%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET090+1 : TPTP v9.2.1. Bugfixed v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n012.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 08:47:20 AM UTC 2026 % Result : Theorem 0.25s 0.51s % Output : Proof 0.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SET090+1 : TPTP v9.2.1. Bugfixed v7.3.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.25 % Computer : n012.cluster.edu % 0.09/0.25 % Model : x86_64 x86_64 % 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.25 % Memory : 8042.1875MB % 0.09/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.25 % CPULimit : 300 % 0.09/0.25 % WCLimit : 300 % 0.09/0.25 % DateTime : Tue Jun 2 14:51:48 EDT 2026 % 0.09/0.25 % CPUTime : % 0.17/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.25/0.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.25/0.51 % SZS status Theorem % 0.25/0.51 % SZS output start Proof % 0.25/0.51 ( % 0.25/0.51 (declare-sort $$unsorted 0) % 0.25/0.51 (declare-const tptp.member_of (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.25/0.51 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.element_relation $$unsorted) % 0.25/0.51 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.universal_class $$unsorted) % 0.25/0.51 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.25/0.51 (declare-const tptp.function (-> $$unsorted Bool)) % 0.25/0.51 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.25/0.51 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.25/0.51 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.null_class $$unsorted) % 0.25/0.51 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.successor_relation $$unsorted) % 0.25/0.51 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.25/0.51 (declare-const tptp.identity_relation $$unsorted) % 0.25/0.51 (define @t1 () (@var "Y" $$unsorted)) % 0.25/0.51 (define @t2 () (@var "U" $$unsorted)) % 0.25/0.51 (define @t3 () (tptp.member @t2 @t1)) % 0.25/0.51 (define @t4 () (@var "X" $$unsorted)) % 0.25/0.51 (define @t5 () (tptp.member @t2 @t4)) % 0.25/0.51 (define @t6 () (@list @t2)) % 0.25/0.51 (define @t7 () (tptp.subclass @t4 @t1)) % 0.25/0.51 (define @t8 () (@list @t4 @t1)) % 0.25/0.51 (define @t9 () (@list @t4)) % 0.25/0.51 (define @t10 () (tptp.member @t2 tptp.universal_class)) % 0.25/0.51 (define @t11 () (tptp.unordered_pair @t4 @t1)) % 0.25/0.51 (define @t12 () (tptp.singleton @t4)) % 0.25/0.51 (define @t13 () (tptp.singleton @t1)) % 0.25/0.51 (define @t14 () (tptp.ordered_pair @t4 @t1)) % 0.25/0.51 (define @t15 () (@var "V" $$unsorted)) % 0.25/0.51 (define @t16 () (tptp.cross_product @t4 @t1)) % 0.25/0.51 (define @t17 () (tptp.ordered_pair @t2 @t15)) % 0.25/0.51 (define @t18 () (tptp.second @t14)) % 0.25/0.51 (define @t19 () (tptp.first @t14)) % 0.25/0.51 (define @t20 () (and (= @t19 @t4) (= @t18 @t1))) % 0.25/0.51 (define @t21 () (tptp.member @t1 tptp.universal_class)) % 0.25/0.51 (define @t22 () (tptp.member @t4 tptp.universal_class)) % 0.25/0.51 (define @t23 () (and @t22 @t21)) % 0.25/0.51 (define @t24 () (=> @t23 @t20)) % 0.25/0.51 (define @t25 () (forall @t8 @t24)) % 0.25/0.51 (define @t26 () (@var "Z" $$unsorted)) % 0.25/0.51 (define @t27 () (@list @t4 @t1 @t26)) % 0.25/0.51 (define @t28 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.25/0.51 (define @t29 () (tptp.member @t26 @t1)) % 0.25/0.51 (define @t30 () (tptp.member @t26 @t4)) % 0.25/0.51 (define @t31 () (tptp.member @t26 tptp.universal_class)) % 0.25/0.51 (define @t32 () (@list @t4 @t26)) % 0.25/0.51 (define @t33 () (@var "XR" $$unsorted)) % 0.25/0.51 (define @t34 () (@var "W" $$unsorted)) % 0.25/0.51 (define @t35 () (tptp.cross_product @t28 tptp.universal_class)) % 0.25/0.51 (define @t36 () (tptp.ordered_pair @t17 @t34)) % 0.25/0.51 (define @t37 () (tptp.member @t36 @t35)) % 0.25/0.51 (define @t38 () (tptp.rotate @t4)) % 0.25/0.51 (define @t39 () (tptp.flip @t4)) % 0.25/0.51 (define @t40 () (tptp.successor @t4)) % 0.25/0.51 (define @t41 () (@list @t1)) % 0.25/0.51 (define @t42 () (@list @t26)) % 0.25/0.51 (define @t43 () (tptp.inductive @t4)) % 0.25/0.51 (define @t44 () (tptp.sum_class @t4)) % 0.25/0.51 (define @t45 () (@list @t2 @t4)) % 0.25/0.51 (define @t46 () (tptp.member @t44 tptp.universal_class)) % 0.25/0.51 (define @t47 () (forall @t9 (=> @t22 @t46))) % 0.25/0.51 (define @t48 () (@var "YR" $$unsorted)) % 0.25/0.51 (define @t49 () (tptp.compose @t48 @t33)) % 0.25/0.51 (define @t50 () (tptp.singleton @t2)) % 0.25/0.51 (define @t51 () (@var "XF" $$unsorted)) % 0.25/0.51 (define @t52 () (tptp.function @t51)) % 0.25/0.51 (define @t53 () (@list @t51)) % 0.25/0.51 (define @t54 () (tptp.member (tptp.image @t51 @t4) tptp.universal_class)) % 0.25/0.51 (define @t55 () (and @t22 @t52)) % 0.25/0.51 (define @t56 () (forall (@list @t4 @t51) (=> @t55 @t54))) % 0.25/0.51 (define @t57 () (tptp.apply @t51 @t1)) % 0.25/0.51 (define @t58 () (tptp.member @t57 @t1)) % 0.25/0.51 (define @t59 () (= @t1 tptp.null_class)) % 0.25/0.51 (define @t60 () (or @t59 @t58)) % 0.25/0.51 (define @t61 () (forall @t41 (=> @t21 @t60))) % 0.25/0.51 (define @t62 () (and @t52 @t61)) % 0.25/0.51 (define @t63 () (exists @t53 @t62)) % 0.25/0.51 (define @t64 () (tptp.member_of @t13)) % 0.25/0.51 (define @t65 () (tptp.member @t64 tptp.universal_class)) % 0.25/0.51 (define @t66 () (forall @t41 (=> @t21 @t65))) % 0.25/0.51 (define @t67 () (tptp.singleton @t64)) % 0.25/0.51 (define @t68 () (=> @t21 (= @t67 @t13))) % 0.25/0.51 (define @t69 () (forall @t41 @t68)) % 0.25/0.51 (define @t70 () (tptp.member_of @t4)) % 0.25/0.51 (define @t71 () (= @t70 @t4)) % 0.25/0.51 (define @t72 () (= @t4 @t50)) % 0.25/0.51 (define @t73 () (and @t10 @t72)) % 0.25/0.51 (define @t74 () (=> @t73 (= @t70 @t2))) % 0.25/0.51 (define @t75 () (@list @t4 @t2)) % 0.25/0.51 (define @t76 () (forall @t75 @t74)) % 0.25/0.51 (define @t77 () (not @t76)) % 0.25/0.51 (define @t78 () (= @t2 (tptp.member_of @t50))) % 0.25/0.51 (define @t79 () (not @t10)) % 0.25/0.51 (define @t80 () (or @t79 @t78)) % 0.25/0.51 (define @t81 () (not (= @t50 @t50))) % 0.25/0.51 (define @t82 () (or @t79 @t81 @t78)) % 0.25/0.51 (define @t83 () (= @t2 @t70)) % 0.25/0.51 (define @t84 () (not @t72)) % 0.25/0.51 (define @t85 () (or @t84 @t79 @t84 @t83)) % 0.25/0.51 (define @t86 () (or @t79 @t84 @t83)) % 0.25/0.51 (define @t87 () (forall @t9 @t86)) % 0.25/0.51 (define @t88 () (forall @t6 @t87)) % 0.25/0.51 (define @t89 () (forall @t45 @t86)) % 0.25/0.51 (define @t90 () (@quantifiers_skolemize (forall @t6 @t80) 0)) % 0.25/0.51 (define @t91 () (tptp.singleton @t90)) % 0.25/0.51 (define @t92 () (tptp.member_of @t91)) % 0.25/0.51 (define @t93 () (= @t90 @t92)) % 0.25/0.51 (define @t94 () (tptp.member @t90 tptp.universal_class)) % 0.25/0.51 (define @t95 () (not @t94)) % 0.25/0.51 (define @t96 () (or @t95 @t93)) % 0.25/0.51 (define @t97 () (not @t93)) % 0.25/0.51 (define @t98 () (@list true)) % 0.25/0.51 (define @t99 () (@list @t96)) % 0.25/0.51 (define @t100 () (= @t13 @t67)) % 0.25/0.51 (define @t101 () (@list @t90)) % 0.25/0.51 (define @t102 () (tptp.singleton @t92)) % 0.25/0.51 (define @t103 () (= @t91 @t102)) % 0.25/0.51 (define @t104 () (or @t95 @t103)) % 0.25/0.51 (define @t105 () (@list false false)) % 0.25/0.51 (define @t106 () (not @t21)) % 0.25/0.51 (define @t107 () (or @t106 @t59 @t58)) % 0.25/0.51 (define @t108 () (forall @t41 @t107)) % 0.25/0.51 (define @t109 () (not @t52)) % 0.25/0.51 (define @t110 () (@quantifiers_skolemize (forall @t53 (or @t109 (not @t108))) 0)) % 0.25/0.51 (define @t111 () (tptp.apply @t110 @t90)) % 0.25/0.51 (define @t112 () (@list @t111 @t90)) % 0.25/0.51 (define @t113 () (tptp.apply @t110 @t92)) % 0.25/0.51 (define @t114 () (@list @t113 @t92)) % 0.25/0.51 (define @t115 () (and (= @t4 @t19) (= @t1 @t18))) % 0.25/0.51 (define @t116 () (not @t22)) % 0.25/0.51 (define @t117 () (tptp.image @t110 @t102)) % 0.25/0.51 (define @t118 () (tptp.member @t102 tptp.universal_class)) % 0.25/0.51 (define @t119 () (and @t52 @t108)) % 0.25/0.51 (define @t120 () (forall @t53 (not @t119))) % 0.25/0.51 (define @t121 () (not @t120)) % 0.25/0.51 (define @t122 () (tptp.function @t110)) % 0.25/0.51 (define @t123 () (not @t122)) % 0.25/0.51 (define @t124 () (or @t123 (not (forall @t41 (or @t106 @t59 (tptp.member (tptp.apply @t110 @t1) @t1)))))) % 0.25/0.51 (define @t125 () (tptp.member @t117 tptp.universal_class)) % 0.25/0.51 (define @t126 () (not @t118)) % 0.25/0.51 (define @t127 () (or @t126 @t123 @t125)) % 0.25/0.51 (define @t128 () (@list false false false)) % 0.25/0.51 (define @t129 () (tptp.sum_class @t117)) % 0.25/0.51 (define @t130 () (tptp.member @t129 tptp.universal_class)) % 0.25/0.51 (define @t131 () (not @t125)) % 0.25/0.51 (define @t132 () (or @t131 @t130)) % 0.25/0.51 (define @t133 () (tptp.member @t113 tptp.universal_class)) % 0.25/0.51 (define @t134 () (tptp.member @t92 tptp.universal_class)) % 0.25/0.51 (define @t135 () (or @t95 @t134)) % 0.25/0.51 (define @t136 () (tptp.ordered_pair @t113 @t92)) % 0.25/0.51 (define @t137 () (= @t92 (tptp.second @t136))) % 0.25/0.51 (define @t138 () (and (= @t113 (tptp.first @t136)) @t137)) % 0.25/0.51 (define @t139 () (not @t134)) % 0.25/0.51 (define @t140 () (not @t133)) % 0.25/0.51 (define @t141 () (or @t140 @t139 @t138)) % 0.25/0.51 (define @t142 () (@list false)) % 0.25/0.51 (define @t143 () (tptp.image @t110 @t91)) % 0.25/0.51 (define @t144 () (tptp.sum_class @t143)) % 0.25/0.51 (define @t145 () (tptp.member @t111 tptp.universal_class)) % 0.25/0.51 (define @t146 () (tptp.ordered_pair @t111 @t90)) % 0.25/0.51 (define @t147 () (tptp.second @t146)) % 0.25/0.51 (define @t148 () (= @t90 @t147)) % 0.25/0.51 (define @t149 () (and (= @t111 (tptp.first @t146)) @t148)) % 0.25/0.51 (define @t150 () (not @t145)) % 0.25/0.51 (define @t151 () (or @t150 @t95 @t149)) % 0.25/0.51 (define @t152 () (not @t148)) % 0.25/0.51 (define @t153 () (not @t137)) % 0.25/0.51 (define @t154 () (= @t136 (tptp.unordered_pair (tptp.singleton @t113) (tptp.unordered_pair @t113 @t102)))) % 0.25/0.51 (define @t155 () (not @t154)) % 0.25/0.51 (define @t156 () (tptp.unordered_pair @t111 @t91)) % 0.25/0.51 (define @t157 () (tptp.singleton @t111)) % 0.25/0.51 (define @t158 () (tptp.unordered_pair @t157 @t156)) % 0.25/0.51 (define @t159 () (= @t146 @t158)) % 0.25/0.51 (define @t160 () (not @t159)) % 0.25/0.51 (define @t161 () (= @t113 @t129)) % 0.25/0.51 (define @t162 () (not @t161)) % 0.25/0.51 (define @t163 () (= @t111 @t144)) % 0.25/0.51 (define @t164 () (not @t163)) % 0.25/0.51 (define @t165 () (not @t103)) % 0.25/0.51 (define @t166 () (and @t97 @t103 @t163 @t161 @t159 @t154 @t137)) % 0.25/0.51 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.25/0.51 (assume @p2 (forall @t9 (tptp.subclass @t4 tptp.universal_class))) % 0.25/0.51 (assume @p3 (forall @t8 (= (= @t4 @t1) (and @t7 (tptp.subclass @t1 @t4))))) % 0.25/0.51 (assume @p4 (forall (@list @t2 @t4 @t1) (= (tptp.member @t2 @t11) (and @t10 (or (= @t2 @t4) (= @t2 @t1)))))) % 0.25/0.51 (assume @p5 (forall @t8 (tptp.member @t11 tptp.universal_class))) % 0.25/0.51 (assume @p6 (forall @t9 (= @t12 (tptp.unordered_pair @t4 @t4)))) % 0.25/0.51 (assume @p7 (forall @t8 (= @t14 (tptp.unordered_pair @t12 (tptp.unordered_pair @t4 @t13))))) % 0.25/0.51 (assume @p8 (forall (@list @t2 @t15 @t4 @t1) (= (tptp.member @t17 @t16) (and @t5 (tptp.member @t15 @t1))))) % 0.25/0.51 (assume @p9 @t25) % 0.25/0.51 (assume @p10 (forall @t27 (=> (tptp.member @t26 @t16) (= @t26 (tptp.ordered_pair (tptp.first @t26) (tptp.second @t26)))))) % 0.25/0.51 (assume @p11 (forall @t8 (= (tptp.member @t14 tptp.element_relation) (and @t21 (tptp.member @t4 @t1))))) % 0.25/0.51 (assume @p12 (tptp.subclass tptp.element_relation @t28)) % 0.25/0.51 (assume @p13 (forall @t27 (= (tptp.member @t26 (tptp.intersection @t4 @t1)) (and @t30 @t29)))) % 0.25/0.51 (assume @p14 (forall @t32 (= (tptp.member @t26 (tptp.complement @t4)) (and @t31 (not @t30))))) % 0.25/0.51 (assume @p15 (forall (@list @t4 @t33 @t1) (= (tptp.restrict @t33 @t4 @t1) (tptp.intersection @t33 @t16)))) % 0.25/0.51 (assume @p16 (forall @t9 (not (tptp.member @t4 tptp.null_class)))) % 0.25/0.51 (assume @p17 (forall @t32 (= (tptp.member @t26 (tptp.domain_of @t4)) (and @t31 (not (= (tptp.restrict @t4 (tptp.singleton @t26) tptp.universal_class) tptp.null_class)))))) % 0.25/0.51 (assume @p18 (forall (@list @t4 @t2 @t15 @t34) (= (tptp.member @t36 @t38) (and @t37 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t15 @t34) @t2) @t4))))) % 0.25/0.51 (assume @p19 (forall @t9 (tptp.subclass @t38 @t35))) % 0.25/0.51 (assume @p20 (forall (@list @t2 @t15 @t34 @t4) (= (tptp.member @t36 @t39) (and @t37 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t15 @t2) @t34) @t4))))) % 0.25/0.51 (assume @p21 (forall @t9 (tptp.subclass @t39 @t35))) % 0.25/0.51 (assume @p22 (forall @t27 (= (tptp.member @t26 (tptp.union @t4 @t1)) (or @t30 @t29)))) % 0.25/0.51 (assume @p23 (forall @t9 (= @t40 (tptp.union @t4 @t12)))) % 0.25/0.51 (assume @p24 (tptp.subclass tptp.successor_relation @t28)) % 0.25/0.51 (assume @p25 (forall @t8 (= (tptp.member @t14 tptp.successor_relation) (and @t22 @t21 (= @t40 @t1))))) % 0.25/0.51 (assume @p26 (forall @t41 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 0.25/0.51 (assume @p27 (forall @t42 (= (tptp.range_of @t26) (tptp.domain_of (tptp.inverse @t26))))) % 0.25/0.51 (assume @p28 (forall (@list @t4 @t33) (= (tptp.image @t33 @t4) (tptp.range_of (tptp.restrict @t33 @t4 tptp.universal_class))))) % 0.25/0.51 (assume @p29 (forall @t9 (= @t43 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 0.25/0.51 (assume @p30 (exists @t9 (and @t22 @t43 (forall @t41 (=> (tptp.inductive @t1) @t7))))) % 0.25/0.51 (assume @p31 (forall @t45 (= (tptp.member @t2 @t44) (exists @t41 (and @t3 (tptp.member @t1 @t4)))))) % 0.25/0.51 (assume @p32 @t47) % 0.25/0.51 (assume @p33 (forall @t45 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t10 (tptp.subclass @t2 @t4))))) % 0.25/0.51 (assume @p34 (forall @t6 (=> @t10 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.25/0.51 (assume @p35 (forall (@list @t33 @t48) (tptp.subclass @t49 @t28))) % 0.25/0.51 (assume @p36 (forall (@list @t33 @t48 @t2 @t15) (= (tptp.member @t17 @t49) (and @t10 (tptp.member @t15 (tptp.image @t48 (tptp.image @t33 @t50))))))) % 0.25/0.51 (assume @p37 (forall @t42 (= (tptp.member @t26 tptp.identity_relation) (exists @t9 (and @t22 (= @t26 (tptp.ordered_pair @t4 @t4))))))) % 0.25/0.51 (assume @p38 (forall @t53 (= @t52 (and (tptp.subclass @t51 @t28) (tptp.subclass (tptp.compose @t51 (tptp.inverse @t51)) tptp.identity_relation))))) % 0.25/0.51 (assume @p39 @t56) % 0.25/0.51 (assume @p40 (forall @t8 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 0.25/0.51 (assume @p41 (forall @t9 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t10 @t5 (tptp.disjoint @t2 @t4)))))) % 0.25/0.51 (assume @p42 (forall (@list @t51 @t1) (= @t57 (tptp.sum_class (tptp.image @t51 @t13))))) % 0.25/0.51 (assume @p43 @t63) % 0.25/0.51 (assume @p44 @t66) % 0.25/0.51 (assume @p45 @t69) % 0.25/0.51 (assume @p46 (forall @t9 (or (tptp.member @t70 tptp.universal_class) @t71))) % 0.25/0.51 (assume @p47 (forall @t9 (or (= (tptp.singleton @t70) @t4) @t71))) % 0.25/0.51 (assume @p48 @t77) % 0.25/0.51 (assume @p49 true) % 0.25/0.51 (step @p50 :rule aci_norm :args ((= (or @t79 false @t78) @t80))) % 0.25/0.51 (step @p51 :rule refl :args (@t78)) % 0.25/0.51 (step @p52 :rule evaluate :args ((not true))) % 0.25/0.51 (step @p53 :rule eq-refl :args (@t50)) % 0.25/0.51 (step @p54 :rule cong :premises (@p53) :args (@t81)) % 0.25/0.51 (step @p55 :rule trans :premises (@p54 @p52)) % 0.25/0.51 (step @p56 :rule refl :args (@t79)) % 0.25/0.51 (step @p57 :rule nary_cong :premises (@p56 @p55 @p51) :args (@t82)) % 0.25/0.51 (step @p58 :rule trans :premises (@p57 @p50)) % 0.25/0.51 (step @p59 :rule cong :premises (@p58) :args ((forall @t6 @t82))) % 0.25/0.51 (step @p60 :rule quant-var-elim-eq :args ((= (forall @t9 @t85) @t82))) % 0.25/0.51 (step @p61 :rule aci_norm :args ((= @t86 @t85))) % 0.25/0.51 (step @p62 :rule cong :premises (@p61) :args (@t87)) % 0.25/0.51 (step @p63 :rule trans :premises (@p62 @p60)) % 0.25/0.51 (step @p64 :rule cong :premises (@p63) :args (@t88)) % 0.25/0.51 (step @p65 :rule quant-merge-prenex :args ((= @t88 @t89))) % 0.25/0.51 (step @p66 :rule symm :premises (@p65)) % 0.25/0.51 (step @p67 :rule quant_var_reordering :args ((= (forall @t75 @t86) @t89))) % 0.25/0.51 (step @p68 :rule trans :premises (@p67 @p66 @p64)) % 0.25/0.51 (step @p69 :rule trans :premises (@p68 @p59)) % 0.25/0.51 (step @p70 :rule aci_norm :args ((= (or (or @t79 @t84) @t83) @t86))) % 0.25/0.51 (step @p71 :rule refl :args (@t83)) % 0.25/0.51 (step @p72 :rule bool-and-de-morgan :args (@t10 @t72 true)) % 0.25/0.51 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or (not @t73) @t83))) % 0.25/0.51 (step @p74 :rule trans :premises (@p73 @p70)) % 0.25/0.51 (step @p75 :rule bool-impl-elim :args (@t73 @t83)) % 0.25/0.51 (step @p76 :rule trans :premises (@p75 @p74)) % 0.25/0.51 (step @p77 :rule cong :premises (@p76) :args ((forall @t75 (=> @t73 @t83)))) % 0.25/0.51 (step @p78 :rule trans :premises (@p77 @p69)) % 0.25/0.51 (step @p79 :rule eq-symm :args (@t70 @t2)) % 0.25/0.51 (step @p80 :rule refl :args (@t73)) % 0.25/0.51 (step @p81 :rule cong :premises (@p80 @p79) :args (@t74)) % 0.25/0.51 (step @p82 :rule cong :premises (@p81) :args (@t76)) % 0.25/0.51 (step @p83 :rule trans :premises (@p82 @p78)) % 0.25/0.51 (step @p84 :rule cong :premises (@p83) :args (@t77)) % 0.25/0.51 (step @p85 :rule eq_resolve :premises (@p48 @p84)) % 0.25/0.51 (step @p86 :rule skolemize :premises (@p85)) % 0.25/0.51 (step @p87 :rule cnf_or_neg :args (@t96 1)) % 0.25/0.51 (step @p88 :rule chain_m_resolution :premises (@p87 @p86) :args (@t97 @t98 @t99)) % 0.25/0.51 (step @p89 :rule bool-impl-elim :args (@t21 @t100)) % 0.25/0.51 (step @p90 :rule cong :premises (@p89) :args ((forall @t41 (=> @t21 @t100)))) % 0.25/0.51 (step @p91 :rule eq-symm :args (@t67 @t13)) % 0.25/0.51 (step @p92 :rule refl :args (@t21)) % 0.25/0.51 (step @p93 :rule cong :premises (@p92 @p91) :args (@t68)) % 0.25/0.51 (step @p94 :rule cong :premises (@p93) :args (@t69)) % 0.25/0.51 (step @p95 :rule trans :premises (@p94 @p90)) % 0.25/0.51 (step @p96 :rule eq_resolve :premises (@p45 @p95)) % 0.25/0.51 (step @p97 :rule instantiate :premises (@p96) :args (@t101)) % 0.25/0.51 (step @p98 :rule bool-double-not-elim :args (@t94)) % 0.25/0.51 (step @p99 :rule refl :args (@t96)) % 0.25/0.51 (step @p100 :rule nary_cong :premises (@p99 @p98) :args ((or @t96 (not @t95)))) % 0.25/0.51 (step @p101 :rule cnf_or_neg :args (@t96 0)) % 0.25/0.51 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 0.25/0.51 (step @p103 :rule reordering :premises (@p102) :args ((or @t94 @t96))) % 0.25/0.51 (step @p104 :rule chain_m_resolution :premises (@p103 @p86) :args (@t94 @t98 @t99)) % 0.25/0.51 (step @p105 :rule cnf_or_pos :args (@t104)) % 0.25/0.51 (step @p106 :rule reordering :premises (@p105) :args ((or @t95 @t103 (not @t104)))) % 0.25/0.51 (step @p107 :rule chain_m_resolution :premises (@p106 @p104 @p97) :args (@t103 @t105 (@list @t94 @t104))) % 0.25/0.51 (step @p108 :rule instantiate :premises (@p42) :args ((@list @t110 @t90))) % 0.25/0.51 (step @p109 :rule instantiate :premises (@p42) :args ((@list @t110 @t92))) % 0.25/0.51 (step @p110 :rule instantiate :premises (@p7) :args (@t112)) % 0.25/0.51 (step @p111 :rule instantiate :premises (@p7) :args (@t114)) % 0.25/0.51 (step @p112 :rule aci_norm :args ((= (or (or @t116 @t106) @t115) (or @t116 @t106 @t115)))) % 0.25/0.51 (step @p113 :rule refl :args (@t115)) % 0.25/0.51 (step @p114 :rule bool-and-de-morgan :args (@t22 @t21 true)) % 0.25/0.51 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or (not @t23) @t115))) % 0.25/0.51 (step @p116 :rule trans :premises (@p115 @p112)) % 0.25/0.51 (step @p117 :rule bool-impl-elim :args (@t23 @t115)) % 0.25/0.51 (step @p118 :rule trans :premises (@p117 @p116)) % 0.25/0.51 (step @p119 :rule cong :premises (@p118) :args ((forall @t8 (=> @t23 @t115)))) % 0.25/0.51 (step @p120 :rule eq-symm :args (@t18 @t1)) % 0.25/0.51 (step @p121 :rule eq-symm :args (@t19 @t4)) % 0.25/0.51 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t20)) % 0.25/0.51 (step @p123 :rule refl :args (@t23)) % 0.25/0.51 (step @p124 :rule cong :premises (@p123 @p122) :args (@t24)) % 0.25/0.51 (step @p125 :rule cong :premises (@p124) :args (@t25)) % 0.25/0.51 (step @p126 :rule trans :premises (@p125 @p119)) % 0.25/0.51 (step @p127 :rule eq_resolve :premises (@p9 @p126)) % 0.25/0.51 (step @p128 :rule instantiate :premises (@p127) :args (@t114)) % 0.25/0.51 (step @p129 :rule bool-impl-elim :args (@t22 @t46)) % 0.25/0.51 (step @p130 :rule cong :premises (@p129) :args (@t47)) % 0.25/0.51 (step @p131 :rule eq_resolve :premises (@p32 @p130)) % 0.25/0.51 (step @p132 :rule instantiate :premises (@p131) :args ((@list @t117))) % 0.25/0.51 (step @p133 :rule aci_norm :args ((= (or (or @t116 @t109) @t54) (or @t116 @t109 @t54)))) % 0.25/0.51 (step @p134 :rule refl :args (@t54)) % 0.25/0.51 (step @p135 :rule bool-and-de-morgan :args (@t22 @t52 true)) % 0.25/0.51 (step @p136 :rule nary_cong :premises (@p135 @p134) :args ((or (not @t55) @t54))) % 0.25/0.51 (step @p137 :rule trans :premises (@p136 @p133)) % 0.25/0.51 (step @p138 :rule bool-impl-elim :args (@t55 @t54)) % 0.25/0.51 (step @p139 :rule trans :premises (@p138 @p137)) % 0.25/0.51 (step @p140 :rule cong :premises (@p139) :args (@t56)) % 0.25/0.51 (step @p141 :rule eq_resolve :premises (@p39 @p140)) % 0.25/0.51 (step @p142 :rule instantiate :premises (@p141) :args ((@list @t102 @t110))) % 0.25/0.51 (step @p143 :rule instantiate :premises (@p5) :args ((@list @t90 @t90))) % 0.25/0.51 (step @p144 :rule true_intro :premises (@p143)) % 0.25/0.51 (step @p145 :rule refl :args (tptp.universal_class)) % 0.25/0.51 (step @p146 :rule instantiate :premises (@p6) :args (@t101)) % 0.25/0.51 (step @p147 :rule symm :premises (@p107)) % 0.25/0.51 (step @p148 :rule trans :premises (@p147 @p146)) % 0.25/0.51 (step @p149 :rule cong :premises (@p148 @p145) :args (@t118)) % 0.25/0.51 (step @p150 :rule trans :premises (@p149 @p144)) % 0.25/0.51 (step @p151 :rule true_elim :premises (@p150)) % 0.25/0.51 (step @p152 :rule bool-and-de-morgan :args (@t52 @t108 true)) % 0.25/0.51 (step @p153 :rule cong :premises (@p152) :args (@t120)) % 0.25/0.51 (step @p154 :rule cong :premises (@p153) :args (@t121)) % 0.25/0.51 (step @p155 :rule exists-elim :args ((= (exists @t53 @t119) @t121))) % 0.25/0.51 (step @p156 :rule trans :premises (@p155 @p154)) % 0.25/0.51 (step @p157 :rule aci_norm :args ((= (or @t106 @t60) @t107))) % 0.25/0.51 (step @p158 :rule bool-impl-elim :args (@t21 @t60)) % 0.25/0.51 (step @p159 :rule trans :premises (@p158 @p157)) % 0.25/0.51 (step @p160 :rule cong :premises (@p159) :args (@t61)) % 0.25/0.51 (step @p161 :rule refl :args (@t52)) % 0.25/0.51 (step @p162 :rule nary_cong :premises (@p161 @p160) :args (@t62)) % 0.25/0.51 (step @p163 :rule cong :premises (@p162) :args (@t63)) % 0.25/0.51 (step @p164 :rule trans :premises (@p163 @p156)) % 0.25/0.51 (step @p165 :rule eq_resolve :premises (@p43 @p164)) % 0.25/0.51 (step @p166 :rule skolemize :premises (@p165)) % 0.25/0.51 (step @p167 :rule bool-double-not-elim :args (@t122)) % 0.25/0.51 (step @p168 :rule refl :args (@t124)) % 0.25/0.51 (step @p169 :rule nary_cong :premises (@p168 @p167) :args ((or @t124 (not @t123)))) % 0.25/0.51 (step @p170 :rule cnf_or_neg :args (@t124 0)) % 0.25/0.51 (step @p171 :rule eq_resolve :premises (@p170 @p169)) % 0.25/0.51 (step @p172 :rule reordering :premises (@p171) :args ((or @t122 @t124))) % 0.25/0.51 (step @p173 :rule chain_m_resolution :premises (@p172 @p166) :args (@t122 @t98 (@list @t124))) % 0.25/0.51 (step @p174 :rule cnf_or_pos :args (@t127)) % 0.25/0.51 (step @p175 :rule reordering :premises (@p174) :args ((or @t123 @t125 @t126 (not @t127)))) % 0.25/0.51 (step @p176 :rule chain_m_resolution :premises (@p175 @p173 @p151 @p142) :args (@t125 @t128 (@list @t122 @t118 @t127))) % 0.25/0.51 (step @p177 :rule cnf_or_pos :args (@t132)) % 0.25/0.51 (step @p178 :rule reordering :premises (@p177) :args ((or @t131 @t130 (not @t132)))) % 0.25/0.51 (step @p179 :rule chain_m_resolution :premises (@p178 @p176 @p132) :args (@t130 @t105 (@list @t125 @t132))) % 0.25/0.51 (step @p180 :rule true_intro :premises (@p179)) % 0.25/0.51 (step @p181 :rule cong :premises (@p109 @p145) :args (@t133)) % 0.25/0.51 (step @p182 :rule trans :premises (@p181 @p180)) % 0.25/0.51 (step @p183 :rule true_elim :premises (@p182)) % 0.25/0.51 (step @p184 :rule bool-impl-elim :args (@t21 @t65)) % 0.25/0.51 (step @p185 :rule cong :premises (@p184) :args (@t66)) % 0.25/0.51 (step @p186 :rule eq_resolve :premises (@p44 @p185)) % 0.25/0.51 (step @p187 :rule instantiate :premises (@p186) :args (@t101)) % 0.25/0.51 (step @p188 :rule cnf_or_pos :args (@t135)) % 0.25/0.51 (step @p189 :rule reordering :premises (@p188) :args ((or @t95 @t134 (not @t135)))) % 0.25/0.51 (step @p190 :rule chain_m_resolution :premises (@p189 @p104 @p187) :args (@t134 @t105 (@list @t94 @t135))) % 0.25/0.51 (step @p191 :rule cnf_or_pos :args (@t141)) % 0.25/0.51 (step @p192 :rule reordering :premises (@p191) :args ((or @t139 @t140 @t138 (not @t141)))) % 0.25/0.51 (step @p193 :rule chain_m_resolution :premises (@p192 @p190 @p183 @p128) :args (@t138 @t128 (@list @t134 @t133 @t141))) % 0.25/0.51 (step @p194 :rule cnf_and_pos :args (@t138 1)) % 0.25/0.51 (step @p195 :rule reordering :premises (@p194) :args ((or @t137 (not @t138)))) % 0.25/0.51 (step @p196 :rule chain_m_resolution :premises (@p195 @p193) :args (@t137 @t142 (@list @t138))) % 0.25/0.51 (step @p197 :rule instantiate :premises (@p127) :args (@t112)) % 0.25/0.51 (step @p198 :rule refl :args (@t110)) % 0.25/0.51 (step @p199 :rule cong :premises (@p198 @p107) :args (@t143)) % 0.25/0.51 (step @p200 :rule cong :premises (@p199) :args (@t144)) % 0.25/0.51 (step @p201 :rule trans :premises (@p108 @p200)) % 0.25/0.51 (step @p202 :rule cong :premises (@p201 @p145) :args (@t145)) % 0.25/0.51 (step @p203 :rule trans :premises (@p202 @p180)) % 0.25/0.51 (step @p204 :rule true_elim :premises (@p203)) % 0.25/0.51 (step @p205 :rule cnf_or_pos :args (@t151)) % 0.25/0.51 (step @p206 :rule reordering :premises (@p205) :args ((or @t95 @t150 @t149 (not @t151)))) % 0.25/0.51 (step @p207 :rule chain_m_resolution :premises (@p206 @p104 @p204 @p197) :args (@t149 @t128 (@list @t94 @t145 @t151))) % 0.25/0.51 (step @p208 :rule cnf_and_pos :args (@t149 1)) % 0.25/0.51 (step @p209 :rule reordering :premises (@p208) :args ((or @t148 (not @t149)))) % 0.25/0.51 (step @p210 :rule chain_m_resolution :premises (@p209 @p207) :args (@t148 @t142 (@list @t149))) % 0.25/0.51 (step @p211 :rule refl :args (@t152)) % 0.25/0.51 (step @p212 :rule refl :args (@t153)) % 0.25/0.51 (step @p213 :rule refl :args (@t155)) % 0.25/0.51 (step @p214 :rule refl :args (@t160)) % 0.25/0.51 (step @p215 :rule refl :args (@t162)) % 0.25/0.51 (step @p216 :rule refl :args (@t164)) % 0.25/0.51 (step @p217 :rule refl :args (@t165)) % 0.25/0.51 (step @p218 :rule bool-double-not-elim :args (@t93)) % 0.25/0.51 (step @p219 :rule nary_cong :premises (@p218 @p217 @p216 @p215 @p214 @p213 @p212 @p211) :args ((or (not @t97) @t165 @t164 @t162 @t160 @t155 @t153 @t152))) % 0.25/0.51 (assume-push @p256 @t97) % 0.25/0.51 (assume-push @p257 @t103) % 0.25/0.51 (assume-push @p258 @t163) % 0.25/0.51 (assume-push @p259 @t161) % 0.25/0.51 (assume-push @p260 @t159) % 0.25/0.51 (assume-push @p261 @t154) % 0.25/0.51 (assume-push @p262 @t137) % 0.25/0.51 (step @p227 :rule false_intro :premises (@p88)) % 0.25/0.51 (step @p228 :rule symm :premises (@p196)) % 0.25/0.51 (step @p229 :rule symm :premises (@p111)) % 0.25/0.51 (step @p230 :rule symm :premises (@p109)) % 0.25/0.51 (step @p231 :rule trans :premises (@p108 @p200 @p230)) % 0.25/0.51 (step @p232 :rule cong :premises (@p231 @p107) :args (@t156)) % 0.25/0.51 (step @p233 :rule cong :premises (@p231) :args (@t157)) % 0.25/0.51 (step @p234 :rule cong :premises (@p233 @p232) :args (@t158)) % 0.25/0.51 (step @p235 :rule trans :premises (@p110 @p234 @p229)) % 0.25/0.51 (step @p236 :rule cong :premises (@p235) :args (@t147)) % 0.25/0.51 (step @p237 :rule trans :premises (@p236 @p228)) % 0.25/0.51 (step @p238 :rule refl :args (@t90)) % 0.25/0.51 (step @p239 :rule cong :premises (@p238 @p237) :args (@t148)) % 0.25/0.51 (step @p240 :rule trans :premises (@p239 @p227)) % 0.25/0.51 (step @p241 :rule false_elim :premises (@p240)) % 0.25/0.51 (step-pop @p263 :rule scope :premises (@p241)) % 0.25/0.51 (step-pop @p264 :rule scope :premises (@p263)) % 0.25/0.51 (step-pop @p265 :rule scope :premises (@p264)) % 0.25/0.51 (step-pop @p266 :rule scope :premises (@p265)) % 0.25/0.51 (step-pop @p267 :rule scope :premises (@p266)) % 0.25/0.51 (step-pop @p268 :rule scope :premises (@p267)) % 0.25/0.51 (step-pop @p269 :rule scope :premises (@p268)) % 0.25/0.51 (step @p242 :rule process_scope :premises (@p269) :args (@t152)) % 0.25/0.51 (step @p250 :rule implies_elim :premises (@p242)) % 0.25/0.51 (step @p251 :rule cnf_and_neg :args (@t166)) % 0.25/0.51 (step @p252 :rule resolution :premises (@p251 @p250) :args (true @t166)) % 0.25/0.51 (step @p253 :rule eq_resolve :premises (@p252 @p219)) % 0.25/0.51 (step @p254 :rule reordering :premises (@p253) :args ((or @t93 @t165 @t164 @t162 @t160 @t155 @t152 @t153))) % 0.25/0.51 (step @p255 false :rule chain_m_resolution :premises (@p254 @p210 @p196 @p111 @p110 @p109 @p108 @p107 @p88) :args (false (@list false false false false false false false true) (@list @t148 @t137 @t154 @t159 @t161 @t163 @t103 @t93))) % 0.25/0.51 ) % 0.25/0.51 % SZS output end Proof % 0.25/0.52 % cvc5 exiting %------------------------------------------------------------------------------