%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV010^5 : 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 : n025.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 08:55:18 AM UTC 2026 % Result : Theorem 169.11s 169.67s % Output : Proof 169.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV010^5 : 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 : n025.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 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 18:07:16 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.49 %----Proving TH0 % 169.11/169.67 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 169.11/169.67 --- 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... % 169.11/169.67 --- 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... % 169.11/169.67 --- Run --ho-elim --full-saturate-quant at 18s... % 169.11/169.67 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 169.11/169.67 % SZS status Theorem % 169.11/169.67 % SZS output start Proof % 169.11/169.67 ( % 169.11/169.67 (declare-sort tptp.a 0) % 169.11/169.67 (define @t1 () (@var "Xp" (-> tptp.a Bool))) % 169.11/169.67 (define @t2 () (@var "Xq" (-> tptp.a Bool))) % 169.11/169.67 (define @t3 () (@var "Xx" tptp.a)) % 169.11/169.67 (define @t4 () (_ @t2 @t3)) % 169.11/169.67 (define @t5 () (@var "Xy" tptp.a)) % 169.11/169.67 (define @t6 () (@var "Xx0" tptp.a)) % 169.11/169.67 (define @t7 () (@var "R" (-> tptp.a tptp.a Bool))) % 169.11/169.67 (define @t8 () (_ (_ @t7 @t6) @t5)) % 169.11/169.67 (define @t9 () (_ @t2 @t5)) % 169.11/169.67 (define @t10 () (@list @t5)) % 169.11/169.67 (define @t11 () (forall @t10 (= @t9 @t8))) % 169.11/169.67 (define @t12 () (_ @t2 @t6)) % 169.11/169.67 (define @t13 () (=> @t12 @t11)) % 169.11/169.67 (define @t14 () (@list @t6)) % 169.11/169.67 (define @t15 () (forall @t14 @t13)) % 169.11/169.67 (define @t16 () (@var "Xz" tptp.a)) % 169.11/169.67 (define @t17 () (_ @t2 @t16)) % 169.11/169.67 (define @t18 () (@list @t16)) % 169.11/169.67 (define @t19 () (exists @t18 @t17)) % 169.11/169.67 (define @t20 () (and @t19 @t15 @t4)) % 169.11/169.67 (define @t21 () (=> @t20 (= @t2 @t1))) % 169.11/169.67 (define @t22 () (@list @t2)) % 169.11/169.67 (define @t23 () (forall @t22 @t21)) % 169.11/169.67 (define @t24 () (_ @t1 @t3)) % 169.11/169.67 (define @t25 () (_ @t1 @t5)) % 169.11/169.67 (define @t26 () (= @t25 @t8)) % 169.11/169.67 (define @t27 () (forall @t10 @t26)) % 169.11/169.67 (define @t28 () (_ @t1 @t6)) % 169.11/169.67 (define @t29 () (=> @t28 @t27)) % 169.11/169.67 (define @t30 () (forall @t14 @t29)) % 169.11/169.67 (define @t31 () (_ @t1 @t16)) % 169.11/169.67 (define @t32 () (exists @t18 @t31)) % 169.11/169.67 (define @t33 () (and @t32 @t30 @t24 @t23)) % 169.11/169.67 (define @t34 () (@list @t1)) % 169.11/169.67 (define @t35 () (exists @t34 @t33)) % 169.11/169.67 (define @t36 () (@list @t3)) % 169.11/169.67 (define @t37 () (forall @t36 @t35)) % 169.11/169.67 (define @t38 () (_ @t7 @t3)) % 169.11/169.67 (define @t39 () (_ @t38 @t5)) % 169.11/169.67 (define @t40 () (forall @t10 (= @t25 @t39))) % 169.11/169.67 (define @t41 () (=> @t24 @t40)) % 169.11/169.67 (define @t42 () (forall @t36 @t41)) % 169.11/169.67 (define @t43 () (and @t32 @t42)) % 169.11/169.67 (define @t44 () (=> @t43 @t32)) % 169.11/169.67 (define @t45 () (forall @t34 @t44)) % 169.11/169.67 (define @t46 () (and @t45 @t37)) % 169.11/169.67 (define @t47 () (_ @t38 @t16)) % 169.11/169.67 (define @t48 () (_ @t7 @t5)) % 169.11/169.67 (define @t49 () (_ @t48 @t16)) % 169.11/169.67 (define @t50 () (and @t39 @t49)) % 169.11/169.67 (define @t51 () (@list @t3 @t5 @t16)) % 169.11/169.67 (define @t52 () (forall @t51 (=> @t50 @t47))) % 169.11/169.67 (define @t53 () (_ @t48 @t3)) % 169.11/169.67 (define @t54 () (@list @t3 @t5)) % 169.11/169.67 (define @t55 () (forall @t54 (=> @t39 @t53))) % 169.11/169.67 (define @t56 () (_ @t38 @t3)) % 169.11/169.67 (define @t57 () (forall @t36 @t56)) % 169.11/169.67 (define @t58 () (and @t57 @t55 @t52)) % 169.11/169.67 (define @t59 () (=> @t58 @t46)) % 169.11/169.67 (define @t60 () (@list @t7)) % 169.11/169.67 (define @t61 () (forall @t60 @t59)) % 169.11/169.67 (define @t62 () (not @t61)) % 169.11/169.67 (define @t63 () (@var "BOUND_VARIABLE_7655" (@ho-elim-sort (-> tptp.a Bool)))) % 169.11/169.67 (define @t64 () (@var "BOUND_VARIABLE_7652" (@ho-elim-sort (-> tptp.a Bool)))) % 169.11/169.67 (define @t65 () (@var "BOUND_VARIABLE_7635" tptp.a)) % 169.11/169.67 (define @t66 () (@const 0 (-> (@ho-elim-sort (-> tptp.a Bool)) tptp.a Bool))) % 169.11/169.67 (define @t67 () (not (_ @t66 @t64 @t65))) % 169.11/169.67 (define @t68 () (@var "BOUND_VARIABLE_7576" tptp.a)) % 169.11/169.67 (define @t69 () (@var "BOUND_VARIABLE_7664" (@ho-elim-sort (-> tptp.a tptp.a Bool)))) % 169.11/169.67 (define @t70 () (@const 1 (-> (@ho-elim-sort (-> tptp.a tptp.a Bool)) tptp.a (@ho-elim-sort (-> tptp.a Bool))))) % 169.11/169.67 (define @t71 () (_ @t70 @t69 @t6)) % 169.11/169.67 (define @t72 () (_ @t66 @t71 @t68)) % 169.11/169.67 (define @t73 () (_ @t66 @t64 @t68)) % 169.11/169.67 (define @t74 () (not (_ @t66 @t64 @t6))) % 169.11/169.67 (define @t75 () (or @t74 (= @t72 @t73))) % 169.11/169.67 (define @t76 () (@list @t6 @t68)) % 169.11/169.67 (define @t77 () (forall @t76 @t75)) % 169.11/169.67 (define @t78 () (not @t77)) % 169.11/169.67 (define @t79 () (@var "BOUND_VARIABLE_7598" tptp.a)) % 169.11/169.67 (define @t80 () (not (_ @t66 @t64 @t79))) % 169.11/169.67 (define @t81 () (or @t80 @t78 @t67 (= @t63 @t64))) % 169.11/169.67 (define @t82 () (@list @t64 @t79)) % 169.11/169.67 (define @t83 () (forall @t82 @t81)) % 169.11/169.67 (define @t84 () (not @t83)) % 169.11/169.67 (define @t85 () (not (_ @t66 @t63 @t65))) % 169.11/169.67 (define @t86 () (@var "BOUND_VARIABLE_7547" tptp.a)) % 169.11/169.67 (define @t87 () (_ @t66 @t63 @t86)) % 169.11/169.67 (define @t88 () (_ @t66 @t71 @t86)) % 169.11/169.68 (define @t89 () (not (_ @t66 @t63 @t6))) % 169.11/169.68 (define @t90 () (or @t89 (= @t87 @t88))) % 169.11/169.68 (define @t91 () (@list @t6 @t86)) % 169.11/169.68 (define @t92 () (forall @t91 @t90)) % 169.11/169.68 (define @t93 () (not @t92)) % 169.11/169.68 (define @t94 () (@var "BOUND_VARIABLE_7616" tptp.a)) % 169.11/169.68 (define @t95 () (not (_ @t66 @t63 @t94))) % 169.11/169.68 (define @t96 () (or @t95 @t93 @t85 @t84)) % 169.11/169.68 (define @t97 () (@list @t63 @t94)) % 169.11/169.68 (define @t98 () (forall @t97 @t96)) % 169.11/169.68 (define @t99 () (not @t98)) % 169.11/169.68 (define @t100 () (_ @t70 @t69 @t3)) % 169.11/169.68 (define @t101 () (_ @t70 @t69 @t5)) % 169.11/169.68 (define @t102 () (not (_ @t66 @t100 @t5))) % 169.11/169.68 (define @t103 () (not (forall @t51 (or @t102 (not (_ @t66 @t101 @t16)) (_ @t66 @t100 @t16))))) % 169.11/169.68 (define @t104 () (not (forall @t54 (or @t102 (_ @t66 @t101 @t3))))) % 169.11/169.68 (define @t105 () (not (forall @t36 (_ @t66 @t100 @t3)))) % 169.11/169.68 (define @t106 () (or @t105 @t104 @t103 @t99)) % 169.11/169.68 (define @t107 () (@list @t69 @t65)) % 169.11/169.68 (define @t108 () (forall @t107 @t106)) % 169.11/169.68 (define @t109 () (not @t108)) % 169.11/169.68 (define @t110 () (= @t1 @t2)) % 169.11/169.68 (define @t111 () (= (_ @t7 @t6 @t68) (_ @t2 @t68))) % 169.11/169.68 (define @t112 () (_ @t2 @t6)) % 169.11/169.68 (define @t113 () (not @t112)) % 169.11/169.68 (define @t114 () (or @t113 @t111)) % 169.11/169.68 (define @t115 () (forall @t76 @t114)) % 169.11/169.68 (define @t116 () (not @t115)) % 169.11/169.68 (define @t117 () (not (_ @t2 @t79))) % 169.11/169.68 (define @t118 () (@list @t2 @t79)) % 169.11/169.68 (define @t119 () (= (_ @t1 @t86) (_ @t7 @t6 @t86))) % 169.11/169.68 (define @t120 () (_ @t1 @t6)) % 169.11/169.68 (define @t121 () (not @t120)) % 169.11/169.68 (define @t122 () (or @t121 @t119)) % 169.11/169.68 (define @t123 () (forall @t91 @t122)) % 169.11/169.68 (define @t124 () (not @t123)) % 169.11/169.68 (define @t125 () (not (_ @t1 @t94))) % 169.11/169.68 (define @t126 () (@list @t1 @t94)) % 169.11/169.68 (define @t127 () (not (forall @t126 (or @t125 @t124 (not (_ @t1 @t65)) (not (forall @t118 (or @t117 @t116 (not (_ @t2 @t65)) @t110))))))) % 169.11/169.68 (define @t128 () (_ @t7 @t3 @t16)) % 169.11/169.68 (define @t129 () (_ @t7 @t5 @t16)) % 169.11/169.68 (define @t130 () (_ @t7 @t3 @t5)) % 169.11/169.68 (define @t131 () (not @t130)) % 169.11/169.68 (define @t132 () (forall @t51 (or @t131 (not @t129) @t128))) % 169.11/169.68 (define @t133 () (not @t132)) % 169.11/169.68 (define @t134 () (_ @t7 @t5 @t3)) % 169.11/169.68 (define @t135 () (forall @t54 (or @t131 @t134))) % 169.11/169.68 (define @t136 () (not @t135)) % 169.11/169.68 (define @t137 () (_ @t7 @t3 @t3)) % 169.11/169.68 (define @t138 () (forall @t36 @t137)) % 169.11/169.68 (define @t139 () (not @t138)) % 169.11/169.68 (define @t140 () (or @t139 @t136 @t133 @t127)) % 169.11/169.68 (define @t141 () (forall (@list @t7 @t65) @t140)) % 169.11/169.68 (define @t142 () (@list @t65)) % 169.11/169.68 (define @t143 () (forall @t142 @t140)) % 169.11/169.68 (define @t144 () (forall @t142 @t127)) % 169.11/169.68 (define @t145 () (or @t139 @t136 @t133 @t144)) % 169.11/169.68 (define @t146 () (_ @t2 @t3)) % 169.11/169.68 (define @t147 () (not @t146)) % 169.11/169.68 (define @t148 () (or @t117 @t116 @t147 @t110)) % 169.11/169.68 (define @t149 () (forall @t118 @t148)) % 169.11/169.68 (define @t150 () (not @t149)) % 169.11/169.68 (define @t151 () (_ @t1 @t3)) % 169.11/169.68 (define @t152 () (not @t151)) % 169.11/169.68 (define @t153 () (or @t125 @t124 @t152 @t150)) % 169.11/169.68 (define @t154 () (forall @t126 @t153)) % 169.11/169.68 (define @t155 () (forall @t36 (not @t154))) % 169.11/169.68 (define @t156 () (or @t139 @t136 @t133 @t155)) % 169.11/169.68 (define @t157 () (or @t139 @t136 @t133)) % 169.11/169.68 (define @t158 () (and @t138 @t135 @t132)) % 169.11/169.68 (define @t159 () (@list @t94)) % 169.11/169.68 (define @t160 () (forall @t159 @t153)) % 169.11/169.68 (define @t161 () (forall @t159 @t125)) % 169.11/169.68 (define @t162 () (@list @t16)) % 169.11/169.68 (define @t163 () (or @t161 @t124 @t152 @t150)) % 169.11/169.68 (define @t164 () (_ @t1 @t16)) % 169.11/169.68 (define @t165 () (forall @t18 (not @t164))) % 169.11/169.68 (define @t166 () (not @t24)) % 169.11/169.68 (define @t167 () (or @t165 @t124 @t166 @t150)) % 169.11/169.68 (define @t168 () (not @t165)) % 169.11/169.68 (define @t169 () (not @t168)) % 169.11/169.68 (define @t170 () (or @t169 @t124 @t166 @t150)) % 169.11/169.68 (define @t171 () (and @t168 @t123 @t24 @t149)) % 169.11/169.68 (define @t172 () (forall @t34 (not @t171))) % 169.11/169.68 (define @t173 () (not @t172)) % 169.11/169.68 (define @t174 () (@list @t79)) % 169.11/169.68 (define @t175 () (forall @t174 @t148)) % 169.11/169.68 (define @t176 () (forall @t174 @t117)) % 169.11/169.68 (define @t177 () (or @t176 @t116 @t147 @t110)) % 169.11/169.68 (define @t178 () (_ @t2 @t16)) % 169.11/169.68 (define @t179 () (forall @t18 (not @t178))) % 169.11/169.68 (define @t180 () (not @t4)) % 169.11/169.68 (define @t181 () (or @t179 @t116 @t180 @t110)) % 169.11/169.68 (define @t182 () (not @t179)) % 169.11/169.68 (define @t183 () (not @t182)) % 169.11/169.68 (define @t184 () (or @t183 @t116 @t180)) % 169.11/169.68 (define @t185 () (and @t182 @t115 @t4)) % 169.11/169.68 (define @t186 () (@list @t68)) % 169.11/169.68 (define @t187 () (forall @t186 @t114)) % 169.11/169.68 (define @t188 () (forall @t186 @t111)) % 169.11/169.68 (define @t189 () (@list @t5)) % 169.11/169.68 (define @t190 () (or @t113 @t188)) % 169.11/169.68 (define @t191 () (_ @t2 @t5)) % 169.11/169.68 (define @t192 () (_ @t7 @t6 @t5)) % 169.11/169.68 (define @t193 () (forall @t10 (= @t192 @t191))) % 169.11/169.68 (define @t194 () (not @t12)) % 169.11/169.68 (define @t195 () (or @t194 @t193)) % 169.11/169.68 (define @t196 () (= @t8 @t9)) % 169.11/169.68 (define @t197 () (not @t17)) % 169.11/169.68 (define @t198 () (forall @t18 @t197)) % 169.11/169.68 (define @t199 () (not @t198)) % 169.11/169.68 (define @t200 () (@list @t86)) % 169.11/169.68 (define @t201 () (forall @t200 @t122)) % 169.11/169.68 (define @t202 () (forall @t200 @t119)) % 169.11/169.68 (define @t203 () (or @t121 @t202)) % 169.11/169.68 (define @t204 () (_ @t1 @t5)) % 169.11/169.68 (define @t205 () (forall @t10 (= @t204 @t192))) % 169.11/169.68 (define @t206 () (not @t28)) % 169.11/169.68 (define @t207 () (or @t206 @t205)) % 169.11/169.68 (define @t208 () (not @t31)) % 169.11/169.68 (define @t209 () (forall @t18 @t208)) % 169.11/169.68 (define @t210 () (not @t209)) % 169.11/169.68 (define @t211 () (@var "BOUND_VARIABLE_7520" tptp.a)) % 169.11/169.68 (define @t212 () (= (_ @t7 @t3 @t211) (_ @t1 @t211))) % 169.11/169.68 (define @t213 () (or @t152 @t212)) % 169.11/169.68 (define @t214 () (forall (@list @t3 @t211) @t213)) % 169.11/169.68 (define @t215 () (not @t214)) % 169.11/169.68 (define @t216 () (and @t168 @t214)) % 169.11/169.68 (define @t217 () (@list @t211)) % 169.11/169.68 (define @t218 () (forall @t217 @t213)) % 169.11/169.68 (define @t219 () (forall @t217 @t212)) % 169.11/169.68 (define @t220 () (or @t152 @t219)) % 169.11/169.68 (define @t221 () (forall @t10 (= @t130 @t204))) % 169.11/169.68 (define @t222 () (or @t166 @t221)) % 169.11/169.68 (define @t223 () (= @t39 @t25)) % 169.11/169.68 (define @t224 () (not @t49)) % 169.11/169.68 (define @t225 () (not @t39)) % 169.11/169.68 (define @t226 () (or @t225 @t224 @t47)) % 169.11/169.68 (define @t227 () (or @t225 @t53)) % 169.11/169.68 (define @t228 () (= @t64 @t63)) % 169.11/169.68 (define @t229 () (forall @t107 (or @t105 @t104 @t103 (not (forall @t97 (or @t95 (not (forall @t91 (or @t89 (= @t88 @t87)))) @t85 (not (forall @t82 (or @t80 (not (forall @t76 (or @t74 (= @t73 @t72)))) @t67 @t228))))))))) % 169.11/169.68 (define @t230 () (@quantifiers_skolemize @t229 1)) % 169.11/169.68 (define @t231 () (not (_ @t66 @t64 @t230))) % 169.11/169.68 (define @t232 () (@quantifiers_skolemize @t229 0)) % 169.11/169.68 (define @t233 () (_ @t70 @t232 @t6)) % 169.11/169.68 (define @t234 () (_ @t66 @t233 @t68)) % 169.11/169.68 (define @t235 () (not (forall @t76 (or @t74 (= @t73 @t234))))) % 169.11/169.68 (define @t236 () (not (forall @t82 (or @t80 @t235 @t231 @t228)))) % 169.11/169.68 (define @t237 () (not (_ @t66 @t63 @t230))) % 169.11/169.68 (define @t238 () (_ @t66 @t233 @t86)) % 169.11/169.68 (define @t239 () (forall @t97 (or @t95 (not (forall @t91 (or @t89 (= @t87 @t238)))) @t237 @t236))) % 169.11/169.68 (define @t240 () (not @t239)) % 169.11/169.68 (define @t241 () (_ @t70 @t232 @t3)) % 169.11/169.68 (define @t242 () (_ @t70 @t232 @t5)) % 169.11/169.68 (define @t243 () (not (_ @t66 @t241 @t5))) % 169.11/169.68 (define @t244 () (forall @t51 (or @t243 (not (_ @t66 @t242 @t16)) (_ @t66 @t241 @t16)))) % 169.11/169.68 (define @t245 () (not @t244)) % 169.11/169.68 (define @t246 () (forall @t54 (or @t243 (_ @t66 @t242 @t3)))) % 169.11/169.68 (define @t247 () (not @t246)) % 169.11/169.68 (define @t248 () (forall @t36 (_ @t66 @t241 @t3))) % 169.11/169.68 (define @t249 () (not @t248)) % 169.11/169.68 (define @t250 () (or @t249 @t247 @t245 @t240)) % 169.11/169.68 (define @t251 () (not @t250)) % 169.11/169.68 (define @t252 () (not @t229)) % 169.11/169.68 (define @t253 () (or @t89 (= @t238 @t87))) % 169.11/169.68 (define @t254 () (forall @t91 @t253)) % 169.11/169.68 (define @t255 () (not @t254)) % 169.11/169.68 (define @t256 () (or @t95 @t255 @t237 @t236)) % 169.11/169.68 (define @t257 () (forall @t97 @t256)) % 169.11/169.68 (define @t258 () (not @t257)) % 169.11/169.68 (define @t259 () (or @t249 @t247 @t245 @t258)) % 169.11/169.68 (define @t260 () (not @t259)) % 169.11/169.68 (define @t261 () (@list true)) % 169.11/169.68 (define @t262 () (@list @t250)) % 169.11/169.68 (define @t263 () (_ @t70 @t232 @t230)) % 169.11/169.68 (define @t264 () (_ @t66 @t263 @t86)) % 169.11/169.68 (define @t265 () (not (_ @t66 @t263 @t6))) % 169.11/169.68 (define @t266 () (forall @t91 (or @t265 (= @t238 @t264)))) % 169.11/169.68 (define @t267 () (@quantifiers_skolemize @t266 0)) % 169.11/169.68 (define @t268 () (forall @t82 (or @t80 @t235 @t231 (= @t64 @t263)))) % 169.11/169.68 (define @t269 () (not @t268)) % 169.11/169.68 (define @t270 () (_ @t66 @t263 @t230)) % 169.11/169.68 (define @t271 () (not @t270)) % 169.11/169.68 (define @t272 () (or @t265 (= @t264 @t238))) % 169.11/169.68 (define @t273 () (forall @t91 @t272)) % 169.11/169.68 (define @t274 () (not @t273)) % 169.11/169.68 (define @t275 () (or @t271 @t274 @t271 @t269)) % 169.11/169.68 (define @t276 () (not @t266)) % 169.11/169.68 (define @t277 () (or @t271 @t276 @t271 @t269)) % 169.11/169.68 (define @t278 () (@list false)) % 169.11/169.68 (define @t279 () (@quantifiers_skolemize @t268 0)) % 169.11/169.68 (define @t280 () (_ @t66 @t279 @t68)) % 169.11/169.68 (define @t281 () (not (_ @t66 @t279 @t6))) % 169.11/169.68 (define @t282 () (forall @t76 (or @t281 (= @t234 @t280)))) % 169.11/169.68 (define @t283 () (= @t263 @t279)) % 169.11/169.68 (define @t284 () (_ @t66 @t279 @t230)) % 169.11/169.68 (define @t285 () (not @t284)) % 169.11/169.68 (define @t286 () (not @t282)) % 169.11/169.68 (define @t287 () (not (_ @t66 @t279 (@quantifiers_skolemize @t268 1)))) % 169.11/169.68 (define @t288 () (or @t287 @t286 @t285 @t283)) % 169.11/169.68 (define @t289 () (@var "y" (@ho-elim-sort (-> tptp.a Bool)))) % 169.11/169.68 (define @t290 () (@var "x" (@ho-elim-sort (-> tptp.a Bool)))) % 169.11/169.68 (define @t291 () (@var "z" tptp.a)) % 169.11/169.68 (define @t292 () (@list @t291)) % 169.11/169.68 (define @t293 () (forall @t292 (= (_ @t66 @t263 @t291) (_ @t66 @t279 @t291)))) % 169.11/169.68 (define @t294 () (not @t293)) % 169.11/169.68 (define @t295 () (or @t294 @t283)) % 169.11/169.68 (define @t296 () (@quantifiers_skolemize @t293 0)) % 169.11/169.68 (define @t297 () (= (_ @t66 @t263 @t296) (_ @t66 @t279 @t296))) % 169.11/169.68 (define @t298 () (not @t297)) % 169.11/169.68 (define @t299 () (or @t285 @t297)) % 169.11/169.68 (define @t300 () (not @t288)) % 169.11/169.68 (define @t301 () (or @t281 (= @t280 @t234))) % 169.11/169.68 (define @t302 () (forall @t76 @t301)) % 169.11/169.68 (define @t303 () (not @t302)) % 169.11/169.68 (define @t304 () (or @t287 @t303 @t285 (= @t279 @t263))) % 169.11/169.68 (define @t305 () (not @t304)) % 169.11/169.68 (define @t306 () (@quantifiers_skolemize @t266 1)) % 169.11/169.68 (define @t307 () (_ @t66 @t263 @t306)) % 169.11/169.68 (define @t308 () (_ @t70 @t232 @t267)) % 169.11/169.68 (define @t309 () (_ @t66 @t308 @t306)) % 169.11/169.68 (define @t310 () (= @t309 @t307)) % 169.11/169.68 (define @t311 () (_ @t66 @t263 @t267)) % 169.11/169.68 (define @t312 () (not @t311)) % 169.11/169.68 (define @t313 () (or @t312 @t310)) % 169.11/169.68 (define @t314 () (not @t313)) % 169.11/169.68 (define @t315 () (@list @t313)) % 169.11/169.68 (define @t316 () (_ @t66 @t308 @t230)) % 169.11/169.68 (define @t317 () (or @t312 @t316)) % 169.11/169.68 (define @t318 () (not @t309)) % 169.11/169.68 (define @t319 () (or @t312 @t318 @t307)) % 169.11/169.68 (define @t320 () (@list true false)) % 169.11/169.68 (define @t321 () (not @t307)) % 169.11/169.68 (define @t322 () (not @t316)) % 169.11/169.68 (define @t323 () (or @t322 @t321 @t309)) % 169.11/169.68 (define @t324 () (not @t323)) % 169.11/169.68 (assume @p1 @t62) % 169.11/169.68 (assume @p2 true) % 169.11/169.68 (step @p3 :rule eq-symm :args (@t63 @t64)) % 169.11/169.68 (step @p4 :rule refl :args (@t67)) % 169.11/169.68 (step @p5 :rule eq-symm :args (@t72 @t73)) % 169.11/169.68 (step @p6 :rule refl :args (@t74)) % 169.11/169.68 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t75)) % 169.11/169.68 (step @p8 :rule cong :premises (@p7) :args 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:args (@t99)) % 169.11/169.68 (step @p24 :rule refl :args (@t103)) % 169.11/169.68 (step @p25 :rule refl :args (@t104)) % 169.11/169.68 (step @p26 :rule refl :args (@t105)) % 169.11/169.68 (step @p27 :rule nary_cong :premises (@p26 @p25 @p24 @p23) :args (@t106)) % 169.11/169.68 (step @p28 :rule cong :premises (@p27) :args (@t108)) % 169.11/169.68 (step @p29 :rule cong :premises (@p28) :args (@t109)) % 169.11/169.68 ; WARNING: add trust step for TRUST % 169.11/169.68 ; trust TRUST PREPROCESS_HO_ELIM % 169.11/169.68 (step @p30 :rule trust :premises () :args ((= (not @t141) @t109))) % 169.11/169.68 (step @p31 :rule quant-merge-prenex :args ((= (forall @t60 @t143) @t141))) % 169.11/169.68 (step @p32 :rule alpha_equiv :args (@t144 (@list @t65) (@list @t3))) % 169.11/169.68 (step @p33 :rule refl :args (@t133)) % 169.11/169.68 (step @p34 :rule refl :args (@t136)) % 169.11/169.68 (step @p35 :rule refl :args (@t139)) % 169.11/169.68 (step @p36 :rule nary_cong :premises (@p35 @p34 @p33 @p32) :args (@t145)) % 169.11/169.68 (step @p37 :rule quant-miniscope-or :args ((= @t143 @t145))) % 169.11/169.68 (step @p38 :rule trans :premises (@p37 @p36)) % 169.11/169.68 (step @p39 :rule symm :premises (@p38)) % 169.11/169.68 (step @p40 :rule cong :premises (@p39) :args ((forall @t60 @t156))) % 169.11/169.68 (step @p41 :rule trans :premises (@p40 @p31)) % 169.11/169.68 (step @p42 :rule aci_norm :args ((= (or @t157 @t155) @t156))) % 169.11/169.68 (step @p43 :rule refl :args (@t155)) % 169.11/169.68 (step @p44 :rule aci_norm :args ((= (or @t139 (or @t136 @t133)) @t157))) % 169.11/169.68 (step @p45 :rule bool-and-de-morgan :args (@t135 @t132 true)) % 169.11/169.68 (step @p46 :rule nary_cong :premises (@p35 @p45) :args ((or @t139 (not (and @t135 @t132))))) % 169.11/169.68 (step @p47 :rule bool-and-de-morgan :args (@t138 @t135 (and @t132))) % 169.11/169.68 (step @p48 :rule trans :premises (@p47 @p46)) % 169.11/169.68 (step @p49 :rule trans :premises (@p48 @p44)) % 169.11/169.68 (step @p50 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(@t166)) % 169.11/169.68 (step @p79 :rule bool-double-not-elim :args (@t165)) % 169.11/169.68 (step @p80 :rule nary_cong :premises (@p79 @p60 @p78 @p58) :args (@t170)) % 169.11/169.68 (step @p81 :rule aci_norm :args ((= (or @t169 (or @t124 (or @t166 @t150))) @t170))) % 169.11/169.68 (step @p82 :rule trans :premises (@p81 @p80)) % 169.11/169.68 (step @p83 :rule bool-and-de-morgan :args (@t24 @t149 true)) % 169.11/169.68 (step @p84 :rule nary_cong :premises (@p60 @p83) :args ((or @t124 (not (and @t24 @t149))))) % 169.11/169.68 (step @p85 :rule bool-and-de-morgan :args (@t123 @t24 (and @t149))) % 169.11/169.68 (step @p86 :rule trans :premises (@p85 @p84)) % 169.11/169.68 (step @p87 :rule refl :args (@t169)) % 169.11/169.68 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((or @t169 (not (and @t123 @t24 @t149))))) % 169.11/169.68 (step @p89 :rule bool-and-de-morgan :args (@t168 @t123 (and @t24 @t149))) % 169.11/169.68 (step @p90 :rule trans :premises (@p89 @p88)) % 169.11/169.68 (step @p91 :rule trans :premises (@p90 @p82)) % 169.11/169.68 (step @p92 :rule cong :premises (@p91) :args (@t172)) % 169.11/169.68 (step @p93 :rule trans :premises (@p92 @p77)) % 169.11/169.68 (step @p94 :rule cong :premises (@p93) :args (@t173)) % 169.11/169.68 (step @p95 :rule exists-elim :args ((= (exists @t34 @t171) @t173))) % 169.11/169.68 (step @p96 :rule trans :premises (@p95 @p94)) % 169.11/169.68 (step @p97 :rule quant-merge-prenex :args ((= (forall @t22 @t175) @t149))) % 169.11/169.68 (step @p98 :rule refl :args (@t110)) % 169.11/169.68 (step @p99 :rule refl :args (@t147)) % 169.11/169.68 (step @p100 :rule refl :args (@t116)) % 169.11/169.68 (step @p101 :rule alpha_equiv :args (@t176 (@list @t79) @t162)) % 169.11/169.68 (step @p102 :rule nary_cong :premises (@p101 @p100 @p99 @p98) :args (@t177)) % 169.11/169.68 (step @p103 :rule quant-miniscope-or :args ((= @t175 @t177))) % 169.11/169.68 (step @p104 :rule trans :premises (@p103 @p102)) % 169.11/169.68 (step @p105 :rule symm 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implies_elim :premises (@p396)) % 169.11/169.68 (step @p398 :rule chain_m_resolution :premises (@p397 @p381) :args (@t277 @t278 (@list @t239))) % 169.11/169.68 (step @p399 :rule bool-double-not-elim :args (@t282)) % 169.11/169.68 (step @p400 :rule refl :args (@t288)) % 169.11/169.68 (step @p401 :rule nary_cong :premises (@p400 @p399) :args ((or @t288 (not @t286)))) % 169.11/169.68 (step @p402 :rule cnf_or_neg :args (@t288 1)) % 169.11/169.68 (step @p403 :rule eq_resolve :premises (@p402 @p401)) % 169.11/169.68 (step @p404 :rule reordering :premises (@p403) :args ((or @t282 @t288))) % 169.11/169.68 (step @p405 :rule bool-double-not-elim :args (@t284)) % 169.11/169.68 (step @p406 :rule nary_cong :premises (@p400 @p405) :args ((or @t288 (not @t285)))) % 169.11/169.68 (step @p407 :rule cnf_or_neg :args (@t288 2)) % 169.11/169.68 (step @p408 :rule eq_resolve :premises (@p407 @p406)) % 169.11/169.68 (step @p409 :rule reordering :premises (@p408) :args ((or @t284 @t288))) % 169.11/169.68 (step @p410 :rule cnf_or_neg :args (@t288 3)) % 169.11/169.68 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 169.11/169.68 (step @p411 :rule trust :premises () :args ((forall (@list @t290 @t289) (or (not (forall @t292 (= (_ @t66 @t290 @t291) (_ @t66 @t289 @t291)))) (= @t290 @t289))))) % 169.11/169.68 (step @p412 :rule instantiate :premises (@p411) :args ((@list @t263 @t279))) % 169.11/169.68 (step @p413 :rule cnf_or_pos :args (@t295)) % 169.11/169.68 (step @p414 :rule reordering :premises (@p413) :args ((or @t283 @t294 (not @t295)))) % 169.11/169.68 (step @p415 :rule refl :args (@t298)) % 169.11/169.68 (step @p416 :rule bool-double-not-elim :args (@t293)) % 169.11/169.68 (step @p417 :rule nary_cong :premises (@p416 @p415) :args ((or (not @t294) @t298))) % 169.11/169.68 (assume-push @p509 @t294) % 169.11/169.68 (step @p419 :rule skolemize :premises (@p509)) % 169.11/169.68 (step-pop @p510 :rule scope :premises (@p419)) % 169.11/169.68 (step @p420 :rule process_scope :premises (@p510) :args (@t298)) % 169.11/169.68 (step @p422 :rule implies_elim :premises (@p420)) % 169.11/169.68 (step @p423 :rule eq_resolve :premises (@p422 @p417)) % 169.11/169.68 (step @p424 :rule cnf_or_pos :args (@t299)) % 169.11/169.68 (step @p425 :rule reordering :premises (@p424) :args ((or @t285 @t297 (not @t299)))) % 169.11/169.68 (assume-push @p511 @t282) % 169.11/169.68 (step @p427 :rule instantiate :premises (@p511) :args ((@list @t230 @t296))) % 169.11/169.68 (step-pop @p512 :rule scope :premises (@p427)) % 169.11/169.68 (step @p428 :rule process_scope :premises (@p512) :args (@t299)) % 169.11/169.68 (step @p430 :rule implies_elim :premises (@p428)) % 169.11/169.68 (step @p431 :rule chain_m_resolution :premises (@p430 @p425 @p423 @p414 @p412 @p410 @p409 @p404) :args (@t288 (@list true true true false true false false) (@list @t299 @t297 @t293 @t295 @t283 @t284 @t282))) % 169.11/169.68 (step @p432 :rule refl :args (@t300)) % 169.11/169.68 (step @p433 :rule bool-double-not-elim :args (@t268)) % 169.11/169.68 (step @p434 :rule nary_cong :premises (@p433 @p432) :args ((or (not @t269) @t300))) % 169.11/169.68 (step @p435 :rule eq-symm :args (@t279 @t263)) % 169.11/169.68 (step @p436 :rule refl :args (@t285)) % 169.11/169.68 (step @p437 :rule eq-symm :args (@t280 @t234)) % 169.11/169.68 (step @p438 :rule refl :args (@t281)) % 169.11/169.68 (step @p439 :rule nary_cong :premises (@p438 @p437) :args (@t301)) % 169.11/169.68 (step @p440 :rule cong :premises (@p439) :args (@t302)) % 169.11/169.68 (step @p441 :rule cong :premises (@p440) :args (@t303)) % 169.11/169.68 (step @p442 :rule refl :args (@t287)) % 169.11/169.68 (step @p443 :rule nary_cong :premises (@p442 @p441 @p436 @p435) :args (@t304)) % 169.11/169.68 (step @p444 :rule cong :premises (@p443) :args (@t305)) % 169.11/169.68 (step @p445 :rule cong :premises (@p382 @p444) :args ((=> @t269 @t305))) % 169.11/169.68 (assume-push @p513 @t269) % 169.11/169.68 (step @p447 :rule skolemize :premises (@p513)) % 169.11/169.68 (step-pop @p514 :rule scope :premises (@p447)) % 169.11/169.68 (step @p448 :rule process_scope :premises (@p514) :args (@t305)) % 169.11/169.68 (step @p450 :rule eq_resolve :premises (@p448 @p445)) % 169.11/169.68 (step @p451 :rule implies_elim :premises (@p450)) % 169.11/169.68 (step @p452 :rule eq_resolve :premises (@p451 @p434)) % 169.11/169.68 (step @p453 :rule chain_m_resolution :premises (@p452 @p431) :args (@t268 @t278 (@list @t288))) % 169.11/169.68 (step @p454 :rule bool-double-not-elim :args (@t248)) % 169.11/169.68 (step @p455 :rule nary_cong :premises (@p363 @p454) :args ((or @t250 (not @t249)))) % 169.11/169.68 (step @p456 :rule cnf_or_neg :args (@t250 0)) % 169.11/169.68 (step @p457 :rule eq_resolve :premises (@p456 @p455)) % 169.11/169.68 (step @p458 :rule reordering :premises (@p457) :args ((or @t248 @t250))) % 169.11/169.68 (step @p459 :rule chain_m_resolution :premises (@p458 @p361) :args (@t248 @t261 @t262)) % 169.11/169.68 (step @p460 :rule instantiate :premises (@p459) :args ((@list @t230))) % 169.11/169.68 (step @p461 :rule cnf_or_pos :args (@t277)) % 169.11/169.68 (step @p462 :rule factoring :premises (@p461)) % 169.11/169.68 (step @p463 :rule reordering :premises (@p462) :args ((or @t271 @t269 @t276 (not @t277)))) % 169.11/169.68 (step @p464 :rule chain_m_resolution :premises (@p463 @p460 @p453 @p398) :args (@t276 (@list false false false) (@list @t270 @t268 @t277))) % 169.11/169.68 (step @p465 :rule refl :args (@t314)) % 169.11/169.68 (step @p466 :rule bool-double-not-elim :args (@t266)) % 169.11/169.68 (step @p467 :rule nary_cong :premises (@p466 @p465) :args ((or (not @t276) @t314))) % 169.11/169.68 (assume-push @p515 @t276) % 169.11/169.68 (step @p469 :rule skolemize :premises (@p515)) % 169.11/169.68 (step-pop @p516 :rule scope :premises (@p469)) % 169.11/169.68 (step @p470 :rule process_scope :premises (@p516) :args (@t314)) % 169.11/169.68 (step @p472 :rule implies_elim :premises (@p470)) % 169.11/169.68 (step @p473 :rule eq_resolve :premises (@p472 @p467)) % 169.11/169.68 (step @p474 :rule chain_m_resolution :premises (@p473 @p464) :args (@t314 @t261 (@list @t266))) % 169.11/169.68 (step @p475 :rule bool-double-not-elim :args (@t311)) % 169.11/169.68 (step @p476 :rule refl :args (@t313)) % 169.11/169.68 (step @p477 :rule nary_cong :premises (@p476 @p475) :args ((or @t313 (not @t312)))) % 169.11/169.68 (step @p478 :rule cnf_or_neg :args (@t313 0)) % 169.11/169.68 (step @p479 :rule eq_resolve :premises (@p478 @p477)) % 169.11/169.68 (step @p480 :rule reordering :premises (@p479) :args ((or @t311 @t313))) % 169.11/169.68 (step @p481 :rule chain_m_resolution :premises (@p480 @p474) :args (@t311 @t261 @t315)) % 169.11/169.68 (step @p482 :rule cnf_or_pos :args (@t317)) % 169.11/169.68 (step @p483 :rule reordering :premises (@p482) :args ((or @t312 @t316 (not @t317)))) % 169.11/169.68 (step @p484 :rule chain_m_resolution :premises (@p483 @p481 @p375) :args (@t316 (@list false false) (@list @t311 @t317))) % 169.11/169.68 (step @p485 :rule cnf_or_neg :args (@t313 1)) % 169.11/169.68 (step @p486 :rule chain_m_resolution :premises (@p485 @p474) :args ((not @t310) @t261 @t315)) % 169.11/169.68 (step @p487 :rule cnf_equiv_neg2 :args (@t310)) % 169.11/169.68 (step @p488 :rule instantiate :premises (@p368) :args ((@list @t230 @t267 @t306))) % 169.11/169.68 (step @p489 :rule cnf_or_pos :args (@t319)) % 169.11/169.68 (step @p490 :rule reordering :premises (@p489) :args ((or @t312 @t307 @t318 (not @t319)))) % 169.11/169.68 (step @p491 :rule chain_m_resolution :premises (@p490 @p488 @p487) :args ((or @t312 @t310 @t318) (@list false true) (@list @t319 @t307))) % 169.11/169.68 (step @p492 :rule chain_m_resolution :premises (@p491 @p486 @p481) :args (@t318 @t320 (@list @t310 @t311))) % 169.11/169.68 (step @p493 :rule cnf_equiv_neg1 :args (@t310)) % 169.11/169.68 (step @p494 :rule reordering :premises (@p493) :args ((or @t309 @t307 @t310))) % 169.11/169.68 (step @p495 :rule chain_m_resolution :premises (@p494 @p492 @p486) :args (@t307 (@list true true) (@list @t309 @t310))) % 169.11/169.68 (step @p496 :rule cnf_or_pos :args (@t323)) % 169.11/169.68 (step @p497 :rule reordering :premises (@p496) :args ((or @t309 @t321 @t322 @t324))) % 169.11/169.68 (step @p498 :rule chain_m_resolution :premises (@p497 @p492 @p495 @p484) :args (@t324 (@list true false false) (@list @t309 @t307 @t316))) % 169.11/169.68 (assume-push @p517 @t244) % 169.11/169.68 (step @p500 :rule instantiate :premises (@p368) :args ((@list @t267 @t230 @t306))) % 169.11/169.68 (step-pop @p518 :rule scope :premises (@p500)) % 169.11/169.68 (step @p501 :rule process_scope :premises (@p518) :args (@t323)) % 169.11/169.68 (step @p503 :rule implies_elim :premises (@p501)) % 169.11/169.68 (step @p504 false :rule chain_m_resolution :premises (@p503 @p498 @p368) :args (false @t320 (@list @t323 @t244))) % 169.11/169.68 ) % 169.11/169.68 % SZS output end Proof % 169.11/169.68 % cvc5 exiting %------------------------------------------------------------------------------