%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET666+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 08:48:23 AM UTC 2026 % Result : Theorem 128.87s 129.05s % Output : Proof 128.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET666+3 : TPTP v9.2.1. Released v2.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n008.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:06:18 EDT 2026 % 0.16/0.35 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 128.87/129.05 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 128.87/129.05 --- Run --no-e-matching --full-saturate-quant at 6... % 128.87/129.05 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 128.87/129.05 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 128.87/129.05 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 128.87/129.05 --- Run --trigger-sel=max --full-saturate-quant at 15... % 128.87/129.05 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 128.87/129.05 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 128.87/129.05 --- Run --prenex-quant=none --full-saturate-quant at 30... % 128.87/129.05 % SZS status Theorem % 128.87/129.05 % SZS output start Proof % 128.87/129.05 ( % 128.87/129.05 (declare-sort $$unsorted 0) % 128.87/129.05 (declare-const tptp.member_type (-> $$unsorted $$unsorted)) % 128.87/129.05 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 128.87/129.05 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 128.87/129.05 (declare-const tptp.ilf_type (-> $$unsorted $$unsorted Bool)) % 128.87/129.05 (declare-const tptp.set_type $$unsorted) % 128.87/129.05 (declare-const tptp.subset_type (-> $$unsorted $$unsorted)) % 128.87/129.05 (declare-const tptp.identity_relation_of (-> $$unsorted $$unsorted)) % 128.87/129.05 (declare-const tptp.identity_relation_of_type (-> $$unsorted $$unsorted)) % 128.87/129.05 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 128.87/129.05 (declare-const tptp.relation_type (-> $$unsorted $$unsorted $$unsorted)) % 128.87/129.05 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 128.87/129.05 (declare-const tptp.empty (-> $$unsorted Bool)) % 128.87/129.05 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 128.87/129.05 (declare-const tptp.binary_relation_type $$unsorted) % 128.87/129.05 (declare-const tptp.relation_like (-> $$unsorted Bool)) % 128.87/129.05 (define @t1 () (@var "C" $$unsorted)) % 128.87/129.05 (define @t2 () (@var "B" $$unsorted)) % 128.87/129.05 (define @t3 () (tptp.cross_product @t2 @t1)) % 128.87/129.05 (define @t4 () (tptp.subset_type @t3)) % 128.87/129.05 (define @t5 () (@var "E" $$unsorted)) % 128.87/129.05 (define @t6 () (tptp.ilf_type @t5 @t4)) % 128.87/129.05 (define @t7 () (tptp.relation_type @t2 @t1)) % 128.87/129.05 (define @t8 () (tptp.ilf_type @t5 @t7)) % 128.87/129.05 (define @t9 () (@list @t5)) % 128.87/129.05 (define @t10 () (forall @t9 (=> @t8 @t6))) % 128.87/129.05 (define @t11 () (@var "D" $$unsorted)) % 128.87/129.05 (define @t12 () (tptp.ilf_type @t11 @t7)) % 128.87/129.05 (define @t13 () (tptp.ilf_type @t11 @t4)) % 128.87/129.05 (define @t14 () (@list @t11)) % 128.87/129.05 (define @t15 () (forall @t14 (=> @t13 @t12))) % 128.87/129.05 (define @t16 () (and @t15 @t10)) % 128.87/129.05 (define @t17 () (tptp.ilf_type @t1 tptp.set_type)) % 128.87/129.05 (define @t18 () (=> @t17 @t16)) % 128.87/129.05 (define @t19 () (@list @t1)) % 128.87/129.05 (define @t20 () (forall @t19 @t18)) % 128.87/129.05 (define @t21 () (tptp.ilf_type @t2 tptp.set_type)) % 128.87/129.05 (define @t22 () (=> @t21 @t20)) % 128.87/129.05 (define @t23 () (@list @t2)) % 128.87/129.05 (define @t24 () (forall @t23 @t22)) % 128.87/129.05 (define @t25 () (tptp.identity_relation_of @t2)) % 128.87/129.05 (define @t26 () (tptp.subset @t25 (tptp.cross_product @t2 @t2))) % 128.87/129.05 (define @t27 () (forall @t23 (=> @t21 @t26))) % 128.87/129.05 (define @t28 () (tptp.member @t1 @t2)) % 128.87/129.05 (define @t29 () (tptp.ilf_type @t11 tptp.set_type)) % 128.87/129.05 (define @t30 () (tptp.identity_relation_of_type @t2)) % 128.87/129.05 (define @t31 () (tptp.ilf_type @t1 @t30)) % 128.87/129.05 (define @t32 () (= @t31 (tptp.ilf_type @t1 (tptp.relation_type @t2 @t2)))) % 128.87/129.05 (define @t33 () (forall @t19 (=> @t17 @t32))) % 128.87/129.05 (define @t34 () (=> @t21 @t33)) % 128.87/129.05 (define @t35 () (forall @t23 @t34)) % 128.87/129.05 (define @t36 () (tptp.ilf_type @t3 tptp.set_type)) % 128.87/129.05 (define @t37 () (forall @t19 (=> @t17 @t36))) % 128.87/129.05 (define @t38 () (=> @t21 @t37)) % 128.87/129.05 (define @t39 () (forall @t23 @t38)) % 128.87/129.05 (define @t40 () (tptp.relation_like @t2)) % 128.87/129.05 (define @t41 () (tptp.ilf_type @t2 tptp.binary_relation_type)) % 128.87/129.05 (define @t42 () (tptp.power_set @t2)) % 128.87/129.05 (define @t43 () (tptp.ilf_type @t1 (tptp.subset_type @t2))) % 128.87/129.05 (define @t44 () (= @t43 (tptp.ilf_type @t1 (tptp.member_type @t42)))) % 128.87/129.05 (define @t45 () (forall @t19 (=> @t17 @t44))) % 128.87/129.05 (define @t46 () (=> @t21 @t45)) % 128.87/129.05 (define @t47 () (forall @t23 @t46)) % 128.87/129.05 (define @t48 () (tptp.member @t11 @t1)) % 128.87/129.05 (define @t49 () (tptp.member @t11 @t2)) % 128.87/129.05 (define @t50 () (=> @t49 @t48)) % 128.87/129.05 (define @t51 () (forall @t14 (=> @t29 @t50))) % 128.87/129.05 (define @t52 () (tptp.subset @t2 @t1)) % 128.87/129.05 (define @t53 () (= @t52 @t51)) % 128.87/129.05 (define @t54 () (=> @t17 @t53)) % 128.87/129.05 (define @t55 () (forall @t19 @t54)) % 128.87/129.05 (define @t56 () (=> @t21 @t55)) % 128.87/129.05 (define @t57 () (forall @t23 @t56)) % 128.87/129.05 (define @t58 () (tptp.power_set @t1)) % 128.87/129.05 (define @t59 () (tptp.member @t2 @t58)) % 128.87/129.05 (define @t60 () (=> @t17 (= @t59 @t51))) % 128.87/129.05 (define @t61 () (forall @t19 @t60)) % 128.87/129.05 (define @t62 () (=> @t21 @t61)) % 128.87/129.05 (define @t63 () (forall @t23 @t62)) % 128.87/129.05 (define @t64 () (and (not (tptp.empty @t42)) (tptp.ilf_type @t42 tptp.set_type))) % 128.87/129.05 (define @t65 () (forall @t23 (=> @t21 @t64))) % 128.87/129.05 (define @t66 () (tptp.member_type @t1)) % 128.87/129.05 (define @t67 () (= (tptp.ilf_type @t2 @t66) (tptp.member @t2 @t1))) % 128.87/129.05 (define @t68 () (tptp.empty @t1)) % 128.87/129.05 (define @t69 () (not @t68)) % 128.87/129.05 (define @t70 () (and @t69 @t17)) % 128.87/129.05 (define @t71 () (forall @t19 (=> @t70 @t67))) % 128.87/129.05 (define @t72 () (=> @t21 @t71)) % 128.87/129.05 (define @t73 () (forall @t23 @t72)) % 128.87/129.05 (define @t74 () (tptp.empty @t2)) % 128.87/129.05 (define @t75 () (tptp.ilf_type @t25 @t30)) % 128.87/129.05 (define @t76 () (forall @t23 (=> @t21 @t75))) % 128.87/129.05 (define @t77 () (not @t76)) % 128.87/129.05 (define @t78 () (not @t49)) % 128.87/129.05 (define @t79 () (not @t29)) % 128.87/129.05 (define @t80 () (or @t79 @t78 @t48)) % 128.87/129.05 (define @t81 () (forall @t14 @t80)) % 128.87/129.05 (define @t82 () (= @t59 @t81)) % 128.87/129.05 (define @t83 () (not @t17)) % 128.87/129.05 (define @t84 () (forall @t19 (or @t83 @t82))) % 128.87/129.05 (define @t85 () (not @t21)) % 128.87/129.05 (define @t86 () (@quantifiers_skolemize (forall @t23 (or @t85 @t75)) 0)) % 128.87/129.05 (define @t87 () (tptp.identity_relation_of @t86)) % 128.87/129.05 (define @t88 () (tptp.member @t87 @t58)) % 128.87/129.05 (define @t89 () (not (tptp.member @t11 @t87))) % 128.87/129.05 (define @t90 () (forall @t14 (or @t79 @t89 @t48))) % 128.87/129.05 (define @t91 () (or @t83 (= @t88 @t90))) % 128.87/129.05 (define @t92 () (forall @t19 @t91)) % 128.87/129.05 (define @t93 () (tptp.ilf_type @t87 tptp.set_type)) % 128.87/129.05 (define @t94 () (not @t93)) % 128.87/129.05 (define @t95 () (or @t94 @t92)) % 128.87/129.05 (define @t96 () (forall @t23 (or @t85 @t84))) % 128.87/129.05 (define @t97 () (@list @t87)) % 128.87/129.05 (define @t98 () (forall @t19 (or @t83 (= @t90 @t88)))) % 128.87/129.05 (define @t99 () (or @t94 @t98)) % 128.87/129.05 (define @t100 () (@list false)) % 128.87/129.05 (define @t101 () (@list false false)) % 128.87/129.05 (define @t102 () (tptp.cross_product @t86 @t86)) % 128.87/129.05 (define @t103 () (@list @t102)) % 128.87/129.05 (define @t104 () (forall @t19 (or @t83 @t36))) % 128.87/129.05 (define @t105 () (@list @t86)) % 128.87/129.05 (define @t106 () (tptp.ilf_type @t86 tptp.set_type)) % 128.87/129.05 (define @t107 () (tptp.identity_relation_of_type @t86)) % 128.87/129.05 (define @t108 () (tptp.ilf_type @t87 @t107)) % 128.87/129.05 (define @t109 () (not @t106)) % 128.87/129.05 (define @t110 () (or @t109 @t108)) % 128.87/129.05 (define @t111 () (@list true)) % 128.87/129.06 (define @t112 () (@list @t110)) % 128.87/129.06 (define @t113 () (tptp.cross_product @t86 @t1)) % 128.87/129.06 (define @t114 () (forall @t19 (or @t83 (tptp.ilf_type @t113 tptp.set_type)))) % 128.87/129.06 (define @t115 () (or @t109 @t114)) % 128.87/129.06 (define @t116 () (tptp.ilf_type @t102 tptp.set_type)) % 128.87/129.06 (define @t117 () (or @t109 @t116)) % 128.87/129.06 (define @t118 () (tptp.power_set @t102)) % 128.87/129.06 (define @t119 () (tptp.member @t87 @t118)) % 128.87/129.06 (define @t120 () (forall @t14 (or @t79 @t89 (tptp.member @t11 @t102)))) % 128.87/129.06 (define @t121 () (= @t120 @t119)) % 128.87/129.06 (define @t122 () (not @t116)) % 128.87/129.06 (define @t123 () (or @t122 @t121)) % 128.87/129.06 (define @t124 () (= @t52 @t81)) % 128.87/129.06 (define @t125 () (forall @t19 (or @t83 @t124))) % 128.87/129.06 (define @t126 () (forall @t19 (or @t83 (= (tptp.subset @t87 @t1) @t90)))) % 128.87/129.06 (define @t127 () (or @t94 @t126)) % 128.87/129.06 (define @t128 () (tptp.subset @t87 @t102)) % 128.87/129.06 (define @t129 () (= @t128 @t120)) % 128.87/129.06 (define @t130 () (or @t122 @t129)) % 128.87/129.06 (define @t131 () (or @t109 @t128)) % 128.87/129.06 (define @t132 () (forall @t19 (or @t83 @t44))) % 128.87/129.06 (define @t133 () (tptp.member_type @t118)) % 128.87/129.06 (define @t134 () (tptp.subset_type @t102)) % 128.87/129.06 (define @t135 () (forall @t19 (or @t83 (= (tptp.ilf_type @t1 @t134) (tptp.ilf_type @t1 @t133))))) % 128.87/129.06 (define @t136 () (or @t122 @t135)) % 128.87/129.06 (define @t137 () (tptp.ilf_type @t87 @t133)) % 128.87/129.06 (define @t138 () (tptp.ilf_type @t87 @t134)) % 128.87/129.06 (define @t139 () (= @t138 @t137)) % 128.87/129.06 (define @t140 () (or @t94 @t139)) % 128.87/129.06 (define @t141 () (and (forall @t14 (or (not @t13) @t12)) (forall @t9 (or (not @t8) @t6)))) % 128.87/129.06 (define @t142 () (forall @t19 (or @t83 @t141))) % 128.87/129.06 (define @t143 () (tptp.subset_type @t113)) % 128.87/129.06 (define @t144 () (tptp.relation_type @t86 @t1)) % 128.87/129.06 (define @t145 () (forall @t19 (or @t83 (and (forall @t14 (or (not (tptp.ilf_type @t11 @t143)) (tptp.ilf_type @t11 @t144))) (forall @t9 (or (not (tptp.ilf_type @t5 @t144)) (tptp.ilf_type @t5 @t143))))))) % 128.87/129.06 (define @t146 () (or @t109 @t145)) % 128.87/129.06 (define @t147 () (tptp.relation_type @t86 @t86)) % 128.87/129.06 (define @t148 () (forall @t14 (or (not (tptp.ilf_type @t11 @t134)) (tptp.ilf_type @t11 @t147)))) % 128.87/129.06 (define @t149 () (and @t148 (forall @t9 (or (not (tptp.ilf_type @t5 @t147)) (tptp.ilf_type @t5 @t134))))) % 128.87/129.06 (define @t150 () (or @t109 @t149)) % 128.87/129.06 (define @t151 () (forall @t19 (or @t83 @t32))) % 128.87/129.06 (define @t152 () (forall @t19 (or @t83 (= (tptp.ilf_type @t1 @t107) (tptp.ilf_type @t1 @t147))))) % 128.87/129.06 (define @t153 () (or @t109 @t152)) % 128.87/129.06 (define @t154 () (tptp.ilf_type @t87 @t147)) % 128.87/129.06 (define @t155 () (= @t108 @t154)) % 128.87/129.06 (define @t156 () (or @t94 @t155)) % 128.87/129.06 (define @t157 () (not @t154)) % 128.87/129.06 (define @t158 () (@list true false)) % 128.87/129.06 (define @t159 () (not @t138)) % 128.87/129.06 (define @t160 () (or @t159 @t154)) % 128.87/129.06 (define @t161 () (not @t137)) % 128.87/129.06 (define @t162 () (or @t68 @t83 @t67)) % 128.87/129.06 (define @t163 () (forall @t19 @t162)) % 128.87/129.06 (define @t164 () (forall @t19 (or @t68 @t83 (= (tptp.ilf_type @t87 @t66) (tptp.member @t87 @t1))))) % 128.87/129.06 (define @t165 () (or @t94 @t164)) % 128.87/129.06 (define @t166 () (tptp.ilf_type @t118 tptp.set_type)) % 128.87/129.06 (define @t167 () (not @t166)) % 128.87/129.06 (define @t168 () (tptp.empty @t118)) % 128.87/129.06 (define @t169 () (or @t168 @t167 (= @t137 @t119))) % 128.87/129.06 (define @t170 () (= @t119 @t137)) % 128.87/129.06 (define @t171 () (or @t168 @t167 @t170)) % 128.87/129.06 (define @t172 () (not @t168)) % 128.87/129.06 (define @t173 () (and @t172 @t166)) % 128.87/129.06 (define @t174 () (or @t122 @t173)) % 128.87/129.06 (define @t175 () (not @t173)) % 128.87/129.06 (define @t176 () (@list @t173)) % 128.87/129.06 (assume @p1 @t24) % 128.87/129.06 (assume @p2 (forall @t23 (=> @t21 (forall @t19 (=> @t17 (exists @t14 (tptp.ilf_type @t11 (tptp.relation_type @t1 @t2)))))))) % 128.87/129.06 (assume @p3 @t27) % 128.87/129.06 (assume @p4 (forall @t23 (=> @t21 (forall @t19 (=> @t17 (forall @t14 (=> @t29 (= (tptp.member (tptp.ordered_pair @t1 @t11) @t25) (and @t28 (= @t1 @t11)))))))))) % 128.87/129.06 (assume @p5 (forall @t23 (=> @t21 (tptp.ilf_type @t25 tptp.binary_relation_type)))) % 128.87/129.06 (assume @p6 @t35) % 128.87/129.06 (assume @p7 (forall @t23 (=> @t21 (exists @t19 @t31)))) % 128.87/129.06 (assume @p8 @t39) % 128.87/129.06 (assume @p9 (forall @t23 (=> @t21 (forall @t19 (=> @t17 (tptp.ilf_type (tptp.ordered_pair @t2 @t1) tptp.set_type)))))) % 128.87/129.06 (assume @p10 (forall @t23 (=> @t21 (= @t41 (and @t40 @t21))))) % 128.87/129.06 (assume @p11 (exists @t23 @t41)) % 128.87/129.06 (assume @p12 @t47) % 128.87/129.06 (assume @p13 (forall @t23 (=> @t21 (exists @t19 @t43)))) % 128.87/129.06 (assume @p14 @t57) % 128.87/129.06 (assume @p15 (forall @t23 (=> @t21 (tptp.subset @t2 @t2)))) % 128.87/129.06 (assume @p16 @t63) % 128.87/129.06 (assume @p17 @t65) % 128.87/129.06 (assume @p18 @t73) % 128.87/129.06 (assume @p19 (forall @t23 (=> (and (not @t74) @t21) (exists @t19 (tptp.ilf_type @t1 (tptp.member_type @t2)))))) % 128.87/129.06 (assume @p20 (forall @t23 (=> @t21 (= @t40 (forall @t19 (=> @t17 (=> @t28 (exists @t14 (and @t29 (exists @t9 (and (tptp.ilf_type @t5 tptp.set_type) (= @t1 (tptp.ordered_pair @t11 @t5))))))))))))) % 128.87/129.06 (assume @p21 (forall @t23 (=> @t21 (forall @t19 (=> @t17 (forall @t14 (=> @t13 (tptp.relation_like @t11)))))))) % 128.87/129.06 (assume @p22 (forall @t23 (=> @t21 (= @t74 (forall @t19 (=> @t17 (not @t28))))))) % 128.87/129.06 (assume @p23 (forall @t23 (=> (and @t74 @t21) @t40))) % 128.87/129.06 (assume @p24 (forall @t23 @t21)) % 128.87/129.06 (assume @p25 @t77) % 128.87/129.06 (assume @p26 true) % 128.87/129.06 (step @p27 :rule bool-impl-elim :args (@t21 @t84)) % 128.87/129.06 (step @p28 :rule cong :premises (@p27) :args ((forall @t23 (=> @t21 @t84)))) % 128.87/129.06 (step @p29 :rule bool-impl-elim :args (@t17 @t82)) % 128.87/129.06 (step @p30 :rule cong :premises (@p29) :args ((forall @t19 (=> @t17 @t82)))) % 128.87/129.06 (step @p31 :rule eq-symm :args (@t81 @t59)) % 128.87/129.06 (step @p32 :rule refl :args (@t59)) % 128.87/129.06 (step @p33 :rule aci_norm :args ((= (or @t79 (or @t78 @t48)) @t80))) % 128.87/129.06 (step @p34 :rule bool-impl-elim :args (@t49 @t48)) % 128.87/129.06 (step @p35 :rule refl :args (@t79)) % 128.87/129.06 (step @p36 :rule nary_cong :premises (@p35 @p34) :args ((or @t79 @t50))) % 128.87/129.06 (step @p37 :rule trans :premises (@p36 @p33)) % 128.87/129.06 (step @p38 :rule bool-impl-elim :args (@t29 @t50)) % 128.87/129.06 (step @p39 :rule trans :premises (@p38 @p37)) % 128.87/129.06 (step @p40 :rule cong :premises (@p39) :args (@t51)) % 128.87/129.06 (step @p41 :rule cong :premises (@p40 @p32) :args ((= @t51 @t59))) % 128.87/129.06 (step @p42 :rule trans :premises (@p41 @p31)) % 128.87/129.06 (step @p43 :rule eq-symm :args (@t59 @t51)) % 128.87/129.06 (step @p44 :rule trans :premises (@p43 @p42)) % 128.87/129.06 (step @p45 :rule refl :args (@t17)) % 128.87/129.06 (step @p46 :rule cong :premises (@p45 @p44) :args (@t60)) % 128.87/129.06 (step @p47 :rule cong :premises (@p46) :args (@t61)) % 128.87/129.06 (step @p48 :rule trans :premises (@p47 @p30)) % 128.87/129.06 (step @p49 :rule refl :args (@t21)) % 128.87/129.06 (step @p50 :rule cong :premises (@p49 @p48) :args (@t62)) % 128.87/129.06 (step @p51 :rule cong :premises (@p50) :args (@t63)) % 128.87/129.06 (step @p52 :rule trans :premises (@p51 @p28)) % 128.87/129.06 (step @p53 :rule eq_resolve :premises (@p16 @p52)) % 128.87/129.06 (step @p54 :rule eq-symm :args (@t88 @t90)) % 128.87/129.06 (step @p55 :rule refl :args (@t83)) % 128.87/129.06 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t91)) % 128.87/129.06 (step @p57 :rule cong :premises (@p56) :args (@t92)) % 128.87/129.06 (step @p58 :rule refl :args (@t94)) % 128.87/129.06 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t95)) % 128.87/129.06 (step @p60 :rule refl :args (@t96)) % 128.87/129.06 (step @p61 :rule cong :premises (@p60 @p59) :args ((=> @t96 @t95))) % 128.87/129.06 (assume-push @p264 @t96) % 128.87/129.06 (step @p63 :rule instantiate :premises (@p53) :args (@t97)) % 128.87/129.06 (step-pop @p265 :rule scope :premises (@p63)) % 128.87/129.06 (step @p64 :rule process_scope :premises (@p265) :args (@t95)) % 128.87/129.06 (step @p66 :rule eq_resolve :premises (@p64 @p61)) % 128.87/129.06 (step @p67 :rule implies_elim :premises (@p66)) % 128.87/129.06 (step @p68 :rule chain_m_resolution :premises (@p67 @p53) :args (@t99 @t100 (@list @t96))) % 128.87/129.06 (step @p69 :rule instantiate :premises (@p24) :args (@t97)) % 128.87/129.06 (step @p70 :rule cnf_or_pos :args (@t99)) % 128.87/129.06 (step @p71 :rule reordering :premises (@p70) :args ((or @t94 @t98 (not @t99)))) % 128.87/129.06 (step @p72 :rule chain_m_resolution :premises (@p71 @p69 @p68) :args (@t98 @t101 (@list @t93 @t99))) % 128.87/129.06 (step @p73 :rule instantiate :premises (@p72) :args (@t103)) % 128.87/129.06 (step @p74 :rule bool-impl-elim :args (@t21 @t104)) % 128.87/129.06 (step @p75 :rule cong :premises (@p74) :args ((forall @t23 (=> @t21 @t104)))) % 128.87/129.06 (step @p76 :rule bool-impl-elim :args (@t17 @t36)) % 128.87/129.06 (step @p77 :rule cong :premises (@p76) :args (@t37)) % 128.87/129.06 (step @p78 :rule cong :premises (@p49 @p77) :args (@t38)) % 128.87/129.06 (step @p79 :rule cong :premises (@p78) :args (@t39)) % 128.87/129.06 (step @p80 :rule trans :premises (@p79 @p75)) % 128.87/129.06 (step @p81 :rule eq_resolve :premises (@p8 @p80)) % 128.87/129.06 (step @p82 :rule instantiate :premises (@p81) :args (@t105)) % 128.87/129.06 (step @p83 :rule bool-impl-elim :args (@t21 @t75)) % 128.87/129.06 (step @p84 :rule cong :premises (@p83) :args (@t76)) % 128.87/129.06 (step @p85 :rule cong :premises (@p84) :args (@t77)) % 128.87/129.06 (step @p86 :rule eq_resolve :premises (@p25 @p85)) % 128.87/129.06 (step @p87 :rule skolemize :premises (@p86)) % 128.87/129.06 (step @p88 :rule bool-double-not-elim :args (@t106)) % 128.87/129.06 (step @p89 :rule refl :args (@t110)) % 128.87/129.06 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or @t110 (not @t109)))) % 128.87/129.06 (step @p91 :rule cnf_or_neg :args (@t110 0)) % 128.87/129.06 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 128.87/129.06 (step @p93 :rule reordering :premises (@p92) :args ((or @t106 @t110))) % 128.87/129.06 (step @p94 :rule chain_m_resolution :premises (@p93 @p87) :args (@t106 @t111 @t112)) % 128.87/129.06 (step @p95 :rule cnf_or_pos :args (@t115)) % 128.87/129.06 (step @p96 :rule reordering :premises (@p95) :args ((or @t109 @t114 (not @t115)))) % 128.87/129.06 (step @p97 :rule chain_m_resolution :premises (@p96 @p94 @p82) :args (@t114 @t101 (@list @t106 @t115))) % 128.87/129.06 (step @p98 :rule instantiate :premises (@p97) :args (@t105)) % 128.87/129.06 (step @p99 :rule cnf_or_pos :args (@t117)) % 128.87/129.06 (step @p100 :rule reordering :premises (@p99) :args ((or @t109 @t116 (not @t117)))) % 128.87/129.06 (step @p101 :rule chain_m_resolution :premises (@p100 @p94 @p98) :args (@t116 @t101 (@list @t106 @t117))) % 128.87/129.06 (step @p102 :rule cnf_or_pos :args (@t123)) % 128.87/129.06 (step @p103 :rule reordering :premises (@p102) :args ((or @t122 @t121 (not @t123)))) % 128.87/129.06 (step @p104 :rule chain_m_resolution :premises (@p103 @p101 @p73) :args (@t121 @t101 (@list @t116 @t123))) % 128.87/129.06 (step @p105 :rule bool-impl-elim :args (@t21 @t125)) % 128.87/129.06 (step @p106 :rule cong :premises (@p105) :args ((forall @t23 (=> @t21 @t125)))) % 128.87/129.06 (step @p107 :rule bool-impl-elim :args (@t17 @t124)) % 128.87/129.06 (step @p108 :rule cong :premises (@p107) :args ((forall @t19 (=> @t17 @t124)))) % 128.87/129.06 (step @p109 :rule refl :args (@t52)) % 128.87/129.06 (step @p110 :rule cong :premises (@p109 @p40) :args (@t53)) % 128.87/129.06 (step @p111 :rule cong :premises (@p45 @p110) :args (@t54)) % 128.87/129.06 (step @p112 :rule cong :premises (@p111) :args (@t55)) % 128.87/129.06 (step @p113 :rule trans :premises (@p112 @p108)) % 128.87/129.06 (step @p114 :rule cong :premises (@p49 @p113) :args (@t56)) % 128.87/129.06 (step @p115 :rule cong :premises (@p114) :args (@t57)) % 128.87/129.06 (step @p116 :rule trans :premises (@p115 @p106)) % 128.87/129.06 (step @p117 :rule eq_resolve :premises (@p14 @p116)) % 128.87/129.06 (step @p118 :rule instantiate :premises (@p117) :args (@t97)) % 128.87/129.06 (step @p119 :rule cnf_or_pos :args (@t127)) % 128.87/129.06 (step @p120 :rule reordering :premises (@p119) :args ((or @t94 @t126 (not @t127)))) % 128.87/129.06 (step @p121 :rule chain_m_resolution :premises (@p120 @p69 @p118) :args (@t126 @t101 (@list @t93 @t127))) % 128.87/129.06 (step @p122 :rule instantiate :premises (@p121) :args (@t103)) % 128.87/129.06 (step @p123 :rule cnf_or_pos :args (@t130)) % 128.87/129.06 (step @p124 :rule reordering :premises (@p123) :args ((or @t122 @t129 (not @t130)))) % 128.87/129.06 (step @p125 :rule chain_m_resolution :premises (@p124 @p101 @p122) :args (@t129 @t101 (@list @t116 @t130))) % 128.87/129.06 (step @p126 :rule bool-impl-elim :args (@t21 @t26)) % 128.87/129.06 (step @p127 :rule cong :premises (@p126) :args (@t27)) % 128.87/129.06 (step @p128 :rule eq_resolve :premises (@p3 @p127)) % 128.87/129.06 (step @p129 :rule instantiate :premises (@p128) :args (@t105)) % 128.87/129.06 (step @p130 :rule cnf_or_pos :args (@t131)) % 128.87/129.06 (step @p131 :rule reordering :premises (@p130) :args ((or @t109 @t128 (not @t131)))) % 128.87/129.06 (step @p132 :rule chain_m_resolution :premises (@p131 @p94 @p129) :args (@t128 @t101 (@list @t106 @t131))) % 128.87/129.06 (step @p133 :rule cnf_equiv_pos1 :args (@t129)) % 128.87/129.06 (step @p134 :rule reordering :premises (@p133) :args ((or (not @t128) @t120 (not @t129)))) % 128.87/129.06 (step @p135 :rule chain_m_resolution :premises (@p134 @p132 @p125) :args (@t120 @t101 (@list @t128 @t129))) % 128.87/129.06 (step @p136 :rule cnf_equiv_pos1 :args (@t121)) % 128.87/129.06 (step @p137 :rule reordering :premises (@p136) :args ((or @t119 (not @t120) (not @t121)))) % 128.87/129.06 (step @p138 :rule chain_m_resolution :premises (@p137 @p135 @p104) :args (@t119 @t101 (@list @t120 @t121))) % 128.87/129.06 (step @p139 :rule bool-impl-elim :args (@t21 @t132)) % 128.87/129.06 (step @p140 :rule cong :premises (@p139) :args ((forall @t23 (=> @t21 @t132)))) % 128.87/129.06 (step @p141 :rule bool-impl-elim :args (@t17 @t44)) % 128.87/129.06 (step @p142 :rule cong :premises (@p141) :args (@t45)) % 128.87/129.06 (step @p143 :rule cong :premises (@p49 @p142) :args (@t46)) % 128.87/129.06 (step @p144 :rule cong :premises (@p143) :args (@t47)) % 128.87/129.06 (step @p145 :rule trans :premises (@p144 @p140)) % 128.87/129.06 (step @p146 :rule eq_resolve :premises (@p12 @p145)) % 128.87/129.06 (step @p147 :rule instantiate :premises (@p146) :args (@t103)) % 128.87/129.06 (step @p148 :rule cnf_or_pos :args (@t136)) % 128.87/129.06 (step @p149 :rule reordering :premises (@p148) :args ((or @t122 @t135 (not @t136)))) % 128.87/129.06 (step @p150 :rule chain_m_resolution :premises (@p149 @p101 @p147) :args (@t135 @t101 (@list @t116 @t136))) % 128.87/129.06 (step @p151 :rule instantiate :premises (@p150) :args (@t97)) % 128.87/129.06 (step @p152 :rule cnf_or_pos :args (@t140)) % 128.87/129.06 (step @p153 :rule reordering :premises (@p152) :args ((or @t94 @t139 (not @t140)))) % 128.87/129.06 (step @p154 :rule chain_m_resolution :premises (@p153 @p69 @p151) :args (@t139 @t101 (@list @t93 @t140))) % 128.87/129.06 (step @p155 :rule bool-impl-elim :args (@t21 @t142)) % 128.87/129.06 (step @p156 :rule cong :premises (@p155) :args ((forall @t23 (=> @t21 @t142)))) % 128.87/129.06 (step @p157 :rule bool-impl-elim :args (@t17 @t141)) % 128.87/129.06 (step @p158 :rule cong :premises (@p157) :args ((forall @t19 (=> @t17 @t141)))) % 128.87/129.06 (step @p159 :rule bool-impl-elim :args (@t8 @t6)) % 128.87/129.06 (step @p160 :rule cong :premises (@p159) :args (@t10)) % 128.87/129.06 (step @p161 :rule bool-impl-elim :args (@t13 @t12)) % 128.87/129.06 (step @p162 :rule cong :premises (@p161) :args (@t15)) % 128.87/129.06 (step @p163 :rule nary_cong :premises (@p162 @p160) :args (@t16)) % 128.87/129.06 (step @p164 :rule cong :premises (@p45 @p163) :args (@t18)) % 128.87/129.06 (step @p165 :rule cong :premises (@p164) :args (@t20)) % 128.87/129.06 (step @p166 :rule trans :premises (@p165 @p158)) % 128.87/129.06 (step @p167 :rule cong :premises (@p49 @p166) :args (@t22)) % 128.87/129.06 (step @p168 :rule cong :premises (@p167) :args (@t24)) % 128.87/129.06 (step @p169 :rule trans :premises (@p168 @p156)) % 128.87/129.06 (step @p170 :rule eq_resolve :premises (@p1 @p169)) % 128.87/129.06 (step @p171 :rule instantiate :premises (@p170) :args (@t105)) % 128.87/129.06 (step @p172 :rule cnf_or_pos :args (@t146)) % 128.87/129.06 (step @p173 :rule reordering :premises (@p172) :args ((or @t109 @t145 (not @t146)))) % 128.87/129.06 (step @p174 :rule chain_m_resolution :premises (@p173 @p94 @p171) :args (@t145 @t101 (@list @t106 @t146))) % 128.87/129.06 (step @p175 :rule instantiate :premises (@p174) :args (@t105)) % 128.87/129.06 (step @p176 :rule cnf_or_pos :args (@t150)) % 128.87/129.06 (step @p177 :rule reordering :premises (@p176) :args ((or @t109 @t149 (not @t150)))) % 128.87/129.06 (step @p178 :rule chain_m_resolution :premises (@p177 @p94 @p175) :args (@t149 @t101 (@list @t106 @t150))) % 128.87/129.06 (step @p179 :rule cnf_and_pos :args (@t149 0)) % 128.87/129.06 (step @p180 :rule reordering :premises (@p179) :args ((or @t148 (not @t149)))) % 128.87/129.06 (step @p181 :rule chain_m_resolution :premises (@p180 @p178) :args (@t148 @t100 (@list @t149))) % 128.87/129.06 (step @p182 :rule instantiate :premises (@p181) :args (@t97)) % 128.87/129.06 (step @p183 :rule bool-impl-elim :args (@t21 @t151)) % 128.87/129.06 (step @p184 :rule cong :premises (@p183) :args ((forall @t23 (=> @t21 @t151)))) % 128.87/129.06 (step @p185 :rule bool-impl-elim :args (@t17 @t32)) % 128.87/129.06 (step @p186 :rule cong :premises (@p185) :args (@t33)) % 128.87/129.06 (step @p187 :rule cong :premises (@p49 @p186) :args (@t34)) % 128.87/129.06 (step @p188 :rule cong :premises (@p187) :args (@t35)) % 128.87/129.06 (step @p189 :rule trans :premises (@p188 @p184)) % 128.87/129.06 (step @p190 :rule eq_resolve :premises (@p6 @p189)) % 128.87/129.06 (step @p191 :rule instantiate :premises (@p190) :args (@t105)) % 128.87/129.06 (step @p192 :rule cnf_or_pos :args (@t153)) % 128.87/129.06 (step @p193 :rule reordering :premises (@p192) :args ((or @t109 @t152 (not @t153)))) % 128.87/129.06 (step @p194 :rule chain_m_resolution :premises (@p193 @p94 @p191) :args (@t152 @t101 (@list @t106 @t153))) % 128.87/129.06 (step @p195 :rule instantiate :premises (@p194) :args (@t97)) % 128.87/129.06 (step @p196 :rule cnf_or_pos :args (@t156)) % 128.87/129.06 (step @p197 :rule reordering :premises (@p196) :args ((or @t94 @t155 (not @t156)))) % 128.87/129.06 (step @p198 :rule chain_m_resolution :premises (@p197 @p69 @p195) :args (@t155 @t101 (@list @t93 @t156))) % 128.87/129.06 (step @p199 :rule cnf_or_neg :args (@t110 1)) % 128.87/129.06 (step @p200 :rule chain_m_resolution :premises (@p199 @p87) :args ((not @t108) @t111 @t112)) % 128.87/129.06 (step @p201 :rule cnf_equiv_pos2 :args (@t155)) % 128.87/129.06 (step @p202 :rule reordering :premises (@p201) :args ((or @t108 @t157 (not @t155)))) % 128.87/129.06 (step @p203 :rule chain_m_resolution :premises (@p202 @p200 @p198) :args (@t157 @t158 (@list @t108 @t155))) % 128.87/129.06 (step @p204 :rule cnf_or_pos :args (@t160)) % 128.87/129.06 (step @p205 :rule reordering :premises (@p204) :args ((or @t154 @t159 (not @t160)))) % 128.87/129.06 (step @p206 :rule chain_m_resolution :premises (@p205 @p203 @p182) :args (@t159 @t158 (@list @t154 @t160))) % 128.87/129.06 (step @p207 :rule cnf_equiv_pos2 :args (@t139)) % 128.87/129.06 (step @p208 :rule reordering :premises (@p207) :args ((or @t138 @t161 (not @t139)))) % 128.87/129.06 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p154) :args (@t161 @t158 (@list @t138 @t139))) % 128.87/129.06 (step @p210 :rule bool-impl-elim :args (@t21 @t163)) % 128.87/129.06 (step @p211 :rule cong :premises (@p210) :args ((forall @t23 (=> @t21 @t163)))) % 128.87/129.06 (step @p212 :rule aci_norm :args ((= (or (or @t68 @t83) @t67) @t162))) % 128.87/129.06 (step @p213 :rule refl :args (@t67)) % 128.87/129.06 (step @p214 :rule refl :args (@t83)) % 128.87/129.06 (step @p215 :rule bool-double-not-elim :args (@t68)) % 128.87/129.06 (step @p216 :rule nary_cong :premises (@p215 @p214) :args ((or (not @t69) @t83))) % 128.87/129.06 (step @p217 :rule bool-and-de-morgan :args (@t69 @t17 true)) % 128.87/129.06 (step @p218 :rule trans :premises (@p217 @p216)) % 128.87/129.06 (step @p219 :rule nary_cong :premises (@p218 @p213) :args ((or (not @t70) @t67))) % 128.87/129.06 (step @p220 :rule trans :premises (@p219 @p212)) % 128.87/129.06 (step @p221 :rule bool-impl-elim :args (@t70 @t67)) % 128.87/129.06 (step @p222 :rule trans :premises (@p221 @p220)) % 128.87/129.06 (step @p223 :rule cong :premises (@p222) :args (@t71)) % 128.87/129.06 (step @p224 :rule cong :premises (@p49 @p223) :args (@t72)) % 128.87/129.06 (step @p225 :rule cong :premises (@p224) :args (@t73)) % 128.87/129.06 (step @p226 :rule trans :premises (@p225 @p211)) % 128.87/129.06 (step @p227 :rule eq_resolve :premises (@p18 @p226)) % 128.87/129.06 (step @p228 :rule instantiate :premises (@p227) :args (@t97)) % 128.87/129.06 (step @p229 :rule cnf_or_pos :args (@t165)) % 128.87/129.06 (step @p230 :rule reordering :premises (@p229) :args ((or @t94 @t164 (not @t165)))) % 128.87/129.06 (step @p231 :rule chain_m_resolution :premises (@p230 @p69 @p228) :args (@t164 @t101 (@list @t93 @t165))) % 128.87/129.06 (step @p232 :rule eq-symm :args (@t137 @t119)) % 128.87/129.06 (step @p233 :rule refl :args (@t167)) % 128.87/129.06 (step @p234 :rule refl :args (@t168)) % 128.87/129.06 (step @p235 :rule nary_cong :premises (@p234 @p233 @p232) :args (@t169)) % 128.87/129.06 (step @p236 :rule refl :args (@t164)) % 128.87/129.06 (step @p237 :rule cong :premises (@p236 @p235) :args ((=> @t164 @t169))) % 128.87/129.06 (assume-push @p266 @t164) % 128.87/129.06 (step @p239 :rule instantiate :premises (@p231) :args ((@list @t118))) % 128.87/129.06 (step-pop @p267 :rule scope :premises (@p239)) % 128.87/129.06 (step @p240 :rule process_scope :premises (@p267) :args (@t169)) % 128.87/129.06 (step @p242 :rule eq_resolve :premises (@p240 @p237)) % 128.87/129.06 (step @p243 :rule implies_elim :premises (@p242)) % 128.87/129.06 (step @p244 :rule chain_m_resolution :premises (@p243 @p231) :args (@t171 @t100 (@list @t164))) % 128.87/129.06 (step @p245 :rule bool-impl-elim :args (@t21 @t64)) % 128.87/129.06 (step @p246 :rule cong :premises (@p245) :args (@t65)) % 128.87/129.06 (step @p247 :rule eq_resolve :premises (@p17 @p246)) % 128.87/129.06 (step @p248 :rule instantiate :premises (@p247) :args (@t103)) % 128.87/129.06 (step @p249 :rule cnf_or_pos :args (@t174)) % 128.87/129.06 (step @p250 :rule reordering :premises (@p249) :args ((or @t122 @t173 (not @t174)))) % 128.87/129.06 (step @p251 :rule chain_m_resolution :premises (@p250 @p101 @p248) :args (@t173 @t101 (@list @t116 @t174))) % 128.87/129.06 (step @p252 :rule cnf_and_pos :args (@t173 1)) % 128.87/129.06 (step @p253 :rule reordering :premises (@p252) :args ((or @t166 @t175))) % 128.87/129.06 (step @p254 :rule chain_m_resolution :premises (@p253 @p251) :args (@t166 @t100 @t176)) % 128.87/129.06 (step @p255 :rule cnf_and_pos :args (@t173 0)) % 128.87/129.06 (step @p256 :rule reordering :premises (@p255) :args ((or @t172 @t175))) % 128.87/129.06 (step @p257 :rule chain_m_resolution :premises (@p256 @p251) :args (@t172 @t100 @t176)) % 128.87/129.06 (step @p258 :rule cnf_or_pos :args (@t171)) % 128.87/129.06 (step @p259 :rule reordering :premises (@p258) :args ((or @t168 @t167 @t170 (not @t171)))) % 128.87/129.06 (step @p260 :rule chain_m_resolution :premises (@p259 @p257 @p254 @p244) :args (@t170 (@list true false false) (@list @t168 @t166 @t171))) % 128.87/129.06 (step @p261 :rule cnf_equiv_pos1 :args (@t170)) % 128.87/129.06 (step @p262 :rule reordering :premises (@p261) :args ((or (not @t119) @t137 (not @t170)))) % 128.87/129.06 (step @p263 false :rule chain_m_resolution :premises (@p262 @p260 @p209 @p138) :args (false (@list false true false) (@list @t170 @t137 @t119))) % 128.87/129.06 ) % 128.87/129.06 % SZS output end Proof % 128.87/129.06 % cvc5 exiting %------------------------------------------------------------------------------