%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET716+4 : TPTP v9.2.1. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:48:30 AM UTC 2026 % Result : Theorem 0.39s 0.62s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET716+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n021.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 16:11:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.62 % SZS status Theorem % 0.39/0.62 % SZS output start Proof % 0.39/0.62 ( % 0.39/0.62 (declare-sort $$unsorted 0) % 0.39/0.62 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.empty_set $$unsorted) % 0.39/0.62 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.62 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (define @t1 () (@var "B" $$unsorted)) % 0.39/0.62 (define @t2 () (@var "X" $$unsorted)) % 0.39/0.62 (define @t3 () (tptp.member @t2 @t1)) % 0.39/0.62 (define @t4 () (@var "A" $$unsorted)) % 0.39/0.62 (define @t5 () (tptp.member @t2 @t4)) % 0.39/0.62 (define @t6 () (@list @t2)) % 0.39/0.62 (define @t7 () (tptp.subset @t4 @t1)) % 0.39/0.62 (define @t8 () (@list @t4 @t1)) % 0.39/0.62 (define @t9 () (@list @t2 @t4)) % 0.39/0.62 (define @t10 () (@list @t2 @t4 @t1)) % 0.39/0.62 (define @t11 () (@var "E" $$unsorted)) % 0.39/0.62 (define @t12 () (= @t2 @t4)) % 0.39/0.62 (define @t13 () (@var "Y" $$unsorted)) % 0.39/0.62 (define @t14 () (tptp.member @t2 @t13)) % 0.39/0.62 (define @t15 () (tptp.member @t13 @t4)) % 0.39/0.62 (define @t16 () (@list @t13)) % 0.39/0.62 (define @t17 () (@var "Y2" $$unsorted)) % 0.39/0.62 (define @t18 () (@var "Y1" $$unsorted)) % 0.39/0.62 (define @t19 () (= @t18 @t17)) % 0.39/0.62 (define @t20 () (@var "F" $$unsorted)) % 0.39/0.62 (define @t21 () (tptp.apply @t20 @t2 @t18)) % 0.39/0.62 (define @t22 () (tptp.member @t17 @t1)) % 0.39/0.62 (define @t23 () (tptp.member @t18 @t1)) % 0.39/0.62 (define @t24 () (and @t5 @t23 @t22)) % 0.39/0.62 (define @t25 () (@list @t2 @t18 @t17)) % 0.39/0.62 (define @t26 () (tptp.apply @t20 @t2 @t13)) % 0.39/0.62 (define @t27 () (tptp.member @t13 @t1)) % 0.39/0.62 (define @t28 () (exists @t16 (and @t27 @t26))) % 0.39/0.62 (define @t29 () (tptp.maps @t20 @t4 @t1)) % 0.39/0.62 (define @t30 () (@list @t20 @t4 @t1)) % 0.39/0.62 (define @t31 () (@var "Z" $$unsorted)) % 0.39/0.62 (define @t32 () (@var "G" $$unsorted)) % 0.39/0.62 (define @t33 () (tptp.apply @t32 @t13 @t31)) % 0.39/0.62 (define @t34 () (and @t27 @t26 @t33)) % 0.39/0.62 (define @t35 () (exists @t16 @t34)) % 0.39/0.62 (define @t36 () (@var "H" $$unsorted)) % 0.39/0.62 (define @t37 () (@var "C" $$unsorted)) % 0.39/0.62 (define @t38 () (tptp.member @t31 @t37)) % 0.39/0.62 (define @t39 () (and @t5 @t38)) % 0.39/0.62 (define @t40 () (tptp.compose_function @t32 @t20 @t4 @t1 @t37)) % 0.39/0.62 (define @t41 () (tptp.apply @t40 @t2 @t31)) % 0.39/0.62 (define @t42 () (=> @t39 (= @t41 @t35))) % 0.39/0.62 (define @t43 () (@list @t32 @t20 @t4 @t1 @t37 @t2 @t31)) % 0.39/0.62 (define @t44 () (forall @t43 @t42)) % 0.39/0.62 (define @t45 () (@var "X2" $$unsorted)) % 0.39/0.62 (define @t46 () (@var "X1" $$unsorted)) % 0.39/0.62 (define @t47 () (= @t46 @t45)) % 0.39/0.62 (define @t48 () (tptp.apply @t20 @t45 @t13)) % 0.39/0.62 (define @t49 () (tptp.apply @t20 @t46 @t13)) % 0.39/0.62 (define @t50 () (and @t49 @t48)) % 0.39/0.62 (define @t51 () (=> @t50 @t47)) % 0.39/0.62 (define @t52 () (tptp.member @t45 @t4)) % 0.39/0.62 (define @t53 () (tptp.member @t46 @t4)) % 0.39/0.62 (define @t54 () (and @t53 @t52 @t27)) % 0.39/0.62 (define @t55 () (@list @t46 @t45 @t13)) % 0.39/0.62 (define @t56 () (forall @t55 (=> @t54 @t51))) % 0.39/0.62 (define @t57 () (tptp.injective @t20 @t4 @t1)) % 0.39/0.62 (define @t58 () (= @t57 @t56)) % 0.39/0.62 (define @t59 () (forall @t30 @t58)) % 0.39/0.62 (define @t60 () (tptp.surjective @t20 @t4 @t1)) % 0.39/0.62 (define @t61 () (tptp.one_to_one @t20 @t4 @t1)) % 0.39/0.62 (define @t62 () (and @t5 @t27)) % 0.39/0.62 (define @t63 () (exists @t6 (and @t5 @t26))) % 0.39/0.62 (define @t64 () (@var "S" $$unsorted)) % 0.39/0.62 (define @t65 () (tptp.apply @t64 @t18 @t17)) % 0.39/0.62 (define @t66 () (tptp.apply @t20 @t45 @t17)) % 0.39/0.62 (define @t67 () (tptp.apply @t20 @t46 @t18)) % 0.39/0.62 (define @t68 () (@var "R" $$unsorted)) % 0.39/0.62 (define @t69 () (tptp.apply @t68 @t46 @t45)) % 0.39/0.62 (define @t70 () (and @t53 @t23 @t52 @t22 @t69 @t67 @t66)) % 0.39/0.62 (define @t71 () (@list @t46 @t18 @t45 @t17)) % 0.39/0.62 (define @t72 () (@list @t20 @t4 @t68 @t1 @t64)) % 0.39/0.62 (define @t73 () (tptp.injective @t40 @t4 @t37)) % 0.39/0.62 (define @t74 () (tptp.injective @t32 @t1 @t37)) % 0.39/0.62 (define @t75 () (tptp.maps @t32 @t1 @t37)) % 0.39/0.62 (define @t76 () (and @t29 @t75 @t57 @t74)) % 0.39/0.62 (define @t77 () (@list @t20 @t32 @t4 @t1 @t37)) % 0.39/0.62 (define @t78 () (forall @t77 (=> @t76 @t73))) % 0.39/0.62 (define @t79 () (not @t78)) % 0.39/0.62 (define @t80 () (not @t33)) % 0.39/0.62 (define @t81 () (not @t26)) % 0.39/0.62 (define @t82 () (not @t27)) % 0.39/0.62 (define @t83 () (or @t82 @t81 @t80)) % 0.39/0.62 (define @t84 () (not (forall @t16 @t83))) % 0.39/0.62 (define @t85 () (= @t41 @t84)) % 0.39/0.62 (define @t86 () (not @t38)) % 0.39/0.62 (define @t87 () (not @t5)) % 0.39/0.62 (define @t88 () (forall @t16 (not @t34))) % 0.39/0.62 (define @t89 () (not @t88)) % 0.39/0.62 (define @t90 () (not @t74)) % 0.39/0.62 (define @t91 () (not @t57)) % 0.39/0.62 (define @t92 () (not @t75)) % 0.39/0.62 (define @t93 () (not @t29)) % 0.39/0.62 (define @t94 () (or @t93 @t92 @t91 @t90 @t73)) % 0.39/0.62 (define @t95 () (forall @t77 @t94)) % 0.39/0.62 (define @t96 () (@quantifiers_skolemize @t95 4)) % 0.39/0.62 (define @t97 () (@quantifiers_skolemize @t95 3)) % 0.39/0.62 (define @t98 () (@quantifiers_skolemize @t95 2)) % 0.39/0.62 (define @t99 () (@quantifiers_skolemize @t95 0)) % 0.39/0.62 (define @t100 () (@quantifiers_skolemize @t95 1)) % 0.39/0.62 (define @t101 () (tptp.compose_function @t100 @t99 @t98 @t97 @t96)) % 0.39/0.62 (define @t102 () (not (tptp.member @t13 @t96))) % 0.39/0.62 (define @t103 () (not (tptp.member @t45 @t98))) % 0.39/0.62 (define @t104 () (not (tptp.member @t46 @t98))) % 0.39/0.62 (define @t105 () (forall @t55 (or @t104 @t103 @t102 (not (tptp.apply @t101 @t46 @t13)) (not (tptp.apply @t101 @t45 @t13)) @t47))) % 0.39/0.62 (define @t106 () (@quantifiers_skolemize @t105 2)) % 0.39/0.62 (define @t107 () (@quantifiers_skolemize @t105 0)) % 0.39/0.62 (define @t108 () (not @t48)) % 0.39/0.62 (define @t109 () (not @t49)) % 0.39/0.62 (define @t110 () (not @t52)) % 0.39/0.62 (define @t111 () (not @t53)) % 0.39/0.62 (define @t112 () (or @t109 @t108 @t47)) % 0.39/0.62 (define @t113 () (or @t111 @t110 @t82)) % 0.39/0.62 (define @t114 () (or @t93 @t92 @t91 @t90)) % 0.39/0.62 (define @t115 () (tptp.injective @t101 @t98 @t96)) % 0.39/0.62 (define @t116 () (tptp.injective @t100 @t97 @t96)) % 0.39/0.62 (define @t117 () (not @t116)) % 0.39/0.62 (define @t118 () (tptp.injective @t99 @t98 @t97)) % 0.39/0.62 (define @t119 () (not @t118)) % 0.39/0.62 (define @t120 () (or (not (tptp.maps @t99 @t98 @t97)) (not (tptp.maps @t100 @t97 @t96)) @t119 @t117 @t115)) % 0.39/0.62 (define @t121 () (@list true)) % 0.39/0.62 (define @t122 () (@list @t120)) % 0.39/0.62 (define @t123 () (= @t115 @t105)) % 0.39/0.62 (define @t124 () (not @t105)) % 0.39/0.62 (define @t125 () (tptp.member @t106 @t96)) % 0.39/0.62 (define @t126 () (@quantifiers_skolemize @t105 1)) % 0.39/0.62 (define @t127 () (= @t107 @t126)) % 0.39/0.62 (define @t128 () (tptp.apply @t101 @t126 @t106)) % 0.39/0.62 (define @t129 () (not @t128)) % 0.39/0.62 (define @t130 () (tptp.apply @t101 @t107 @t106)) % 0.39/0.62 (define @t131 () (not @t130)) % 0.39/0.62 (define @t132 () (not @t125)) % 0.39/0.62 (define @t133 () (tptp.member @t126 @t98)) % 0.39/0.62 (define @t134 () (not @t133)) % 0.39/0.62 (define @t135 () (tptp.member @t107 @t98)) % 0.39/0.62 (define @t136 () (not @t135)) % 0.39/0.62 (define @t137 () (or @t136 @t134 @t132 @t131 @t129 @t127)) % 0.39/0.62 (define @t138 () (@list @t137)) % 0.39/0.62 (define @t139 () (not (tptp.apply @t100 @t13 @t106))) % 0.39/0.62 (define @t140 () (not (tptp.member @t13 @t97))) % 0.39/0.62 (define @t141 () (forall @t16 (or @t140 (not (tptp.apply @t99 @t107 @t13)) @t139))) % 0.39/0.62 (define @t142 () (not @t141)) % 0.39/0.62 (define @t143 () (= @t130 @t142)) % 0.39/0.62 (define @t144 () (or @t136 @t132 @t143)) % 0.39/0.62 (define @t145 () (@list false false false)) % 0.39/0.62 (define @t146 () (@list false false)) % 0.39/0.62 (define @t147 () (@quantifiers_skolemize @t141 0)) % 0.39/0.62 (define @t148 () (tptp.apply @t99 @t107 @t147)) % 0.39/0.62 (define @t149 () (tptp.apply @t100 @t147 @t106)) % 0.39/0.62 (define @t150 () (not @t149)) % 0.39/0.62 (define @t151 () (not @t148)) % 0.39/0.62 (define @t152 () (tptp.member @t147 @t97)) % 0.39/0.62 (define @t153 () (not @t152)) % 0.39/0.62 (define @t154 () (or @t153 @t151 @t150)) % 0.39/0.62 (define @t155 () (@list @t154)) % 0.39/0.62 (define @t156 () (forall @t55 (or (not (tptp.member @t46 @t97)) (not (tptp.member @t45 @t97)) @t102 (not (tptp.apply @t100 @t46 @t13)) (not (tptp.apply @t100 @t45 @t13)) @t47))) % 0.39/0.62 (define @t157 () (= @t116 @t156)) % 0.39/0.62 (define @t158 () (forall @t16 (or @t140 (not (tptp.apply @t99 @t126 @t13)) @t139))) % 0.39/0.62 (define @t159 () (@quantifiers_skolemize @t158 0)) % 0.39/0.62 (define @t160 () (not @t158)) % 0.39/0.62 (define @t161 () (= @t128 @t160)) % 0.39/0.62 (define @t162 () (or @t134 @t132 @t161)) % 0.39/0.62 (define @t163 () (tptp.apply @t100 @t159 @t106)) % 0.39/0.62 (define @t164 () (not @t163)) % 0.39/0.62 (define @t165 () (tptp.apply @t99 @t126 @t159)) % 0.39/0.62 (define @t166 () (not @t165)) % 0.39/0.62 (define @t167 () (tptp.member @t159 @t97)) % 0.39/0.62 (define @t168 () (not @t167)) % 0.39/0.62 (define @t169 () (or @t168 @t166 @t164)) % 0.39/0.62 (define @t170 () (@list @t169)) % 0.39/0.62 (define @t171 () (= @t147 @t159)) % 0.39/0.62 (define @t172 () (or @t153 @t168 @t132 @t150 @t164 @t171)) % 0.39/0.62 (define @t173 () (tptp.apply @t99 @t107 @t159)) % 0.39/0.62 (define @t174 () (forall @t55 (or @t104 @t103 @t140 (not (tptp.apply @t99 @t46 @t13)) (not (tptp.apply @t99 @t45 @t13)) @t47))) % 0.39/0.62 (define @t175 () (= @t118 @t174)) % 0.39/0.62 (define @t176 () (not @t173)) % 0.39/0.62 (define @t177 () (or @t134 @t136 @t168 @t166 @t176 (= @t126 @t107))) % 0.39/0.62 (define @t178 () (or @t134 @t136 @t168 @t166 @t176 @t127)) % 0.39/0.62 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.39/0.62 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.39/0.62 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.39/0.62 (assume @p4 (forall @t10 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.39/0.62 (assume @p5 (forall @t10 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.39/0.62 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.39/0.62 (assume @p7 (forall (@list @t1 @t4 @t11) (= (tptp.member @t1 (tptp.difference @t11 @t4)) (and (tptp.member @t1 @t11) (not (tptp.member @t1 @t4)))))) % 0.39/0.62 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t12))) % 0.39/0.62 (assume @p9 (forall @t10 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t12 (= @t2 @t1))))) % 0.39/0.62 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t16 (and @t15 @t14))))) % 0.39/0.62 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t16 (=> @t15 @t14))))) % 0.39/0.62 (assume @p12 (forall @t30 (= @t29 (and (forall @t6 (=> @t5 @t28)) (forall @t25 (=> @t24 (=> (and @t21 (tptp.apply @t20 @t2 @t17)) @t19))))))) % 0.39/0.62 (assume @p13 (forall (@list @t36 @t32 @t20 @t4 @t1 @t37) (= (tptp.compose_predicate @t36 @t32 @t20 @t4 @t1 @t37) (forall (@list @t2 @t31) (=> @t39 (= (tptp.apply @t36 @t2 @t31) @t35)))))) % 0.39/0.62 (assume @p14 @t44) % 0.39/0.62 (assume @p15 (forall (@list @t20 @t32 @t4 @t1) (= (tptp.equal_maps @t20 @t32 @t4 @t1) (forall @t25 (=> @t24 (=> (and @t21 (tptp.apply @t32 @t2 @t17)) @t19)))))) % 0.39/0.62 (assume @p16 (forall (@list @t20 @t4) (= (tptp.identity @t20 @t4) (forall @t6 (=> @t5 (tptp.apply @t20 @t2 @t2)))))) % 0.39/0.62 (assume @p17 @t59) % 0.39/0.62 (assume @p18 (forall @t30 (= @t60 (forall @t16 (=> @t27 (exists (@list @t11) (and (tptp.member @t11 @t4) (tptp.apply @t20 @t11 @t13)))))))) % 0.39/0.62 (assume @p19 (forall @t30 (= @t61 (and @t57 @t60)))) % 0.39/0.62 (assume @p20 (forall (@list @t32 @t20 @t4 @t1) (= (tptp.inverse_predicate @t32 @t20 @t4 @t1) (forall (@list @t2 @t13) (=> @t62 (= @t26 (tptp.apply @t32 @t13 @t2))))))) % 0.39/0.62 (assume @p21 (forall (@list @t20 @t4 @t1 @t2 @t13) (=> @t62 (= @t26 (tptp.apply (tptp.inverse_function @t20 @t4 @t1) @t13 @t2))))) % 0.39/0.62 (assume @p22 (forall (@list @t20 @t4 @t13) (= (tptp.member @t13 (tptp.image2 @t20 @t4)) @t63))) % 0.39/0.62 (assume @p23 (forall (@list @t20 @t4 @t1 @t13) (= (tptp.member @t13 (tptp.image3 @t20 @t4 @t1)) (and @t27 @t63)))) % 0.39/0.62 (assume @p24 (forall (@list @t20 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t20 @t1)) @t28))) % 0.39/0.62 (assume @p25 (forall (@list @t20 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t20 @t1 @t4)) (and @t5 @t28)))) % 0.39/0.62 (assume @p26 (forall @t72 (= (tptp.increasing @t20 @t4 @t68 @t1 @t64) (forall @t71 (=> @t70 @t65))))) % 0.39/0.62 (assume @p27 (forall @t72 (= (tptp.decreasing @t20 @t4 @t68 @t1 @t64) (forall @t71 (=> @t70 (tptp.apply @t64 @t17 @t18)))))) % 0.39/0.62 (assume @p28 (forall @t72 (= (tptp.isomorphism @t20 @t4 @t68 @t1 @t64) (and @t29 @t61 (forall @t71 (=> (and @t53 @t23 @t52 @t22 @t67 @t66) (= @t69 @t65))))))) % 0.39/0.62 (assume @p29 @t79) % 0.39/0.62 (assume @p30 true) % 0.39/0.62 (step @p31 :rule evaluate :args ((= false true))) % 0.39/0.62 (step @p32 :rule aci_norm :args ((= (or (or @t87 @t86) @t85) (or @t87 @t86 @t85)))) % 0.39/0.62 (step @p33 :rule refl :args (@t85)) % 0.39/0.62 (step @p34 :rule bool-and-de-morgan :args (@t5 @t38 true)) % 0.39/0.62 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or (not @t39) @t85))) % 0.39/0.62 (step @p36 :rule trans :premises (@p35 @p32)) % 0.39/0.62 (step @p37 :rule bool-impl-elim :args (@t39 @t85)) % 0.39/0.62 (step @p38 :rule trans :premises (@p37 @p36)) % 0.39/0.62 (step @p39 :rule cong :premises (@p38) :args ((forall @t43 (=> @t39 @t85)))) % 0.39/0.62 (step @p40 :rule eq-symm :args (@t84 @t41)) % 0.39/0.62 (step @p41 :rule refl :args (@t41)) % 0.39/0.62 (step @p42 :rule aci_norm :args ((= (or @t82 (or @t81 @t80)) @t83))) % 0.39/0.62 (step @p43 :rule bool-and-de-morgan :args (@t26 @t33 true)) % 0.39/0.62 (step @p44 :rule refl :args (@t82)) % 0.39/0.62 (step @p45 :rule nary_cong :premises (@p44 @p43) :args ((or @t82 (not (and @t26 @t33))))) % 0.39/0.62 (step @p46 :rule bool-and-de-morgan :args (@t27 @t26 (and @t33))) % 0.39/0.62 (step @p47 :rule trans :premises (@p46 @p45)) % 0.39/0.62 (step @p48 :rule trans :premises (@p47 @p42)) % 0.39/0.62 (step @p49 :rule cong :premises (@p48) :args (@t88)) % 0.39/0.62 (step @p50 :rule cong :premises (@p49) :args (@t89)) % 0.39/0.62 (step @p51 :rule exists-elim :args ((= @t35 @t89))) % 0.39/0.62 (step @p52 :rule trans :premises (@p51 @p50)) % 0.39/0.62 (step @p53 :rule cong :premises (@p52 @p41) :args ((= @t35 @t41))) % 0.39/0.62 (step @p54 :rule trans :premises (@p53 @p40)) % 0.39/0.62 (step @p55 :rule eq-symm :args (@t41 @t35)) % 0.39/0.62 (step @p56 :rule trans :premises (@p55 @p54)) % 0.39/0.62 (step @p57 :rule refl :args (@t39)) % 0.39/0.62 (step @p58 :rule cong :premises (@p57 @p56) :args (@t42)) % 0.39/0.62 (step @p59 :rule cong :premises (@p58) :args (@t44)) % 0.39/0.62 (step @p60 :rule trans :premises (@p59 @p39)) % 0.39/0.62 (step @p61 :rule eq_resolve :premises (@p14 @p60)) % 0.39/0.62 (step @p62 :rule instantiate :premises (@p61) :args ((@list @t100 @t99 @t98 @t97 @t96 @t107 @t106))) % 0.39/0.62 (step @p63 :rule aci_norm :args ((= (or @t113 @t112) (or @t111 @t110 @t82 @t109 @t108 @t47)))) % 0.39/0.62 (step @p64 :rule aci_norm :args ((= (or (or @t109 @t108) @t47) @t112))) % 0.39/0.62 (step @p65 :rule refl :args (@t47)) % 0.39/0.62 (step @p66 :rule bool-and-de-morgan :args (@t49 @t48 true)) % 0.39/0.62 (step @p67 :rule nary_cong :premises (@p66 @p65) :args ((or (not @t50) @t47))) % 0.39/0.62 (step @p68 :rule trans :premises (@p67 @p64)) % 0.39/0.62 (step @p69 :rule bool-impl-elim :args (@t50 @t47)) % 0.39/0.62 (step @p70 :rule trans :premises (@p69 @p68)) % 0.39/0.62 (step @p71 :rule aci_norm :args ((= (or @t111 (or @t110 @t82)) @t113))) % 0.39/0.62 (step @p72 :rule bool-and-de-morgan :args (@t52 @t27 true)) % 0.39/0.62 (step @p73 :rule refl :args (@t111)) % 0.39/0.62 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t111 (not (and @t52 @t27))))) % 0.39/0.62 (step @p75 :rule bool-and-de-morgan :args (@t53 @t52 (and @t27))) % 0.39/0.62 (step @p76 :rule trans :premises (@p75 @p74)) % 0.39/0.62 (step @p77 :rule trans :premises (@p76 @p71)) % 0.39/0.62 (step @p78 :rule nary_cong :premises (@p77 @p70) :args ((or (not @t54) @t51))) % 0.39/0.62 (step @p79 :rule trans :premises (@p78 @p63)) % 0.39/0.62 (step @p80 :rule bool-impl-elim :args (@t54 @t51)) % 0.39/0.62 (step @p81 :rule trans :premises (@p80 @p79)) % 0.39/0.62 (step @p82 :rule cong :premises (@p81) :args (@t56)) % 0.39/0.62 (step @p83 :rule refl :args (@t57)) % 0.39/0.62 (step @p84 :rule cong :premises (@p83 @p82) :args (@t58)) % 0.39/0.62 (step @p85 :rule cong :premises (@p84) :args (@t59)) % 0.39/0.62 (step @p86 :rule eq_resolve :premises (@p17 @p85)) % 0.39/0.62 (step @p87 :rule instantiate :premises (@p86) :args ((@list @t101 @t98 @t96))) % 0.39/0.62 (step @p88 :rule aci_norm :args ((= (or @t114 @t73) @t94))) % 0.39/0.62 (step @p89 :rule refl :args (@t73)) % 0.39/0.62 (step @p90 :rule aci_norm :args ((= (or @t93 (or @t92 (or @t91 @t90))) @t114))) % 0.39/0.62 (step @p91 :rule bool-and-de-morgan :args (@t57 @t74 true)) % 0.39/0.62 (step @p92 :rule refl :args (@t92)) % 0.39/0.62 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or @t92 (not (and @t57 @t74))))) % 0.39/0.62 (step @p94 :rule bool-and-de-morgan :args (@t75 @t57 (and @t74))) % 0.39/0.62 (step @p95 :rule trans :premises (@p94 @p93)) % 0.39/0.62 (step @p96 :rule refl :args (@t93)) % 0.39/0.62 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or @t93 (not (and @t75 @t57 @t74))))) % 0.39/0.62 (step @p98 :rule bool-and-de-morgan :args (@t29 @t75 (and @t57 @t74))) % 0.39/0.62 (step @p99 :rule trans :premises (@p98 @p97)) % 0.39/0.62 (step @p100 :rule trans :premises (@p99 @p90)) % 0.39/0.62 (step @p101 :rule nary_cong :premises (@p100 @p89) :args ((or (not @t76) @t73))) % 0.39/0.62 (step @p102 :rule trans :premises (@p101 @p88)) % 0.39/0.62 (step @p103 :rule bool-impl-elim :args (@t76 @t73)) % 0.39/0.62 (step @p104 :rule trans :premises (@p103 @p102)) % 0.39/0.62 (step @p105 :rule cong :premises (@p104) :args (@t78)) % 0.39/0.62 (step @p106 :rule cong :premises (@p105) :args (@t79)) % 0.39/0.62 (step @p107 :rule eq_resolve :premises (@p29 @p106)) % 0.39/0.62 (step @p108 :rule skolemize :premises (@p107)) % 0.39/0.62 (step @p109 :rule cnf_or_neg :args (@t120 4)) % 0.39/0.62 (step @p110 :rule chain_m_resolution :premises (@p109 @p108) :args ((not @t115) @t121 @t122)) % 0.39/0.62 (step @p111 :rule cnf_equiv_pos2 :args (@t123)) % 0.39/0.62 (step @p112 :rule reordering :premises (@p111) :args ((or @t115 @t124 (not @t123)))) % 0.39/0.62 (step @p113 :rule chain_m_resolution :premises (@p112 @p110 @p87) :args (@t124 (@list true false) (@list @t115 @t123))) % 0.39/0.62 (step @p114 :rule skolemize :premises (@p113)) % 0.39/0.62 (step @p115 :rule bool-double-not-elim :args (@t125)) % 0.39/0.62 (step @p116 :rule refl :args (@t137)) % 0.39/0.62 (step @p117 :rule nary_cong :premises (@p116 @p115) :args ((or @t137 (not @t132)))) % 0.39/0.62 (step @p118 :rule cnf_or_neg :args (@t137 2)) % 0.39/0.62 (step @p119 :rule eq_resolve :premises (@p118 @p117)) % 0.39/0.62 (step @p120 :rule reordering :premises (@p119) :args ((or @t125 @t137))) % 0.39/0.62 (step @p121 :rule chain_m_resolution :premises (@p120 @p114) :args (@t125 @t121 @t138)) % 0.39/0.62 (step @p122 :rule bool-double-not-elim :args (@t135)) % 0.39/0.62 (step @p123 :rule nary_cong :premises (@p116 @p122) :args ((or @t137 (not @t136)))) % 0.39/0.62 (step @p124 :rule cnf_or_neg :args (@t137 0)) % 0.39/0.62 (step @p125 :rule eq_resolve :premises (@p124 @p123)) % 0.39/0.62 (step @p126 :rule reordering :premises (@p125) :args ((or @t135 @t137))) % 0.39/0.62 (step @p127 :rule chain_m_resolution :premises (@p126 @p114) :args (@t135 @t121 @t138)) % 0.39/0.62 (step @p128 :rule cnf_or_pos :args (@t144)) % 0.39/0.62 (step @p129 :rule reordering :premises (@p128) :args ((or @t136 @t132 @t143 (not @t144)))) % 0.39/0.62 (step @p130 :rule chain_m_resolution :premises (@p129 @p127 @p121 @p62) :args (@t143 @t145 (@list @t135 @t125 @t144))) % 0.39/0.62 (step @p131 :rule bool-double-not-elim :args (@t130)) % 0.39/0.62 (step @p132 :rule nary_cong :premises (@p116 @p131) :args ((or @t137 (not @t131)))) % 0.39/0.62 (step @p133 :rule cnf_or_neg :args (@t137 3)) % 0.39/0.62 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.39/0.62 (step @p135 :rule reordering :premises (@p134) :args ((or @t130 @t137))) % 0.39/0.62 (step @p136 :rule chain_m_resolution :premises (@p135 @p114) :args (@t130 @t121 @t138)) % 0.39/0.62 (step @p137 :rule cnf_equiv_pos1 :args (@t143)) % 0.39/0.62 (step @p138 :rule reordering :premises (@p137) :args ((or @t131 @t142 (not @t143)))) % 0.39/0.62 (step @p139 :rule chain_m_resolution :premises (@p138 @p136 @p130) :args (@t142 @t146 (@list @t130 @t143))) % 0.39/0.62 (step @p140 :rule skolemize :premises (@p139)) % 0.39/0.62 (step @p141 :rule bool-double-not-elim :args (@t148)) % 0.39/0.62 (step @p142 :rule refl :args (@t154)) % 0.39/0.62 (step @p143 :rule nary_cong :premises (@p142 @p141) :args ((or @t154 (not @t151)))) % 0.39/0.62 (step @p144 :rule cnf_or_neg :args (@t154 1)) % 0.39/0.62 (step @p145 :rule eq_resolve :premises (@p144 @p143)) % 0.39/0.62 (step @p146 :rule reordering :premises (@p145) :args ((or @t148 @t154))) % 0.39/0.62 (step @p147 :rule chain_m_resolution :premises (@p146 @p140) :args (@t148 @t121 @t155)) % 0.39/0.62 (step @p148 :rule true_intro :premises (@p147)) % 0.39/0.62 (step @p149 :rule instantiate :premises (@p86) :args ((@list @t100 @t97 @t96))) % 0.39/0.62 (step @p150 :rule bool-double-not-elim :args (@t116)) % 0.39/0.62 (step @p151 :rule refl :args (@t120)) % 0.39/0.62 (step @p152 :rule nary_cong :premises (@p151 @p150) :args ((or @t120 (not @t117)))) % 0.39/0.62 (step @p153 :rule cnf_or_neg :args (@t120 3)) % 0.39/0.62 (step @p154 :rule eq_resolve :premises (@p153 @p152)) % 0.39/0.62 (step @p155 :rule reordering :premises (@p154) :args ((or @t116 @t120))) % 0.39/0.62 (step @p156 :rule chain_m_resolution :premises (@p155 @p108) :args (@t116 @t121 @t122)) % 0.39/0.62 (step @p157 :rule cnf_equiv_pos1 :args (@t157)) % 0.39/0.62 (step @p158 :rule reordering :premises (@p157) :args ((or @t117 @t156 (not @t157)))) % 0.39/0.62 (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p149) :args (@t156 @t146 (@list @t116 @t157))) % 0.39/0.62 (step @p160 :rule instantiate :premises (@p159) :args ((@list @t147 @t159 @t106))) % 0.39/0.62 (step @p161 :rule instantiate :premises (@p61) :args ((@list @t100 @t99 @t98 @t97 @t96 @t126 @t106))) % 0.39/0.62 (step @p162 :rule bool-double-not-elim :args (@t133)) % 0.39/0.62 (step @p163 :rule nary_cong :premises (@p116 @p162) :args ((or @t137 (not @t134)))) % 0.39/0.62 (step @p164 :rule cnf_or_neg :args (@t137 1)) % 0.39/0.62 (step @p165 :rule eq_resolve :premises (@p164 @p163)) % 0.39/0.62 (step @p166 :rule reordering :premises (@p165) :args ((or @t133 @t137))) % 0.39/0.62 (step @p167 :rule chain_m_resolution :premises (@p166 @p114) :args (@t133 @t121 @t138)) % 0.39/0.62 (step @p168 :rule cnf_or_pos :args (@t162)) % 0.39/0.62 (step @p169 :rule reordering :premises (@p168) :args ((or @t134 @t132 @t161 (not @t162)))) % 0.39/0.62 (step @p170 :rule chain_m_resolution :premises (@p169 @p167 @p121 @p161) :args (@t161 @t145 (@list @t133 @t125 @t162))) % 0.39/0.62 (step @p171 :rule bool-double-not-elim :args (@t128)) % 0.39/0.62 (step @p172 :rule nary_cong :premises (@p116 @p171) :args ((or @t137 (not @t129)))) % 0.39/0.62 (step @p173 :rule cnf_or_neg :args (@t137 4)) % 0.39/0.62 (step @p174 :rule eq_resolve :premises (@p173 @p172)) % 0.39/0.62 (step @p175 :rule reordering :premises (@p174) :args ((or @t128 @t137))) % 0.39/0.62 (step @p176 :rule chain_m_resolution :premises (@p175 @p114) :args (@t128 @t121 @t138)) % 0.39/0.62 (step @p177 :rule cnf_equiv_pos1 :args (@t161)) % 0.39/0.62 (step @p178 :rule reordering :premises (@p177) :args ((or @t129 @t160 (not @t161)))) % 0.39/0.62 (step @p179 :rule chain_m_resolution :premises (@p178 @p176 @p170) :args (@t160 @t146 (@list @t128 @t161))) % 0.39/0.62 (step @p180 :rule skolemize :premises (@p179)) % 0.39/0.62 (step @p181 :rule bool-double-not-elim :args (@t163)) % 0.39/0.62 (step @p182 :rule refl :args (@t169)) % 0.39/0.62 (step @p183 :rule nary_cong :premises (@p182 @p181) :args ((or @t169 (not @t164)))) % 0.39/0.62 (step @p184 :rule cnf_or_neg :args (@t169 2)) % 0.39/0.62 (step @p185 :rule eq_resolve :premises (@p184 @p183)) % 0.39/0.62 (step @p186 :rule reordering :premises (@p185) :args ((or @t163 @t169))) % 0.39/0.62 (step @p187 :rule chain_m_resolution :premises (@p186 @p180) :args (@t163 @t121 @t170)) % 0.39/0.62 (step @p188 :rule bool-double-not-elim :args (@t167)) % 0.39/0.62 (step @p189 :rule nary_cong :premises (@p182 @p188) :args ((or @t169 (not @t168)))) % 0.39/0.62 (step @p190 :rule cnf_or_neg :args (@t169 0)) % 0.39/0.62 (step @p191 :rule eq_resolve :premises (@p190 @p189)) % 0.39/0.62 (step @p192 :rule reordering :premises (@p191) :args ((or @t167 @t169))) % 0.39/0.62 (step @p193 :rule chain_m_resolution :premises (@p192 @p180) :args (@t167 @t121 @t170)) % 0.39/0.62 (step @p194 :rule bool-double-not-elim :args (@t149)) % 0.39/0.62 (step @p195 :rule nary_cong :premises (@p142 @p194) :args ((or @t154 (not @t150)))) % 0.39/0.62 (step @p196 :rule cnf_or_neg :args (@t154 2)) % 0.39/0.62 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 0.39/0.62 (step @p198 :rule reordering :premises (@p197) :args ((or @t149 @t154))) % 0.39/0.62 (step @p199 :rule chain_m_resolution :premises (@p198 @p140) :args (@t149 @t121 @t155)) % 0.39/0.62 (step @p200 :rule bool-double-not-elim :args (@t152)) % 0.39/0.62 (step @p201 :rule nary_cong :premises (@p142 @p200) :args ((or @t154 (not @t153)))) % 0.39/0.62 (step @p202 :rule cnf_or_neg :args (@t154 0)) % 0.39/0.62 (step @p203 :rule eq_resolve :premises (@p202 @p201)) % 0.39/0.62 (step @p204 :rule reordering :premises (@p203) :args ((or @t152 @t154))) % 0.39/0.62 (step @p205 :rule chain_m_resolution :premises (@p204 @p140) :args (@t152 @t121 @t155)) % 0.39/0.62 (step @p206 :rule cnf_or_pos :args (@t172)) % 0.39/0.62 (step @p207 :rule reordering :premises (@p206) :args ((or @t132 @t153 @t150 @t168 @t164 @t171 (not @t172)))) % 0.39/0.62 (step @p208 :rule chain_m_resolution :premises (@p207 @p121 @p205 @p199 @p193 @p187 @p160) :args (@t171 (@list false false false false false false) (@list @t125 @t152 @t149 @t167 @t163 @t172))) % 0.39/0.62 (step @p209 :rule symm :premises (@p208)) % 0.39/0.62 (step @p210 :rule refl :args (@t107)) % 0.39/0.62 (step @p211 :rule refl :args (@t99)) % 0.39/0.62 (step @p212 :rule cong :premises (@p211 @p210 @p209) :args (@t173)) % 0.39/0.63 (step @p213 :rule instantiate :premises (@p86) :args ((@list @t99 @t98 @t97))) % 0.39/0.63 (step @p214 :rule bool-double-not-elim :args (@t118)) % 0.39/0.63 (step @p215 :rule nary_cong :premises (@p151 @p214) :args ((or @t120 (not @t119)))) % 0.39/0.63 (step @p216 :rule cnf_or_neg :args (@t120 2)) % 0.39/0.63 (step @p217 :rule eq_resolve :premises (@p216 @p215)) % 0.39/0.63 (step @p218 :rule reordering :premises (@p217) :args ((or @t118 @t120))) % 0.39/0.63 (step @p219 :rule chain_m_resolution :premises (@p218 @p108) :args (@t118 @t121 @t122)) % 0.39/0.63 (step @p220 :rule cnf_equiv_pos1 :args (@t175)) % 0.39/0.63 (step @p221 :rule reordering :premises (@p220) :args ((or @t119 @t174 (not @t175)))) % 0.39/0.63 (step @p222 :rule chain_m_resolution :premises (@p221 @p219 @p213) :args (@t174 @t146 (@list @t118 @t175))) % 0.39/0.63 (step @p223 :rule eq-symm :args (@t126 @t107)) % 0.39/0.63 (step @p224 :rule refl :args (@t176)) % 0.39/0.63 (step @p225 :rule refl :args (@t166)) % 0.39/0.63 (step @p226 :rule refl :args (@t168)) % 0.39/0.63 (step @p227 :rule refl :args (@t136)) % 0.39/0.63 (step @p228 :rule refl :args (@t134)) % 0.39/0.63 (step @p229 :rule nary_cong :premises (@p228 @p227 @p226 @p225 @p224 @p223) :args (@t177)) % 0.39/0.63 (step @p230 :rule refl :args (@t174)) % 0.39/0.63 (step @p231 :rule cong :premises (@p230 @p229) :args ((=> @t174 @t177))) % 0.39/0.63 (assume-push @p254 @t174) % 0.39/0.63 (step @p233 :rule instantiate :premises (@p222) :args ((@list @t126 @t107 @t159))) % 0.39/0.63 (step-pop @p255 :rule scope :premises (@p233)) % 0.39/0.63 (step @p234 :rule process_scope :premises (@p255) :args (@t177)) % 0.39/0.63 (step @p236 :rule eq_resolve :premises (@p234 @p231)) % 0.39/0.63 (step @p237 :rule implies_elim :premises (@p236)) % 0.39/0.63 (step @p238 :rule chain_m_resolution :premises (@p237 @p222) :args (@t178 (@list false) (@list @t174))) % 0.39/0.63 (step @p239 :rule bool-double-not-elim :args (@t165)) % 0.39/0.63 (step @p240 :rule nary_cong :premises (@p182 @p239) :args ((or @t169 (not @t166)))) % 0.39/0.63 (step @p241 :rule cnf_or_neg :args (@t169 1)) % 0.39/0.63 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.39/0.63 (step @p243 :rule reordering :premises (@p242) :args ((or @t165 @t169))) % 0.39/0.63 (step @p244 :rule chain_m_resolution :premises (@p243 @p180) :args (@t165 @t121 @t170)) % 0.39/0.63 (step @p245 :rule cnf_or_neg :args (@t137 5)) % 0.39/0.63 (step @p246 :rule chain_m_resolution :premises (@p245 @p114) :args ((not @t127) @t121 @t138)) % 0.39/0.63 (step @p247 :rule cnf_or_pos :args (@t178)) % 0.39/0.63 (step @p248 :rule reordering :premises (@p247) :args ((or @t136 @t134 @t127 @t168 @t166 @t176 (not @t178)))) % 0.39/0.63 (step @p249 :rule chain_m_resolution :premises (@p248 @p127 @p167 @p246 @p193 @p244 @p238) :args (@t176 (@list false false true false false false) (@list @t135 @t133 @t127 @t167 @t165 @t178))) % 0.39/0.63 (step @p250 :rule false_intro :premises (@p249)) % 0.39/0.63 (step @p251 :rule symm :premises (@p250)) % 0.39/0.63 (step @p252 :rule trans :premises (@p251 @p212 @p148)) % 0.39/0.63 (step @p253 false :rule eq_resolve :premises (@p252 @p31)) % 0.39/0.63 ) % 0.39/0.63 % SZS output end Proof % 0.39/0.63 % cvc5 exiting %------------------------------------------------------------------------------