%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV107^5 : 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 : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:55:27 AM UTC 2026 % Result : Theorem 2.41s 2.68s % Output : Proof 2.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV107^5 : 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 % 0.17/0.34 % Computer : n017.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 18:12:01 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 2.41/2.68 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 2.41/2.68 % SZS status Theorem % 2.41/2.68 % SZS output start Proof % 2.41/2.68 ( % 2.41/2.68 (declare-sort $$unsorted 0) % 2.41/2.68 (declare-sort tptp.a 0) % 2.41/2.68 (declare-const tptp.cS (-> $$unsorted $$unsorted Bool)) % 2.41/2.68 (declare-const tptp.f (-> tptp.a $$unsorted Bool)) % 2.41/2.68 (declare-const tptp.cR (-> tptp.a tptp.a Bool)) % 2.41/2.68 (declare-const tptp.z tptp.a) % 2.41/2.68 (define @t1 () (@var "Xx" tptp.a)) % 2.41/2.68 (define @t2 () (_ tptp.cR @t1)) % 2.41/2.68 (define @t3 () (_ @t2 tptp.z)) % 2.41/2.68 (define @t4 () (@var "Xy" $$unsorted)) % 2.41/2.68 (define @t5 () (@var "Xw" tptp.a)) % 2.41/2.68 (define @t6 () (not (_ (_ tptp.f @t5) @t4))) % 2.41/2.68 (define @t7 () (and @t6 @t3)) % 2.41/2.68 (define @t8 () (_ tptp.f @t1)) % 2.41/2.68 (define @t9 () (_ @t8 @t4)) % 2.41/2.68 (define @t10 () (@list @t5)) % 2.41/2.68 (define @t11 () (forall @t10 (or @t9 @t7))) % 2.41/2.68 (define @t12 () (@list @t1)) % 2.41/2.68 (define @t13 () (exists @t12 @t11)) % 2.41/2.68 (define @t14 () (@list @t4)) % 2.41/2.68 (define @t15 () (forall @t14 @t13)) % 2.41/2.68 (define @t16 () (@var "Xx2" tptp.a)) % 2.41/2.68 (define @t17 () (@var "Xx1" tptp.a)) % 2.41/2.68 (define @t18 () (_ tptp.cR @t17)) % 2.41/2.68 (define @t19 () (_ @t18 @t16)) % 2.41/2.68 (define @t20 () (_ (_ tptp.cR @t16) tptp.z)) % 2.41/2.68 (define @t21 () (and @t6 @t20)) % 2.41/2.68 (define @t22 () (_ (_ tptp.f @t16) @t4)) % 2.41/2.68 (define @t23 () (forall @t10 (or @t22 @t21))) % 2.41/2.68 (define @t24 () (_ @t18 tptp.z)) % 2.41/2.68 (define @t25 () (and @t6 @t24)) % 2.41/2.68 (define @t26 () (_ (_ tptp.f @t17) @t4)) % 2.41/2.68 (define @t27 () (forall @t10 (or @t26 @t25))) % 2.41/2.68 (define @t28 () (and @t27 @t23)) % 2.41/2.68 (define @t29 () (=> @t28 @t19)) % 2.41/2.68 (define @t30 () (@list @t4 @t17 @t16)) % 2.41/2.68 (define @t31 () (forall @t30 @t29)) % 2.41/2.68 (define @t32 () (exists @t14 @t11)) % 2.41/2.68 (define @t33 () (forall @t12 @t32)) % 2.41/2.68 (define @t34 () (and @t33 @t31 @t15)) % 2.41/2.68 (define @t35 () (and @t26 @t22)) % 2.41/2.68 (define @t36 () (@list @t17 @t16 @t4)) % 2.41/2.68 (define @t37 () (forall @t36 (=> @t35 @t19))) % 2.41/2.68 (define @t38 () (@var "Xy2" $$unsorted)) % 2.41/2.68 (define @t39 () (@var "Xy1" $$unsorted)) % 2.41/2.68 (define @t40 () (_ (_ tptp.cS @t39) @t38)) % 2.41/2.68 (define @t41 () (_ @t8 @t38)) % 2.41/2.68 (define @t42 () (_ @t8 @t39)) % 2.41/2.68 (define @t43 () (and @t42 @t41)) % 2.41/2.68 (define @t44 () (@list @t1 @t39 @t38)) % 2.41/2.68 (define @t45 () (forall @t44 (=> @t43 @t40))) % 2.41/2.68 (define @t46 () (exists @t14 @t9)) % 2.41/2.68 (define @t47 () (forall @t12 @t46)) % 2.41/2.68 (define @t48 () (and @t47 @t45 @t37)) % 2.41/2.68 (define @t49 () (=> @t48 @t34)) % 2.41/2.68 (define @t50 () (_ @t2 @t1)) % 2.41/2.68 (define @t51 () (forall @t12 @t50)) % 2.41/2.68 (define @t52 () (@var "Xu" tptp.a)) % 2.41/2.68 (define @t53 () (_ tptp.cR @t52)) % 2.41/2.68 (define @t54 () (_ @t53 @t5)) % 2.41/2.68 (define @t55 () (@var "Xv" tptp.a)) % 2.41/2.68 (define @t56 () (_ (_ tptp.cR @t5) @t55)) % 2.41/2.68 (define @t57 () (_ @t53 @t55)) % 2.41/2.68 (define @t58 () (and @t57 @t56)) % 2.41/2.68 (define @t59 () (@list @t52 @t55 @t5)) % 2.41/2.68 (define @t60 () (forall @t59 (=> @t58 @t54))) % 2.41/2.68 (define @t61 () (and @t60 @t51)) % 2.41/2.68 (define @t62 () (=> @t61 @t49)) % 2.41/2.68 (define @t63 () (not @t62)) % 2.41/2.68 (define @t64 () (@var "BOUND_VARIABLE_7678" tptp.a)) % 2.41/2.68 (define @t65 () (tptp.cR @t64 tptp.z)) % 2.41/2.68 (define @t66 () (@list @t64)) % 2.41/2.68 (define @t67 () (forall @t66 (not @t65))) % 2.41/2.68 (define @t68 () (not @t67)) % 2.41/2.68 (define @t69 () (@var "BOUND_VARIABLE_7705" tptp.a)) % 2.41/2.68 (define @t70 () (not (tptp.f @t69 @t4))) % 2.41/2.68 (define @t71 () (and @t70 @t68)) % 2.41/2.68 (define @t72 () (@var "BOUND_VARIABLE_7671" tptp.a)) % 2.41/2.68 (define @t73 () (tptp.f @t72 @t4)) % 2.41/2.68 (define @t74 () (@list @t72)) % 2.41/2.68 (define @t75 () (forall @t74 (not @t73))) % 2.41/2.68 (define @t76 () (not @t75)) % 2.41/2.68 (define @t77 () (or @t76 @t71)) % 2.41/2.68 (define @t78 () (forall (@list @t4 @t69) @t77)) % 2.41/2.68 (define @t79 () (@list @t69)) % 2.41/2.68 (define @t80 () (forall @t79 @t77)) % 2.41/2.68 (define @t81 () (forall @t79 @t68)) % 2.41/2.68 (define @t82 () (forall @t79 @t70)) % 2.41/2.68 (define @t83 () (@var "BOUND_VARIABLE_7545" tptp.a)) % 2.41/2.68 (define @t84 () (@list @t83)) % 2.41/2.68 (define @t85 () (and @t82 @t81)) % 2.41/2.68 (define @t86 () (forall @t79 @t71)) % 2.41/2.68 (define @t87 () (or @t76 @t86)) % 2.41/2.68 (define @t88 () (tptp.f @t83 @t4)) % 2.41/2.68 (define @t89 () (@list @t83)) % 2.41/2.68 (define @t90 () (forall @t89 (not @t88))) % 2.41/2.68 (define @t91 () (not @t90)) % 2.41/2.68 (define @t92 () (or @t91 @t67)) % 2.41/2.68 (define @t93 () (_ (_ tptp.cR @t64) tptp.z)) % 2.41/2.68 (define @t94 () (not @t93)) % 2.41/2.68 (define @t95 () (forall @t66 @t94)) % 2.41/2.68 (define @t96 () (or @t91 @t95)) % 2.41/2.68 (define @t97 () (forall @t66 (or @t91 @t94))) % 2.41/2.68 (define @t98 () (_ (_ tptp.f @t72) @t4)) % 2.41/2.68 (define @t99 () (not @t98)) % 2.41/2.68 (define @t100 () (forall @t74 @t99)) % 2.41/2.68 (define @t101 () (not @t3)) % 2.41/2.68 (define @t102 () (or @t91 @t101)) % 2.41/2.68 (define @t103 () (forall @t12 @t102)) % 2.41/2.68 (define @t104 () (@list @t1)) % 2.41/2.68 (define @t105 () (not @t9)) % 2.41/2.68 (define @t106 () (forall @t12 @t105)) % 2.41/2.68 (define @t107 () (and @t106 @t103)) % 2.41/2.68 (define @t108 () (and @t105 @t102)) % 2.41/2.68 (define @t109 () (and @t90 @t3)) % 2.41/2.68 (define @t110 () (or @t9 @t109)) % 2.41/2.68 (define @t111 () (not @t110)) % 2.41/2.68 (define @t112 () (forall @t12 @t111)) % 2.41/2.68 (define @t113 () (not @t112)) % 2.41/2.68 (define @t114 () (_ (_ tptp.f @t83) @t4)) % 2.41/2.68 (define @t115 () (not @t114)) % 2.41/2.68 (define @t116 () (forall @t89 @t115)) % 2.41/2.68 (define @t117 () (forall @t10 @t3)) % 2.41/2.68 (define @t118 () (forall @t10 @t6)) % 2.41/2.68 (define @t119 () (@list @t5)) % 2.41/2.68 (define @t120 () (and @t118 @t117)) % 2.41/2.68 (define @t121 () (forall @t10 @t7)) % 2.41/2.68 (define @t122 () (or @t9 @t121)) % 2.41/2.68 (define @t123 () (tptp.cR @t17 @t16)) % 2.41/2.68 (define @t124 () (tptp.cR @t16 tptp.z)) % 2.41/2.68 (define @t125 () (not @t20)) % 2.41/2.68 (define @t126 () (@var "BOUND_VARIABLE_7623" tptp.a)) % 2.41/2.68 (define @t127 () (tptp.f @t126 @t4)) % 2.41/2.68 (define @t128 () (@list @t126)) % 2.41/2.68 (define @t129 () (forall @t128 (not @t127))) % 2.41/2.68 (define @t130 () (not @t129)) % 2.41/2.68 (define @t131 () (or @t130 @t125)) % 2.41/2.68 (define @t132 () (tptp.f @t16 @t4)) % 2.41/2.68 (define @t133 () (not @t22)) % 2.41/2.68 (define @t134 () (and @t133 @t131)) % 2.41/2.68 (define @t135 () (tptp.cR @t17 tptp.z)) % 2.41/2.68 (define @t136 () (not @t24)) % 2.41/2.68 (define @t137 () (@var "BOUND_VARIABLE_7606" tptp.a)) % 2.41/2.68 (define @t138 () (tptp.f @t137 @t4)) % 2.41/2.68 (define @t139 () (@list @t137)) % 2.41/2.68 (define @t140 () (forall @t139 (not @t138))) % 2.41/2.68 (define @t141 () (not @t140)) % 2.41/2.68 (define @t142 () (or @t141 @t136)) % 2.41/2.68 (define @t143 () (tptp.f @t17 @t4)) % 2.41/2.68 (define @t144 () (not @t26)) % 2.41/2.68 (define @t145 () (and @t144 @t142)) % 2.41/2.68 (define @t146 () (or @t145 @t134 @t19)) % 2.41/2.68 (define @t147 () (and @t129 @t20)) % 2.41/2.68 (define @t148 () (and @t140 @t24)) % 2.41/2.68 (define @t149 () (or @t22 @t147)) % 2.41/2.68 (define @t150 () (or @t26 @t148)) % 2.41/2.68 (define @t151 () (and @t150 @t149)) % 2.41/2.68 (define @t152 () (_ (_ tptp.f @t126) @t4)) % 2.41/2.68 (define @t153 () (not @t152)) % 2.41/2.68 (define @t154 () (forall @t128 @t153)) % 2.41/2.68 (define @t155 () (forall @t10 @t20)) % 2.41/2.68 (define @t156 () (@list @t126)) % 2.41/2.68 (define @t157 () (and @t118 @t155)) % 2.41/2.68 (define @t158 () (forall @t10 @t21)) % 2.41/2.68 (define @t159 () (or @t22 @t158)) % 2.41/2.68 (define @t160 () (_ (_ tptp.f @t137) @t4)) % 2.41/2.68 (define @t161 () (not @t160)) % 2.41/2.68 (define @t162 () (forall @t139 @t161)) % 2.41/2.68 (define @t163 () (forall @t10 @t24)) % 2.41/2.68 (define @t164 () (@list @t137)) % 2.41/2.68 (define @t165 () (and @t118 @t163)) % 2.41/2.68 (define @t166 () (forall @t10 @t25)) % 2.41/2.68 (define @t167 () (or @t26 @t166)) % 2.41/2.68 (define @t168 () (@var "BOUND_VARIABLE_7576" $$unsorted)) % 2.41/2.68 (define @t169 () (not (forall @t89 (not (tptp.f @t83 @t168))))) % 2.41/2.68 (define @t170 () (@list @t168)) % 2.41/2.68 (define @t171 () (forall @t170 @t169)) % 2.41/2.68 (define @t172 () (not @t171)) % 2.41/2.68 (define @t173 () (tptp.cR @t1 tptp.z)) % 2.41/2.68 (define @t174 () (and @t3 @t172)) % 2.41/2.68 (define @t175 () (@var "BOUND_VARIABLE_7570" $$unsorted)) % 2.41/2.68 (define @t176 () (tptp.f @t1 @t175)) % 2.41/2.68 (define @t177 () (@list @t175)) % 2.41/2.68 (define @t178 () (forall @t177 (not @t176))) % 2.41/2.68 (define @t179 () (not @t178)) % 2.41/2.68 (define @t180 () (or @t179 @t174)) % 2.41/2.68 (define @t181 () (or @t101 @t171)) % 2.41/2.68 (define @t182 () (or @t101 @t169)) % 2.41/2.68 (define @t183 () (or @t169 @t101)) % 2.41/2.68 (define @t184 () (forall @t170 @t183)) % 2.41/2.68 (define @t185 () (_ @t8 @t175)) % 2.41/2.68 (define @t186 () (not @t185)) % 2.41/2.68 (define @t187 () (forall @t177 @t186)) % 2.41/2.68 (define @t188 () (forall @t14 @t102)) % 2.41/2.68 (define @t189 () (@list @t4)) % 2.41/2.68 (define @t190 () (forall @t14 @t105)) % 2.41/2.68 (define @t191 () (@list @t175)) % 2.41/2.68 (define @t192 () (and @t190 @t188)) % 2.41/2.68 (define @t193 () (forall @t14 @t111)) % 2.41/2.68 (define @t194 () (not @t193)) % 2.41/2.68 (define @t195 () (or @t144 @t133 @t19)) % 2.41/2.68 (define @t196 () (tptp.cS @t39 @t38)) % 2.41/2.68 (define @t197 () (tptp.f @t1 @t38)) % 2.41/2.68 (define @t198 () (not @t41)) % 2.41/2.68 (define @t199 () (tptp.f @t1 @t39)) % 2.41/2.68 (define @t200 () (not @t42)) % 2.41/2.68 (define @t201 () (or @t200 @t198 @t40)) % 2.41/2.68 (define @t202 () (tptp.f @t1 @t4)) % 2.41/2.68 (define @t203 () (not @t190)) % 2.41/2.68 (define @t204 () (tptp.cR @t1 @t1)) % 2.41/2.68 (define @t205 () (tptp.cR @t52 @t5)) % 2.41/2.68 (define @t206 () (tptp.cR @t5 @t55)) % 2.41/2.68 (define @t207 () (not @t56)) % 2.41/2.68 (define @t208 () (tptp.cR @t52 @t55)) % 2.41/2.68 (define @t209 () (not @t57)) % 2.41/2.68 (define @t210 () (or @t209 @t207 @t54)) % 2.41/2.68 (define @t211 () (forall @t30 (or (and (not @t143) (or @t141 (not @t135))) (and (not @t132) (or @t130 (not @t124))) @t123))) % 2.41/2.68 (define @t212 () (@quantifiers_skolemize @t211 2)) % 2.41/2.68 (define @t213 () (@quantifiers_skolemize @t211 1)) % 2.41/2.68 (define @t214 () (tptp.cR @t213 @t212)) % 2.41/2.68 (define @t215 () (tptp.cR @t212 tptp.z)) % 2.41/2.68 (define @t216 () (not @t215)) % 2.41/2.68 (define @t217 () (@quantifiers_skolemize @t211 0)) % 2.41/2.68 (define @t218 () (forall @t128 (not (tptp.f @t126 @t217)))) % 2.41/2.68 (define @t219 () (not @t218)) % 2.41/2.68 (define @t220 () (or @t219 @t216)) % 2.41/2.68 (define @t221 () (tptp.f @t212 @t217)) % 2.41/2.68 (define @t222 () (not @t221)) % 2.41/2.68 (define @t223 () (and @t222 @t220)) % 2.41/2.68 (define @t224 () (tptp.cR @t213 tptp.z)) % 2.41/2.68 (define @t225 () (not @t224)) % 2.41/2.68 (define @t226 () (forall @t139 (not (tptp.f @t137 @t217)))) % 2.41/2.68 (define @t227 () (not @t226)) % 2.41/2.68 (define @t228 () (or @t227 @t225)) % 2.41/2.68 (define @t229 () (tptp.f @t213 @t217)) % 2.41/2.68 (define @t230 () (not @t229)) % 2.41/2.68 (define @t231 () (and @t230 @t228)) % 2.41/2.68 (define @t232 () (or @t231 @t223 @t214)) % 2.41/2.68 (define @t233 () (not @t228)) % 2.41/2.68 (define @t234 () (not @t220)) % 2.41/2.68 (define @t235 () (or @t225 @t216 @t214)) % 2.41/2.68 (define @t236 () (or @t230 @t222 @t214)) % 2.41/2.68 (define @t237 () (not @t232)) % 2.41/2.68 (define @t238 () (not @t211)) % 2.41/2.68 (define @t239 () (@list false)) % 2.41/2.68 (define @t240 () (forall @t12 (or @t179 (and @t173 @t172)))) % 2.41/2.68 (define @t241 () (@quantifiers_skolemize @t240 0)) % 2.41/2.68 (define @t242 () (forall @t177 (not (tptp.f @t241 @t175)))) % 2.41/2.68 (define @t243 () (not @t242)) % 2.41/2.68 (define @t244 () (@list true)) % 2.41/2.68 (define @t245 () (or @t243 (and (tptp.cR @t241 tptp.z) @t172))) % 2.41/2.68 (define @t246 () (not @t245)) % 2.41/2.68 (define @t247 () (not @t240)) % 2.41/2.68 (define @t248 () (not @t78)) % 2.41/2.68 (define @t249 () (@quantifiers_skolemize @t78 0)) % 2.41/2.68 (define @t250 () (@quantifiers_skolemize @t78 1)) % 2.41/2.68 (define @t251 () (tptp.f @t250 @t249)) % 2.41/2.68 (define @t252 () (not @t251)) % 2.41/2.68 (define @t253 () (and @t252 @t68)) % 2.41/2.68 (define @t254 () (forall @t74 (not (tptp.f @t72 @t249)))) % 2.41/2.68 (define @t255 () (not @t254)) % 2.41/2.68 (define @t256 () (or @t255 @t253)) % 2.41/2.68 (define @t257 () (not @t256)) % 2.41/2.68 (define @t258 () (@list @t256)) % 2.41/2.68 (define @t259 () (@list tptp.z)) % 2.41/2.68 (define @t260 () (tptp.cR tptp.z tptp.z)) % 2.41/2.68 (define @t261 () (not @t260)) % 2.41/2.68 (define @t262 () (forall @t12 @t204)) % 2.41/2.68 (assume @p1 @t63) % 2.41/2.68 (assume @p2 true) % 2.41/2.68 (step @p3 :rule quant-merge-prenex :args ((= (forall @t14 @t80) @t78))) % 2.41/2.68 (step @p4 :rule quant-unused-vars :args ((= @t81 @t68))) % 2.41/2.68 (step @p5 :rule alpha_equiv :args (@t82 (@list @t69) @t84)) % 2.41/2.68 (step @p6 :rule nary_cong :premises (@p5 @p4) :args (@t85)) % 2.41/2.68 (step @p7 :rule quant-miniscope-and :args ((= @t86 @t85))) % 2.41/2.68 (step @p8 :rule trans :premises (@p7 @p6)) % 2.41/2.68 (step @p9 :rule refl :args (@t76)) % 2.41/2.68 (step @p10 :rule nary_cong :premises (@p9 @p8) :args (@t87)) % 2.41/2.68 (step @p11 :rule quant-miniscope-or :args ((= @t80 @t87))) % 2.41/2.68 (step @p12 :rule trans :premises (@p11 @p10)) % 2.41/2.68 (step @p13 :rule symm :premises (@p12)) % 2.41/2.68 (step @p14 :rule cong :premises (@p13) :args ((forall @t14 (or @t76 (and @t90 @t68))))) % 2.41/2.68 (step @p15 :rule trans :premises (@p14 @p3)) % 2.41/2.68 (step @p16 :rule refl :args (@t68)) % 2.41/2.68 (step @p17 :rule bool-double-not-elim :args (@t90)) % 2.41/2.68 (step @p18 :rule nary_cong :premises (@p17 @p16) :args ((and (not @t91) @t68))) % 2.41/2.68 (step @p19 :rule bool-or-de-morgan :args (@t91 @t67 false)) % 2.41/2.68 (step @p20 :rule trans :premises (@p19 @p18)) % 2.41/2.68 (step @p21 :rule nary_cong :premises (@p9 @p20) :args ((or @t76 (not @t92)))) % 2.41/2.68 (step @p22 :rule bool-and-de-morgan :args (@t75 @t92 true)) % 2.41/2.68 (step @p23 :rule trans :premises (@p22 @p21)) % 2.41/2.68 (step @p24 :rule cong :premises (@p23) :args ((forall @t14 (not (and @t75 @t92))))) % 2.41/2.68 (step @p25 :rule trans :premises (@p24 @p15)) % 2.41/2.68 (step @p26 :rule refl :args (@t65)) % 2.41/2.68 (step @p27 :rule refl :args (@t93)) % 2.41/2.68 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t93 @t65))) % 2.41/2.68 (step @p29 :rule symm :premises (@p28)) % 2.41/2.68 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 2.41/2.68 (step @p31 :rule cong :premises (@p30) :args (@t94)) % 2.41/2.68 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@p271 :rule symm :premises (@p270)) % 2.41/2.69 (step @p272 :rule eq_resolve :premises (@p269 @p271)) % 2.41/2.69 (step @p273 :rule cong :premises (@p272) :args (@t105)) % 2.41/2.69 (step @p274 :rule cong :premises (@p273) :args (@t190)) % 2.41/2.69 (step @p275 :rule cong :premises (@p274) :args (@t203)) % 2.41/2.69 (step @p276 :rule exists-elim :args ((= @t46 @t203))) % 2.41/2.69 (step @p277 :rule trans :premises (@p276 @p275)) % 2.41/2.69 (step @p278 :rule cong :premises (@p277) :args (@t47)) % 2.41/2.69 (step @p279 :rule nary_cong :premises (@p278 @p267 @p240) :args (@t48)) % 2.41/2.69 (step @p280 :rule cong :premises (@p279 @p230) :args (@t49)) % 2.41/2.69 (step @p281 :rule refl :args (@t204)) % 2.41/2.69 (step @p282 :rule refl :args (@t50)) % 2.41/2.69 (step @p283 :rule cong :premises (@p282 @p281) :args ((= @t50 @t204))) % 2.41/2.69 (step @p284 :rule symm :premises (@p283)) % 2.41/2.69 (step @p285 :rule eq_resolve :premises (@p282 @p284)) % 2.41/2.69 (step @p286 :rule cong :premises (@p285) :args (@t51)) % 2.41/2.69 (step @p287 :rule refl :args (@t205)) % 2.41/2.69 (step @p288 :rule refl :args (@t54)) % 2.41/2.69 (step @p289 :rule cong :premises (@p288 @p287) :args ((= @t54 @t205))) % 2.41/2.69 (step @p290 :rule symm :premises (@p289)) % 2.41/2.69 (step @p291 :rule eq_resolve :premises (@p288 @p290)) % 2.41/2.69 (step @p292 :rule refl :args (@t206)) % 2.41/2.69 (step @p293 :rule refl :args (@t56)) % 2.41/2.69 (step @p294 :rule cong :premises (@p293 @p292) :args ((= @t56 @t206))) % 2.41/2.69 (step @p295 :rule symm :premises (@p294)) % 2.41/2.69 (step @p296 :rule eq_resolve :premises (@p293 @p295)) % 2.41/2.69 (step @p297 :rule cong :premises (@p296) :args (@t207)) % 2.41/2.69 (step @p298 :rule refl :args (@t208)) % 2.41/2.69 (step @p299 :rule refl :args (@t57)) % 2.41/2.69 (step @p300 :rule cong :premises (@p299 @p298) :args ((= @t57 @t208))) % 2.41/2.69 (step @p301 :rule symm :premises (@p300)) % 2.41/2.69 (step @p302 :rule eq_resolve :premises (@p299 @p301)) % 2.41/2.69 (step @p303 :rule cong :premises (@p302) :args (@t209)) % 2.41/2.69 (step @p304 :rule nary_cong :premises (@p303 @p297 @p291) :args (@t210)) % 2.41/2.69 (step @p305 :rule cong :premises (@p304) :args ((forall @t59 @t210))) % 2.41/2.69 (step @p306 :rule aci_norm :args ((= (or (or @t209 @t207) @t54) @t210))) % 2.41/2.69 (step @p307 :rule bool-and-de-morgan :args (@t57 @t56 true)) % 2.41/2.69 (step @p308 :rule nary_cong :premises (@p307 @p288) :args ((or (not @t58) @t54))) % 2.41/2.69 (step @p309 :rule trans :premises (@p308 @p306)) % 2.41/2.69 (step @p310 :rule bool-impl-elim :args (@t58 @t54)) % 2.41/2.69 (step @p311 :rule trans :premises (@p310 @p309)) % 2.41/2.69 (step @p312 :rule cong :premises (@p311) :args (@t60)) % 2.41/2.69 (step @p313 :rule trans :premises (@p312 @p305)) % 2.41/2.69 (step @p314 :rule nary_cong :premises (@p313 @p286) :args (@t61)) % 2.41/2.69 (step @p315 :rule cong :premises (@p314 @p280) :args (@t62)) % 2.41/2.69 (step @p316 :rule cong :premises (@p315) :args (@t63)) % 2.41/2.69 (step @p317 :rule eq_resolve :premises (@p1 @p316)) % 2.41/2.69 (step @p318 :rule not_implies_elim1 :premises (@p317)) % 2.41/2.69 (step @p319 :rule and_elim :premises (@p318) :args (1)) % 2.41/2.69 (step @p320 :rule cnf_or_neg :args (@t232 0)) % 2.41/2.69 (step @p321 :rule cnf_or_neg :args (@t232 1)) % 2.41/2.69 (step @p322 :rule cnf_or_neg :args (@t232 2)) % 2.41/2.69 (assume-push @p464 @t226) % 2.41/2.69 (step @p324 :rule instantiate :premises (@p464) :args ((@list @t213))) % 2.41/2.69 (step-pop @p465 :rule scope :premises (@p324)) % 2.41/2.69 (step @p325 :rule process_scope :premises (@p465) :args (@t230)) % 2.41/2.69 (step @p327 :rule implies_elim :premises (@p325)) % 2.41/2.69 (step @p328 :rule reordering :premises (@p327) :args ((or @t230 @t227))) % 2.41/2.69 (assume-push @p466 @t226) % 2.41/2.69 (step @p330 :rule instantiate :premises (@p466) :args ((@list @t212))) % 2.41/2.69 (step-pop @p467 :rule scope :premises (@p330)) % 2.41/2.69 (step @p331 :rule process_scope :premises (@p467) :args (@t222)) % 2.41/2.69 (step @p333 :rule implies_elim :premises (@p331)) % 2.41/2.69 (step @p334 :rule refl :args (@t233)) % 2.41/2.69 (step @p335 :rule bool-double-not-elim :args (@t229)) % 2.41/2.69 (step @p336 :rule refl :args (@t231)) % 2.41/2.69 (step @p337 :rule nary_cong :premises (@p336 @p335 @p334) :args ((or @t231 (not @t230) @t233))) % 2.41/2.69 (step @p338 :rule cnf_and_neg :args (@t231)) % 2.41/2.69 (step @p339 :rule eq_resolve :premises (@p338 @p337)) % 2.41/2.69 (step @p340 :rule reordering :premises (@p339) :args ((or @t229 @t231 @t233))) % 2.41/2.69 (step @p341 :rule refl :args (@t234)) % 2.41/2.69 (step @p342 :rule bool-double-not-elim :args (@t221)) % 2.41/2.69 (step @p343 :rule refl :args (@t223)) % 2.41/2.69 (step @p344 :rule nary_cong :premises (@p343 @p342 @p341) :args ((or @t223 (not @t222) @t234))) % 2.41/2.69 (step @p345 :rule cnf_and_neg :args (@t223)) % 2.41/2.69 (step @p346 :rule eq_resolve :premises (@p345 @p344)) % 2.41/2.69 (step @p347 :rule reordering :premises (@p346) :args ((or @t221 @t223 @t234))) % 2.41/2.69 (step @p348 :rule bool-double-not-elim :args (@t224)) % 2.41/2.69 (step @p349 :rule refl :args (@t228)) % 2.41/2.69 (step @p350 :rule nary_cong :premises (@p349 @p348) :args ((or @t228 (not @t225)))) % 2.41/2.69 (step @p351 :rule cnf_or_neg :args (@t228 1)) % 2.41/2.69 (step @p352 :rule eq_resolve :premises (@p351 @p350)) % 2.41/2.69 (step @p353 :rule reordering :premises (@p352) :args ((or @t224 @t228))) % 2.41/2.69 (step @p354 :rule bool-double-not-elim :args (@t215)) % 2.41/2.69 (step @p355 :rule refl :args (@t220)) % 2.41/2.69 (step @p356 :rule nary_cong :premises (@p355 @p354) :args ((or @t220 (not @t216)))) % 2.41/2.69 (step @p357 :rule cnf_or_neg :args (@t220 1)) % 2.41/2.69 (step @p358 :rule eq_resolve :premises (@p357 @p356)) % 2.41/2.69 (step @p359 :rule reordering :premises (@p358) :args ((or @t215 @t220))) % 2.41/2.69 (step @p360 :rule and_elim :premises (@p318) :args (0)) % 2.41/2.69 (step @p361 :rule instantiate :premises (@p360) :args ((@list @t213 tptp.z @t212))) % 2.41/2.69 (step @p362 :rule cnf_or_pos :args (@t235)) % 2.41/2.69 (step @p363 :rule reordering :premises (@p362) :args ((or @t225 @t216 @t214 (not @t235)))) % 2.41/2.69 (step @p364 :rule chain_m_resolution :premises (@p363 @p361 @p359 @p353 @p347 @p340 @p333 @p328) :args ((or @t227 @t231 @t223 @t214) (@list false false false true true true true) (@list @t235 @t215 @t224 @t220 @t228 @t221 @t229))) % 2.41/2.69 (step @p365 :rule bool-double-not-elim :args (@t226)) % 2.41/2.69 (step @p366 :rule nary_cong :premises (@p349 @p365) :args ((or @t228 (not @t227)))) % 2.41/2.69 (step @p367 :rule cnf_or_neg :args (@t228 0)) % 2.41/2.69 (step @p368 :rule eq_resolve :premises (@p367 @p366)) % 2.41/2.69 (step @p369 :rule reordering :premises (@p368) :args ((or @t226 @t228))) % 2.41/2.69 (step @p370 :rule alpha_equiv :args (@t226 @t164 @t156)) % 2.41/2.69 (step @p371 :rule equiv_elim2 :premises (@p370)) % 2.41/2.69 (step @p372 :rule bool-double-not-elim :args (@t218)) % 2.41/2.69 (step @p373 :rule nary_cong :premises (@p355 @p372) :args ((or @t220 (not @t219)))) % 2.41/2.69 (step @p374 :rule cnf_or_neg :args (@t220 0)) % 2.41/2.69 (step @p375 :rule eq_resolve :premises (@p374 @p373)) % 2.41/2.69 (step @p376 :rule reordering :premises (@p375) :args ((or @t218 @t220))) % 2.41/2.69 (step @p377 :rule not_implies_elim2 :premises (@p317)) % 2.41/2.69 (step @p378 :rule not_implies_elim1 :premises (@p377)) % 2.41/2.69 (step @p379 :rule and_elim :premises (@p378) :args (2)) % 2.41/2.69 (step @p380 :rule instantiate :premises (@p379) :args ((@list @t213 @t212 @t217))) % 2.41/2.69 (step @p381 :rule cnf_or_pos :args (@t236)) % 2.41/2.69 (step @p382 :rule reordering :premises (@p381) :args ((or @t230 @t222 @t214 (not @t236)))) % 2.41/2.69 (step @p383 :rule chain_m_resolution :premises (@p347 @p382 @p380 @p376 @p340 @p371 @p369 @p364 @p322 @p321 @p320) :args (@t232 (@list true false false false true false true true true true) (@list @t221 @t236 @t220 @t229 @t218 @t228 @t226 @t214 @t223 @t231))) % 2.41/2.69 (step @p384 :rule refl :args (@t237)) % 2.41/2.69 (step @p385 :rule bool-double-not-elim :args (@t211)) % 2.41/2.69 (step @p386 :rule nary_cong :premises (@p385 @p384) :args ((or (not @t238) @t237))) % 2.41/2.69 (assume-push @p468 @t238) % 2.41/2.69 (step @p388 :rule skolemize :premises (@p468)) % 2.41/2.69 (step-pop @p469 :rule scope :premises (@p388)) % 2.41/2.69 (step @p389 :rule process_scope :premises (@p469) :args (@t237)) % 2.41/2.69 (step @p391 :rule implies_elim :premises (@p389)) % 2.41/2.69 (step @p392 :rule eq_resolve :premises (@p391 @p386)) % 2.41/2.69 (step @p393 :rule chain_m_resolution :premises (@p392 @p383) :args (@t211 @t239 (@list @t232))) % 2.41/2.69 (step @p394 :rule and_elim :premises (@p378) :args (0)) % 2.41/2.69 (step @p395 :rule instantiate :premises (@p394) :args ((@list @t241))) % 2.41/2.69 (step @p396 :rule alpha_equiv :args (@t242 @t191 @t189)) % 2.41/2.69 (step @p397 :rule equiv_elim1 :premises (@p396)) % 2.41/2.69 (step @p398 :rule chain_m_resolution :premises (@p397 @p395) :args (@t243 @t244 (@list (forall @t14 (not (tptp.f @t241 @t4)))))) % 2.41/2.69 (step @p399 :rule bool-double-not-elim :args (@t242)) % 2.41/2.69 (step @p400 :rule refl :args (@t245)) % 2.41/2.69 (step @p401 :rule nary_cong :premises (@p400 @p399) :args ((or @t245 (not @t243)))) % 2.41/2.69 (step @p402 :rule cnf_or_neg :args (@t245 0)) % 2.41/2.69 (step @p403 :rule eq_resolve :premises (@p402 @p401)) % 2.41/2.69 (step @p404 :rule reordering :premises (@p403) :args ((or @t242 @t245))) % 2.41/2.69 (step @p405 :rule chain_m_resolution :premises (@p404 @p398) :args (@t245 @t244 (@list @t242))) % 2.41/2.69 (step @p406 :rule refl :args (@t246)) % 2.41/2.69 (step @p407 :rule bool-double-not-elim :args (@t240)) % 2.41/2.69 (step @p408 :rule nary_cong :premises (@p407 @p406) :args ((or (not @t247) @t246))) % 2.41/2.69 (assume-push @p470 @t247) % 2.41/2.69 (step @p410 :rule skolemize :premises (@p470)) % 2.41/2.69 (step-pop @p471 :rule scope :premises (@p410)) % 2.41/2.69 (step @p411 :rule process_scope :premises (@p471) :args (@t246)) % 2.41/2.69 (step @p413 :rule implies_elim :premises (@p411)) % 2.41/2.69 (step @p414 :rule eq_resolve :premises (@p413 @p408)) % 2.41/2.69 (step @p415 :rule chain_m_resolution :premises (@p414 @p405) :args (@t240 @t239 (@list @t245))) % 2.41/2.69 (step @p416 :rule not_implies_elim2 :premises (@p377)) % 2.41/2.69 (step @p417 :rule not_and :premises (@p416)) % 2.41/2.69 (step @p418 :rule chain_m_resolution :premises (@p417 @p415 @p393) :args (@t248 (@list false false) (@list @t240 @t211))) % 2.41/2.69 (step @p419 :rule refl :args (@t257)) % 2.41/2.69 (step @p420 :rule bool-double-not-elim :args (@t78)) % 2.41/2.69 (step @p421 :rule nary_cong :premises (@p420 @p419) :args ((or (not @t248) @t257))) % 2.41/2.69 (assume-push @p472 @t248) % 2.41/2.69 (step @p423 :rule skolemize :premises (@p472)) % 2.41/2.69 (step-pop @p473 :rule scope :premises (@p423)) % 2.41/2.69 (step @p424 :rule process_scope :premises (@p473) :args (@t257)) % 2.41/2.69 (step @p426 :rule implies_elim :premises (@p424)) % 2.41/2.69 (step @p427 :rule eq_resolve :premises (@p426 @p421)) % 2.41/2.69 (step @p428 :rule chain_m_resolution :premises (@p427 @p418) :args (@t257 @t244 (@list @t78))) % 2.41/2.69 (step @p429 :rule cnf_or_neg :args (@t256 1)) % 2.41/2.69 (step @p430 :rule chain_m_resolution :premises (@p429 @p428) :args ((not @t253) @t244 @t258)) % 2.41/2.69 (step @p431 :rule bool-double-not-elim :args (@t254)) % 2.41/2.69 (step @p432 :rule refl :args (@t256)) % 2.41/2.69 (step @p433 :rule nary_cong :premises (@p432 @p431) :args ((or @t256 (not @t255)))) % 2.41/2.69 (step @p434 :rule cnf_or_neg :args (@t256 0)) % 2.41/2.69 (step @p435 :rule eq_resolve :premises (@p434 @p433)) % 2.41/2.69 (step @p436 :rule reordering :premises (@p435) :args ((or @t254 @t256))) % 2.41/2.69 (step @p437 :rule chain_m_resolution :premises (@p436 @p428) :args (@t254 @t244 @t258)) % 2.41/2.69 (assume-push @p474 @t254) % 2.41/2.69 (step @p439 :rule instantiate :premises (@p474) :args ((@list @t250))) % 2.41/2.69 (step-pop @p475 :rule scope :premises (@p439)) % 2.41/2.69 (step @p440 :rule process_scope :premises (@p475) :args (@t252)) % 2.41/2.69 (step @p442 :rule implies_elim :premises (@p440)) % 2.41/2.69 (step @p443 :rule chain_m_resolution :premises (@p442 @p437) :args (@t252 @t239 (@list @t254))) % 2.41/2.69 (step @p444 :rule bool-double-not-elim :args (@t67)) % 2.41/2.69 (step @p445 :rule bool-double-not-elim :args (@t251)) % 2.41/2.69 (step @p446 :rule refl :args (@t253)) % 2.41/2.69 (step @p447 :rule nary_cong :premises (@p446 @p445 @p444) :args ((or @t253 (not @t252) (not @t68)))) % 2.41/2.69 (step @p448 :rule cnf_and_neg :args (@t253)) % 2.41/2.69 (step @p449 :rule eq_resolve :premises (@p448 @p447)) % 2.41/2.69 (step @p450 :rule reordering :premises (@p449) :args ((or @t67 @t251 @t253))) % 2.41/2.69 (step @p451 :rule chain_m_resolution :premises (@p450 @p443 @p430) :args (@t67 (@list true true) (@list @t251 @t253))) % 2.41/2.69 (assume-push @p476 @t67) % 2.41/2.69 (step @p453 :rule instantiate :premises (@p476) :args (@t259)) % 2.41/2.69 (step-pop @p477 :rule scope :premises (@p453)) % 2.41/2.69 (step @p454 :rule process_scope :premises (@p477) :args (@t261)) % 2.41/2.69 (step @p456 :rule implies_elim :premises (@p454)) % 2.41/2.69 (step @p457 :rule chain_m_resolution :premises (@p456 @p451) :args (@t261 @t239 (@list @t67))) % 2.41/2.69 (assume-push @p478 @t262) % 2.41/2.69 (step @p459 :rule instantiate :premises (@p319) :args (@t259)) % 2.41/2.69 (step-pop @p479 :rule scope :premises (@p459)) % 2.41/2.69 (step @p460 :rule process_scope :premises (@p479) :args (@t260)) % 2.41/2.69 (step @p462 :rule implies_elim :premises (@p460)) % 2.41/2.69 (step @p463 false :rule chain_m_resolution :premises (@p462 @p457 @p319) :args (false (@list true false) (@list @t260 @t262))) % 2.41/2.69 ) % 2.41/2.69 % SZS output end Proof % 2.41/2.69 % cvc5 exiting %------------------------------------------------------------------------------