%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PLA054_4 : TPTP v9.2.1. Released v8.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n026.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 08:43:31 AM UTC 2026 % Result : Theorem 0.45s 0.69s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PLA054_4 : TPTP v9.2.1. Released v8.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n026.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 13:05:10 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.69 % SZS status Theorem % 0.45/0.69 % SZS output start Proof % 0.45/0.69 ( % 0.45/0.69 (declare-sort |tptp.'$ki_world'| 0) % 0.45/0.69 (declare-sort $$unsorted 0) % 0.45/0.69 (declare-const tptp.n $$unsorted) % 0.45/0.69 (declare-const tptp.d $$unsorted) % 0.45/0.69 (declare-const tptp.open (-> |tptp.'$ki_world'| $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.combo (-> |tptp.'$ki_world'| $$unsorted $$unsorted Bool)) % 0.45/0.69 (declare-const |tptp.'$ki_local_world'| |tptp.'$ki_world'|) % 0.45/0.69 (declare-const tptp.o $$unsorted) % 0.45/0.69 (declare-const tptp.closed (-> |tptp.'$ki_world'| $$unsorted Bool)) % 0.45/0.69 (declare-const |tptp.'$ki_exists_in_world_$i'| (-> |tptp.'$ki_world'| $$unsorted Bool)) % 0.45/0.69 (declare-const tptp.h (-> |tptp.'$ki_world'| $$unsorted Bool)) % 0.45/0.69 (declare-const |tptp.'$ki_accessible'| (-> |tptp.'$ki_world'| |tptp.'$ki_world'| Bool)) % 0.45/0.69 (define @t1 () (@var "W" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t2 () (@list @t1)) % 0.45/0.69 (define @t3 () (@var "U" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t4 () (@var "V" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t5 () (@var "X" $$unsorted)) % 0.45/0.69 (define @t6 () (|tptp.'$ki_exists_in_world_$i'| @t1 @t5)) % 0.45/0.69 (define @t7 () (forall (@list @t1 @t5) @t6)) % 0.45/0.69 (define @t8 () (@var "S" $$unsorted)) % 0.45/0.69 (define @t9 () (@var "W1" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t10 () (tptp.closed @t9 @t8)) % 0.45/0.69 (define @t11 () (@var "W0" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t12 () (|tptp.'$ki_accessible'| @t11 @t9)) % 0.45/0.69 (define @t13 () (@list @t9)) % 0.45/0.69 (define @t14 () (forall @t13 (=> @t12 @t10))) % 0.45/0.69 (define @t15 () (tptp.h @t11 tptp.o)) % 0.45/0.69 (define @t16 () (@var "V" $$unsorted)) % 0.45/0.69 (define @t17 () (tptp.combo @t11 @t8 @t16)) % 0.45/0.69 (define @t18 () (not @t17)) % 0.45/0.69 (define @t19 () (tptp.closed @t11 @t8)) % 0.45/0.69 (define @t20 () (and @t19 @t18 @t15)) % 0.45/0.69 (define @t21 () (=> @t20 @t14)) % 0.45/0.69 (define @t22 () (|tptp.'$ki_accessible'| @t1 @t11)) % 0.45/0.69 (define @t23 () (=> @t22 @t21)) % 0.45/0.69 (define @t24 () (@list @t11)) % 0.45/0.69 (define @t25 () (forall @t24 @t23)) % 0.45/0.69 (define @t26 () (tptp.open @t9 @t8)) % 0.45/0.69 (define @t27 () (forall @t13 (=> @t12 @t26))) % 0.45/0.69 (define @t28 () (@var "O" $$unsorted)) % 0.45/0.69 (define @t29 () (tptp.h @t11 @t28)) % 0.45/0.69 (define @t30 () (and @t19 @t17 @t29)) % 0.45/0.69 (define @t31 () (=> @t30 @t27)) % 0.45/0.69 (define @t32 () (=> @t22 @t31)) % 0.45/0.69 (define @t33 () (forall @t24 @t32)) % 0.45/0.69 (define @t34 () (|tptp.'$ki_exists_in_world_$i'| @t1 @t28)) % 0.45/0.69 (define @t35 () (and @t34 @t33 @t25)) % 0.45/0.69 (define @t36 () (@list @t28)) % 0.45/0.69 (define @t37 () (exists @t36 @t35)) % 0.45/0.69 (define @t38 () (|tptp.'$ki_exists_in_world_$i'| @t1 @t16)) % 0.45/0.69 (define @t39 () (=> @t38 @t37)) % 0.45/0.69 (define @t40 () (@list @t16)) % 0.45/0.69 (define @t41 () (forall @t40 @t39)) % 0.45/0.69 (define @t42 () (|tptp.'$ki_exists_in_world_$i'| @t1 @t8)) % 0.45/0.69 (define @t43 () (=> @t42 @t41)) % 0.45/0.69 (define @t44 () (@list @t8)) % 0.45/0.69 (define @t45 () (forall @t44 @t43)) % 0.45/0.69 (define @t46 () (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| @t1)) % 0.45/0.69 (define @t47 () (=> @t46 @t45)) % 0.45/0.69 (define @t48 () (forall @t2 @t47)) % 0.45/0.69 (define @t49 () (tptp.closed @t1 tptp.d)) % 0.45/0.69 (define @t50 () (forall @t2 (=> @t46 @t49))) % 0.45/0.69 (define @t51 () (tptp.combo @t1 tptp.d tptp.n)) % 0.45/0.69 (define @t52 () (tptp.combo @t1 tptp.d @t16)) % 0.45/0.69 (define @t53 () (forall @t2 (=> @t46 @t52))) % 0.45/0.69 (define @t54 () (|tptp.'$ki_exists_in_world_$i'| |tptp.'$ki_local_world'| @t16)) % 0.45/0.69 (define @t55 () (and @t54 @t53)) % 0.45/0.69 (define @t56 () (exists @t40 @t55)) % 0.45/0.69 (define @t57 () (tptp.open @t11 tptp.d)) % 0.45/0.69 (define @t58 () (forall @t24 (=> @t22 @t57))) % 0.45/0.69 (define @t59 () (and (tptp.combo @t11 tptp.d @t16) @t29)) % 0.45/0.69 (define @t60 () (forall @t24 (=> @t22 @t59))) % 0.45/0.69 (define @t61 () (=> @t60 @t58)) % 0.45/0.69 (define @t62 () (and @t34 @t61)) % 0.45/0.69 (define @t63 () (exists @t36 @t62)) % 0.45/0.69 (define @t64 () (and @t38 @t63)) % 0.45/0.69 (define @t65 () (exists @t40 @t64)) % 0.45/0.69 (define @t66 () (=> @t46 @t65)) % 0.45/0.69 (define @t67 () (forall @t2 @t66)) % 0.45/0.69 (define @t68 () (not @t67)) % 0.45/0.69 (define @t69 () (not @t22)) % 0.45/0.69 (define @t70 () (forall @t24 (or @t69 @t57))) % 0.45/0.69 (define @t71 () (not @t70)) % 0.45/0.69 (define @t72 () (@var "BOUND_VARIABLE_7785" $$unsorted)) % 0.45/0.69 (define @t73 () (@var "BOUND_VARIABLE_7787" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t74 () (and (tptp.combo @t73 tptp.d @t16) (tptp.h @t73 @t72))) % 0.45/0.69 (define @t75 () (and (or (not (|tptp.'$ki_accessible'| @t1 @t73)) @t74) @t71)) % 0.45/0.69 (define @t76 () (not (|tptp.'$ki_exists_in_world_$i'| @t1 @t72))) % 0.45/0.69 (define @t77 () (not @t38)) % 0.45/0.69 (define @t78 () (or @t77 @t76 @t75)) % 0.45/0.69 (define @t79 () (@list @t16 @t72 @t73)) % 0.45/0.69 (define @t80 () (not (forall @t79 @t78))) % 0.45/0.69 (define @t81 () (or @t76 @t75)) % 0.45/0.69 (define @t82 () (or @t77 @t81)) % 0.45/0.69 (define @t83 () (forall @t79 @t82)) % 0.45/0.69 (define @t84 () (@list @t72 @t73)) % 0.45/0.69 (define @t85 () (forall @t84 @t82)) % 0.45/0.69 (define @t86 () (forall @t84 @t81)) % 0.45/0.69 (define @t87 () (@var "BOUND_VARIABLE_7765" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t88 () (or @t77 @t86)) % 0.45/0.69 (define @t89 () (or (not (|tptp.'$ki_accessible'| @t1 @t87)) (and (tptp.combo @t87 tptp.d @t16) (tptp.h @t87 @t28)))) % 0.45/0.69 (define @t90 () (and @t89 @t71)) % 0.45/0.69 (define @t91 () (not @t34)) % 0.45/0.69 (define @t92 () (or @t91 @t90)) % 0.45/0.69 (define @t93 () (forall (@list @t28 @t87) @t92)) % 0.45/0.69 (define @t94 () (not @t93)) % 0.45/0.69 (define @t95 () (and @t38 @t94)) % 0.45/0.69 (define @t96 () (forall @t40 (not @t95))) % 0.45/0.69 (define @t97 () (not @t96)) % 0.45/0.69 (define @t98 () (@list @t87)) % 0.45/0.69 (define @t99 () (forall @t98 @t92)) % 0.45/0.69 (define @t100 () (forall @t98 @t71)) % 0.45/0.69 (define @t101 () (forall @t98 @t89)) % 0.45/0.69 (define @t102 () (and @t101 @t100)) % 0.45/0.69 (define @t103 () (forall @t98 @t90)) % 0.45/0.69 (define @t104 () (or @t91 @t103)) % 0.45/0.69 (define @t105 () (forall @t24 (or @t69 @t59))) % 0.45/0.69 (define @t106 () (=> @t105 @t70)) % 0.45/0.69 (define @t107 () (and @t34 @t106)) % 0.45/0.69 (define @t108 () (forall @t36 (not @t107))) % 0.45/0.69 (define @t109 () (not @t108)) % 0.45/0.69 (define @t110 () (not @t46)) % 0.45/0.69 (define @t111 () (@quantifiers_skolemize (forall @t2 (or @t110 @t80)) 0)) % 0.45/0.69 (define @t112 () (forall @t24 (or (not (|tptp.'$ki_accessible'| @t111 @t11)) @t57))) % 0.45/0.69 (define @t113 () (not @t112)) % 0.45/0.69 (define @t114 () (forall @t79 (or (not (|tptp.'$ki_exists_in_world_$i'| @t111 @t16)) (not (|tptp.'$ki_exists_in_world_$i'| @t111 @t72)) (and (or (not (|tptp.'$ki_accessible'| @t111 @t73)) @t74) @t113)))) % 0.45/0.69 (define @t115 () (not @t114)) % 0.45/0.69 (define @t116 () (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| @t111)) % 0.45/0.69 (define @t117 () (not @t116)) % 0.45/0.69 (define @t118 () (or @t117 @t115)) % 0.45/0.69 (define @t119 () (@list true)) % 0.45/0.69 (define @t120 () (@list @t118)) % 0.45/0.69 (define @t121 () (@var "BOUND_VARIABLE_7547" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t122 () (tptp.open @t121 tptp.d)) % 0.45/0.69 (define @t123 () (not (|tptp.'$ki_accessible'| @t11 @t121))) % 0.45/0.69 (define @t124 () (not @t29)) % 0.45/0.69 (define @t125 () (forall @t2 (or @t110 @t52))) % 0.45/0.69 (define @t126 () (@quantifiers_skolemize (forall @t40 (or (not @t54) (not @t125))) 0)) % 0.45/0.69 (define @t127 () (not (tptp.combo @t11 tptp.d @t126))) % 0.45/0.69 (define @t128 () (not (tptp.closed @t11 tptp.d))) % 0.45/0.69 (define @t129 () (not (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| @t11))) % 0.45/0.69 (define @t130 () (@list @t11 @t121)) % 0.45/0.69 (define @t131 () (forall @t36 (or (not (|tptp.'$ki_exists_in_world_$i'| |tptp.'$ki_local_world'| @t28)) (not (forall @t130 (or @t129 @t128 @t127 @t124 @t123 @t122)))))) % 0.45/0.69 (define @t132 () (@quantifiers_skolemize @t131 0)) % 0.45/0.69 (define @t133 () (@var "BOUND_VARIABLE_7664" $$unsorted)) % 0.45/0.69 (define @t134 () (@var "BOUND_VARIABLE_7666" $$unsorted)) % 0.45/0.69 (define @t135 () (@var "BOUND_VARIABLE_7670" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t136 () (@var "BOUND_VARIABLE_7668" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t137 () (and (or (not (|tptp.'$ki_accessible'| @t1 @t136)) (not (tptp.closed @t136 @t133)) (tptp.combo @t136 @t133 @t134) (not (tptp.h @t136 tptp.o)) (not (|tptp.'$ki_accessible'| @t136 @t135)) (tptp.closed @t135 @t133)) (not (forall @t36 (or @t91 (not (forall @t130 (or @t69 (not (tptp.closed @t11 @t133)) (not (tptp.combo @t11 @t133 @t134)) @t124 @t123 (tptp.open @t121 @t133))))))))) % 0.45/0.69 (define @t138 () (not (|tptp.'$ki_exists_in_world_$i'| @t1 @t134))) % 0.45/0.69 (define @t139 () (not (|tptp.'$ki_exists_in_world_$i'| @t1 @t133))) % 0.45/0.69 (define @t140 () (or @t139 @t138 @t137)) % 0.45/0.69 (define @t141 () (or @t110 @t140)) % 0.45/0.69 (define @t142 () (forall (@list @t1 @t133 @t134 @t136 @t135) @t141)) % 0.45/0.69 (define @t143 () (@list @t133 @t134 @t136 @t135)) % 0.45/0.69 (define @t144 () (forall @t143 @t141)) % 0.45/0.69 (define @t145 () (forall @t143 @t140)) % 0.45/0.69 (define @t146 () (@var "BOUND_VARIABLE_7629" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t147 () (@var "BOUND_VARIABLE_7627" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t148 () (@var "BOUND_VARIABLE_7625" $$unsorted)) % 0.45/0.69 (define @t149 () (or @t110 @t145)) % 0.45/0.69 (define @t150 () (tptp.open @t121 @t8)) % 0.45/0.69 (define @t151 () (not @t19)) % 0.45/0.69 (define @t152 () (and (or (not (|tptp.'$ki_accessible'| @t1 @t147)) (not (tptp.closed @t147 @t8)) (tptp.combo @t147 @t8 @t148) (not (tptp.h @t147 tptp.o)) (not (|tptp.'$ki_accessible'| @t147 @t146)) (tptp.closed @t146 @t8)) (not (forall @t36 (or @t91 (not (forall @t130 (or @t69 @t151 (not (tptp.combo @t11 @t8 @t148)) @t124 @t123 @t150)))))))) % 0.45/0.69 (define @t153 () (not (|tptp.'$ki_exists_in_world_$i'| @t1 @t148))) % 0.45/0.69 (define @t154 () (not @t42)) % 0.45/0.69 (define @t155 () (or @t154 @t153 @t152)) % 0.45/0.69 (define @t156 () (@list @t8 @t148 @t147 @t146)) % 0.45/0.69 (define @t157 () (forall @t156 @t155)) % 0.45/0.69 (define @t158 () (or @t153 @t152)) % 0.45/0.69 (define @t159 () (or @t154 @t158)) % 0.45/0.69 (define @t160 () (forall @t156 @t159)) % 0.45/0.69 (define @t161 () (@list @t148 @t147 @t146)) % 0.45/0.69 (define @t162 () (forall @t161 @t159)) % 0.45/0.69 (define @t163 () (forall @t161 @t158)) % 0.45/0.69 (define @t164 () (@var "BOUND_VARIABLE_7603" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t165 () (@var "BOUND_VARIABLE_7601" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t166 () (or @t154 @t163)) % 0.45/0.69 (define @t167 () (or @t69 @t151 @t18 @t124 @t123 @t150)) % 0.45/0.69 (define @t168 () (forall @t130 @t167)) % 0.45/0.69 (define @t169 () (not @t168)) % 0.45/0.69 (define @t170 () (or @t91 @t169)) % 0.45/0.69 (define @t171 () (forall @t36 @t170)) % 0.45/0.69 (define @t172 () (not @t171)) % 0.45/0.69 (define @t173 () (or (not (|tptp.'$ki_accessible'| @t1 @t165)) (not (tptp.closed @t165 @t8)) (tptp.combo @t165 @t8 @t16) (not (tptp.h @t165 tptp.o)) (not (|tptp.'$ki_accessible'| @t165 @t164)) (tptp.closed @t164 @t8))) % 0.45/0.69 (define @t174 () (and @t173 @t172)) % 0.45/0.69 (define @t175 () (or @t77 @t174)) % 0.45/0.69 (define @t176 () (forall (@list @t16 @t165 @t164) @t175)) % 0.45/0.69 (define @t177 () (@list @t165 @t164)) % 0.45/0.69 (define @t178 () (forall @t177 @t175)) % 0.45/0.69 (define @t179 () (forall @t177 @t172)) % 0.45/0.69 (define @t180 () (forall @t177 @t173)) % 0.45/0.69 (define @t181 () (@var "BOUND_VARIABLE_7569" |tptp.'$ki_world'|)) % 0.45/0.69 (define @t182 () (and @t180 @t179)) % 0.45/0.69 (define @t183 () (forall @t177 @t174)) % 0.45/0.69 (define @t184 () (or @t77 @t183)) % 0.45/0.69 (define @t185 () (tptp.closed @t181 @t8)) % 0.45/0.69 (define @t186 () (not (|tptp.'$ki_accessible'| @t11 @t181))) % 0.45/0.69 (define @t187 () (not @t15)) % 0.45/0.69 (define @t188 () (or @t69 @t151 @t17 @t187 @t186 @t185)) % 0.45/0.69 (define @t189 () (@list @t11 @t181)) % 0.45/0.69 (define @t190 () (forall @t189 @t188)) % 0.45/0.69 (define @t191 () (not @t190)) % 0.45/0.69 (define @t192 () (or @t191 @t171)) % 0.45/0.69 (define @t193 () (not @t192)) % 0.45/0.69 (define @t194 () (or @t191 @t170)) % 0.45/0.69 (define @t195 () (or @t91 @t169 @t191)) % 0.45/0.69 (define @t196 () (and @t34 @t168 @t190)) % 0.45/0.69 (define @t197 () (forall @t36 (not @t196))) % 0.45/0.69 (define @t198 () (not @t197)) % 0.45/0.69 (define @t199 () (or @t186 @t185)) % 0.45/0.69 (define @t200 () (or @t69 @t151 @t17 @t187 @t199)) % 0.45/0.69 (define @t201 () (forall @t189 @t200)) % 0.45/0.69 (define @t202 () (@list @t181)) % 0.45/0.69 (define @t203 () (forall @t202 @t200)) % 0.45/0.69 (define @t204 () (forall @t202 @t199)) % 0.45/0.69 (define @t205 () (@list @t9)) % 0.45/0.69 (define @t206 () (or @t69 @t151 @t17 @t187 @t204)) % 0.45/0.69 (define @t207 () (not @t12)) % 0.45/0.69 (define @t208 () (forall @t13 (or @t207 @t10))) % 0.45/0.69 (define @t209 () (or @t69 @t151 @t17 @t187 @t208)) % 0.45/0.69 (define @t210 () (or @t151 @t17 @t187 @t208)) % 0.45/0.69 (define @t211 () (not @t18)) % 0.45/0.69 (define @t212 () (or @t151 @t211 @t187)) % 0.45/0.69 (define @t213 () (=> @t20 @t208)) % 0.45/0.69 (define @t214 () (or @t123 @t150)) % 0.45/0.69 (define @t215 () (or @t69 @t151 @t18 @t124 @t214)) % 0.45/0.69 (define @t216 () (forall @t130 @t215)) % 0.45/0.69 (define @t217 () (@list @t121)) % 0.45/0.69 (define @t218 () (forall @t217 @t215)) % 0.45/0.69 (define @t219 () (forall @t217 @t214)) % 0.45/0.69 (define @t220 () (or @t69 @t151 @t18 @t124 @t219)) % 0.45/0.69 (define @t221 () (forall @t13 (or @t207 @t26))) % 0.45/0.69 (define @t222 () (or @t69 @t151 @t18 @t124 @t221)) % 0.45/0.69 (define @t223 () (or @t151 @t18 @t124 @t221)) % 0.45/0.69 (define @t224 () (or @t151 @t18 @t124)) % 0.45/0.69 (define @t225 () (=> @t30 @t221)) % 0.45/0.69 (define @t226 () (and @t54 @t125)) % 0.45/0.69 (define @t227 () (forall @t40 (not @t226))) % 0.45/0.69 (define @t228 () (not @t227)) % 0.45/0.69 (define @t229 () (|tptp.'$ki_exists_in_world_$i'| |tptp.'$ki_local_world'| @t126)) % 0.45/0.69 (define @t230 () (forall @t2 (or @t110 (tptp.combo @t1 tptp.d @t126)))) % 0.45/0.69 (define @t231 () (not @t230)) % 0.45/0.69 (define @t232 () (not @t229)) % 0.45/0.69 (define @t233 () (or @t232 @t231)) % 0.45/0.69 (define @t234 () (@list @t233)) % 0.45/0.69 (define @t235 () (not @t131)) % 0.45/0.69 (define @t236 () (tptp.closed @t111 tptp.d)) % 0.45/0.69 (define @t237 () (tptp.h |tptp.'$ki_local_world'| tptp.o)) % 0.45/0.69 (define @t238 () (tptp.combo |tptp.'$ki_local_world'| tptp.d @t126)) % 0.45/0.69 (define @t239 () (|tptp.'$ki_accessible'| |tptp.'$ki_local_world'| |tptp.'$ki_local_world'|)) % 0.45/0.69 (define @t240 () (not @t239)) % 0.45/0.69 (define @t241 () (and (or @t240 (not (tptp.closed |tptp.'$ki_local_world'| tptp.d)) @t238 (not @t237) @t117 @t236) @t235)) % 0.45/0.69 (define @t242 () (|tptp.'$ki_exists_in_world_$i'| |tptp.'$ki_local_world'| tptp.d)) % 0.45/0.69 (define @t243 () (not @t242)) % 0.45/0.69 (define @t244 () (or @t240 @t243 @t232 @t241)) % 0.45/0.69 (define @t245 () (@list false)) % 0.45/0.69 (define @t246 () (forall @t130 (or @t129 @t128 @t127 (not (tptp.h @t11 @t132)) @t123 @t122))) % 0.45/0.69 (define @t247 () (not @t246)) % 0.45/0.69 (define @t248 () (or (not (|tptp.'$ki_exists_in_world_$i'| |tptp.'$ki_local_world'| @t132)) @t247)) % 0.45/0.69 (define @t249 () (@quantifiers_skolemize @t112 0)) % 0.45/0.69 (define @t250 () (and (or (not (|tptp.'$ki_accessible'| @t111 |tptp.'$ki_local_world'|)) (and @t238 @t237)) @t113)) % 0.45/0.69 (define @t251 () (|tptp.'$ki_exists_in_world_$i'| @t111 tptp.o)) % 0.45/0.69 (define @t252 () (not @t251)) % 0.45/0.69 (define @t253 () (|tptp.'$ki_exists_in_world_$i'| @t111 @t126)) % 0.45/0.69 (define @t254 () (not @t253)) % 0.45/0.69 (define @t255 () (or @t254 @t252 @t250)) % 0.45/0.69 (define @t256 () (tptp.open @t249 tptp.d)) % 0.45/0.69 (define @t257 () (|tptp.'$ki_accessible'| @t111 @t249)) % 0.45/0.69 (define @t258 () (not @t257)) % 0.45/0.69 (define @t259 () (or @t258 @t256)) % 0.45/0.69 (define @t260 () (@list @t259)) % 0.45/0.69 (define @t261 () (@list @t111)) % 0.45/0.69 (define @t262 () (tptp.combo @t111 tptp.d @t126)) % 0.45/0.69 (define @t263 () (or @t117 @t262)) % 0.45/0.69 (define @t264 () (@list false false)) % 0.45/0.69 (define @t265 () (or @t117 @t236)) % 0.45/0.69 (define @t266 () (tptp.h @t111 @t132)) % 0.45/0.69 (define @t267 () (not @t266)) % 0.45/0.69 (define @t268 () (not @t262)) % 0.45/0.69 (define @t269 () (not @t236)) % 0.45/0.69 (define @t270 () (or @t117 @t269 @t268 @t267 @t258 @t256)) % 0.45/0.69 (define @t271 () (and @t262 @t266)) % 0.45/0.69 (define @t272 () (not @t271)) % 0.45/0.69 (define @t273 () (|tptp.'$ki_accessible'| @t111 @t111)) % 0.45/0.69 (define @t274 () (not @t273)) % 0.45/0.69 (define @t275 () (or @t274 @t271)) % 0.45/0.69 (define @t276 () (not @t275)) % 0.45/0.69 (define @t277 () (and @t275 @t113)) % 0.45/0.69 (define @t278 () (not @t277)) % 0.45/0.69 (define @t279 () (|tptp.'$ki_exists_in_world_$i'| @t111 @t132)) % 0.45/0.69 (define @t280 () (not @t279)) % 0.45/0.69 (define @t281 () (or @t254 @t280 @t277)) % 0.45/0.69 (assume @p1 (forall @t2 (|tptp.'$ki_accessible'| @t1 @t1))) % 0.45/0.69 (assume @p2 (forall (@list @t1 @t4 @t3) (=> (and (|tptp.'$ki_accessible'| @t1 @t4) (|tptp.'$ki_accessible'| @t4 @t3)) (|tptp.'$ki_accessible'| @t1 @t3)))) % 0.45/0.69 (assume @p3 @t7) % 0.45/0.69 (assume @p4 (forall @t2 (exists (@list @t5) @t6))) % 0.45/0.69 (assume @p5 @t48) % 0.45/0.69 (assume @p6 @t50) % 0.45/0.69 (assume @p7 (forall @t2 (=> @t46 (or @t51 (not @t51))))) % 0.45/0.69 (assume @p8 (forall @t2 (=> @t46 (forall @t44 (=> @t42 (not (and (tptp.open @t1 @t8) (tptp.closed @t1 @t8)))))))) % 0.45/0.69 (assume @p9 @t56) % 0.45/0.69 (assume @p10 @t68) % 0.45/0.69 (assume @p11 true) % 0.45/0.69 (step @p12 :rule bool-impl-elim :args (@t46 @t80)) % 0.45/0.69 (step @p13 :rule cong :premises (@p12) :args ((forall @t2 (=> @t46 @t80)))) % 0.45/0.69 (step @p14 :rule aci_norm :args ((= @t82 @t78))) % 0.45/0.69 (step @p15 :rule cong :premises (@p14) :args (@t83)) % 0.45/0.69 (step @p16 :rule quant-merge-prenex :args ((= (forall @t40 @t85) @t83))) % 0.45/0.69 (step @p17 :rule alpha_equiv :args (@t86 (@list @t72 @t73) (@list @t28 @t87))) % 0.45/0.69 (step @p18 :rule refl :args (@t77)) % 0.45/0.69 (step @p19 :rule nary_cong :premises (@p18 @p17) :args (@t88)) % 0.45/0.69 (step @p20 :rule quant-miniscope-or :args ((= @t85 @t88))) % 0.45/0.69 (step @p21 :rule trans :premises (@p20 @p19)) % 0.45/0.69 (step @p22 :rule symm :premises (@p21)) % 0.45/0.69 (step @p23 :rule cong :premises (@p22) :args ((forall @t40 (or @t77 @t93)))) % 0.45/0.69 (step @p24 :rule trans :premises (@p23 @p16)) % 0.45/0.69 (step @p25 :rule trans :premises (@p24 @p15)) % 0.45/0.69 (step @p26 :rule bool-double-not-elim :args (@t93)) % 0.45/0.69 (step @p27 :rule nary_cong :premises (@p18 @p26) :args ((or @t77 (not @t94)))) % 0.45/0.69 (step @p28 :rule bool-and-de-morgan :args (@t38 @t94 true)) % 0.45/0.69 (step @p29 :rule trans :premises (@p28 @p27)) % 0.45/0.69 (step @p30 :rule cong :premises (@p29) :args (@t96)) % 0.45/0.69 (step @p31 :rule trans :premises (@p30 @p25)) % 0.45/0.69 (step @p32 :rule cong :premises (@p31) :args (@t97)) % 0.45/0.69 (step @p33 :rule exists-elim :args ((= (exists @t40 @t95) @t97))) % 0.45/0.69 (step @p34 :rule trans :premises (@p33 @p32)) % 0.45/0.69 (step @p35 :rule quant-merge-prenex :args ((= (forall @t36 @t99) @t93))) % 0.45/0.69 (step @p36 :rule quant-unused-vars :args ((= @t100 @t71))) % 0.45/0.69 (step @p37 :rule alpha_equiv :args (@t101 (@list @t87) (@list @t11))) % 0.45/0.69 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t102)) % 0.45/0.69 (step @p39 :rule quant-miniscope-and :args ((= @t103 @t102))) % 0.45/0.69 (step @p40 :rule trans :premises (@p39 @p38)) % 0.45/0.69 (step @p41 :rule refl :args (@t91)) % 0.45/0.69 (step @p42 :rule nary_cong :premises (@p41 @p40) :args (@t104)) % 0.45/0.69 (step @p43 :rule quant-miniscope-or :args ((= @t99 @t104))) % 0.45/0.69 (step @p44 :rule trans :premises (@p43 @p42)) % 0.45/0.69 (step @p45 :rule symm :premises (@p44)) % 0.45/0.69 (step @p46 :rule cong :premises (@p45) :args ((forall @t36 (or @t91 (and @t105 @t71))))) % 0.45/0.69 (step @p47 :rule trans :premises (@p46 @p35)) % 0.45/0.69 (step @p48 :rule bool-implies-de-morgan :args (@t105 @t70)) % 0.45/0.69 (step @p49 :rule nary_cong :premises (@p41 @p48) :args ((or @t91 (not @t106)))) % 0.45/0.69 (step @p50 :rule bool-and-de-morgan :args (@t34 @t106 true)) % 0.45/0.69 (step @p51 :rule trans :premises (@p50 @p49)) % 0.45/0.69 (step @p52 :rule cong :premises (@p51) :args (@t108)) % 0.45/0.69 (step @p53 :rule trans :premises (@p52 @p47)) % 0.45/0.69 (step @p54 :rule cong :premises (@p53) :args (@t109)) % 0.45/0.69 (step @p55 :rule exists-elim :args ((= (exists @t36 @t107) @t109))) % 0.45/0.69 (step @p56 :rule trans :premises (@p55 @p54)) % 0.45/0.69 (step @p57 :rule bool-impl-elim :args (@t22 @t57)) % 0.45/0.69 (step @p58 :rule cong :premises (@p57) :args (@t58)) % 0.45/0.69 (step @p59 :rule bool-impl-elim :args (@t22 @t59)) % 0.45/0.69 (step @p60 :rule cong :premises (@p59) :args (@t60)) % 0.45/0.69 (step @p61 :rule cong :premises (@p60 @p58) :args (@t61)) % 0.45/0.69 (step @p62 :rule refl :args (@t34)) % 0.45/0.69 (step @p63 :rule nary_cong :premises (@p62 @p61) :args (@t62)) % 0.45/0.69 (step @p64 :rule cong :premises (@p63) :args (@t63)) % 0.45/0.69 (step @p65 :rule trans :premises (@p64 @p56)) % 0.45/0.69 (step @p66 :rule refl :args (@t38)) % 0.45/0.69 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t64)) % 0.45/0.69 (step @p68 :rule cong :premises (@p67) :args (@t65)) % 0.45/0.69 (step @p69 :rule trans :premises (@p68 @p34)) % 0.45/0.69 (step @p70 :rule refl :args (@t46)) % 0.45/0.69 (step @p71 :rule cong :premises (@p70 @p69) :args (@t66)) % 0.45/0.69 (step @p72 :rule cong :premises (@p71) :args (@t67)) % 0.45/0.69 (step @p73 :rule trans :premises (@p72 @p13)) % 0.45/0.69 (step @p74 :rule cong :premises (@p73) :args (@t68)) % 0.45/0.69 (step @p75 :rule eq_resolve :premises (@p10 @p74)) % 0.45/0.69 (step @p76 :rule skolemize :premises (@p75)) % 0.45/0.69 (step @p77 :rule bool-double-not-elim :args (@t114)) % 0.45/0.69 (step @p78 :rule refl :args (@t118)) % 0.45/0.69 (step @p79 :rule nary_cong :premises (@p78 @p77) :args ((or @t118 (not @t115)))) % 0.45/0.69 (step @p80 :rule cnf_or_neg :args (@t118 1)) % 0.45/0.69 (step @p81 :rule eq_resolve :premises (@p80 @p79)) % 0.45/0.69 (step @p82 :rule reordering :premises (@p81) :args ((or @t114 @t118))) % 0.45/0.69 (step @p83 :rule chain_m_resolution :premises (@p82 @p76) :args (@t114 @t119 @t120)) % 0.45/0.69 (step @p84 :rule instantiate :premises (@p83) :args ((@list @t126 @t132 @t111))) % 0.45/0.69 (step @p85 :rule aci_norm :args ((= @t141 (or @t110 @t139 @t138 @t137)))) % 0.45/0.69 (step @p86 :rule cong :premises (@p85) :args (@t142)) % 0.45/0.69 (step @p87 :rule quant-merge-prenex :args ((= (forall @t2 @t144) @t142))) % 0.45/0.69 (step @p88 :rule alpha_equiv :args (@t145 (@list @t133 @t134 @t136 @t135) (@list @t8 @t148 @t147 @t146))) % 0.45/0.69 (step @p89 :rule refl :args (@t110)) % 0.45/0.69 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t149)) % 0.45/0.69 (step @p91 :rule quant-miniscope-or :args ((= @t144 @t149))) % 0.45/0.69 (step @p92 :rule trans :premises (@p91 @p90)) % 0.45/0.69 (step @p93 :rule symm :premises (@p92)) % 0.45/0.69 (step @p94 :rule cong :premises (@p93) :args ((forall @t2 (or @t110 @t157)))) % 0.45/0.69 (step @p95 :rule trans :premises (@p94 @p87)) % 0.45/0.69 (step @p96 :rule trans :premises (@p95 @p86)) % 0.45/0.69 (step @p97 :rule bool-impl-elim :args (@t46 @t157)) % 0.45/0.69 (step @p98 :rule cong :premises (@p97) :args ((forall @t2 (=> @t46 @t157)))) % 0.45/0.69 (step @p99 :rule trans :premises (@p98 @p96)) % 0.45/0.69 (step @p100 :rule aci_norm :args ((= @t159 @t155))) % 0.45/0.69 (step @p101 :rule cong :premises (@p100) :args (@t160)) % 0.45/0.69 (step @p102 :rule quant-merge-prenex :args ((= (forall @t44 @t162) @t160))) % 0.45/0.69 (step @p103 :rule alpha_equiv :args (@t163 (@list @t148 @t147 @t146) (@list @t16 @t165 @t164))) % 0.45/0.69 (step @p104 :rule refl :args (@t154)) % 0.45/0.69 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t166)) % 0.45/0.69 (step @p106 :rule quant-miniscope-or :args ((= @t162 @t166))) % 0.45/0.69 (step @p107 :rule trans :premises (@p106 @p105)) % 0.45/0.69 (step @p108 :rule symm :premises (@p107)) % 0.45/0.69 (step @p109 :rule cong :premises (@p108) :args ((forall @t44 (or @t154 @t176)))) % 0.45/0.69 (step @p110 :rule trans :premises (@p109 @p102)) % 0.45/0.69 (step @p111 :rule trans :premises (@p110 @p101)) % 0.45/0.69 (step @p112 :rule bool-impl-elim :args (@t42 @t176)) % 0.45/0.69 (step @p113 :rule cong :premises (@p112) :args ((forall @t44 (=> @t42 @t176)))) % 0.45/0.69 (step @p114 :rule trans :premises (@p113 @p111)) % 0.45/0.69 (step @p115 :rule quant-merge-prenex :args ((= (forall @t40 @t178) @t176))) % 0.45/0.69 (step @p116 :rule quant-unused-vars :args ((= @t179 @t172))) % 0.45/0.69 (step @p117 :rule alpha_equiv :args (@t180 (@list @t165 @t164) (@list @t11 @t181))) % 0.45/0.69 (step @p118 :rule nary_cong :premises (@p117 @p116) :args (@t182)) % 0.45/0.69 (step @p119 :rule quant-miniscope-and :args ((= @t183 @t182))) % 0.45/0.69 (step @p120 :rule trans :premises (@p119 @p118)) % 0.45/0.69 (step @p121 :rule nary_cong :premises (@p18 @p120) :args (@t184)) % 0.45/0.69 (step @p122 :rule quant-miniscope-or :args ((= @t178 @t184))) % 0.45/0.69 (step @p123 :rule trans :premises (@p122 @p121)) % 0.45/0.69 (step @p124 :rule symm :premises (@p123)) % 0.45/0.69 (step @p125 :rule cong :premises (@p124) :args ((forall @t40 (or @t77 (and @t190 @t172))))) % 0.45/0.69 (step @p126 :rule trans :premises (@p125 @p115)) % 0.45/0.69 (step @p127 :rule refl :args (@t172)) % 0.45/0.69 (step @p128 :rule bool-double-not-elim :args (@t190)) % 0.45/0.69 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((and (not @t191) @t172))) % 0.45/0.69 (step @p130 :rule bool-or-de-morgan :args (@t191 @t171 false)) % 0.45/0.69 (step @p131 :rule trans :premises (@p130 @p129)) % 0.45/0.69 (step @p132 :rule nary_cong :premises (@p18 @p131) :args ((or @t77 @t193))) % 0.45/0.69 (step @p133 :rule bool-impl-elim :args (@t38 @t193)) % 0.45/0.69 (step @p134 :rule trans :premises (@p133 @p132)) % 0.45/0.69 (step @p135 :rule cong :premises (@p134) :args ((forall @t40 (=> @t38 @t193)))) % 0.45/0.69 (step @p136 :rule trans :premises (@p135 @p126)) % 0.45/0.69 (step @p137 :rule quant-miniscope-or :args ((= (forall @t36 @t194) @t192))) % 0.45/0.69 (step @p138 :rule aci_norm :args ((= @t195 @t194))) % 0.45/0.69 (step @p139 :rule cong :premises (@p138) :args ((forall @t36 @t195))) % 0.45/0.69 (step @p140 :rule trans :premises (@p139 @p137)) % 0.45/0.69 (step @p141 :rule aci_norm :args ((= (or @t91 (or @t169 @t191)) @t195))) % 0.45/0.69 (step @p142 :rule bool-and-de-morgan :args (@t168 @t190 true)) % 0.45/0.69 (step @p143 :rule nary_cong :premises (@p41 @p142) :args ((or @t91 (not (and @t168 @t190))))) % 0.45/0.69 (step @p144 :rule bool-and-de-morgan :args (@t34 @t168 (and @t190))) % 0.45/0.69 (step @p145 :rule trans :premises (@p144 @p143)) % 0.45/0.69 (step @p146 :rule trans :premises (@p145 @p141)) % 0.45/0.69 (step @p147 :rule cong :premises (@p146) :args (@t197)) % 0.45/0.69 (step @p148 :rule trans :premises (@p147 @p140)) % 0.45/0.69 (step @p149 :rule cong :premises (@p148) :args (@t198)) % 0.45/0.69 (step @p150 :rule exists-elim :args ((= (exists @t36 @t196) @t198))) % 0.45/0.69 (step @p151 :rule trans :premises (@p150 @p149)) % 0.45/0.69 (step @p152 :rule aci_norm :args ((= @t200 @t188))) % 0.45/0.69 (step @p153 :rule cong :premises (@p152) :args (@t201)) % 0.45/0.69 (step @p154 :rule quant-merge-prenex :args ((= (forall @t24 @t203) @t201))) % 0.45/0.69 (step @p155 :rule alpha_equiv :args (@t204 (@list @t181) @t205)) % 0.45/0.69 (step @p156 :rule refl :args (@t187)) % 0.45/0.69 (step @p157 :rule refl :args (@t17)) % 0.45/0.69 (step @p158 :rule refl :args (@t151)) % 0.45/0.69 (step @p159 :rule refl :args (@t69)) % 0.45/0.69 (step @p160 :rule nary_cong :premises (@p159 @p158 @p157 @p156 @p155) :args (@t206)) % 0.45/0.69 (step @p161 :rule quant-miniscope-or :args ((= @t203 @t206))) % 0.45/0.69 (step @p162 :rule trans :premises (@p161 @p160)) % 0.45/0.69 (step @p163 :rule symm :premises (@p162)) % 0.45/0.69 (step @p164 :rule cong :premises (@p163) :args ((forall @t24 @t209))) % 0.45/0.69 (step @p165 :rule trans :premises (@p164 @p154)) % 0.45/0.69 (step @p166 :rule trans :premises (@p165 @p153)) % 0.45/0.69 (step @p167 :rule aci_norm :args ((= (or @t69 @t210) @t209))) % 0.45/0.69 (step @p168 :rule aci_norm :args ((= (or (or @t151 @t17 @t187) @t208) @t210))) % 0.45/0.69 (step @p169 :rule refl :args (@t208)) % 0.45/0.69 (step @p170 :rule bool-double-not-elim :args (@t17)) % 0.45/0.69 (step @p171 :rule nary_cong :premises (@p158 @p170 @p156) :args (@t212)) % 0.45/0.69 (step @p172 :rule aci_norm :args ((= (or @t151 (or @t211 @t187)) @t212))) % 0.45/0.69 (step @p173 :rule trans :premises (@p172 @p171)) % 0.45/0.69 (step @p174 :rule bool-and-de-morgan :args (@t18 @t15 true)) % 0.45/0.69 (step @p175 :rule nary_cong :premises (@p158 @p174) :args ((or @t151 (not (and @t18 @t15))))) % 0.45/0.69 (step @p176 :rule bool-and-de-morgan :args (@t19 @t18 (and @t15))) % 0.45/0.69 (step @p177 :rule trans :premises (@p176 @p175)) % 0.45/0.69 (step @p178 :rule trans :premises (@p177 @p173)) % 0.45/0.69 (step @p179 :rule nary_cong :premises (@p178 @p169) :args ((or (not @t20) @t208))) % 0.45/0.69 (step @p180 :rule trans :premises (@p179 @p168)) % 0.45/0.69 (step @p181 :rule bool-impl-elim :args (@t20 @t208)) % 0.45/0.69 (step @p182 :rule trans :premises (@p181 @p180)) % 0.45/0.69 (step @p183 :rule nary_cong :premises (@p159 @p182) :args ((or @t69 @t213))) % 0.45/0.69 (step @p184 :rule trans :premises (@p183 @p167)) % 0.45/0.69 (step @p185 :rule bool-impl-elim :args (@t22 @t213)) % 0.45/0.69 (step @p186 :rule trans :premises (@p185 @p184)) % 0.45/0.69 (step @p187 :rule cong :premises (@p186) :args ((forall @t24 (=> @t22 @t213)))) % 0.45/0.69 (step @p188 :rule trans :premises (@p187 @p166)) % 0.45/0.69 (step @p189 :rule bool-impl-elim :args (@t12 @t10)) % 0.45/0.69 (step @p190 :rule cong :premises (@p189) :args (@t14)) % 0.45/0.69 (step @p191 :rule refl :args (@t20)) % 0.45/0.69 (step @p192 :rule cong :premises (@p191 @p190) :args (@t21)) % 0.45/0.69 (step @p193 :rule refl :args (@t22)) % 0.45/0.69 (step @p194 :rule cong :premises (@p193 @p192) :args (@t23)) % 0.45/0.69 (step @p195 :rule cong :premises (@p194) :args (@t25)) % 0.45/0.69 (step @p196 :rule trans :premises (@p195 @p188)) % 0.45/0.69 (step @p197 :rule aci_norm :args ((= @t215 @t167))) % 0.45/0.69 (step @p198 :rule cong :premises (@p197) :args (@t216)) % 0.45/0.69 (step @p199 :rule quant-merge-prenex :args ((= (forall @t24 @t218) @t216))) % 0.45/0.69 (step @p200 :rule alpha_equiv :args (@t219 (@list @t121) @t205)) % 0.45/0.69 (step @p201 :rule refl :args (@t124)) % 0.45/0.69 (step @p202 :rule refl :args (@t18)) % 0.45/0.69 (step @p203 :rule nary_cong :premises (@p159 @p158 @p202 @p201 @p200) :args (@t220)) % 0.45/0.69 (step @p204 :rule quant-miniscope-or :args ((= @t218 @t220))) % 0.45/0.69 (step @p205 :rule trans :premises (@p204 @p203)) % 0.45/0.69 (step @p206 :rule symm :premises (@p205)) % 0.45/0.69 (step @p207 :rule cong :premises (@p206) :args ((forall @t24 @t222))) % 0.45/0.69 (step @p208 :rule trans :premises (@p207 @p199)) % 0.45/0.69 (step @p209 :rule trans :premises (@p208 @p198)) % 0.45/0.69 (step @p210 :rule aci_norm :args ((= (or @t69 @t223) @t222))) % 0.45/0.69 (step @p211 :rule aci_norm :args ((= (or @t224 @t221) @t223))) % 0.45/0.69 (step @p212 :rule refl :args (@t221)) % 0.45/0.69 (step @p213 :rule aci_norm :args ((= (or @t151 (or @t18 @t124)) @t224))) % 0.45/0.69 (step @p214 :rule bool-and-de-morgan :args (@t17 @t29 true)) % 0.45/0.69 (step @p215 :rule nary_cong :premises (@p158 @p214) :args ((or @t151 (not (and @t17 @t29))))) % 0.45/0.69 (step @p216 :rule bool-and-de-morgan :args (@t19 @t17 (and @t29))) % 0.45/0.69 (step @p217 :rule trans :premises (@p216 @p215)) % 0.45/0.69 (step @p218 :rule trans :premises (@p217 @p213)) % 0.45/0.69 (step @p219 :rule nary_cong :premises (@p218 @p212) :args ((or (not @t30) @t221))) % 0.45/0.69 (step @p220 :rule trans :premises (@p219 @p211)) % 0.45/0.69 (step @p221 :rule bool-impl-elim :args (@t30 @t221)) % 0.45/0.69 (step @p222 :rule trans :premises (@p221 @p220)) % 0.45/0.69 (step @p223 :rule nary_cong :premises (@p159 @p222) :args ((or @t69 @t225))) % 0.45/0.69 (step @p224 :rule trans :premises (@p223 @p210)) % 0.45/0.69 (step @p225 :rule bool-impl-elim :args (@t22 @t225)) % 0.45/0.69 (step @p226 :rule trans :premises (@p225 @p224)) % 0.45/0.69 (step @p227 :rule cong :premises (@p226) :args ((forall @t24 (=> @t22 @t225)))) % 0.45/0.69 (step @p228 :rule trans :premises (@p227 @p209)) % 0.45/0.69 (step @p229 :rule bool-impl-elim :args (@t12 @t26)) % 0.45/0.69 (step @p230 :rule cong :premises (@p229) :args (@t27)) % 0.45/0.69 (step @p231 :rule refl :args (@t30)) % 0.45/0.69 (step @p232 :rule cong :premises (@p231 @p230) :args (@t31)) % 0.45/0.69 (step @p233 :rule cong :premises (@p193 @p232) :args (@t32)) % 0.45/0.69 (step @p234 :rule cong :premises (@p233) :args (@t33)) % 0.45/0.69 (step @p235 :rule trans :premises (@p234 @p228)) % 0.45/0.69 (step @p236 :rule nary_cong :premises (@p62 @p235 @p196) :args (@t35)) % 0.45/0.69 (step @p237 :rule cong :premises (@p236) :args (@t37)) % 0.45/0.69 (step @p238 :rule trans :premises (@p237 @p151)) % 0.45/0.69 (step @p239 :rule cong :premises (@p66 @p238) :args (@t39)) % 0.45/0.69 (step @p240 :rule cong :premises (@p239) :args (@t41)) % 0.45/0.69 (step @p241 :rule trans :premises (@p240 @p136)) % 0.45/0.69 (step @p242 :rule refl :args (@t42)) % 0.45/0.69 (step @p243 :rule cong :premises (@p242 @p241) :args (@t43)) % 0.45/0.69 (step @p244 :rule cong :premises (@p243) :args (@t45)) % 0.45/0.69 (step @p245 :rule trans :premises (@p244 @p114)) % 0.45/0.69 (step @p246 :rule cong :premises (@p70 @p245) :args (@t47)) % 0.45/0.69 (step @p247 :rule cong :premises (@p246) :args (@t48)) % 0.45/0.69 (step @p248 :rule trans :premises (@p247 @p99)) % 0.45/0.69 (step @p249 :rule eq_resolve :premises (@p5 @p248)) % 0.45/0.69 (step @p250 :rule instantiate :premises (@p249) :args ((@list |tptp.'$ki_local_world'| tptp.d @t126 |tptp.'$ki_local_world'| @t111))) % 0.45/0.69 (step @p251 :rule instantiate :premises (@p3) :args ((@list |tptp.'$ki_local_world'| tptp.d))) % 0.45/0.69 (step @p252 :rule instantiate :premises (@p1) :args ((@list |tptp.'$ki_local_world'|))) % 0.45/0.69 (step @p253 :rule bool-and-de-morgan :args (@t54 @t125 true)) % 0.45/0.69 (step @p254 :rule cong :premises (@p253) :args (@t227)) % 0.45/0.69 (step @p255 :rule cong :premises (@p254) :args (@t228)) % 0.45/0.69 (step @p256 :rule exists-elim :args ((= (exists @t40 @t226) @t228))) % 0.45/0.69 (step @p257 :rule trans :premises (@p256 @p255)) % 0.45/0.69 (step @p258 :rule bool-impl-elim :args (@t46 @t52)) % 0.45/0.69 (step @p259 :rule cong :premises (@p258) :args (@t53)) % 0.45/0.69 (step @p260 :rule refl :args (@t54)) % 0.45/0.69 (step @p261 :rule nary_cong :premises (@p260 @p259) :args (@t55)) % 0.45/0.69 (step @p262 :rule cong :premises (@p261) :args (@t56)) % 0.45/0.69 (step @p263 :rule trans :premises (@p262 @p257)) % 0.45/0.69 (step @p264 :rule eq_resolve :premises (@p9 @p263)) % 0.45/0.69 (step @p265 :rule skolemize :premises (@p264)) % 0.45/0.69 (step @p266 :rule bool-double-not-elim :args (@t229)) % 0.45/0.69 (step @p267 :rule refl :args (@t233)) % 0.45/0.69 (step @p268 :rule nary_cong :premises (@p267 @p266) :args ((or @t233 (not @t232)))) % 0.45/0.69 (step @p269 :rule cnf_or_neg :args (@t233 0)) % 0.45/0.69 (step @p270 :rule eq_resolve :premises (@p269 @p268)) % 0.45/0.69 (step @p271 :rule reordering :premises (@p270) :args ((or @t229 @t233))) % 0.45/0.69 (step @p272 :rule chain_m_resolution :premises (@p271 @p265) :args (@t229 @t119 @t234)) % 0.45/0.69 (step @p273 :rule cnf_or_pos :args (@t244)) % 0.45/0.69 (step @p274 :rule reordering :premises (@p273) :args ((or @t232 @t240 @t243 @t241 (not @t244)))) % 0.45/0.69 (step @p275 :rule chain_m_resolution :premises (@p274 @p272 @p252 @p251 @p250) :args (@t241 (@list false false false false) (@list @t229 @t239 @t242 @t244))) % 0.45/0.69 (step @p276 :rule cnf_and_pos :args (@t241 1)) % 0.45/0.69 (step @p277 :rule reordering :premises (@p276) :args ((or @t235 (not @t241)))) % 0.45/0.69 (step @p278 :rule chain_m_resolution :premises (@p277 @p275) :args (@t235 @t245 (@list @t241))) % 0.45/0.69 (step @p279 :rule skolemize :premises (@p278)) % 0.45/0.69 (step @p280 :rule bool-double-not-elim :args (@t246)) % 0.45/0.69 (step @p281 :rule refl :args (@t248)) % 0.45/0.69 (step @p282 :rule nary_cong :premises (@p281 @p280) :args ((or @t248 (not @t247)))) % 0.45/0.69 (step @p283 :rule cnf_or_neg :args (@t248 1)) % 0.45/0.69 (step @p284 :rule eq_resolve :premises (@p283 @p282)) % 0.45/0.69 (step @p285 :rule reordering :premises (@p284) :args ((or @t246 @t248))) % 0.45/0.69 (step @p286 :rule chain_m_resolution :premises (@p285 @p279) :args (@t246 @t119 (@list @t248))) % 0.45/0.69 (step @p287 :rule instantiate :premises (@p286) :args ((@list @t111 @t249))) % 0.45/0.69 (step @p288 :rule instantiate :premises (@p83) :args ((@list @t126 tptp.o |tptp.'$ki_local_world'|))) % 0.45/0.69 (step @p289 :rule instantiate :premises (@p3) :args ((@list @t111 tptp.o))) % 0.45/0.69 (step @p290 :rule instantiate :premises (@p3) :args ((@list @t111 @t126))) % 0.45/0.69 (step @p291 :rule cnf_or_pos :args (@t255)) % 0.45/0.69 (step @p292 :rule reordering :premises (@p291) :args ((or @t254 @t252 @t250 (not @t255)))) % 0.45/0.69 (step @p293 :rule chain_m_resolution :premises (@p292 @p290 @p289 @p288) :args (@t250 (@list false false false) (@list @t253 @t251 @t255))) % 0.45/0.69 (step @p294 :rule cnf_and_pos :args (@t250 1)) % 0.45/0.69 (step @p295 :rule reordering :premises (@p294) :args ((or @t113 (not @t250)))) % 0.45/0.69 (step @p296 :rule chain_m_resolution :premises (@p295 @p293) :args (@t113 @t245 (@list @t250))) % 0.45/0.69 (step @p297 :rule skolemize :premises (@p296)) % 0.45/0.69 (step @p298 :rule cnf_or_neg :args (@t259 1)) % 0.45/0.69 (step @p299 :rule chain_m_resolution :premises (@p298 @p297) :args ((not @t256) @t119 @t260)) % 0.45/0.69 (step @p300 :rule bool-double-not-elim :args (@t257)) % 0.45/0.69 (step @p301 :rule refl :args (@t259)) % 0.45/0.69 (step @p302 :rule nary_cong :premises (@p301 @p300) :args ((or @t259 (not @t258)))) % 0.45/0.69 (step @p303 :rule cnf_or_neg :args (@t259 0)) % 0.45/0.69 (step @p304 :rule eq_resolve :premises (@p303 @p302)) % 0.45/0.69 (step @p305 :rule reordering :premises (@p304) :args ((or @t257 @t259))) % 0.45/0.69 (step @p306 :rule chain_m_resolution :premises (@p305 @p297) :args (@t257 @t119 @t260)) % 0.45/0.69 (step @p307 :rule bool-double-not-elim :args (@t230)) % 0.45/0.69 (step @p308 :rule nary_cong :premises (@p267 @p307) :args ((or @t233 (not @t231)))) % 0.45/0.69 (step @p309 :rule cnf_or_neg :args (@t233 1)) % 0.45/0.69 (step @p310 :rule eq_resolve :premises (@p309 @p308)) % 0.45/0.69 (step @p311 :rule reordering :premises (@p310) :args ((or @t230 @t233))) % 0.45/0.69 (step @p312 :rule chain_m_resolution :premises (@p311 @p265) :args (@t230 @t119 @t234)) % 0.45/0.69 (step @p313 :rule instantiate :premises (@p312) :args (@t261)) % 0.45/0.69 (step @p314 :rule bool-double-not-elim :args (@t116)) % 0.45/0.69 (step @p315 :rule nary_cong :premises (@p78 @p314) :args ((or @t118 (not @t117)))) % 0.45/0.69 (step @p316 :rule cnf_or_neg :args (@t118 0)) % 0.45/0.69 (step @p317 :rule eq_resolve :premises (@p316 @p315)) % 0.45/0.69 (step @p318 :rule reordering :premises (@p317) :args ((or @t116 @t118))) % 0.45/0.69 (step @p319 :rule chain_m_resolution :premises (@p318 @p76) :args (@t116 @t119 @t120)) % 0.45/0.69 (step @p320 :rule cnf_or_pos :args (@t263)) % 0.45/0.69 (step @p321 :rule reordering :premises (@p320) :args ((or @t117 @t262 (not @t263)))) % 0.45/0.69 (step @p322 :rule chain_m_resolution :premises (@p321 @p319 @p313) :args (@t262 @t264 (@list @t116 @t263))) % 0.45/0.69 (step @p323 :rule bool-impl-elim :args (@t46 @t49)) % 0.45/0.69 (step @p324 :rule cong :premises (@p323) :args (@t50)) % 0.45/0.69 (step @p325 :rule eq_resolve :premises (@p6 @p324)) % 0.45/0.69 (step @p326 :rule instantiate :premises (@p325) :args (@t261)) % 0.45/0.69 (step @p327 :rule cnf_or_pos :args (@t265)) % 0.45/0.69 (step @p328 :rule reordering :premises (@p327) :args ((or @t117 @t236 (not @t265)))) % 0.45/0.69 (step @p329 :rule chain_m_resolution :premises (@p328 @p319 @p326) :args (@t236 @t264 (@list @t116 @t265))) % 0.45/0.69 (step @p330 :rule cnf_or_pos :args (@t270)) % 0.45/0.69 (step @p331 :rule reordering :premises (@p330) :args ((or @t117 @t269 @t268 @t258 @t256 @t267 (not @t270)))) % 0.45/0.69 (step @p332 :rule chain_m_resolution :premises (@p331 @p319 @p329 @p322 @p306 @p299 @p287) :args (@t267 (@list false false false false true false) (@list @t116 @t236 @t262 @t257 @t256 @t270))) % 0.45/0.69 (step @p333 :rule cnf_and_pos :args (@t271 1)) % 0.45/0.69 (step @p334 :rule reordering :premises (@p333) :args ((or @t266 @t272))) % 0.45/0.69 (step @p335 :rule chain_m_resolution :premises (@p334 @p332) :args (@t272 @t119 (@list @t266))) % 0.45/0.69 (step @p336 :rule instantiate :premises (@p1) :args (@t261)) % 0.45/0.69 (step @p337 :rule cnf_or_pos :args (@t275)) % 0.45/0.69 (step @p338 :rule reordering :premises (@p337) :args ((or @t274 @t271 @t276))) % 0.45/0.69 (step @p339 :rule chain_m_resolution :premises (@p338 @p336 @p335) :args (@t276 (@list false true) (@list @t273 @t271))) % 0.45/0.69 (step @p340 :rule cnf_and_pos :args (@t277 0)) % 0.45/0.69 (step @p341 :rule reordering :premises (@p340) :args ((or @t275 @t278))) % 0.45/0.69 (step @p342 :rule chain_m_resolution :premises (@p341 @p339) :args (@t278 @t119 (@list @t275))) % 0.45/0.69 (step @p343 :rule cnf_or_pos :args (@t281)) % 0.45/0.69 (step @p344 :rule reordering :premises (@p343) :args ((or @t254 @t280 @t277 (not @t281)))) % 0.45/0.69 (step @p345 :rule chain_m_resolution :premises (@p344 @p290 @p342 @p84) :args (@t280 (@list false true false) (@list @t253 @t277 @t281))) % 0.45/0.69 (assume-push @p352 @t7) % 0.45/0.69 (step @p347 :rule instantiate :premises (@p3) :args ((@list @t111 @t132))) % 0.45/0.69 (step-pop @p353 :rule scope :premises (@p347)) % 0.45/0.69 (step @p348 :rule process_scope :premises (@p353) :args (@t279)) % 0.45/0.69 (step @p350 :rule implies_elim :premises (@p348)) % 0.45/0.69 (step @p351 false :rule chain_m_resolution :premises (@p350 @p345 @p3) :args (false (@list true false) (@list @t279 @t7))) % 0.45/0.69 ) % 0.45/0.69 % SZS output end Proof % 0.45/0.69 % cvc5 exiting %------------------------------------------------------------------------------