%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO362^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:12:30 AM UTC 2026 % Result : Theorem 169.02s 169.57s % Output : Proof 169.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SYO362^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n017.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Wed Jun 3 00:04:16 EDT 2026 % 0.16/0.35 % CPUTime : % 0.27/0.52 %----Proving TH0 % 169.02/169.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 169.02/169.57 --- 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... % 169.02/169.57 --- 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... % 169.02/169.57 --- Run --ho-elim --full-saturate-quant at 18s... % 169.02/169.57 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 169.02/169.57 % SZS status Theorem % 169.02/169.57 % SZS output start Proof % 169.02/169.57 ( % 169.02/169.57 (declare-sort $$unsorted 0) % 169.02/169.57 (declare-const tptp.cK (-> (-> $$unsorted Bool) $$unsorted Bool)) % 169.02/169.57 (define @t1 () (@var "Xx" $$unsorted)) % 169.02/169.57 (define @t2 () (@var "Y" (-> $$unsorted Bool))) % 169.02/169.57 (define @t3 () (_ tptp.cK @t2)) % 169.02/169.57 (define @t4 () (_ @t3 @t1)) % 169.02/169.57 (define @t5 () (@var "X" (-> $$unsorted Bool))) % 169.02/169.57 (define @t6 () (_ tptp.cK @t5)) % 169.02/169.57 (define @t7 () (_ @t6 @t1)) % 169.02/169.57 (define @t8 () (@list @t1)) % 169.02/169.57 (define @t9 () (forall @t8 (=> @t7 @t4))) % 169.02/169.57 (define @t10 () (_ @t2 @t1)) % 169.02/169.57 (define @t11 () (_ @t5 @t1)) % 169.02/169.57 (define @t12 () (forall @t8 (=> @t11 @t10))) % 169.02/169.57 (define @t13 () (=> @t12 @t9)) % 169.02/169.57 (define @t14 () (@list @t5 @t2)) % 169.02/169.57 (define @t15 () (forall @t14 @t13)) % 169.02/169.57 (define @t16 () (@var "Xw" $$unsorted)) % 169.02/169.57 (define @t17 () (_ @t3 @t16)) % 169.02/169.57 (define @t18 () (_ @t6 @t16)) % 169.02/169.57 (define @t19 () (or @t18 @t17)) % 169.02/169.57 (define @t20 () (@list @t16)) % 169.02/169.57 (define @t21 () (lambda @t20 @t19)) % 169.02/169.57 (define @t22 () (@var "Xz" $$unsorted)) % 169.02/169.57 (define @t23 () (_ @t2 @t22)) % 169.02/169.57 (define @t24 () (_ @t5 @t22)) % 169.02/169.57 (define @t25 () (or @t24 @t23)) % 169.02/169.57 (define @t26 () (@list @t22)) % 169.02/169.57 (define @t27 () (lambda @t26 @t25)) % 169.02/169.57 (define @t28 () (= (_ tptp.cK @t27) @t21)) % 169.02/169.57 (define @t29 () (forall @t14 @t28)) % 169.02/169.57 (define @t30 () (=> @t29 @t15)) % 169.02/169.57 (define @t31 () (not @t30)) % 169.02/169.57 (define @t32 () (@var "BOUND_VARIABLE_7476" $$unsorted)) % 169.02/169.57 (define @t33 () (@var "BOUND_VARIABLE_7558" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t34 () (@const 0 (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool)))) % 169.02/169.57 (define @t35 () (@const 1 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool)) (@ho-elim-sort (-> $$unsorted Bool)) (@ho-elim-sort (-> $$unsorted Bool))))) % 169.02/169.57 (define @t36 () (@const 2 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 169.02/169.57 (define @t37 () (@var "BOUND_VARIABLE_7568" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t38 () (forall (@list @t37 @t33 @t32) (or (not (forall @t8 (or (not (_ @t36 @t37 @t1)) (_ @t36 @t33 @t1)))) (not (_ @t36 (_ @t35 @t34 @t37) @t32)) (_ @t36 (_ @t35 @t34 @t33) @t32)))) % 169.02/169.57 (define @t39 () (@const 3 (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool)))) % 169.02/169.57 (define @t40 () (@const 4 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool)) (@ho-elim-sort (-> $$unsorted Bool)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))))) % 169.02/169.57 (define @t41 () (_ @t35 (_ @t40 @t39 @t37) @t33)) % 169.02/169.57 (define @t42 () (@const 5 (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool)))) % 169.02/169.57 (define @t43 () (_ @t35 @t34 (_ @t35 (_ @t40 @t42 @t37) @t33))) % 169.02/169.57 (define @t44 () (forall (@list @t37 @t33) (= @t41 @t43))) % 169.02/169.57 (define @t45 () (=> @t44 @t38)) % 169.02/169.57 (define @t46 () (not @t45)) % 169.02/169.57 (define @t47 () (tptp.cK @t2 @t32)) % 169.02/169.57 (define @t48 () (not (tptp.cK @t5 @t32))) % 169.02/169.57 (define @t49 () (_ @t2 @t1)) % 169.02/169.57 (define @t50 () (_ @t5 @t1)) % 169.02/169.57 (define @t51 () (forall @t8 (or (not @t50) @t49))) % 169.02/169.57 (define @t52 () (not @t51)) % 169.02/169.57 (define @t53 () (or @t52 @t48 @t47)) % 169.02/169.57 (define @t54 () (@list @t5 @t2 @t32)) % 169.02/169.57 (define @t55 () (forall @t54 @t53)) % 169.02/169.57 (define @t56 () (@const 6 (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool))) % 169.02/169.57 (define @t57 () (_ tptp.cK (_ (_ @t56 @t5) @t2))) % 169.02/169.57 (define @t58 () (@const 7 (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool))) % 169.02/169.57 (define @t59 () (_ (_ @t58 @t5) @t2)) % 169.02/169.57 (define @t60 () (forall @t14 (= @t57 @t59))) % 169.02/169.57 (define @t61 () (=> @t60 @t55)) % 169.02/169.57 (define @t62 () (not @t61)) % 169.02/169.57 (define @t63 () (tptp.cK @t2 @t16)) % 169.02/169.57 (define @t64 () (tptp.cK @t5 @t16)) % 169.02/169.57 (define @t65 () (_ @t2 @t22)) % 169.02/169.57 (define @t66 () (_ @t5 @t22)) % 169.02/169.57 (define @t67 () (or @t48 @t47)) % 169.02/169.57 (define @t68 () (or @t52 @t67)) % 169.02/169.57 (define @t69 () (forall @t54 @t68)) % 169.02/169.57 (define @t70 () (@list @t32)) % 169.02/169.57 (define @t71 () (forall @t70 @t68)) % 169.02/169.57 (define @t72 () (forall @t70 @t67)) % 169.02/169.57 (define @t73 () (or @t52 @t72)) % 169.02/169.57 (define @t74 () (tptp.cK @t2 @t1)) % 169.02/169.57 (define @t75 () (tptp.cK @t5 @t1)) % 169.02/169.57 (define @t76 () (forall @t8 (or (not @t75) @t74))) % 169.02/169.57 (define @t77 () (not @t7)) % 169.02/169.57 (define @t78 () (or @t77 @t4)) % 169.02/169.57 (define @t79 () (not @t11)) % 169.02/169.57 (define @t80 () (or @t79 @t10)) % 169.02/169.57 (define @t81 () (@quantifiers_skolemize @t38 2)) % 169.02/169.57 (define @t82 () (@quantifiers_skolemize @t38 1)) % 169.02/169.57 (define @t83 () (_ @t35 @t34 @t82)) % 169.02/169.57 (define @t84 () (_ @t36 @t83 @t81)) % 169.02/169.57 (define @t85 () (@quantifiers_skolemize @t38 0)) % 169.02/169.57 (define @t86 () (_ @t36 (_ @t35 @t34 @t85) @t81)) % 169.02/169.57 (define @t87 () (not @t86)) % 169.02/169.57 (define @t88 () (forall @t8 (or (not (_ @t36 @t85 @t1)) (_ @t36 @t82 @t1)))) % 169.02/169.57 (define @t89 () (not @t88)) % 169.02/169.57 (define @t90 () (or @t89 @t87 @t84)) % 169.02/169.57 (define @t91 () (not @t84)) % 169.02/169.57 (define @t92 () (@list true)) % 169.02/169.57 (define @t93 () (@list @t90)) % 169.02/169.57 (define @t94 () (@list @t85 @t82)) % 169.02/169.57 (define @t95 () (@var "BOUND_VARIABLE_7533" $$unsorted)) % 169.02/169.57 (define @t96 () (@var "BOUND_VARIABLE_7613" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t97 () (@var "BOUND_VARIABLE_7614" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t98 () (or (_ @t36 (_ @t35 @t34 @t97) @t95) (_ @t36 (_ @t35 @t34 @t96) @t95))) % 169.02/169.57 (define @t99 () (_ @t36 (_ @t35 (_ @t40 @t39 @t97) @t96) @t95)) % 169.02/169.57 (define @t100 () (forall (@list @t97 @t96 @t95) (= @t98 @t99))) % 169.02/169.57 (define @t101 () (@var "BOUND_VARIABLE_7532" (-> $$unsorted Bool))) % 169.02/169.57 (define @t102 () (@var "BOUND_VARIABLE_7531" (-> $$unsorted Bool))) % 169.02/169.57 (define @t103 () (forall (@list @t102 @t101 @t95) (= (or (tptp.cK @t102 @t95) (tptp.cK @t101 @t95)) (_ @t58 @t102 @t101 @t95)))) % 169.02/169.57 (define @t104 () (or @t86 @t84)) % 169.02/169.57 (define @t105 () (@list false)) % 169.02/169.57 (define @t106 () (_ @t35 (_ @t40 @t39 @t85) @t82)) % 169.02/169.57 (define @t107 () (_ @t36 @t106 @t81)) % 169.02/169.57 (define @t108 () (= @t107 @t104)) % 169.02/169.57 (define @t109 () (@list false false)) % 169.02/169.57 (define @t110 () (@var "ii" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t111 () (@var "u" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool)))) % 169.02/169.57 (define @t112 () (@var "e" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t113 () (@var "i" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t114 () (@var "v" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool)))) % 169.02/169.57 (define @t115 () (_ @t35 @t114 @t110)) % 169.02/169.57 (define @t116 () (@list @t110)) % 169.02/169.57 (define @t117 () (@list @t114)) % 169.02/169.57 (define @t118 () (forall (@list @t111 @t112 @t113) (not (forall @t117 (not (forall @t116 (= @t115 (ite (= @t113 @t110) @t112 (_ @t35 @t111 @t110))))))))) % 169.02/169.57 (define @t119 () (_ @t35 @t34 @t110)) % 169.02/169.57 (define @t120 () (ite (= @t85 @t110) @t82 @t119)) % 169.02/169.57 (define @t121 () (= @t115 @t120)) % 169.02/169.57 (define @t122 () (forall @t116 @t121)) % 169.02/169.57 (define @t123 () (not @t122)) % 169.02/169.57 (define @t124 () (forall @t117 @t123)) % 169.02/169.57 (define @t125 () (not @t124)) % 169.02/169.57 (define @t126 () (ite (= @t110 @t85) @t82 @t119)) % 169.02/169.57 (define @t127 () (forall @t117 (not (forall @t116 (= @t115 @t126))))) % 169.02/169.57 (define @t128 () (not @t127)) % 169.02/169.57 (define @t129 () (@quantifiers_skolemize @t127 0)) % 169.02/169.57 (define @t130 () (_ @t35 @t129 @t110)) % 169.02/169.57 (define @t131 () (forall @t116 (= @t126 @t130))) % 169.02/169.57 (define @t132 () (forall @t116 (= @t130 @t126))) % 169.02/169.57 (define @t133 () (not (not @t132))) % 169.02/169.57 (define @t134 () (= @t85 @t82)) % 169.02/169.57 (define @t135 () (ite @t134 @t82 @t83)) % 169.02/169.57 (define @t136 () (@purify @t135)) % 169.02/169.57 (define @t137 () (_ @t35 @t129 @t82)) % 169.02/169.57 (define @t138 () (= @t137 @t135)) % 169.02/169.57 (define @t139 () (ite (= @t82 @t85) @t82 @t83)) % 169.02/169.57 (define @t140 () (= @t139 @t137)) % 169.02/169.57 (define @t141 () (= @t137 @t136)) % 169.02/169.57 (define @t142 () (@list @t131)) % 169.02/169.57 (define @t143 () (not @t134)) % 169.02/169.57 (define @t144 () (not @t91)) % 169.02/169.57 (define @t145 () (and @t86 @t134 @t91)) % 169.02/169.57 (define @t146 () (@list false true)) % 169.02/169.57 (define @t147 () (= @t135 @t83)) % 169.02/169.57 (define @t148 () (= @t135 @t82)) % 169.02/169.57 (define @t149 () (= @t83 @t136)) % 169.02/169.57 (define @t150 () (_ @t35 (_ @t40 @t42 @t85) @t82)) % 169.02/169.57 (define @t151 () (_ @t35 @t34 @t150)) % 169.02/169.57 (define @t152 () (= @t85 @t150)) % 169.02/169.57 (define @t153 () (ite @t152 @t82 @t151)) % 169.02/169.57 (define @t154 () (@purify @t153)) % 169.02/169.57 (define @t155 () (_ @t35 @t129 @t150)) % 169.02/169.57 (define @t156 () (= @t155 @t153)) % 169.02/169.57 (define @t157 () (ite (= @t150 @t85) @t82 @t151)) % 169.02/169.57 (define @t158 () (= @t157 @t155)) % 169.02/169.57 (define @t159 () (= @t155 @t154)) % 169.02/169.57 (define @t160 () (@var "BOUND_VARIABLE_7543" $$unsorted)) % 169.02/169.57 (define @t161 () (@var "BOUND_VARIABLE_7638" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t162 () (@var "BOUND_VARIABLE_7639" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t163 () (or (_ @t36 @t162 @t160) (_ @t36 @t161 @t160))) % 169.02/169.57 (define @t164 () (_ @t36 (_ @t35 (_ @t40 @t42 @t162) @t161) @t160)) % 169.02/169.57 (define @t165 () (forall (@list @t162 @t161 @t160) (= @t163 @t164))) % 169.02/169.57 (define @t166 () (@var "BOUND_VARIABLE_7542" (-> $$unsorted Bool))) % 169.02/169.57 (define @t167 () (@var "BOUND_VARIABLE_7541" (-> $$unsorted Bool))) % 169.02/169.57 (define @t168 () (forall (@list @t167 @t166 @t160) (= (or (_ @t167 @t160) (_ @t166 @t160)) (_ @t56 @t167 @t166 @t160)))) % 169.02/169.57 (define @t169 () (@var "z" $$unsorted)) % 169.02/169.57 (define @t170 () (_ @t36 @t82 @t169)) % 169.02/169.57 (define @t171 () (@list @t169)) % 169.02/169.57 (define @t172 () (forall @t171 (= (_ @t36 @t85 @t169) @t170))) % 169.02/169.57 (define @t173 () (@quantifiers_skolemize @t172 0)) % 169.02/169.57 (define @t174 () (@var "y" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t175 () (@var "x" (@ho-elim-sort (-> $$unsorted Bool)))) % 169.02/169.57 (define @t176 () (not @t172)) % 169.02/169.57 (define @t177 () (or @t176 @t134)) % 169.02/169.57 (define @t178 () (@list true false)) % 169.02/169.57 (define @t179 () (_ @t36 @t82 @t173)) % 169.02/169.57 (define @t180 () (_ @t36 @t85 @t173)) % 169.02/169.57 (define @t181 () (= @t180 @t179)) % 169.02/169.57 (define @t182 () (not @t181)) % 169.02/169.57 (define @t183 () (not @t180)) % 169.02/169.57 (define @t184 () (or @t183 @t179)) % 169.02/169.57 (define @t185 () (or @t180 @t179)) % 169.02/169.57 (define @t186 () (_ @t36 @t150 @t173)) % 169.02/169.57 (define @t187 () (= @t186 @t185)) % 169.02/169.57 (define @t188 () (not @t186)) % 169.02/169.57 (define @t189 () (not @t152)) % 169.02/169.57 (define @t190 () (= true false)) % 169.02/169.57 (define @t191 () (and @t186 @t152 @t183)) % 169.02/169.57 (define @t192 () (= @t153 @t151)) % 169.02/169.57 (define @t193 () (= @t153 @t82)) % 169.02/169.57 (define @t194 () (= @t151 @t154)) % 169.02/169.57 (define @t195 () (forall @t171 (= @t170 (_ @t36 @t150 @t169)))) % 169.02/169.57 (define @t196 () (@quantifiers_skolemize @t195 0)) % 169.02/169.57 (define @t197 () (_ @t36 @t150 @t196)) % 169.02/169.57 (define @t198 () (_ @t36 @t82 @t196)) % 169.02/169.57 (define @t199 () (= @t198 @t197)) % 169.02/169.57 (define @t200 () (_ @t36 @t85 @t196)) % 169.02/169.57 (define @t201 () (or @t200 @t198)) % 169.02/169.57 (define @t202 () (not @t198)) % 169.02/169.57 (define @t203 () (= @t197 @t201)) % 169.02/169.57 (define @t204 () (not @t203)) % 169.02/169.57 (define @t205 () (not @t201)) % 169.02/169.57 (define @t206 () (not @t200)) % 169.02/169.57 (define @t207 () (or @t206 @t198)) % 169.02/169.57 (define @t208 () (not @t199)) % 169.02/169.57 (define @t209 () (not @t195)) % 169.02/169.57 (define @t210 () (= @t82 @t150)) % 169.02/169.57 (define @t211 () (or @t209 @t210)) % 169.02/169.57 (define @t212 () (not @t194)) % 169.02/169.57 (define @t213 () (not @t159)) % 169.02/169.57 (define @t214 () (not @t210)) % 169.02/169.57 (define @t215 () (not @t149)) % 169.02/169.57 (define @t216 () (not @t141)) % 169.02/169.57 (define @t217 () (not @t107)) % 169.02/169.57 (define @t218 () (= @t151 @t106)) % 169.02/169.57 (define @t219 () (not @t218)) % 169.02/169.57 (define @t220 () (and @t91 @t149 @t141 @t210 @t159 @t194 @t218 @t107)) % 169.02/169.57 (assume @p1 @t31) % 169.02/169.57 (assume @p2 true) % 169.02/169.57 (step @p3 :rule refl :args (@t38)) % 169.02/169.57 (step @p4 :rule eq-symm :args (@t41 @t43)) % 169.02/169.57 (step @p5 :rule cong :premises (@p4) :args (@t44)) % 169.02/169.57 (step @p6 :rule cong :premises (@p5 @p3) :args (@t45)) % 169.02/169.57 (step @p7 :rule cong :premises (@p6) :args (@t46)) % 169.02/169.57 ; WARNING: add trust step for TRUST % 169.02/169.57 ; trust TRUST PREPROCESS_HO_ELIM % 169.02/169.57 (step @p8 :rule trust :premises () :args ((= (not (=> (forall @t14 (= @t59 @t57)) @t55)) @t46))) % 169.02/169.57 (step @p9 :rule refl :args (@t55)) % 169.02/169.57 (step @p10 :rule eq-symm :args (@t57 @t59)) % 169.02/169.57 (step @p11 :rule cong :premises (@p10) :args (@t60)) % 169.02/169.57 (step @p12 :rule cong :premises (@p11 @p9) :args (@t61)) % 169.02/169.57 (step @p13 :rule cong :premises (@p12) :args (@t62)) % 169.02/169.57 ; trust TRUST PREPROCESS_HO_ELIM % 169.02/169.57 (step @p14 :rule trust :premises () :args ((= (not (=> (forall @t14 (= (_ tptp.cK (lambda @t26 (or @t66 @t65))) (lambda @t20 (or @t64 @t63)))) @t55)) @t62))) % 169.02/169.57 (step @p15 :rule aci_norm :args ((= @t68 @t53))) % 169.02/169.57 (step @p16 :rule cong :premises (@p15) :args (@t69)) % 169.02/169.57 (step @p17 :rule quant-merge-prenex :args ((= (forall @t14 @t71) @t69))) % 169.02/169.57 (step @p18 :rule alpha_equiv :args (@t72 (@list @t32) (@list @t1))) % 169.02/169.57 (step @p19 :rule refl :args (@t52)) % 169.02/169.57 (step @p20 :rule nary_cong :premises (@p19 @p18) :args (@t73)) % 169.02/169.57 (step @p21 :rule quant-miniscope-or :args ((= @t71 @t73))) % 169.02/169.57 (step @p22 :rule trans :premises (@p21 @p20)) % 169.02/169.57 (step @p23 :rule symm :premises (@p22)) % 169.02/169.57 (step @p24 :rule cong :premises (@p23) :args ((forall @t14 (or @t52 @t76)))) % 169.02/169.57 (step @p25 :rule trans :premises (@p24 @p17)) % 169.02/169.57 (step @p26 :rule trans :premises (@p25 @p16)) % 169.02/169.57 (step @p27 :rule bool-impl-elim :args (@t51 @t76)) % 169.02/169.57 (step @p28 :rule cong :premises (@p27) :args ((forall @t14 (=> @t51 @t76)))) % 169.02/169.57 (step @p29 :rule trans :premises (@p28 @p26)) % 169.02/169.57 (step @p30 :rule refl :args (@t74)) % 169.02/169.57 (step @p31 :rule refl :args (@t4)) % 169.02/169.57 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t4 @t74))) % 169.02/169.57 (step @p33 :rule symm :premises (@p32)) % 169.02/169.57 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 169.02/169.57 (step @p35 :rule refl :args (@t75)) % 169.02/169.57 (step @p36 :rule refl :args (@t7)) % 169.02/169.57 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t7 @t75))) % 169.02/169.57 (step @p38 :rule symm :premises (@p37)) % 169.02/169.57 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 169.02/169.57 (step @p40 :rule cong :premises (@p39) :args (@t77)) % 169.02/169.57 (step @p41 :rule nary_cong :premises (@p40 @p34) :args (@t78)) % 169.02/169.57 (step @p42 :rule cong :premises (@p41) :args ((forall @t8 @t78))) % 169.02/169.57 (step @p43 :rule bool-impl-elim :args (@t7 @t4)) % 169.02/169.57 (step @p44 :rule cong :premises (@p43) :args (@t9)) % 169.02/169.57 (step @p45 :rule trans :premises (@p44 @p42)) % 169.02/169.57 (step @p46 :rule refl :args (@t49)) % 169.02/169.57 (step @p47 :rule refl :args (@t10)) % 169.02/169.57 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t10 @t49))) % 169.02/169.57 (step @p49 :rule symm :premises (@p48)) % 169.02/169.57 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 169.02/169.57 (step @p51 :rule refl :args (@t50)) % 169.02/169.57 (step @p52 :rule refl :args (@t11)) % 169.02/169.57 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t11 @t50))) % 169.02/169.57 (step @p54 :rule symm :premises (@p53)) % 169.02/169.57 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 169.02/169.57 (step @p56 :rule cong :premises (@p55) :args (@t79)) % 169.02/169.57 (step @p57 :rule nary_cong :premises (@p56 @p50) :args (@t80)) % 169.02/169.57 (step @p58 :rule cong :premises (@p57) :args ((forall @t8 @t80))) % 169.02/169.57 (step @p59 :rule bool-impl-elim :args (@t11 @t10)) % 169.02/169.57 (step @p60 :rule cong :premises (@p59) :args (@t12)) % 169.02/169.57 (step @p61 :rule trans :premises (@p60 @p58)) % 169.02/169.57 (step @p62 :rule cong :premises (@p61 @p45) :args (@t13)) % 169.02/169.57 (step @p63 :rule cong :premises (@p62) :args (@t15)) % 169.02/169.57 (step @p64 :rule trans :premises (@p63 @p29)) % 169.02/169.57 (step @p65 :rule refl :args (@t63)) % 169.02/169.57 (step @p66 :rule refl :args (@t17)) % 169.02/169.57 (step @p67 :rule cong :premises (@p66 @p65) :args ((= @t17 @t63))) % 169.02/169.57 (step @p68 :rule symm :premises (@p67)) % 169.02/169.57 (step @p69 :rule eq_resolve :premises (@p66 @p68)) % 169.02/169.57 (step @p70 :rule refl :args (@t64)) % 169.02/169.57 (step @p71 :rule refl :args (@t18)) % 169.02/169.57 (step @p72 :rule cong :premises (@p71 @p70) :args ((= @t18 @t64))) % 169.02/169.57 (step @p73 :rule symm :premises (@p72)) % 169.02/169.57 (step @p74 :rule eq_resolve :premises (@p71 @p73)) % 169.02/169.57 (step @p75 :rule nary_cong :premises (@p74 @p69) :args (@t19)) % 169.02/169.57 (step @p76 :rule cong :premises (@p75) :args (@t21)) % 169.02/169.57 (step @p77 :rule refl :args (@t65)) % 169.02/169.57 (step @p78 :rule refl :args (@t23)) % 169.02/169.57 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t23 @t65))) % 169.02/169.57 (step @p80 :rule symm :premises (@p79)) % 169.02/169.57 (step @p81 :rule eq_resolve :premises (@p78 @p80)) % 169.02/169.57 (step @p82 :rule refl :args (@t66)) % 169.02/169.57 (step @p83 :rule refl :args (@t24)) % 169.02/169.57 (step @p84 :rule cong :premises (@p83 @p82) :args ((= @t24 @t66))) % 169.02/169.57 (step @p85 :rule symm :premises (@p84)) % 169.02/169.57 (step @p86 :rule eq_resolve :premises (@p83 @p85)) % 169.02/169.57 (step @p87 :rule nary_cong :premises (@p86 @p81) :args (@t25)) % 169.02/169.57 (step @p88 :rule cong :premises (@p87) :args (@t27)) % 169.02/169.57 (step @p89 :rule refl :args (tptp.cK)) % 169.02/169.57 (step @p90 :rule ho_cong :premises (@p89 @p88)) % 169.02/169.57 (step @p91 :rule cong :premises (@p90 @p76) :args (@t28)) % 169.02/169.57 (step @p92 :rule cong :premises (@p91) :args (@t29)) % 169.02/169.57 (step @p93 :rule cong :premises (@p92 @p64) :args (@t30)) % 169.02/169.57 (step @p94 :rule cong :premises (@p93) :args (@t31)) % 169.02/169.57 (step @p95 :rule trans :premises (@p94 @p14 @p13 @p8 @p7)) % 169.02/169.57 (step @p96 :rule eq_resolve :premises (@p1 @p95)) % 169.02/169.57 (step @p97 :rule not_implies_elim2 :premises (@p96)) % 169.02/169.57 (step @p98 :rule skolemize :premises (@p97)) % 169.02/169.57 (step @p99 :rule cnf_or_neg :args (@t90 2)) % 169.02/169.57 (step @p100 :rule chain_m_resolution :premises (@p99 @p98) :args (@t91 @t92 @t93)) % 169.02/169.57 (step @p101 :rule not_implies_elim1 :premises (@p96)) % 169.02/169.57 (step @p102 :rule instantiate :premises (@p101) :args (@t94)) % 169.02/169.57 (step @p103 :rule eq-symm :args (@t98 @t99)) % 169.02/169.57 (step @p104 :rule cong :premises (@p103) :args (@t100)) % 169.02/169.57 ; trust TRUST PREPROCESS_HO_ELIM % 169.02/169.57 (step @p105 :rule trust :premises () :args ((= @t103 @t100))) % 169.02/169.57 (step @p106 :rule trans :premises (@p105 @p104)) % 169.02/169.57 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 169.02/169.57 (step @p107 :rule trust :premises () :args (@t103)) % 169.02/169.57 (step @p108 :rule eq_resolve :premises (@p107 @p106)) % 169.02/169.57 (step @p109 :rule instantiate :premises (@p108) :args ((@list @t85 @t82 @t81))) % 169.02/169.57 (step @p110 :rule bool-double-not-elim :args (@t86)) % 169.02/169.57 (step @p111 :rule refl :args (@t90)) % 169.02/169.57 (step @p112 :rule nary_cong :premises (@p111 @p110) :args ((or @t90 (not @t87)))) % 169.02/169.57 (step @p113 :rule cnf_or_neg :args (@t90 1)) % 169.02/169.57 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 169.02/169.57 (step @p115 :rule reordering :premises (@p114) :args ((or @t86 @t90))) % 169.02/169.57 (step @p116 :rule chain_m_resolution :premises (@p115 @p98) :args (@t86 @t92 @t93)) % 169.02/169.57 (step @p117 :rule cnf_or_neg :args (@t104 0)) % 169.02/169.57 (step @p118 :rule reordering :premises (@p117) :args ((or @t87 @t104))) % 169.02/169.57 (step @p119 :rule chain_m_resolution :premises (@p118 @p116) :args (@t104 @t105 (@list @t86))) % 169.02/169.57 (step @p120 :rule cnf_equiv_pos2 :args (@t108)) % 169.02/169.57 (step @p121 :rule reordering :premises (@p120) :args ((or @t107 (not @t104) (not @t108)))) % 169.02/169.57 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p109) :args (@t107 @t109 (@list @t104 @t108))) % 169.02/169.57 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 169.02/169.57 (step @p123 :rule trust :premises () :args (@t118)) % 169.02/169.57 (step @p124 :rule refl :args (@t119)) % 169.02/169.57 (step @p125 :rule refl :args (@t82)) % 169.02/169.57 (step @p126 :rule eq-symm :args (@t85 @t110)) % 169.02/169.57 (step @p127 :rule cong :premises (@p126 @p125 @p124) :args (@t120)) % 169.02/169.57 (step @p128 :rule refl :args (@t115)) % 169.02/169.57 (step @p129 :rule cong :premises (@p128 @p127) :args (@t121)) % 169.02/169.57 (step @p130 :rule cong :premises (@p129) :args (@t122)) % 169.02/169.57 (step @p131 :rule cong :premises (@p130) :args (@t123)) % 169.02/169.57 (step @p132 :rule cong :premises (@p131) :args (@t124)) % 169.02/169.57 (step @p133 :rule cong :premises (@p132) :args (@t125)) % 169.02/169.57 (step @p134 :rule refl :args (@t118)) % 169.02/169.57 (step @p135 :rule cong :premises (@p134 @p133) :args ((=> @t118 @t125))) % 169.02/169.57 (assume-push @p434 @t118) % 169.02/169.57 (step @p137 :rule instantiate :premises (@p123) :args ((@list @t34 @t82 @t85))) % 169.02/169.57 (step-pop @p435 :rule scope :premises (@p137)) % 169.02/169.57 (step @p138 :rule process_scope :premises (@p435) :args (@t125)) % 169.02/169.57 (step @p140 :rule eq_resolve :premises (@p138 @p135)) % 169.02/169.57 (step @p141 :rule implies_elim :premises (@p140)) % 169.02/169.57 (step @p142 :rule chain_m_resolution :premises (@p141 @p123) :args (@t128 @t105 (@list @t118))) % 169.02/169.57 (step @p143 :rule refl :args (@t131)) % 169.02/169.57 (step @p144 :rule bool-double-not-elim :args (@t127)) % 169.02/169.57 (step @p145 :rule nary_cong :premises (@p144 @p143) :args ((or (not @t128) @t131))) % 169.02/169.57 (step @p146 :rule eq-symm :args (@t130 @t126)) % 169.02/169.57 (step @p147 :rule cong :premises (@p146) :args (@t132)) % 169.02/169.57 (step @p148 :rule bool-double-not-elim :args (@t132)) % 169.02/169.57 (step @p149 :rule trans :premises (@p148 @p147)) % 169.02/169.57 (step @p150 :rule refl :args (@t128)) % 169.02/169.57 (step @p151 :rule cong :premises (@p150 @p149) :args ((=> @t128 @t133))) % 169.02/169.57 (assume-push @p436 @t128) % 169.02/169.57 (step @p153 :rule skolemize :premises (@p142)) % 169.02/169.57 (step-pop @p437 :rule scope :premises (@p153)) % 169.02/169.57 (step @p154 :rule process_scope :premises (@p437) :args (@t133)) % 169.02/169.57 (step @p156 :rule eq_resolve :premises (@p154 @p151)) % 169.02/169.57 (step @p157 :rule implies_elim :premises (@p156)) % 169.02/169.57 (step @p158 :rule eq_resolve :premises (@p157 @p145)) % 169.02/169.57 (step @p159 :rule chain_m_resolution :premises (@p158 @p142) :args (@t131 @t92 (@list @t127))) % 169.02/169.57 (step @p160 :rule eq-refl :args (@t135)) % 169.02/169.57 (step @p161 :rule skolem_intro :args (@t136)) % 169.02/169.57 (step @p162 :rule refl :args (@t135)) % 169.02/169.57 (step @p163 :rule cong :premises (@p162 @p161) :args ((= @t135 @t136))) % 169.02/169.57 (step @p164 :rule trans :premises (@p163 @p160)) % 169.02/169.57 (step @p165 :rule true_elim :premises (@p164)) % 169.02/169.57 (step @p166 :rule refl :args (@t137)) % 169.02/169.57 (step @p167 :rule cong :premises (@p166 @p165) :args (@t138)) % 169.02/169.57 (step @p168 :rule cong :premises (@p143 @p167) :args ((=> @t131 @t138))) % 169.02/169.57 (step @p169 :rule eq-symm :args (@t135 @t137)) % 169.02/169.57 (step @p170 :rule refl :args (@t83)) % 169.02/169.57 (step @p171 :rule eq-symm :args (@t82 @t85)) % 169.02/169.57 (step @p172 :rule cong :premises (@p171 @p125 @p170) :args (@t139)) % 169.02/169.57 (step @p173 :rule cong :premises (@p172 @p166) :args (@t140)) % 169.02/169.57 (step @p174 :rule trans :premises (@p173 @p169)) % 169.02/169.57 (step @p175 :rule cong :premises (@p143 @p174) :args ((=> @t131 @t140))) % 169.02/169.57 (assume-push @p438 @t131) % 169.02/169.57 (step @p177 :rule instantiate :premises (@p159) :args ((@list @t82))) % 169.02/169.57 (step-pop @p439 :rule scope :premises (@p177)) % 169.02/169.57 (step @p178 :rule process_scope :premises (@p439) :args (@t140)) % 169.02/169.57 (step @p180 :rule eq_resolve :premises (@p178 @p175)) % 169.02/169.57 (step @p181 :rule eq_resolve :premises (@p180 @p168)) % 169.02/169.57 (step @p182 :rule implies_elim :premises (@p181)) % 169.02/169.57 (step @p183 :rule chain_m_resolution :premises (@p182 @p159) :args (@t141 @t105 @t142)) % 169.02/169.57 (step @p184 :rule refl :args (@t143)) % 169.02/169.57 (step @p185 :rule bool-double-not-elim :args (@t84)) % 169.02/169.57 (step @p186 :rule refl :args (@t87)) % 169.02/169.57 (step @p187 :rule nary_cong :premises (@p186 @p185 @p184) :args ((or @t87 @t144 @t143))) % 169.02/169.57 (assume-push @p440 @t86) % 169.02/169.57 (assume-push @p441 @t134) % 169.02/169.57 (assume-push @p442 @t91) % 169.02/169.57 (step @p191 :rule evaluate :args ((= false true))) % 169.02/169.57 (step @p192 :rule true_intro :premises (@p116)) % 169.02/169.57 (step @p193 :rule refl :args (@t81)) % 169.02/169.57 (step @p194 :rule symm :premises (@p441)) % 169.02/169.57 (step @p195 :rule refl :args (@t34)) % 169.02/169.57 (step @p196 :rule cong :premises (@p195 @p194) :args (@t83)) % 169.02/169.57 (step @p197 :rule cong :premises (@p196 @p193) :args (@t84)) % 169.02/169.57 (step @p198 :rule false_intro :premises (@p100)) % 169.02/169.57 (step @p199 :rule symm :premises (@p198)) % 169.02/169.57 (step @p200 :rule trans :premises (@p199 @p197 @p192)) % 169.02/169.57 (step @p201 false :rule eq_resolve :premises (@p200 @p191)) % 169.02/169.57 (step-pop @p443 :rule scope :premises (@p201)) % 169.02/169.57 (step-pop @p444 :rule scope :premises (@p443)) % 169.02/169.57 (step-pop @p445 :rule scope :premises (@p444)) % 169.02/169.57 (step @p202 :rule process_scope :premises (@p445) :args (false)) % 169.02/169.57 (assume-push @p446 @t86) % 169.02/169.57 (assume-push @p447 @t91) % 169.02/169.57 (assume-push @p448 @t134) % 169.02/169.57 (step @p209 :rule and_intro :premises (@p116 @p448 @p100)) % 169.02/169.57 (step-pop @p449 :rule scope :premises (@p209)) % 169.02/169.57 (step-pop @p450 :rule scope :premises (@p449)) % 169.02/169.57 (step-pop @p451 :rule scope :premises (@p450)) % 169.02/169.57 (step @p210 :rule process_scope :premises (@p451) :args (@t145)) % 169.02/169.57 (step @p214 :rule implies_elim :premises (@p210)) % 169.02/169.57 (step @p215 :rule resolution :premises (@p214 @p202) :args (true @t145)) % 169.02/169.57 (step @p216 :rule not_and :premises (@p215)) % 169.02/169.57 (step @p217 :rule eq_resolve :premises (@p216 @p187)) % 169.02/169.57 (step @p218 :rule chain_m_resolution :premises (@p217 @p116 @p100) :args (@t143 @t146 (@list @t86 @t84))) % 169.02/169.57 (step @p219 :rule eq-symm :args (@t136 @t83)) % 169.02/169.57 (step @p220 :rule eq-symm :args (@t136 @t82)) % 169.02/169.57 (step @p221 :rule refl :args (@t134)) % 169.02/169.57 (step @p222 :rule cong :premises (@p221 @p220 @p219) :args ((ite @t134 (= @t136 @t82) (= @t136 @t83)))) % 169.02/169.57 (step @p223 :rule cong :premises (@p165 @p170) :args (@t147)) % 169.02/169.57 (step @p224 :rule cong :premises (@p165 @p125) :args (@t148)) % 169.02/169.57 (step @p225 :rule cong :premises (@p221 @p224 @p223) :args ((ite @t134 @t148 @t147))) % 169.02/169.57 (step @p226 :rule ite_eq :args (@t135)) % 169.02/169.57 (step @p227 :rule eq_resolve :premises (@p226 @p225)) % 169.02/169.57 (step @p228 :rule eq_resolve :premises (@p227 @p222)) % 169.02/169.57 (step @p229 :rule ite_elim2 :premises (@p228)) % 169.02/169.57 (step @p230 :rule chain_m_resolution :premises (@p229 @p218) :args (@t149 @t92 (@list @t134))) % 169.02/169.57 (step @p231 :rule eq-refl :args (@t153)) % 169.02/169.57 (step @p232 :rule skolem_intro :args (@t154)) % 169.02/169.57 (step @p233 :rule refl :args (@t153)) % 169.02/169.57 (step @p234 :rule cong :premises (@p233 @p232) :args ((= @t153 @t154))) % 169.02/169.57 (step @p235 :rule trans :premises (@p234 @p231)) % 169.02/169.57 (step @p236 :rule true_elim :premises (@p235)) % 169.02/169.57 (step @p237 :rule refl :args (@t155)) % 169.02/169.57 (step @p238 :rule cong :premises (@p237 @p236) :args (@t156)) % 169.02/169.57 (step @p239 :rule cong :premises (@p143 @p238) :args ((=> @t131 @t156))) % 169.02/169.57 (step @p240 :rule eq-symm :args (@t153 @t155)) % 169.02/169.57 (step @p241 :rule refl :args (@t151)) % 169.02/169.57 (step @p242 :rule eq-symm :args (@t150 @t85)) % 169.02/169.57 (step @p243 :rule cong :premises (@p242 @p125 @p241) :args (@t157)) % 169.02/169.57 (step @p244 :rule cong :premises (@p243 @p237) :args (@t158)) % 169.02/169.57 (step @p245 :rule trans :premises (@p244 @p240)) % 169.02/169.57 (step @p246 :rule cong :premises (@p143 @p245) :args ((=> @t131 @t158))) % 169.02/169.57 (assume-push @p452 @t131) % 169.02/169.57 (step @p248 :rule instantiate :premises (@p159) :args ((@list @t150))) % 169.02/169.57 (step-pop @p453 :rule scope :premises (@p248)) % 169.02/169.57 (step @p249 :rule process_scope :premises (@p453) :args (@t158)) % 169.02/169.57 (step @p251 :rule eq_resolve :premises (@p249 @p246)) % 169.02/169.57 (step @p252 :rule eq_resolve :premises (@p251 @p239)) % 169.02/169.57 (step @p253 :rule implies_elim :premises (@p252)) % 169.02/169.57 (step @p254 :rule chain_m_resolution :premises (@p253 @p159) :args (@t159 @t105 @t142)) % 169.02/169.57 (step @p255 :rule eq-symm :args (@t163 @t164)) % 169.02/169.57 (step @p256 :rule cong :premises (@p255) :args (@t165)) % 169.02/169.57 ; trust TRUST PREPROCESS_HO_ELIM % 169.02/169.57 (step @p257 :rule trust :premises () :args ((= @t168 @t165))) % 169.02/169.57 (step @p258 :rule trans :premises (@p257 @p256)) % 169.02/169.57 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 169.02/169.57 (step @p259 :rule trust :premises () :args (@t168)) % 169.02/169.57 (step @p260 :rule eq_resolve :premises (@p259 @p258)) % 169.02/169.57 (step @p261 :rule instantiate :premises (@p260) :args ((@list @t85 @t82 @t173))) % 169.02/169.57 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 169.02/169.57 (step @p262 :rule trust :premises () :args ((forall (@list @t175 @t174) (or (not (forall @t171 (= (_ @t36 @t175 @t169) (_ @t36 @t174 @t169)))) (= @t175 @t174))))) % 169.02/169.57 (step @p263 :rule instantiate :premises (@p262) :args (@t94)) % 169.02/169.57 (step @p264 :rule cnf_or_pos :args (@t177)) % 169.02/169.57 (step @p265 :rule reordering :premises (@p264) :args ((or @t176 @t134 (not @t177)))) % 169.02/169.57 (step @p266 :rule chain_m_resolution :premises (@p265 @p218 @p263) :args (@t176 @t178 (@list @t134 @t177))) % 169.02/169.57 (step @p267 :rule refl :args (@t182)) % 169.02/169.57 (step @p268 :rule bool-double-not-elim :args (@t172)) % 169.02/169.57 (step @p269 :rule nary_cong :premises (@p268 @p267) :args ((or (not @t176) @t182))) % 169.02/169.57 (assume-push @p454 @t176) % 169.02/169.57 (step @p271 :rule skolemize :premises (@p454)) % 169.02/169.57 (step-pop @p455 :rule scope :premises (@p271)) % 169.02/169.57 (step @p272 :rule process_scope :premises (@p455) :args (@t182)) % 169.02/169.57 (step @p274 :rule implies_elim :premises (@p272)) % 169.02/169.57 (step @p275 :rule eq_resolve :premises (@p274 @p269)) % 169.02/169.57 (step @p276 :rule chain_m_resolution :premises (@p275 @p266) :args (@t182 @t92 (@list @t172))) % 169.02/169.57 (step @p277 :rule cnf_equiv_neg2 :args (@t181)) % 169.02/169.57 (step @p278 :rule bool-double-not-elim :args (@t88)) % 169.02/169.57 (step @p279 :rule nary_cong :premises (@p111 @p278) :args ((or @t90 (not @t89)))) % 169.02/169.57 (step @p280 :rule cnf_or_neg :args (@t90 0)) % 169.02/169.57 (step @p281 :rule eq_resolve :premises (@p280 @p279)) % 169.02/169.57 (step @p282 :rule reordering :premises (@p281) :args ((or @t88 @t90))) % 169.02/169.57 (step @p283 :rule chain_m_resolution :premises (@p282 @p98) :args (@t88 @t92 @t93)) % 169.02/169.57 (step @p284 :rule instantiate :premises (@p283) :args ((@list @t173))) % 169.02/169.57 (step @p285 :rule cnf_or_pos :args (@t184)) % 169.02/169.57 (step @p286 :rule reordering :premises (@p285) :args ((or @t179 @t183 (not @t184)))) % 169.02/169.57 (step @p287 :rule chain_m_resolution :premises (@p286 @p284 @p277) :args ((or @t181 @t183) @t146 (@list @t184 @t179))) % 169.02/169.57 (step @p288 :rule chain_m_resolution :premises (@p287 @p276) :args (@t183 @t92 (@list @t181))) % 169.02/169.57 (step @p289 :rule cnf_equiv_neg1 :args (@t181)) % 169.02/169.57 (step @p290 :rule reordering :premises (@p289) :args ((or @t180 @t179 @t181))) % 169.02/169.57 (step @p291 :rule chain_m_resolution :premises (@p290 @p288 @p276) :args (@t179 (@list true true) (@list @t180 @t181))) % 169.02/169.57 (step @p292 :rule cnf_or_neg :args (@t185 1)) % 169.02/169.57 (step @p293 :rule reordering :premises (@p292) :args ((or (not @t179) @t185))) % 169.02/169.57 (step @p294 :rule chain_m_resolution :premises (@p293 @p291) :args (@t185 @t105 (@list @t179))) % 169.02/169.57 (step @p295 :rule cnf_equiv_pos2 :args (@t187)) % 169.02/169.57 (step @p296 :rule reordering :premises (@p295) :args ((or @t186 (not @t185) (not @t187)))) % 169.02/169.57 (step @p297 :rule chain_m_resolution :premises (@p296 @p294 @p261) :args (@t186 @t109 (@list @t185 @t187))) % 169.02/169.57 (step @p298 :rule refl :args (@t188)) % 169.02/169.57 (step @p299 :rule refl :args (@t189)) % 169.02/169.57 (step @p300 :rule bool-double-not-elim :args (@t180)) % 169.02/169.57 (step @p301 :rule nary_cong :premises (@p300 @p299 @p298) :args ((or (not @t183) @t189 @t188))) % 169.02/169.57 (assume-push @p456 @t186) % 169.02/169.57 (assume-push @p457 @t152) % 169.02/169.57 (assume-push @p458 @t183) % 169.02/169.57 (step @p305 :rule evaluate :args (@t190)) % 169.02/169.57 (step @p306 :rule false_intro :premises (@p458)) % 169.02/169.57 (step @p307 :rule refl :args (@t173)) % 169.02/169.57 (step @p308 :rule symm :premises (@p457)) % 169.02/169.57 (step @p309 :rule cong :premises (@p308 @p307) :args (@t186)) % 169.02/169.57 (step @p310 :rule true_intro :premises (@p456)) % 169.02/169.57 (step @p311 :rule symm :premises (@p310)) % 169.02/169.57 (step @p312 :rule trans :premises (@p311 @p309 @p306)) % 169.02/169.57 (step @p313 false :rule eq_resolve :premises (@p312 @p305)) % 169.02/169.57 (step-pop @p459 :rule scope :premises (@p313)) % 169.02/169.57 (step-pop @p460 :rule scope :premises (@p459)) % 169.02/169.57 (step-pop @p461 :rule scope :premises (@p460)) % 169.02/169.57 (step @p314 :rule process_scope :premises (@p461) :args (false)) % 169.02/169.57 (assume-push @p462 @t183) % 169.02/169.57 (assume-push @p463 @t152) % 169.02/169.57 (assume-push @p464 @t186) % 169.02/169.57 (step @p321 :rule and_intro :premises (@p464 @p463 @p462)) % 169.02/169.57 (step-pop @p465 :rule scope :premises (@p321)) % 169.02/169.57 (step-pop @p466 :rule scope :premises (@p465)) % 169.02/169.57 (step-pop @p467 :rule scope :premises (@p466)) % 169.02/169.57 (step @p322 :rule process_scope :premises (@p467) :args (@t191)) % 169.02/169.57 (step @p326 :rule implies_elim :premises (@p322)) % 169.02/169.57 (step @p327 :rule resolution :premises (@p326 @p314) :args (true @t191)) % 169.02/169.57 (step @p328 :rule not_and :premises (@p327)) % 169.02/169.57 (step @p329 :rule eq_resolve :premises (@p328 @p301)) % 169.02/169.57 (step @p330 :rule chain_m_resolution :premises (@p329 @p288 @p297) :args (@t189 @t178 (@list @t180 @t186))) % 169.02/169.57 (step @p331 :rule eq-symm :args (@t154 @t151)) % 169.02/169.57 (step @p332 :rule eq-symm :args (@t154 @t82)) % 169.02/169.57 (step @p333 :rule refl :args (@t152)) % 169.02/169.57 (step @p334 :rule cong :premises (@p333 @p332 @p331) :args ((ite @t152 (= @t154 @t82) (= @t154 @t151)))) % 169.02/169.57 (step @p335 :rule cong :premises (@p236 @p241) :args (@t192)) % 169.02/169.57 (step @p336 :rule cong :premises (@p236 @p125) :args (@t193)) % 169.02/169.57 (step @p337 :rule cong :premises (@p333 @p336 @p335) :args ((ite @t152 @t193 @t192))) % 169.02/169.57 (step @p338 :rule ite_eq :args (@t153)) % 169.02/169.57 (step @p339 :rule eq_resolve :premises (@p338 @p337)) % 169.02/169.57 (step @p340 :rule eq_resolve :premises (@p339 @p334)) % 169.02/169.57 (step @p341 :rule ite_elim2 :premises (@p340)) % 169.02/169.57 (step @p342 :rule chain_m_resolution :premises (@p341 @p330) :args (@t194 @t92 (@list @t152))) % 169.02/169.57 (step @p343 :rule instantiate :premises (@p262) :args ((@list @t82 @t150))) % 169.02/169.57 (step @p344 :rule cnf_equiv_neg2 :args (@t199)) % 169.02/169.57 (step @p345 :rule cnf_or_neg :args (@t201 1)) % 169.02/169.57 (step @p346 :rule reordering :premises (@p345) :args ((or @t202 @t201))) % 169.02/169.57 (step @p347 :rule instantiate :premises (@p260) :args ((@list @t85 @t82 @t196))) % 169.02/169.57 (step @p348 :rule cnf_equiv_pos2 :args (@t203)) % 169.02/169.57 (step @p349 :rule reordering :premises (@p348) :args ((or @t197 @t205 @t204))) % 169.02/169.57 (step @p350 :rule chain_m_resolution :premises (@p349 @p347 @p346 @p344) :args ((or @t199 @t202) (@list false false true) (@list @t203 @t201 @t197))) % 169.02/169.57 (step @p351 :rule cnf_equiv_neg1 :args (@t199)) % 169.02/169.57 (step @p352 :rule reordering :premises (@p351) :args ((or @t198 @t197 @t199))) % 169.02/169.57 (step @p353 :rule instantiate :premises (@p283) :args ((@list @t196))) % 169.02/169.57 (step @p354 :rule cnf_or_pos :args (@t207)) % 169.02/169.57 (step @p355 :rule reordering :premises (@p354) :args ((or @t198 @t206 (not @t207)))) % 169.02/169.57 (step @p356 :rule cnf_equiv_pos1 :args (@t203)) % 169.02/169.57 (step @p357 :rule reordering :premises (@p356) :args ((or (not @t197) @t201 @t204))) % 169.02/169.57 (step @p358 :rule cnf_or_pos :args (@t201)) % 169.02/169.57 (step @p359 :rule reordering :premises (@p358) :args ((or @t198 @t200 @t205))) % 169.02/169.57 (step @p360 :rule chain_m_resolution :premises (@p359 @p357 @p347 @p355 @p353 @p352 @p350) :args (@t199 (@list false false true false false true) (@list @t201 @t203 @t200 @t207 @t197 @t198))) % 169.02/169.57 (step @p361 :rule refl :args (@t208)) % 169.02/169.57 (step @p362 :rule bool-double-not-elim :args (@t195)) % 169.02/169.57 (step @p363 :rule nary_cong :premises (@p362 @p361) :args ((or (not @t209) @t208))) % 169.02/169.57 (assume-push @p468 @t209) % 169.02/169.57 (step @p365 :rule skolemize :premises (@p468)) % 169.02/169.57 (step-pop @p469 :rule scope :premises (@p365)) % 169.02/169.57 (step @p366 :rule process_scope :premises (@p469) :args (@t208)) % 169.02/169.57 (step @p368 :rule implies_elim :premises (@p366)) % 169.02/169.57 (step @p369 :rule eq_resolve :premises (@p368 @p363)) % 169.02/169.57 (step @p370 :rule chain_m_resolution :premises (@p369 @p360) :args (@t195 @t105 (@list @t199))) % 169.02/169.57 (step @p371 :rule cnf_or_pos :args (@t211)) % 169.02/169.57 (step @p372 :rule reordering :premises (@p371) :args ((or @t210 @t209 (not @t211)))) % 169.02/169.57 (step @p373 :rule chain_m_resolution :premises (@p372 @p370 @p343) :args (@t210 @t109 (@list @t195 @t211))) % 169.02/169.57 (step @p374 :rule refl :args (@t212)) % 169.02/169.57 (step @p375 :rule refl :args (@t213)) % 169.02/169.57 (step @p376 :rule refl :args (@t214)) % 169.02/169.57 (step @p377 :rule refl :args (@t215)) % 169.02/169.57 (step @p378 :rule refl :args (@t216)) % 169.02/169.57 (step @p379 :rule refl :args (@t217)) % 169.02/169.57 (step @p380 :rule refl :args (@t219)) % 169.02/169.57 (step @p381 :rule nary_cong :premises (@p185 @p380 @p379 @p378 @p377 @p376 @p375 @p374) :args ((or @t144 @t219 @t217 @t216 @t215 @t214 @t213 @t212))) % 169.02/169.57 (assume-push @p470 @t91) % 169.02/169.57 (assume-push @p471 @t149) % 169.02/169.57 (assume-push @p472 @t141) % 169.02/169.57 (assume-push @p473 @t210) % 169.02/169.57 (assume-push @p474 @t159) % 169.02/169.57 (assume-push @p475 @t194) % 169.02/169.57 (assume-push @p476 @t218) % 169.02/169.57 (assume-push @p477 @t107) % 169.02/169.57 (step @p305 :rule evaluate :args (@t190)) % 169.02/169.57 (step @p198 :rule false_intro :premises (@p100)) % 169.02/169.57 (step @p193 :rule refl :args (@t81)) % 169.02/169.57 (step @p390 :rule symm :premises (@p471)) % 169.02/169.57 (step @p391 :rule symm :premises (@p473)) % 169.02/169.57 (step @p392 :rule refl :args (@t129)) % 169.02/169.57 (step @p393 :rule cong :premises (@p392 @p391) :args (@t155)) % 169.02/169.57 (step @p394 :rule symm :premises (@p254)) % 169.02/169.57 (step @p395 :rule symm :premises (@p102)) % 169.02/169.57 (step @p396 :rule trans :premises (@p395 @p475 @p394 @p393 @p183 @p390)) % 169.02/169.57 (step @p397 :rule cong :premises (@p396 @p193) :args (@t107)) % 169.02/169.57 (step @p398 :rule true_intro :premises (@p122)) % 169.02/169.57 (step @p399 :rule symm :premises (@p398)) % 169.02/169.57 (step @p400 :rule trans :premises (@p399 @p397 @p198)) % 169.02/169.57 (step @p401 false :rule eq_resolve :premises (@p400 @p305)) % 169.02/169.57 (step-pop @p478 :rule scope :premises (@p401)) % 169.02/169.57 (step-pop @p479 :rule scope :premises (@p478)) % 169.02/169.57 (step-pop @p480 :rule scope :premises (@p479)) % 169.02/169.57 (step-pop @p481 :rule scope :premises (@p480)) % 169.02/169.57 (step-pop @p482 :rule scope :premises (@p481)) % 169.02/169.57 (step-pop @p483 :rule scope :premises (@p482)) % 169.02/169.57 (step-pop @p484 :rule scope :premises (@p483)) % 169.02/169.57 (step-pop @p485 :rule scope :premises (@p484)) % 169.02/169.57 (step @p402 :rule process_scope :premises (@p485) :args (false)) % 169.02/169.57 (assume-push @p486 @t91) % 169.02/169.57 (assume-push @p487 @t218) % 169.02/169.57 (assume-push @p488 @t107) % 169.02/169.57 (assume-push @p489 @t141) % 169.02/169.57 (assume-push @p490 @t149) % 169.02/169.57 (assume-push @p491 @t210) % 169.02/169.57 (assume-push @p492 @t159) % 169.02/169.57 (assume-push @p493 @t194) % 169.02/169.57 (step @p419 :rule and_intro :premises (@p100 @p490 @p183 @p491 @p254 @p493 @p102 @p122)) % 169.02/169.57 (step-pop @p494 :rule scope :premises (@p419)) % 169.02/169.57 (step-pop @p495 :rule scope :premises (@p494)) % 169.02/169.57 (step-pop @p496 :rule scope :premises (@p495)) % 169.02/169.57 (step-pop @p497 :rule scope :premises (@p496)) % 169.02/169.57 (step-pop @p498 :rule scope :premises (@p497)) % 169.02/169.57 (step-pop @p499 :rule scope :premises (@p498)) % 169.02/169.57 (step-pop @p500 :rule scope :premises (@p499)) % 169.02/169.57 (step-pop @p501 :rule scope :premises (@p500)) % 169.02/169.57 (step @p420 :rule process_scope :premises (@p501) :args (@t220)) % 169.02/169.57 (step @p429 :rule implies_elim :premises (@p420)) % 169.02/169.57 (step @p430 :rule resolution :premises (@p429 @p402) :args (true @t220)) % 169.02/169.57 (step @p431 :rule not_and :premises (@p430)) % 169.02/169.57 (step @p432 :rule eq_resolve :premises (@p431 @p381)) % 169.02/169.57 (step @p433 false :rule chain_m_resolution :premises (@p432 @p373 @p342 @p254 @p230 @p183 @p122 @p102 @p100) :args (false (@list false false false false false false false true) (@list @t210 @t194 @t159 @t149 @t141 @t107 @t218 @t84))) % 169.02/169.57 ) % 169.02/169.57 % SZS output end Proof % 169.02/169.57 % cvc5 exiting %------------------------------------------------------------------------------