 2)) % 152.51/152.82 (step @p446 :rule chain_m_resolution :premises (@p445 @p418) :args ((not @t272) @t218 @t277)) % 152.51/152.82 (step @p447 :rule cnf_equiv_pos2 :args (@t281)) % 152.51/152.82 (step @p448 :rule reordering :premises (@p447) :args ((or @t272 (not @t278) @t282))) % 152.51/152.82 (step @p449 :rule chain_m_resolution :premises (@p448 @p446 @p444) :args (@t282 (@list true false) (@list @t272 @t278))) % 152.51/152.82 (step @p450 :rule cnf_or_pos :args (@t284)) % 152.51/152.82 (step @p451 :rule reordering :premises (@p450) :args ((or @t283 @t281 (not @t284)))) % 152.51/152.82 (step @p452 false :rule chain_m_resolution :premises (@p451 @p449 @p431 @p313) :args (false (@list true false false) (@list @t281 @t222 @t284))) % 152.51/152.82 ) % 152.51/152.82 % SZS output end Proof % 152.51/152.82 % cvc5 exiting %------------------------------------------------------------------------------