%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET642+3 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n008.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 08:48:21 AM UTC 2026 % Result : Theorem 0.41s 0.62s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET642+3 : TPTP v9.2.1. Released v2.2.0. % 0.13/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n008.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:05:48 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.41/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.41/0.62 % SZS status Theorem % 0.41/0.62 % SZS output start Proof % 0.41/0.62 ( % 0.41/0.62 (declare-sort $$unsorted 0) % 0.41/0.62 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.62 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.41/0.62 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.41/0.62 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.41/0.62 (declare-const tptp.subset_type (-> $$unsorted $$unsorted)) % 0.41/0.62 (declare-const tptp.member_type (-> $$unsorted $$unsorted)) % 0.41/0.62 (declare-const tptp.set_type $$unsorted) % 0.41/0.62 (declare-const tptp.ilf_type (-> $$unsorted $$unsorted Bool)) % 0.41/0.62 (declare-const tptp.relation_type (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.62 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.41/0.62 (declare-const tptp.relation_like (-> $$unsorted Bool)) % 0.41/0.62 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.62 (define @t1 () (@var "D" $$unsorted)) % 0.41/0.62 (define @t2 () (@var "C" $$unsorted)) % 0.41/0.62 (define @t3 () (@var "B" $$unsorted)) % 0.41/0.62 (define @t4 () (tptp.subset @t3 (tptp.cross_product @t2 @t1))) % 0.41/0.62 (define @t5 () (@var "E" $$unsorted)) % 0.41/0.62 (define @t6 () (tptp.subset @t3 @t5)) % 0.41/0.62 (define @t7 () (=> @t6 @t4)) % 0.41/0.62 (define @t8 () (tptp.relation_type @t2 @t1)) % 0.41/0.62 (define @t9 () (tptp.ilf_type @t5 @t8)) % 0.41/0.62 (define @t10 () (@list @t5)) % 0.41/0.62 (define @t11 () (forall @t10 (=> @t9 @t7))) % 0.41/0.62 (define @t12 () (tptp.ilf_type @t1 tptp.set_type)) % 0.41/0.62 (define @t13 () (=> @t12 @t11)) % 0.41/0.62 (define @t14 () (@list @t1)) % 0.41/0.62 (define @t15 () (forall @t14 @t13)) % 0.41/0.62 (define @t16 () (tptp.ilf_type @t2 tptp.set_type)) % 0.41/0.62 (define @t17 () (=> @t16 @t15)) % 0.41/0.62 (define @t18 () (@list @t2)) % 0.41/0.62 (define @t19 () (forall @t18 @t17)) % 0.41/0.62 (define @t20 () (tptp.ilf_type @t3 tptp.set_type)) % 0.41/0.62 (define @t21 () (=> @t20 @t19)) % 0.41/0.62 (define @t22 () (@list @t3)) % 0.41/0.62 (define @t23 () (forall @t22 @t21)) % 0.41/0.62 (define @t24 () (tptp.ilf_type @t3 @t8)) % 0.41/0.62 (define @t25 () (=> @t4 @t24)) % 0.41/0.62 (define @t26 () (forall @t14 (=> @t12 @t25))) % 0.41/0.62 (define @t27 () (=> @t16 @t26)) % 0.41/0.62 (define @t28 () (forall @t18 @t27)) % 0.41/0.62 (define @t29 () (=> @t20 @t28)) % 0.41/0.62 (define @t30 () (forall @t22 @t29)) % 0.41/0.62 (define @t31 () (tptp.cross_product @t3 @t2)) % 0.41/0.62 (define @t32 () (tptp.subset_type @t31)) % 0.41/0.62 (define @t33 () (tptp.relation_type @t3 @t2)) % 0.41/0.62 (define @t34 () (tptp.ilf_type @t1 @t32)) % 0.41/0.62 (define @t35 () (forall @t14 (=> @t12 (=> (tptp.member @t1 @t3) (tptp.member @t1 @t2))))) % 0.41/0.62 (define @t36 () (tptp.power_set @t3)) % 0.41/0.62 (define @t37 () (tptp.ilf_type @t2 (tptp.subset_type @t3))) % 0.41/0.62 (define @t38 () (tptp.empty @t3)) % 0.41/0.62 (define @t39 () (tptp.member @t2 @t3)) % 0.41/0.62 (define @t40 () (tptp.relation_like @t3)) % 0.41/0.62 (define @t41 () (=> @t6 @t24)) % 0.41/0.62 (define @t42 () (forall @t10 (=> @t9 @t41))) % 0.41/0.62 (define @t43 () (=> @t12 @t42)) % 0.41/0.62 (define @t44 () (forall @t14 @t43)) % 0.41/0.62 (define @t45 () (=> @t16 @t44)) % 0.41/0.62 (define @t46 () (forall @t18 @t45)) % 0.41/0.62 (define @t47 () (=> @t20 @t46)) % 0.41/0.62 (define @t48 () (forall @t22 @t47)) % 0.41/0.62 (define @t49 () (not @t48)) % 0.41/0.62 (define @t50 () (@var "BOUND_VARIABLE_8107" $$unsorted)) % 0.41/0.62 (define @t51 () (not (tptp.subset @t3 @t50))) % 0.41/0.62 (define @t52 () (@var "BOUND_VARIABLE_8105" $$unsorted)) % 0.41/0.62 (define @t53 () (@var "BOUND_VARIABLE_8103" $$unsorted)) % 0.41/0.62 (define @t54 () (tptp.relation_type @t53 @t52)) % 0.41/0.62 (define @t55 () (not (tptp.ilf_type @t50 @t54))) % 0.41/0.62 (define @t56 () (tptp.ilf_type @t3 @t54)) % 0.41/0.62 (define @t57 () (not (tptp.ilf_type @t52 tptp.set_type))) % 0.41/0.62 (define @t58 () (not (tptp.ilf_type @t53 tptp.set_type))) % 0.41/0.62 (define @t59 () (not @t20)) % 0.41/0.62 (define @t60 () (or @t59 @t58 @t57 @t56 @t55 @t51)) % 0.41/0.62 (define @t61 () (or @t58 @t57 @t56 @t55 @t51)) % 0.41/0.62 (define @t62 () (or @t59 @t61)) % 0.41/0.62 (define @t63 () (@list @t3 @t53 @t52 @t50)) % 0.41/0.62 (define @t64 () (forall @t63 @t62)) % 0.41/0.62 (define @t65 () (@list @t53 @t52 @t50)) % 0.41/0.62 (define @t66 () (forall @t65 @t62)) % 0.41/0.62 (define @t67 () (forall @t65 @t61)) % 0.41/0.62 (define @t68 () (@var "BOUND_VARIABLE_8083" $$unsorted)) % 0.41/0.62 (define @t69 () (@var "BOUND_VARIABLE_8081" $$unsorted)) % 0.41/0.62 (define @t70 () (or @t59 @t67)) % 0.41/0.62 (define @t71 () (not (tptp.subset @t3 @t68))) % 0.41/0.62 (define @t72 () (tptp.relation_type @t2 @t69)) % 0.41/0.62 (define @t73 () (not (tptp.ilf_type @t68 @t72))) % 0.41/0.62 (define @t74 () (tptp.ilf_type @t3 @t72)) % 0.41/0.62 (define @t75 () (not (tptp.ilf_type @t69 tptp.set_type))) % 0.41/0.62 (define @t76 () (not @t16)) % 0.41/0.62 (define @t77 () (or @t76 @t75 @t74 @t73 @t71)) % 0.41/0.62 (define @t78 () (@list @t2 @t69 @t68)) % 0.41/0.62 (define @t79 () (forall @t78 @t77)) % 0.41/0.62 (define @t80 () (or @t75 @t74 @t73 @t71)) % 0.41/0.62 (define @t81 () (or @t76 @t80)) % 0.41/0.62 (define @t82 () (forall @t78 @t81)) % 0.41/0.62 (define @t83 () (@list @t69 @t68)) % 0.41/0.62 (define @t84 () (forall @t83 @t81)) % 0.41/0.62 (define @t85 () (forall @t83 @t80)) % 0.41/0.62 (define @t86 () (@var "BOUND_VARIABLE_8065" $$unsorted)) % 0.41/0.62 (define @t87 () (or @t76 @t85)) % 0.41/0.62 (define @t88 () (not (tptp.subset @t3 @t86))) % 0.41/0.62 (define @t89 () (not (tptp.ilf_type @t86 @t8))) % 0.41/0.62 (define @t90 () (not @t12)) % 0.41/0.62 (define @t91 () (or @t90 @t24 @t89 @t88)) % 0.41/0.62 (define @t92 () (@list @t1 @t86)) % 0.41/0.62 (define @t93 () (forall @t92 @t91)) % 0.41/0.62 (define @t94 () (or @t89 @t88)) % 0.41/0.62 (define @t95 () (or @t90 @t24 @t94)) % 0.41/0.62 (define @t96 () (forall @t92 @t95)) % 0.41/0.62 (define @t97 () (@list @t86)) % 0.41/0.62 (define @t98 () (forall @t97 @t95)) % 0.41/0.62 (define @t99 () (forall @t97 @t94)) % 0.41/0.62 (define @t100 () (@list @t5)) % 0.41/0.62 (define @t101 () (or @t90 @t24 @t99)) % 0.41/0.62 (define @t102 () (not @t6)) % 0.41/0.62 (define @t103 () (not @t9)) % 0.41/0.62 (define @t104 () (or @t103 @t102)) % 0.41/0.62 (define @t105 () (forall @t10 @t104)) % 0.41/0.62 (define @t106 () (or @t90 @t24 @t105)) % 0.41/0.62 (define @t107 () (or @t24 @t105)) % 0.41/0.62 (define @t108 () (or @t24 @t104)) % 0.41/0.62 (define @t109 () (or @t103 @t102 @t24)) % 0.41/0.62 (define @t110 () (forall @t63 @t60)) % 0.41/0.62 (define @t111 () (@quantifiers_skolemize @t110 0)) % 0.41/0.62 (define @t112 () (tptp.ilf_type @t111 tptp.set_type)) % 0.41/0.62 (define @t113 () (@quantifiers_skolemize @t110 3)) % 0.41/0.62 (define @t114 () (tptp.subset @t111 @t113)) % 0.41/0.62 (define @t115 () (not @t114)) % 0.41/0.62 (define @t116 () (@quantifiers_skolemize @t110 2)) % 0.41/0.62 (define @t117 () (@quantifiers_skolemize @t110 1)) % 0.41/0.62 (define @t118 () (tptp.relation_type @t117 @t116)) % 0.41/0.62 (define @t119 () (tptp.ilf_type @t113 @t118)) % 0.41/0.62 (define @t120 () (not @t119)) % 0.41/0.62 (define @t121 () (tptp.ilf_type @t111 @t118)) % 0.41/0.62 (define @t122 () (tptp.ilf_type @t116 tptp.set_type)) % 0.41/0.62 (define @t123 () (not @t122)) % 0.41/0.62 (define @t124 () (tptp.ilf_type @t117 tptp.set_type)) % 0.41/0.62 (define @t125 () (not @t124)) % 0.41/0.62 (define @t126 () (not @t112)) % 0.41/0.62 (define @t127 () (or @t126 @t125 @t123 @t121 @t120 @t115)) % 0.41/0.62 (define @t128 () (@list true)) % 0.41/0.62 (define @t129 () (@list @t127)) % 0.41/0.62 (define @t130 () (@var "BOUND_VARIABLE_7698" $$unsorted)) % 0.41/0.62 (define @t131 () (@var "BOUND_VARIABLE_7696" $$unsorted)) % 0.41/0.62 (define @t132 () (tptp.ilf_type @t3 (tptp.relation_type @t131 @t130))) % 0.41/0.62 (define @t133 () (not (tptp.subset @t3 (tptp.cross_product @t131 @t130)))) % 0.41/0.62 (define @t134 () (not (tptp.ilf_type @t130 tptp.set_type))) % 0.41/0.62 (define @t135 () (not (tptp.ilf_type @t131 tptp.set_type))) % 0.41/0.62 (define @t136 () (or @t135 @t134 @t133 @t132)) % 0.41/0.62 (define @t137 () (or @t59 @t136)) % 0.41/0.62 (define @t138 () (forall (@list @t3 @t131 @t130) @t137)) % 0.41/0.62 (define @t139 () (@list @t131 @t130)) % 0.41/0.62 (define @t140 () (forall @t139 @t137)) % 0.41/0.62 (define @t141 () (forall @t139 @t136)) % 0.41/0.62 (define @t142 () (@var "BOUND_VARIABLE_7677" $$unsorted)) % 0.41/0.62 (define @t143 () (or @t59 @t141)) % 0.41/0.62 (define @t144 () (tptp.ilf_type @t3 (tptp.relation_type @t2 @t142))) % 0.41/0.62 (define @t145 () (not (tptp.subset @t3 (tptp.cross_product @t2 @t142)))) % 0.41/0.62 (define @t146 () (not (tptp.ilf_type @t142 tptp.set_type))) % 0.41/0.62 (define @t147 () (or @t76 @t146 @t145 @t144)) % 0.41/0.62 (define @t148 () (@list @t2 @t142)) % 0.41/0.62 (define @t149 () (forall @t148 @t147)) % 0.41/0.62 (define @t150 () (or @t146 @t145 @t144)) % 0.41/0.62 (define @t151 () (or @t76 @t150)) % 0.41/0.62 (define @t152 () (forall @t148 @t151)) % 0.41/0.62 (define @t153 () (@list @t142)) % 0.41/0.62 (define @t154 () (forall @t153 @t151)) % 0.41/0.62 (define @t155 () (forall @t153 @t150)) % 0.41/0.62 (define @t156 () (or @t76 @t155)) % 0.41/0.62 (define @t157 () (not @t4)) % 0.41/0.62 (define @t158 () (or @t90 @t157 @t24)) % 0.41/0.62 (define @t159 () (forall @t14 @t158)) % 0.41/0.62 (define @t160 () (@var "BOUND_VARIABLE_7649" $$unsorted)) % 0.41/0.62 (define @t161 () (not (tptp.subset @t3 @t160))) % 0.41/0.62 (define @t162 () (@var "BOUND_VARIABLE_7647" $$unsorted)) % 0.41/0.62 (define @t163 () (@var "BOUND_VARIABLE_7645" $$unsorted)) % 0.41/0.62 (define @t164 () (not (tptp.ilf_type @t160 (tptp.relation_type @t163 @t162)))) % 0.41/0.62 (define @t165 () (tptp.subset @t3 (tptp.cross_product @t163 @t162))) % 0.41/0.62 (define @t166 () (not (tptp.ilf_type @t162 tptp.set_type))) % 0.41/0.62 (define @t167 () (not (tptp.ilf_type @t163 tptp.set_type))) % 0.41/0.62 (define @t168 () (or @t167 @t166 @t165 @t164 @t161)) % 0.41/0.62 (define @t169 () (or @t59 @t168)) % 0.41/0.62 (define @t170 () (forall (@list @t3 @t163 @t162 @t160) @t169)) % 0.41/0.62 (define @t171 () (@list @t163 @t162 @t160)) % 0.41/0.62 (define @t172 () (forall @t171 @t169)) % 0.41/0.62 (define @t173 () (forall @t171 @t168)) % 0.41/0.62 (define @t174 () (@var "BOUND_VARIABLE_7623" $$unsorted)) % 0.41/0.62 (define @t175 () (@var "BOUND_VARIABLE_7621" $$unsorted)) % 0.41/0.62 (define @t176 () (or @t59 @t173)) % 0.41/0.62 (define @t177 () (not (tptp.subset @t3 @t174))) % 0.41/0.62 (define @t178 () (not (tptp.ilf_type @t174 (tptp.relation_type @t2 @t175)))) % 0.41/0.62 (define @t179 () (tptp.subset @t3 (tptp.cross_product @t2 @t175))) % 0.41/0.62 (define @t180 () (not (tptp.ilf_type @t175 tptp.set_type))) % 0.41/0.62 (define @t181 () (or @t76 @t180 @t179 @t178 @t177)) % 0.41/0.62 (define @t182 () (@list @t2 @t175 @t174)) % 0.41/0.62 (define @t183 () (forall @t182 @t181)) % 0.41/0.62 (define @t184 () (or @t180 @t179 @t178 @t177)) % 0.41/0.62 (define @t185 () (or @t76 @t184)) % 0.41/0.62 (define @t186 () (forall @t182 @t185)) % 0.41/0.62 (define @t187 () (@list @t175 @t174)) % 0.41/0.62 (define @t188 () (forall @t187 @t185)) % 0.41/0.62 (define @t189 () (forall @t187 @t184)) % 0.41/0.62 (define @t190 () (@var "BOUND_VARIABLE_7604" $$unsorted)) % 0.41/0.62 (define @t191 () (or @t76 @t189)) % 0.41/0.62 (define @t192 () (not (tptp.subset @t3 @t190))) % 0.41/0.62 (define @t193 () (not (tptp.ilf_type @t190 @t8))) % 0.41/0.62 (define @t194 () (or @t90 @t4 @t193 @t192)) % 0.41/0.62 (define @t195 () (@list @t1 @t190)) % 0.41/0.62 (define @t196 () (forall @t195 @t194)) % 0.41/0.62 (define @t197 () (or @t193 @t192)) % 0.41/0.62 (define @t198 () (or @t90 @t4 @t197)) % 0.41/0.62 (define @t199 () (forall @t195 @t198)) % 0.41/0.62 (define @t200 () (@list @t190)) % 0.41/0.62 (define @t201 () (forall @t200 @t198)) % 0.41/0.62 (define @t202 () (forall @t200 @t197)) % 0.41/0.62 (define @t203 () (or @t90 @t4 @t202)) % 0.41/0.62 (define @t204 () (or @t90 @t4 @t105)) % 0.41/0.62 (define @t205 () (or @t4 @t105)) % 0.41/0.62 (define @t206 () (or @t4 @t104)) % 0.41/0.62 (define @t207 () (or @t103 @t102 @t4)) % 0.41/0.62 (define @t208 () (tptp.subset @t111 (tptp.cross_product @t117 @t116))) % 0.41/0.62 (define @t209 () (or @t126 @t125 @t123 @t208 @t120 @t115)) % 0.41/0.62 (define @t210 () (not @t208)) % 0.41/0.62 (define @t211 () (or @t126 @t125 @t123 @t210 @t121)) % 0.41/0.62 (assume @p1 @t23) % 0.41/0.62 (assume @p2 @t30) % 0.41/0.62 (assume @p3 (forall @t22 (=> @t20 (forall @t18 (=> @t16 (and (forall @t14 (=> @t34 (tptp.ilf_type @t1 @t33))) (forall @t10 (=> (tptp.ilf_type @t5 @t33) (tptp.ilf_type @t5 @t32))))))))) % 0.41/0.62 (assume @p4 (forall @t22 (=> @t20 (forall @t18 (=> @t16 (exists @t14 (tptp.ilf_type @t1 (tptp.relation_type @t2 @t3)))))))) % 0.41/0.62 (assume @p5 (forall @t22 (=> @t20 (forall @t18 (=> @t16 (= (tptp.subset @t3 @t2) @t35)))))) % 0.41/0.62 (assume @p6 (forall @t22 (=> @t20 (forall @t18 (=> @t16 (tptp.ilf_type @t31 tptp.set_type)))))) % 0.41/0.62 (assume @p7 (forall @t22 (=> @t20 (forall @t18 (=> @t16 (= @t37 (tptp.ilf_type @t2 (tptp.member_type @t36)))))))) % 0.41/0.62 (assume @p8 (forall @t22 (=> @t20 (exists @t18 @t37)))) % 0.41/0.62 (assume @p9 (forall @t22 (=> @t20 (tptp.subset @t3 @t3)))) % 0.41/0.62 (assume @p10 (forall @t22 (=> @t20 (forall @t18 (=> @t16 (= (tptp.member @t3 (tptp.power_set @t2)) @t35)))))) % 0.41/0.62 (assume @p11 (forall @t22 (=> @t20 (and (not (tptp.empty @t36)) (tptp.ilf_type @t36 tptp.set_type))))) % 0.41/0.62 (assume @p12 (forall @t22 (=> @t20 (forall @t18 (=> (and (not (tptp.empty @t2)) @t16) (= (tptp.ilf_type @t3 (tptp.member_type @t2)) (tptp.member @t3 @t2))))))) % 0.41/0.62 (assume @p13 (forall @t22 (=> (and (not @t38) @t20) (exists @t18 (tptp.ilf_type @t2 (tptp.member_type @t3)))))) % 0.41/0.62 (assume @p14 (forall @t22 (=> @t20 (= @t38 (forall @t18 (=> @t16 (not @t39))))))) % 0.41/0.62 (assume @p15 (forall @t22 (=> @t20 (= @t40 (forall @t18 (=> @t16 (=> @t39 (exists @t14 (and @t12 (exists @t10 (and (tptp.ilf_type @t5 tptp.set_type) (= @t2 (tptp.ordered_pair @t1 @t5))))))))))))) % 0.41/0.62 (assume @p16 (forall @t22 (=> (and @t38 @t20) @t40))) % 0.41/0.62 (assume @p17 (forall @t22 (=> @t20 (forall @t18 (=> @t16 (forall @t14 (=> @t34 (tptp.relation_like @t1)))))))) % 0.41/0.62 (assume @p18 (forall @t22 (=> @t20 (forall @t18 (=> @t16 (tptp.ilf_type (tptp.ordered_pair @t3 @t2) tptp.set_type)))))) % 0.41/0.62 (assume @p19 (forall @t22 @t20)) % 0.41/0.62 (assume @p20 @t49) % 0.41/0.62 (assume @p21 true) % 0.41/0.62 (step @p22 :rule aci_norm :args ((= @t62 @t60))) % 0.41/0.62 (step @p23 :rule cong :premises (@p22) :args (@t64)) % 0.41/0.62 (step @p24 :rule quant-merge-prenex :args ((= (forall @t22 @t66) @t64))) % 0.41/0.62 (step @p25 :rule alpha_equiv :args (@t67 (@list @t53 @t52 @t50) (@list @t2 @t69 @t68))) % 0.41/0.62 (step @p26 :rule refl :args (@t59)) % 0.41/0.62 (step @p27 :rule nary_cong :premises (@p26 @p25) :args (@t70)) % 0.41/0.62 (step @p28 :rule quant-miniscope-or :args ((= @t66 @t70))) % 0.41/0.62 (step @p29 :rule trans :premises (@p28 @p27)) % 0.41/0.62 (step @p30 :rule symm :premises (@p29)) % 0.41/0.62 (step @p31 :rule cong :premises (@p30) :args ((forall @t22 (or @t59 @t79)))) % 0.41/0.62 (step @p32 :rule trans :premises (@p31 @p24)) % 0.41/0.62 (step @p33 :rule trans :premises (@p32 @p23)) % 0.41/0.62 (step @p34 :rule bool-impl-elim :args (@t20 @t79)) % 0.41/0.62 (step @p35 :rule cong :premises (@p34) :args ((forall @t22 (=> @t20 @t79)))) % 0.41/0.62 (step @p36 :rule trans :premises (@p35 @p33)) % 0.41/0.62 (step @p37 :rule aci_norm :args ((= @t81 @t77))) % 0.41/0.62 (step @p38 :rule cong :premises (@p37) :args (@t82)) % 0.41/0.62 (step @p39 :rule quant-merge-prenex :args ((= (forall @t18 @t84) @t82))) % 0.41/0.62 (step @p40 :rule alpha_equiv :args (@t85 (@list @t69 @t68) (@list @t1 @t86))) % 0.41/0.62 (step @p41 :rule refl :args (@t76)) % 0.41/0.62 (step @p42 :rule nary_cong :premises (@p41 @p40) :args (@t87)) % 0.41/0.62 (step @p43 :rule quant-miniscope-or :args ((= @t84 @t87))) % 0.41/0.62 (step @p44 :rule trans :premises (@p43 @p42)) % 0.41/0.62 (step @p45 :rule symm :premises (@p44)) % 0.41/0.62 (step @p46 :rule cong :premises (@p45) :args ((forall @t18 (or @t76 @t93)))) % 0.41/0.62 (step @p47 :rule trans :premises (@p46 @p39)) % 0.41/0.62 (step @p48 :rule trans :premises (@p47 @p38)) % 0.41/0.62 (step @p49 :rule bool-impl-elim :args (@t16 @t93)) % 0.41/0.62 (step @p50 :rule cong :premises (@p49) :args ((forall @t18 (=> @t16 @t93)))) % 0.41/0.62 (step @p51 :rule trans :premises (@p50 @p48)) % 0.41/0.62 (step @p52 :rule aci_norm :args ((= @t95 @t91))) % 0.41/0.62 (step @p53 :rule cong :premises (@p52) :args (@t96)) % 0.41/0.62 (step @p54 :rule quant-merge-prenex :args ((= (forall @t14 @t98) @t96))) % 0.41/0.62 (step @p55 :rule alpha_equiv :args (@t99 (@list @t86) @t100)) % 0.41/0.62 (step @p56 :rule refl :args (@t24)) % 0.41/0.62 (step @p57 :rule refl :args (@t90)) % 0.41/0.62 (step @p58 :rule nary_cong :premises (@p57 @p56 @p55) :args (@t101)) % 0.41/0.62 (step @p59 :rule quant-miniscope-or :args ((= @t98 @t101))) % 0.41/0.62 (step @p60 :rule trans :premises (@p59 @p58)) % 0.41/0.62 (step @p61 :rule symm :premises (@p60)) % 0.41/0.62 (step @p62 :rule cong :premises (@p61) :args ((forall @t14 @t106))) % 0.41/0.62 (step @p63 :rule trans :premises (@p62 @p54)) % 0.41/0.62 (step @p64 :rule trans :premises (@p63 @p53)) % 0.41/0.62 (step @p65 :rule aci_norm :args ((= (or @t90 @t107) @t106))) % 0.41/0.62 (step @p66 :rule bool-impl-elim :args (@t12 @t107)) % 0.41/0.62 (step @p67 :rule trans :premises (@p66 @p65)) % 0.41/0.62 (step @p68 :rule cong :premises (@p67) :args ((forall @t14 (=> @t12 @t107)))) % 0.41/0.62 (step @p69 :rule trans :premises (@p68 @p64)) % 0.41/0.62 (step @p70 :rule quant-miniscope-or :args ((= (forall @t10 @t108) @t107))) % 0.41/0.62 (step @p71 :rule aci_norm :args ((= @t109 @t108))) % 0.41/0.62 (step @p72 :rule cong :premises (@p71) :args ((forall @t10 @t109))) % 0.41/0.62 (step @p73 :rule trans :premises (@p72 @p70)) % 0.41/0.62 (step @p74 :rule aci_norm :args ((= (or @t103 (or @t102 @t24)) @t109))) % 0.41/0.62 (step @p75 :rule bool-impl-elim :args (@t6 @t24)) % 0.41/0.62 (step @p76 :rule refl :args (@t103)) % 0.41/0.62 (step @p77 :rule nary_cong :premises (@p76 @p75) :args ((or @t103 @t41))) % 0.41/0.62 (step @p78 :rule trans :premises (@p77 @p74)) % 0.41/0.62 (step @p79 :rule bool-impl-elim :args (@t9 @t41)) % 0.41/0.62 (step @p80 :rule trans :premises (@p79 @p78)) % 0.41/0.62 (step @p81 :rule cong :premises (@p80) :args (@t42)) % 0.41/0.62 (step @p82 :rule trans :premises (@p81 @p73)) % 0.41/0.62 (step @p83 :rule refl :args (@t12)) % 0.41/0.62 (step @p84 :rule cong :premises (@p83 @p82) :args (@t43)) % 0.41/0.62 (step @p85 :rule cong :premises (@p84) :args (@t44)) % 0.41/0.62 (step @p86 :rule trans :premises (@p85 @p69)) % 0.41/0.62 (step @p87 :rule refl :args (@t16)) % 0.41/0.62 (step @p88 :rule cong :premises (@p87 @p86) :args (@t45)) % 0.41/0.62 (step @p89 :rule cong :premises (@p88) :args (@t46)) % 0.41/0.62 (step @p90 :rule trans :premises (@p89 @p51)) % 0.41/0.62 (step @p91 :rule refl :args (@t20)) % 0.41/0.62 (step @p92 :rule cong :premises (@p91 @p90) :args (@t47)) % 0.41/0.62 (step @p93 :rule cong :premises (@p92) :args (@t48)) % 0.41/0.62 (step @p94 :rule trans :premises (@p93 @p36)) % 0.41/0.62 (step @p95 :rule cong :premises (@p94) :args (@t49)) % 0.41/0.62 (step @p96 :rule eq_resolve :premises (@p20 @p95)) % 0.41/0.62 (step @p97 :rule skolemize :premises (@p96)) % 0.41/0.62 (step @p98 :rule bool-double-not-elim :args (@t112)) % 0.41/0.62 (step @p99 :rule refl :args (@t127)) % 0.41/0.62 (step @p100 :rule nary_cong :premises (@p99 @p98) :args ((or @t127 (not @t126)))) % 0.41/0.62 (step @p101 :rule cnf_or_neg :args (@t127 0)) % 0.41/0.62 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 0.41/0.62 (step @p103 :rule reordering :premises (@p102) :args ((or @t112 @t127))) % 0.41/0.62 (step @p104 :rule chain_m_resolution :premises (@p103 @p97) :args (@t112 @t128 @t129)) % 0.41/0.62 (step @p105 :rule bool-double-not-elim :args (@t124)) % 0.41/0.62 (step @p106 :rule nary_cong :premises (@p99 @p105) :args ((or @t127 (not @t125)))) % 0.41/0.62 (step @p107 :rule cnf_or_neg :args (@t127 1)) % 0.41/0.62 (step @p108 :rule eq_resolve :premises (@p107 @p106)) % 0.41/0.62 (step @p109 :rule reordering :premises (@p108) :args ((or @t124 @t127))) % 0.41/0.62 (step @p110 :rule chain_m_resolution :premises (@p109 @p97) :args (@t124 @t128 @t129)) % 0.41/0.62 (step @p111 :rule bool-double-not-elim :args (@t122)) % 0.41/0.62 (step @p112 :rule nary_cong :premises (@p99 @p111) :args ((or @t127 (not @t123)))) % 0.41/0.62 (step @p113 :rule cnf_or_neg :args (@t127 2)) % 0.41/0.62 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 0.41/0.62 (step @p115 :rule reordering :premises (@p114) :args ((or @t122 @t127))) % 0.41/0.62 (step @p116 :rule chain_m_resolution :premises (@p115 @p97) :args (@t122 @t128 @t129)) % 0.41/0.62 (step @p117 :rule cnf_or_neg :args (@t127 3)) % 0.41/0.62 (step @p118 :rule chain_m_resolution :premises (@p117 @p97) :args ((not @t121) @t128 @t129)) % 0.41/0.62 (step @p119 :rule aci_norm :args ((= @t137 (or @t59 @t135 @t134 @t133 @t132)))) % 0.41/0.62 (step @p120 :rule cong :premises (@p119) :args (@t138)) % 0.41/0.62 (step @p121 :rule quant-merge-prenex :args ((= (forall @t22 @t140) @t138))) % 0.41/0.62 (step @p122 :rule alpha_equiv :args (@t141 (@list @t131 @t130) (@list @t2 @t142))) % 0.41/0.62 (step @p123 :rule nary_cong :premises (@p26 @p122) :args (@t143)) % 0.41/0.62 (step @p124 :rule quant-miniscope-or :args ((= @t140 @t143))) % 0.41/0.62 (step @p125 :rule trans :premises (@p124 @p123)) % 0.41/0.62 (step @p126 :rule symm :premises (@p125)) % 0.41/0.62 (step @p127 :rule cong :premises (@p126) :args ((forall @t22 (or @t59 @t149)))) % 0.41/0.62 (step @p128 :rule trans :premises (@p127 @p121)) % 0.41/0.62 (step @p129 :rule trans :premises (@p128 @p120)) % 0.41/0.62 (step @p130 :rule bool-impl-elim :args (@t20 @t149)) % 0.41/0.62 (step @p131 :rule cong :premises (@p130) :args ((forall @t22 (=> @t20 @t149)))) % 0.41/0.62 (step @p132 :rule trans :premises (@p131 @p129)) % 0.41/0.62 (step @p133 :rule aci_norm :args ((= @t151 @t147))) % 0.41/0.62 (step @p134 :rule cong :premises (@p133) :args (@t152)) % 0.41/0.62 (step @p135 :rule quant-merge-prenex :args ((= (forall @t18 @t154) @t152))) % 0.41/0.62 (step @p136 :rule alpha_equiv :args (@t155 (@list @t142) (@list @t1))) % 0.41/0.62 (step @p137 :rule nary_cong :premises (@p41 @p136) :args (@t156)) % 0.41/0.62 (step @p138 :rule quant-miniscope-or :args ((= @t154 @t156))) % 0.41/0.62 (step @p139 :rule trans :premises (@p138 @p137)) % 0.41/0.62 (step @p140 :rule symm :premises (@p139)) % 0.41/0.62 (step @p141 :rule cong :premises (@p140) :args ((forall @t18 (or @t76 @t159)))) % 0.41/0.62 (step @p142 :rule trans :premises (@p141 @p135)) % 0.41/0.62 (step @p143 :rule trans :premises (@p142 @p134)) % 0.41/0.62 (step @p144 :rule bool-impl-elim :args (@t16 @t159)) % 0.41/0.62 (step @p145 :rule cong :premises (@p144) :args ((forall @t18 (=> @t16 @t159)))) % 0.41/0.62 (step @p146 :rule trans :premises (@p145 @p143)) % 0.41/0.62 (step @p147 :rule aci_norm :args ((= (or @t90 (or @t157 @t24)) @t158))) % 0.41/0.62 (step @p148 :rule bool-impl-elim :args (@t4 @t24)) % 0.41/0.62 (step @p149 :rule nary_cong :premises (@p57 @p148) :args ((or @t90 @t25))) % 0.41/0.62 (step @p150 :rule trans :premises (@p149 @p147)) % 0.41/0.62 (step @p151 :rule bool-impl-elim :args (@t12 @t25)) % 0.41/0.62 (step @p152 :rule trans :premises (@p151 @p150)) % 0.41/0.62 (step @p153 :rule cong :premises (@p152) :args (@t26)) % 0.41/0.62 (step @p154 :rule cong :premises (@p87 @p153) :args (@t27)) % 0.41/0.62 (step @p155 :rule cong :premises (@p154) :args (@t28)) % 0.41/0.62 (step @p156 :rule trans :premises (@p155 @p146)) % 0.41/0.62 (step @p157 :rule cong :premises (@p91 @p156) :args (@t29)) % 0.41/0.62 (step @p158 :rule cong :premises (@p157) :args (@t30)) % 0.41/0.62 (step @p159 :rule trans :premises (@p158 @p132)) % 0.41/0.62 (step @p160 :rule eq_resolve :premises (@p2 @p159)) % 0.41/0.62 (step @p161 :rule instantiate :premises (@p160) :args ((@list @t111 @t117 @t116))) % 0.41/0.62 (step @p162 :rule aci_norm :args ((= @t169 (or @t59 @t167 @t166 @t165 @t164 @t161)))) % 0.41/0.62 (step @p163 :rule cong :premises (@p162) :args (@t170)) % 0.41/0.62 (step @p164 :rule quant-merge-prenex :args ((= (forall @t22 @t172) @t170))) % 0.41/0.62 (step @p165 :rule alpha_equiv :args (@t173 (@list @t163 @t162 @t160) (@list @t2 @t175 @t174))) % 0.41/0.62 (step @p166 :rule nary_cong :premises (@p26 @p165) :args (@t176)) % 0.41/0.62 (step @p167 :rule quant-miniscope-or :args ((= @t172 @t176))) % 0.41/0.62 (step @p168 :rule trans :premises (@p167 @p166)) % 0.41/0.62 (step @p169 :rule symm :premises (@p168)) % 0.41/0.62 (step @p170 :rule cong :premises (@p169) :args ((forall @t22 (or @t59 @t183)))) % 0.41/0.62 (step @p171 :rule trans :premises (@p170 @p164)) % 0.41/0.62 (step @p172 :rule trans :premises (@p171 @p163)) % 0.41/0.62 (step @p173 :rule bool-impl-elim :args (@t20 @t183)) % 0.41/0.62 (step @p174 :rule cong :premises (@p173) :args ((forall @t22 (=> @t20 @t183)))) % 0.41/0.62 (step @p175 :rule trans :premises (@p174 @p172)) % 0.41/0.62 (step @p176 :rule aci_norm :args ((= @t185 @t181))) % 0.41/0.62 (step @p177 :rule cong :premises (@p176) :args (@t186)) % 0.41/0.62 (step @p178 :rule quant-merge-prenex :args ((= (forall @t18 @t188) @t186))) % 0.41/0.62 (step @p179 :rule alpha_equiv :args (@t189 (@list @t175 @t174) (@list @t1 @t190))) % 0.41/0.62 (step @p180 :rule nary_cong :premises (@p41 @p179) :args (@t191)) % 0.41/0.62 (step @p181 :rule quant-miniscope-or :args ((= @t188 @t191))) % 0.41/0.62 (step @p182 :rule trans :premises (@p181 @p180)) % 0.41/0.62 (step @p183 :rule symm :premises (@p182)) % 0.41/0.62 (step @p184 :rule cong :premises (@p183) :args ((forall @t18 (or @t76 @t196)))) % 0.41/0.62 (step @p185 :rule trans :premises (@p184 @p178)) % 0.41/0.62 (step @p186 :rule trans :premises (@p185 @p177)) % 0.41/0.62 (step @p187 :rule bool-impl-elim :args (@t16 @t196)) % 0.41/0.62 (step @p188 :rule cong :premises (@p187) :args ((forall @t18 (=> @t16 @t196)))) % 0.41/0.62 (step @p189 :rule trans :premises (@p188 @p186)) % 0.41/0.62 (step @p190 :rule aci_norm :args ((= @t198 @t194))) % 0.41/0.62 (step @p191 :rule cong :premises (@p190) :args (@t199)) % 0.41/0.62 (step @p192 :rule quant-merge-prenex :args ((= (forall @t14 @t201) @t199))) % 0.41/0.62 (step @p193 :rule alpha_equiv :args (@t202 (@list @t190) @t100)) % 0.41/0.62 (step @p194 :rule refl :args (@t4)) % 0.41/0.62 (step @p195 :rule nary_cong :premises (@p57 @p194 @p193) :args (@t203)) % 0.41/0.62 (step @p196 :rule quant-miniscope-or :args ((= @t201 @t203))) % 0.41/0.62 (step @p197 :rule trans :premises (@p196 @p195)) % 0.41/0.62 (step @p198 :rule symm :premises (@p197)) % 0.41/0.62 (step @p199 :rule cong :premises (@p198) :args ((forall @t14 @t204))) % 0.41/0.62 (step @p200 :rule trans :premises (@p199 @p192)) % 0.41/0.62 (step @p201 :rule trans :premises (@p200 @p191)) % 0.41/0.62 (step @p202 :rule aci_norm :args ((= (or @t90 @t205) @t204))) % 0.41/0.62 (step @p203 :rule bool-impl-elim :args (@t12 @t205)) % 0.41/0.62 (step @p204 :rule trans :premises (@p203 @p202)) % 0.41/0.62 (step @p205 :rule cong :premises (@p204) :args ((forall @t14 (=> @t12 @t205)))) % 0.41/0.62 (step @p206 :rule trans :premises (@p205 @p201)) % 0.41/0.62 (step @p207 :rule quant-miniscope-or :args ((= (forall @t10 @t206) @t205))) % 0.41/0.62 (step @p208 :rule aci_norm :args ((= @t207 @t206))) % 0.41/0.62 (step @p209 :rule cong :premises (@p208) :args ((forall @t10 @t207))) % 0.41/0.62 (step @p210 :rule trans :premises (@p209 @p207)) % 0.41/0.62 (step @p211 :rule aci_norm :args ((= (or @t103 (or @t102 @t4)) @t207))) % 0.41/0.62 (step @p212 :rule bool-impl-elim :args (@t6 @t4)) % 0.41/0.62 (step @p213 :rule nary_cong :premises (@p76 @p212) :args ((or @t103 @t7))) % 0.41/0.62 (step @p214 :rule trans :premises (@p213 @p211)) % 0.41/0.62 (step @p215 :rule bool-impl-elim :args (@t9 @t7)) % 0.41/0.62 (step @p216 :rule trans :premises (@p215 @p214)) % 0.41/0.62 (step @p217 :rule cong :premises (@p216) :args (@t11)) % 0.41/0.62 (step @p218 :rule trans :premises (@p217 @p210)) % 0.41/0.62 (step @p219 :rule cong :premises (@p83 @p218) :args (@t13)) % 0.41/0.62 (step @p220 :rule cong :premises (@p219) :args (@t15)) % 0.41/0.62 (step @p221 :rule trans :premises (@p220 @p206)) % 0.41/0.62 (step @p222 :rule cong :premises (@p87 @p221) :args (@t17)) % 0.41/0.62 (step @p223 :rule cong :premises (@p222) :args (@t19)) % 0.41/0.62 (step @p224 :rule trans :premises (@p223 @p189)) % 0.41/0.62 (step @p225 :rule cong :premises (@p91 @p224) :args (@t21)) % 0.41/0.62 (step @p226 :rule cong :premises (@p225) :args (@t23)) % 0.41/0.62 (step @p227 :rule trans :premises (@p226 @p175)) % 0.41/0.62 (step @p228 :rule eq_resolve :premises (@p1 @p227)) % 0.41/0.62 (step @p229 :rule instantiate :premises (@p228) :args ((@list @t111 @t117 @t116 @t113))) % 0.41/0.62 (step @p230 :rule bool-double-not-elim :args (@t114)) % 0.41/0.62 (step @p231 :rule nary_cong :premises (@p99 @p230) :args ((or @t127 (not @t115)))) % 0.41/0.62 (step @p232 :rule cnf_or_neg :args (@t127 5)) % 0.41/0.62 (step @p233 :rule eq_resolve :premises (@p232 @p231)) % 0.41/0.62 (step @p234 :rule reordering :premises (@p233) :args ((or @t114 @t127))) % 0.41/0.62 (step @p235 :rule chain_m_resolution :premises (@p234 @p97) :args (@t114 @t128 @t129)) % 0.41/0.62 (step @p236 :rule bool-double-not-elim :args (@t119)) % 0.41/0.62 (step @p237 :rule nary_cong :premises (@p99 @p236) :args ((or @t127 (not @t120)))) % 0.41/0.62 (step @p238 :rule cnf_or_neg :args (@t127 4)) % 0.41/0.62 (step @p239 :rule eq_resolve :premises (@p238 @p237)) % 0.41/0.62 (step @p240 :rule reordering :premises (@p239) :args ((or @t119 @t127))) % 0.41/0.62 (step @p241 :rule chain_m_resolution :premises (@p240 @p97) :args (@t119 @t128 @t129)) % 0.41/0.62 (step @p242 :rule cnf_or_pos :args (@t209)) % 0.41/0.62 (step @p243 :rule reordering :premises (@p242) :args ((or @t126 @t125 @t123 @t120 @t115 @t208 (not @t209)))) % 0.41/0.62 (step @p244 :rule chain_m_resolution :premises (@p243 @p104 @p110 @p116 @p241 @p235 @p229) :args (@t208 (@list false false false false false false) (@list @t112 @t124 @t122 @t119 @t114 @t209))) % 0.41/0.62 (step @p245 :rule cnf_or_pos :args (@t211)) % 0.41/0.62 (step @p246 :rule reordering :premises (@p245) :args ((or @t126 @t125 @t123 @t121 @t210 (not @t211)))) % 0.41/0.62 (step @p247 false :rule chain_m_resolution :premises (@p246 @p244 @p161 @p118 @p116 @p110 @p104) :args (false (@list false false true false false false) (@list @t208 @t211 @t121 @t122 @t124 @t112))) % 0.41/0.62 ) % 0.41/0.62 % SZS output end Proof % 0.41/0.62 % cvc5 exiting %------------------------------------------------------------------------------