%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET108+1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:47:25 AM UTC 2026 % Result : Theorem 0.54s 0.75s % Output : Proof 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET108+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.14/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n014.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 14:56:43 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.54/0.75 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.54/0.75 % SZS status Theorem % 0.54/0.75 % SZS output start Proof % 0.54/0.75 ( % 0.54/0.75 (declare-sort $$unsorted 0) % 0.54/0.75 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.54/0.75 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.element_relation $$unsorted) % 0.54/0.75 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.universal_class $$unsorted) % 0.54/0.75 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.inductive (-> $$unsorted Bool)) % 0.54/0.75 (declare-const tptp.function (-> $$unsorted Bool)) % 0.54/0.75 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 0.54/0.75 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.54/0.75 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.null_class $$unsorted) % 0.54/0.75 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.successor_relation $$unsorted) % 0.54/0.75 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.54/0.75 (declare-const tptp.identity_relation $$unsorted) % 0.54/0.75 (define @t1 () (@var "Y" $$unsorted)) % 0.54/0.75 (define @t2 () (@var "U" $$unsorted)) % 0.54/0.75 (define @t3 () (tptp.member @t2 @t1)) % 0.54/0.75 (define @t4 () (@var "X" $$unsorted)) % 0.54/0.75 (define @t5 () (tptp.member @t2 @t4)) % 0.54/0.75 (define @t6 () (@list @t2)) % 0.54/0.75 (define @t7 () (tptp.subclass @t4 @t1)) % 0.54/0.75 (define @t8 () (@list @t4 @t1)) % 0.54/0.75 (define @t9 () (@list @t4)) % 0.54/0.75 (define @t10 () (= @t2 @t4)) % 0.54/0.75 (define @t11 () (tptp.member @t2 tptp.universal_class)) % 0.54/0.75 (define @t12 () (tptp.unordered_pair @t4 @t1)) % 0.54/0.75 (define @t13 () (tptp.singleton @t4)) % 0.54/0.75 (define @t14 () (tptp.singleton @t1)) % 0.54/0.75 (define @t15 () (tptp.ordered_pair @t4 @t1)) % 0.54/0.75 (define @t16 () (@var "V" $$unsorted)) % 0.54/0.75 (define @t17 () (tptp.cross_product @t4 @t1)) % 0.54/0.75 (define @t18 () (tptp.ordered_pair @t2 @t16)) % 0.54/0.75 (define @t19 () (tptp.member @t1 tptp.universal_class)) % 0.54/0.75 (define @t20 () (tptp.member @t4 tptp.universal_class)) % 0.54/0.75 (define @t21 () (@var "Z" $$unsorted)) % 0.54/0.75 (define @t22 () (@list @t4 @t1 @t21)) % 0.54/0.75 (define @t23 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 0.54/0.75 (define @t24 () (tptp.member @t21 @t1)) % 0.54/0.75 (define @t25 () (tptp.member @t21 @t4)) % 0.54/0.75 (define @t26 () (tptp.member @t21 tptp.universal_class)) % 0.54/0.75 (define @t27 () (@list @t4 @t21)) % 0.54/0.75 (define @t28 () (@var "XR" $$unsorted)) % 0.54/0.75 (define @t29 () (@var "W" $$unsorted)) % 0.54/0.75 (define @t30 () (tptp.cross_product @t23 tptp.universal_class)) % 0.54/0.75 (define @t31 () (tptp.ordered_pair @t18 @t29)) % 0.54/0.75 (define @t32 () (tptp.member @t31 @t30)) % 0.54/0.75 (define @t33 () (tptp.rotate @t4)) % 0.54/0.75 (define @t34 () (tptp.flip @t4)) % 0.54/0.75 (define @t35 () (tptp.successor @t4)) % 0.54/0.75 (define @t36 () (@list @t1)) % 0.54/0.75 (define @t37 () (@list @t21)) % 0.54/0.75 (define @t38 () (tptp.inductive @t4)) % 0.54/0.75 (define @t39 () (tptp.sum_class @t4)) % 0.54/0.75 (define @t40 () (@list @t2 @t4)) % 0.54/0.75 (define @t41 () (@var "YR" $$unsorted)) % 0.54/0.75 (define @t42 () (tptp.compose @t41 @t28)) % 0.54/0.75 (define @t43 () (@var "XF" $$unsorted)) % 0.54/0.75 (define @t44 () (tptp.function @t43)) % 0.54/0.75 (define @t45 () (@list @t43)) % 0.54/0.75 (define @t46 () (tptp.apply @t43 @t1)) % 0.54/0.75 (define @t47 () (= @t4 (tptp.ordered_pair @t1 @t21))) % 0.54/0.75 (define @t48 () (and @t19 @t26 @t47)) % 0.54/0.75 (define @t49 () (@list @t1 @t21)) % 0.54/0.75 (define @t50 () (exists @t49 @t48)) % 0.54/0.75 (define @t51 () (not @t50)) % 0.54/0.75 (define @t52 () (and @t51 @t10 (= @t16 @t4))) % 0.54/0.75 (define @t53 () (= @t4 @t18)) % 0.54/0.75 (define @t54 () (tptp.member @t16 tptp.universal_class)) % 0.54/0.75 (define @t55 () (and @t11 @t54 @t53)) % 0.54/0.75 (define @t56 () (or @t55 @t52)) % 0.54/0.75 (define @t57 () (@list @t2 @t16)) % 0.54/0.75 (define @t58 () (exists @t57 @t56)) % 0.54/0.75 (define @t59 () (forall @t9 @t58)) % 0.54/0.75 (define @t60 () (not @t59)) % 0.54/0.75 (define @t61 () (@var "BOUND_VARIABLE_7910" $$unsorted)) % 0.54/0.75 (define @t62 () (not (tptp.member @t61 tptp.universal_class))) % 0.54/0.75 (define @t63 () (@var "BOUND_VARIABLE_7908" $$unsorted)) % 0.54/0.75 (define @t64 () (not (tptp.member @t63 tptp.universal_class))) % 0.54/0.75 (define @t65 () (tptp.ordered_pair @t63 @t61)) % 0.54/0.75 (define @t66 () (@var "BOUND_VARIABLE_7870" $$unsorted)) % 0.54/0.75 (define @t67 () (@var "BOUND_VARIABLE_7868" $$unsorted)) % 0.54/0.75 (define @t68 () (tptp.ordered_pair @t67 @t66)) % 0.54/0.75 (define @t69 () (not (tptp.member @t66 tptp.universal_class))) % 0.54/0.75 (define @t70 () (not (tptp.member @t67 tptp.universal_class))) % 0.54/0.75 (define @t71 () (@list @t67 @t66)) % 0.54/0.75 (define @t72 () (not (forall @t71 (or @t70 @t69 (not (= @t68 @t65)))))) % 0.54/0.75 (define @t73 () (or @t72 @t64 @t62)) % 0.54/0.75 (define @t74 () (not (= @t65 @t65))) % 0.54/0.75 (define @t75 () (not (= @t65 @t68))) % 0.54/0.75 (define @t76 () (or @t70 @t69 @t75)) % 0.54/0.75 (define @t77 () (forall @t71 @t76)) % 0.54/0.75 (define @t78 () (not @t77)) % 0.54/0.75 (define @t79 () (or @t78 @t64 @t62 @t74)) % 0.54/0.75 (define @t80 () (@list @t63 @t61)) % 0.54/0.75 (define @t81 () (not (= @t4 @t65))) % 0.54/0.75 (define @t82 () (forall @t71 (or @t70 @t69 (not (= @t4 @t68))))) % 0.54/0.75 (define @t83 () (not @t82)) % 0.54/0.75 (define @t84 () (or @t81 @t83 @t64 @t62 @t81)) % 0.54/0.75 (define @t85 () (or @t83 @t64 @t62 @t81)) % 0.54/0.75 (define @t86 () (forall @t9 @t85)) % 0.54/0.75 (define @t87 () (forall @t80 @t86)) % 0.54/0.75 (define @t88 () (forall (@list @t63 @t61 @t4) @t85)) % 0.54/0.75 (define @t89 () (@list @t4 @t63 @t61)) % 0.54/0.75 (define @t90 () (or @t64 @t62 @t81)) % 0.54/0.75 (define @t91 () (or @t83 @t90)) % 0.54/0.75 (define @t92 () (forall @t89 @t91)) % 0.54/0.75 (define @t93 () (forall @t80 @t91)) % 0.54/0.75 (define @t94 () (forall @t80 @t90)) % 0.54/0.75 (define @t95 () (or @t83 @t94)) % 0.54/0.75 (define @t96 () (not @t47)) % 0.54/0.75 (define @t97 () (not @t26)) % 0.54/0.75 (define @t98 () (not @t19)) % 0.54/0.75 (define @t99 () (or @t98 @t97 @t96)) % 0.54/0.75 (define @t100 () (forall @t49 @t99)) % 0.54/0.75 (define @t101 () (not @t100)) % 0.54/0.75 (define @t102 () (not (= @t4 @t4))) % 0.54/0.75 (define @t103 () (@var "BOUND_VARIABLE_7884" $$unsorted)) % 0.54/0.75 (define @t104 () (not (= @t4 @t103))) % 0.54/0.75 (define @t105 () (@list @t103)) % 0.54/0.75 (define @t106 () (or @t104 @t104)) % 0.54/0.75 (define @t107 () (forall @t105 @t104)) % 0.54/0.75 (define @t108 () (@var "BOUND_VARIABLE_7882" $$unsorted)) % 0.54/0.75 (define @t109 () (not (= @t4 @t108))) % 0.54/0.75 (define @t110 () (@list @t108)) % 0.54/0.75 (define @t111 () (or @t109 @t109)) % 0.54/0.75 (define @t112 () (forall @t110 @t109)) % 0.54/0.75 (define @t113 () (or @t101 @t112 @t107)) % 0.54/0.75 (define @t114 () (forall (@list @t108 @t103) (or @t101 @t109 @t104))) % 0.54/0.75 (define @t115 () (= @t4 @t16)) % 0.54/0.75 (define @t116 () (not @t115)) % 0.54/0.75 (define @t117 () (= @t4 @t2)) % 0.54/0.75 (define @t118 () (not @t117)) % 0.54/0.75 (define @t119 () (or @t101 @t118 @t116)) % 0.54/0.75 (define @t120 () (forall @t57 @t119)) % 0.54/0.75 (define @t121 () (@list @t2 @t16)) % 0.54/0.75 (define @t122 () (not @t53)) % 0.54/0.75 (define @t123 () (not @t54)) % 0.54/0.75 (define @t124 () (not @t11)) % 0.54/0.75 (define @t125 () (or @t124 @t123 @t122)) % 0.54/0.75 (define @t126 () (forall @t57 @t125)) % 0.54/0.75 (define @t127 () (and @t126 @t120)) % 0.54/0.75 (define @t128 () (and @t100 @t117 @t115)) % 0.54/0.75 (define @t129 () (or @t55 @t128)) % 0.54/0.75 (define @t130 () (forall @t57 (not @t129))) % 0.54/0.75 (define @t131 () (not @t130)) % 0.54/0.75 (define @t132 () (forall @t49 (not @t48))) % 0.54/0.75 (define @t133 () (not @t132)) % 0.54/0.75 (define @t134 () (forall @t80 @t73)) % 0.54/0.75 (define @t135 () (@quantifiers_skolemize @t134 1)) % 0.54/0.75 (define @t136 () (@quantifiers_skolemize @t134 0)) % 0.54/0.75 (define @t137 () (tptp.ordered_pair @t136 @t135)) % 0.54/0.75 (define @t138 () (forall @t71 (or @t70 @t69 (not (= @t68 @t137))))) % 0.54/0.75 (define @t139 () (tptp.member @t135 tptp.universal_class)) % 0.54/0.75 (define @t140 () (not @t139)) % 0.54/0.75 (define @t141 () (tptp.member @t136 tptp.universal_class)) % 0.54/0.75 (define @t142 () (not @t141)) % 0.54/0.75 (define @t143 () (not @t138)) % 0.54/0.75 (define @t144 () (or @t143 @t142 @t140)) % 0.54/0.75 (define @t145 () (@list true)) % 0.54/0.75 (define @t146 () (@list @t144)) % 0.54/0.75 (define @t147 () (or @t142 @t140)) % 0.54/0.75 (define @t148 () (not @t147)) % 0.54/0.75 (define @t149 () (not (= @t137 @t137))) % 0.54/0.75 (define @t150 () (or @t142 @t140 @t149)) % 0.54/0.75 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.54/0.75 (assume @p2 (forall @t9 (tptp.subclass @t4 tptp.universal_class))) % 0.54/0.75 (assume @p3 (forall @t8 (= (= @t4 @t1) (and @t7 (tptp.subclass @t1 @t4))))) % 0.54/0.75 (assume @p4 (forall (@list @t2 @t4 @t1) (= (tptp.member @t2 @t12) (and @t11 (or @t10 (= @t2 @t1)))))) % 0.54/0.75 (assume @p5 (forall @t8 (tptp.member @t12 tptp.universal_class))) % 0.54/0.75 (assume @p6 (forall @t9 (= @t13 (tptp.unordered_pair @t4 @t4)))) % 0.54/0.75 (assume @p7 (forall @t8 (= @t15 (tptp.unordered_pair @t13 (tptp.unordered_pair @t4 @t14))))) % 0.54/0.75 (assume @p8 (forall (@list @t2 @t16 @t4 @t1) (= (tptp.member @t18 @t17) (and @t5 (tptp.member @t16 @t1))))) % 0.54/0.75 (assume @p9 (forall @t8 (=> (and @t20 @t19) (and (= (tptp.first @t15) @t4) (= (tptp.second @t15) @t1))))) % 0.54/0.75 (assume @p10 (forall @t22 (=> (tptp.member @t21 @t17) (= @t21 (tptp.ordered_pair (tptp.first @t21) (tptp.second @t21)))))) % 0.54/0.75 (assume @p11 (forall @t8 (= (tptp.member @t15 tptp.element_relation) (and @t19 (tptp.member @t4 @t1))))) % 0.54/0.75 (assume @p12 (tptp.subclass tptp.element_relation @t23)) % 0.54/0.75 (assume @p13 (forall @t22 (= (tptp.member @t21 (tptp.intersection @t4 @t1)) (and @t25 @t24)))) % 0.54/0.75 (assume @p14 (forall @t27 (= (tptp.member @t21 (tptp.complement @t4)) (and @t26 (not @t25))))) % 0.54/0.75 (assume @p15 (forall (@list @t4 @t28 @t1) (= (tptp.restrict @t28 @t4 @t1) (tptp.intersection @t28 @t17)))) % 0.54/0.75 (assume @p16 (forall @t9 (not (tptp.member @t4 tptp.null_class)))) % 0.54/0.75 (assume @p17 (forall @t27 (= (tptp.member @t21 (tptp.domain_of @t4)) (and @t26 (not (= (tptp.restrict @t4 (tptp.singleton @t21) tptp.universal_class) tptp.null_class)))))) % 0.54/0.75 (assume @p18 (forall (@list @t4 @t2 @t16 @t29) (= (tptp.member @t31 @t33) (and @t32 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t16 @t29) @t2) @t4))))) % 0.54/0.75 (assume @p19 (forall @t9 (tptp.subclass @t33 @t30))) % 0.54/0.75 (assume @p20 (forall (@list @t2 @t16 @t29 @t4) (= (tptp.member @t31 @t34) (and @t32 (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t16 @t2) @t29) @t4))))) % 0.54/0.75 (assume @p21 (forall @t9 (tptp.subclass @t34 @t30))) % 0.54/0.75 (assume @p22 (forall @t22 (= (tptp.member @t21 (tptp.union @t4 @t1)) (or @t25 @t24)))) % 0.54/0.75 (assume @p23 (forall @t9 (= @t35 (tptp.union @t4 @t13)))) % 0.54/0.75 (assume @p24 (tptp.subclass tptp.successor_relation @t23)) % 0.54/0.75 (assume @p25 (forall @t8 (= (tptp.member @t15 tptp.successor_relation) (and @t20 @t19 (= @t35 @t1))))) % 0.54/0.75 (assume @p26 (forall @t36 (= (tptp.inverse @t1) (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class)))))) % 0.54/0.75 (assume @p27 (forall @t37 (= (tptp.range_of @t21) (tptp.domain_of (tptp.inverse @t21))))) % 0.54/0.75 (assume @p28 (forall (@list @t4 @t28) (= (tptp.image @t28 @t4) (tptp.range_of (tptp.restrict @t28 @t4 tptp.universal_class))))) % 0.54/0.75 (assume @p29 (forall @t9 (= @t38 (and (tptp.member tptp.null_class @t4) (tptp.subclass (tptp.image tptp.successor_relation @t4) @t4))))) % 0.54/0.75 (assume @p30 (exists @t9 (and @t20 @t38 (forall @t36 (=> (tptp.inductive @t1) @t7))))) % 0.54/0.75 (assume @p31 (forall @t40 (= (tptp.member @t2 @t39) (exists @t36 (and @t3 (tptp.member @t1 @t4)))))) % 0.54/0.75 (assume @p32 (forall @t9 (=> @t20 (tptp.member @t39 tptp.universal_class)))) % 0.54/0.75 (assume @p33 (forall @t40 (= (tptp.member @t2 (tptp.power_class @t4)) (and @t11 (tptp.subclass @t2 @t4))))) % 0.54/0.75 (assume @p34 (forall @t6 (=> @t11 (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 0.54/0.75 (assume @p35 (forall (@list @t28 @t41) (tptp.subclass @t42 @t23))) % 0.54/0.75 (assume @p36 (forall (@list @t28 @t41 @t2 @t16) (= (tptp.member @t18 @t42) (and @t11 (tptp.member @t16 (tptp.image @t41 (tptp.image @t28 (tptp.singleton @t2)))))))) % 0.54/0.75 (assume @p37 (forall @t37 (= (tptp.member @t21 tptp.identity_relation) (exists @t9 (and @t20 (= @t21 (tptp.ordered_pair @t4 @t4))))))) % 0.54/0.75 (assume @p38 (forall @t45 (= @t44 (and (tptp.subclass @t43 @t23) (tptp.subclass (tptp.compose @t43 (tptp.inverse @t43)) tptp.identity_relation))))) % 0.54/0.75 (assume @p39 (forall (@list @t4 @t43) (=> (and @t20 @t44) (tptp.member (tptp.image @t43 @t4) tptp.universal_class)))) % 0.54/0.75 (assume @p40 (forall @t8 (= (tptp.disjoint @t4 @t1) (forall @t6 (not (and @t5 @t3)))))) % 0.54/0.75 (assume @p41 (forall @t9 (=> (not (= @t4 tptp.null_class)) (exists @t6 (and @t11 @t5 (tptp.disjoint @t2 @t4)))))) % 0.54/0.75 (assume @p42 (forall (@list @t43 @t1) (= @t46 (tptp.sum_class (tptp.image @t43 @t14))))) % 0.54/0.75 (assume @p43 (exists @t45 (and @t44 (forall @t36 (=> @t19 (or (= @t1 tptp.null_class) (tptp.member @t46 @t1))))))) % 0.54/0.75 (assume @p44 @t60) % 0.54/0.75 (assume @p45 true) % 0.54/0.75 (step @p46 :rule aci_norm :args ((= (or @t72 @t64 @t62 false) @t73))) % 0.54/0.75 (step @p47 :rule evaluate :args ((not true))) % 0.54/0.75 (step @p48 :rule eq-refl :args (@t65)) % 0.54/0.75 (step @p49 :rule cong :premises (@p48) :args (@t74)) % 0.54/0.75 (step @p50 :rule trans :premises (@p49 @p47)) % 0.54/0.75 (step @p51 :rule refl :args (@t62)) % 0.54/0.75 (step @p52 :rule refl :args (@t64)) % 0.54/0.75 (step @p53 :rule eq-symm :args (@t65 @t68)) % 0.54/0.75 (step @p54 :rule cong :premises (@p53) :args (@t75)) % 0.54/0.75 (step @p55 :rule refl :args (@t69)) % 0.54/0.75 (step @p56 :rule refl :args (@t70)) % 0.54/0.75 (step @p57 :rule nary_cong :premises (@p56 @p55 @p54) :args (@t76)) % 0.54/0.75 (step @p58 :rule cong :premises (@p57) :args (@t77)) % 0.54/0.75 (step @p59 :rule cong :premises (@p58) :args (@t78)) % 0.54/0.75 (step @p60 :rule nary_cong :premises (@p59 @p52 @p51 @p50) :args (@t79)) % 0.54/0.75 (step @p61 :rule trans :premises (@p60 @p46)) % 0.54/0.75 (step @p62 :rule cong :premises (@p61) :args ((forall @t80 @t79))) % 0.54/0.75 (step @p63 :rule quant-var-elim-eq :args ((= (forall @t9 @t84) @t79))) % 0.54/0.75 (step @p64 :rule aci_norm :args ((= @t85 @t84))) % 0.54/0.75 (step @p65 :rule cong :premises (@p64) :args (@t86)) % 0.54/0.75 (step @p66 :rule trans :premises (@p65 @p63)) % 0.54/0.75 (step @p67 :rule cong :premises (@p66) :args (@t87)) % 0.54/0.75 (step @p68 :rule quant-merge-prenex :args ((= @t87 @t88))) % 0.54/0.75 (step @p69 :rule symm :premises (@p68)) % 0.54/0.75 (step @p70 :rule quant_var_reordering :args ((= (forall @t89 @t85) @t88))) % 0.54/0.75 (step @p71 :rule trans :premises (@p70 @p69 @p67)) % 0.54/0.75 (step @p72 :rule trans :premises (@p71 @p62)) % 0.54/0.75 (step @p73 :rule aci_norm :args ((= @t91 @t85))) % 0.54/0.75 (step @p74 :rule cong :premises (@p73) :args (@t92)) % 0.54/0.75 (step @p75 :rule trans :premises (@p74 @p72)) % 0.54/0.75 (step @p76 :rule quant-merge-prenex :args ((= (forall @t9 @t93) @t92))) % 0.54/0.75 (step @p77 :rule alpha_equiv :args (@t94 (@list @t63 @t61) (@list @t1 @t21))) % 0.54/0.75 (step @p78 :rule refl :args (@t83)) % 0.54/0.75 (step @p79 :rule nary_cong :premises (@p78 @p77) :args (@t95)) % 0.54/0.75 (step @p80 :rule quant-miniscope-or :args ((= @t93 @t95))) % 0.54/0.75 (step @p81 :rule trans :premises (@p80 @p79)) % 0.54/0.75 (step @p82 :rule symm :premises (@p81)) % 0.54/0.75 (step @p83 :rule cong :premises (@p82) :args ((forall @t9 (or @t83 @t100)))) % 0.54/0.75 (step @p84 :rule trans :premises (@p83 @p76)) % 0.54/0.75 (step @p85 :rule trans :premises (@p84 @p75)) % 0.54/0.75 (step @p86 :rule bool-double-not-elim :args (@t100)) % 0.54/0.75 (step @p87 :rule nary_cong :premises (@p78 @p86) :args ((or @t83 (not @t101)))) % 0.54/0.75 (step @p88 :rule bool-and-de-morgan :args (@t82 @t101 true)) % 0.54/0.75 (step @p89 :rule trans :premises (@p88 @p87)) % 0.54/0.75 (step @p90 :rule cong :premises (@p89) :args ((forall @t9 (not (and @t82 @t101))))) % 0.54/0.75 (step @p91 :rule trans :premises (@p90 @p85)) % 0.54/0.75 (step @p92 :rule aci_norm :args ((= (or @t101 false false) @t101))) % 0.54/0.75 (step @p93 :rule eq-refl :args (@t4)) % 0.54/0.75 (step @p94 :rule cong :premises (@p93) :args (@t102)) % 0.54/0.75 (step @p95 :rule trans :premises (@p94 @p47)) % 0.54/0.75 (step @p96 :rule quant-var-elim-eq :args ((= (forall @t105 (or (not (= @t103 @t4)) @t104)) @t102))) % 0.54/0.75 (step @p97 :rule refl :args (@t104)) % 0.54/0.75 (step @p98 :rule eq-symm :args (@t4 @t103)) % 0.54/0.75 (step @p99 :rule cong :premises (@p98) :args (@t104)) % 0.54/0.75 (step @p100 :rule nary_cong :premises (@p99 @p97) :args (@t106)) % 0.54/0.75 (step @p101 :rule aci_norm :args ((= @t104 @t106))) % 0.54/0.75 (step @p102 :rule trans :premises (@p101 @p100)) % 0.54/0.75 (step @p103 :rule cong :premises (@p102) :args (@t107)) % 0.54/0.75 (step @p104 :rule trans :premises (@p103 @p96)) % 0.54/0.75 (step @p105 :rule trans :premises (@p104 @p95)) % 0.54/0.75 (step @p106 :rule quant-var-elim-eq :args ((= (forall @t110 (or (not (= @t108 @t4)) @t109)) @t102))) % 0.54/0.75 (step @p107 :rule refl :args (@t109)) % 0.54/0.75 (step @p108 :rule eq-symm :args (@t4 @t108)) % 0.54/0.75 (step @p109 :rule cong :premises (@p108) :args (@t109)) % 0.54/0.75 (step @p110 :rule nary_cong :premises (@p109 @p107) :args (@t111)) % 0.54/0.75 (step @p111 :rule aci_norm :args ((= @t109 @t111))) % 0.54/0.75 (step @p112 :rule trans :premises (@p111 @p110)) % 0.54/0.75 (step @p113 :rule cong :premises (@p112) :args (@t112)) % 0.54/0.75 (step @p114 :rule trans :premises (@p113 @p106)) % 0.54/0.75 (step @p115 :rule trans :premises (@p114 @p95)) % 0.54/0.75 (step @p116 :rule refl :args (@t101)) % 0.54/0.75 (step @p117 :rule nary_cong :premises (@p116 @p115 @p105) :args (@t113)) % 0.54/0.75 (step @p118 :rule trans :premises (@p117 @p92)) % 0.54/0.75 (step @p119 :rule quant-miniscope-or :args ((= @t114 @t113))) % 0.54/0.75 (step @p120 :rule trans :premises (@p119 @p118)) % 0.54/0.75 (step @p121 :rule refl :args (@t82)) % 0.54/0.75 (step @p122 :rule nary_cong :premises (@p121 @p120) :args ((and @t82 @t114))) % 0.54/0.75 (step @p123 :rule alpha_equiv :args (@t120 @t121 (@list @t108 @t103))) % 0.54/0.75 (step @p124 :rule alpha_equiv :args (@t126 @t121 (@list @t67 @t66))) % 0.54/0.75 (step @p125 :rule nary_cong :premises (@p124 @p123) :args (@t127)) % 0.54/0.75 (step @p126 :rule quant-miniscope-and :args ((= (forall @t57 (and @t125 @t119)) @t127))) % 0.54/0.75 (step @p127 :rule trans :premises (@p126 @p125)) % 0.54/0.75 (step @p128 :rule trans :premises (@p127 @p122)) % 0.54/0.75 (step @p129 :rule aci_norm :args ((= (or @t101 (or @t118 @t116)) @t119))) % 0.54/0.75 (step @p130 :rule bool-and-de-morgan :args (@t117 @t115 true)) % 0.54/0.75 (step @p131 :rule refl :args (@t101)) % 0.54/0.75 (step @p132 :rule nary_cong :premises (@p131 @p130) :args ((or @t101 (not (and @t117 @t115))))) % 0.54/0.75 (step @p133 :rule bool-and-de-morgan :args (@t100 @t117 (and @t115))) % 0.54/0.75 (step @p134 :rule trans :premises (@p133 @p132)) % 0.54/0.75 (step @p135 :rule trans :premises (@p134 @p129)) % 0.54/0.75 (step @p136 :rule aci_norm :args ((= (or @t124 (or @t123 @t122)) @t125))) % 0.54/0.75 (step @p137 :rule bool-and-de-morgan :args (@t54 @t53 true)) % 0.54/0.75 (step @p138 :rule refl :args (@t124)) % 0.54/0.75 (step @p139 :rule nary_cong :premises (@p138 @p137) :args ((or @t124 (not (and @t54 @t53))))) % 0.54/0.75 (step @p140 :rule bool-and-de-morgan :args (@t11 @t54 (and @t53))) % 0.54/0.75 (step @p141 :rule trans :premises (@p140 @p139)) % 0.54/0.75 (step @p142 :rule trans :premises (@p141 @p136)) % 0.54/0.75 (step @p143 :rule nary_cong :premises (@p142 @p135) :args ((and (not @t55) (not @t128)))) % 0.54/0.75 (step @p144 :rule bool-or-de-morgan :args (@t55 @t128 false)) % 0.54/0.75 (step @p145 :rule trans :premises (@p144 @p143)) % 0.54/0.75 (step @p146 :rule cong :premises (@p145) :args (@t130)) % 0.54/0.75 (step @p147 :rule trans :premises (@p146 @p128)) % 0.54/0.75 (step @p148 :rule cong :premises (@p147) :args (@t131)) % 0.54/0.75 (step @p149 :rule exists-elim :args ((= (exists @t57 @t129) @t131))) % 0.54/0.75 (step @p150 :rule trans :premises (@p149 @p148)) % 0.54/0.75 (step @p151 :rule eq-symm :args (@t16 @t4)) % 0.54/0.75 (step @p152 :rule eq-symm :args (@t2 @t4)) % 0.54/0.75 (step @p153 :rule aci_norm :args ((= (or @t98 (or @t97 @t96)) @t99))) % 0.54/0.75 (step @p154 :rule bool-and-de-morgan :args (@t26 @t47 true)) % 0.54/0.75 (step @p155 :rule refl :args (@t98)) % 0.54/0.75 (step @p156 :rule nary_cong :premises (@p155 @p154) :args ((or @t98 (not (and @t26 @t47))))) % 0.54/0.75 (step @p157 :rule bool-and-de-morgan :args (@t19 @t26 (and @t47))) % 0.54/0.75 (step @p158 :rule trans :premises (@p157 @p156)) % 0.54/0.75 (step @p159 :rule trans :premises (@p158 @p153)) % 0.54/0.75 (step @p160 :rule cong :premises (@p159) :args (@t132)) % 0.54/0.75 (step @p161 :rule cong :premises (@p160) :args (@t133)) % 0.54/0.75 (step @p162 :rule exists-elim :args ((= @t50 @t133))) % 0.54/0.75 (step @p163 :rule trans :premises (@p162 @p161)) % 0.54/0.75 (step @p164 :rule cong :premises (@p163) :args (@t51)) % 0.54/0.75 (step @p165 :rule trans :premises (@p164 @p86)) % 0.54/0.75 (step @p166 :rule nary_cong :premises (@p165 @p152 @p151) :args (@t52)) % 0.54/0.75 (step @p167 :rule refl :args (@t55)) % 0.54/0.75 (step @p168 :rule nary_cong :premises (@p167 @p166) :args (@t56)) % 0.54/0.75 (step @p169 :rule cong :premises (@p168) :args (@t58)) % 0.54/0.75 (step @p170 :rule trans :premises (@p169 @p150)) % 0.54/0.75 (step @p171 :rule cong :premises (@p170) :args (@t59)) % 0.54/0.75 (step @p172 :rule trans :premises (@p171 @p91)) % 0.54/0.75 (step @p173 :rule cong :premises (@p172) :args (@t60)) % 0.54/0.75 (step @p174 :rule eq_resolve :premises (@p44 @p173)) % 0.54/0.75 (step @p175 :rule skolemize :premises (@p174)) % 0.54/0.75 (step @p176 :rule bool-double-not-elim :args (@t138)) % 0.54/0.75 (step @p177 :rule refl :args (@t144)) % 0.54/0.75 (step @p178 :rule nary_cong :premises (@p177 @p176) :args ((or @t144 (not @t143)))) % 0.54/0.75 (step @p179 :rule cnf_or_neg :args (@t144 0)) % 0.54/0.75 (step @p180 :rule eq_resolve :premises (@p179 @p178)) % 0.54/0.75 (step @p181 :rule reordering :premises (@p180) :args ((or @t138 @t144))) % 0.54/0.75 (step @p182 :rule chain_m_resolution :premises (@p181 @p175) :args (@t138 @t145 @t146)) % 0.54/0.75 (step @p183 :rule bool-double-not-elim :args (@t139)) % 0.54/0.75 (step @p184 :rule nary_cong :premises (@p177 @p183) :args ((or @t144 (not @t140)))) % 0.54/0.75 (step @p185 :rule cnf_or_neg :args (@t144 2)) % 0.54/0.75 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.54/0.75 (step @p187 :rule reordering :premises (@p186) :args ((or @t139 @t144))) % 0.54/0.75 (step @p188 :rule chain_m_resolution :premises (@p187 @p175) :args (@t139 @t145 @t146)) % 0.54/0.76 (step @p189 :rule bool-double-not-elim :args (@t141)) % 0.54/0.76 (step @p190 :rule nary_cong :premises (@p177 @p189) :args ((or @t144 (not @t142)))) % 0.54/0.76 (step @p191 :rule cnf_or_neg :args (@t144 1)) % 0.54/0.76 (step @p192 :rule eq_resolve :premises (@p191 @p190)) % 0.54/0.76 (step @p193 :rule reordering :premises (@p192) :args ((or @t141 @t144))) % 0.54/0.76 (step @p194 :rule chain_m_resolution :premises (@p193 @p175) :args (@t141 @t145 @t146)) % 0.54/0.76 (step @p195 :rule cnf_or_pos :args (@t147)) % 0.54/0.76 (step @p196 :rule reordering :premises (@p195) :args ((or @t142 @t140 @t148))) % 0.54/0.76 (step @p197 :rule chain_m_resolution :premises (@p196 @p194 @p188) :args (@t148 (@list false false) (@list @t141 @t139))) % 0.54/0.76 (step @p198 :rule aci_norm :args ((= (or @t142 @t140 false) @t147))) % 0.54/0.76 (step @p199 :rule eq-refl :args (@t137)) % 0.54/0.76 (step @p200 :rule cong :premises (@p199) :args (@t149)) % 0.54/0.76 (step @p201 :rule trans :premises (@p200 @p47)) % 0.54/0.76 (step @p202 :rule refl :args (@t140)) % 0.54/0.76 (step @p203 :rule refl :args (@t142)) % 0.54/0.76 (step @p204 :rule nary_cong :premises (@p203 @p202 @p201) :args (@t150)) % 0.54/0.76 (step @p205 :rule trans :premises (@p204 @p198)) % 0.54/0.76 (step @p206 :rule refl :args (@t138)) % 0.54/0.76 (step @p207 :rule cong :premises (@p206 @p205) :args ((=> @t138 @t150))) % 0.54/0.76 (assume-push @p215 @t138) % 0.54/0.76 (step @p209 :rule instantiate :premises (@p182) :args ((@list @t136 @t135))) % 0.54/0.76 (step-pop @p216 :rule scope :premises (@p209)) % 0.54/0.76 (step @p210 :rule process_scope :premises (@p216) :args (@t150)) % 0.54/0.76 (step @p212 :rule eq_resolve :premises (@p210 @p207)) % 0.54/0.76 (step @p213 :rule implies_elim :premises (@p212)) % 0.54/0.76 (step @p214 false :rule chain_m_resolution :premises (@p213 @p197 @p182) :args (false (@list true false) (@list @t147 @t138))) % 0.54/0.76 ) % 0.54/0.76 % SZS output end Proof % 0.54/0.76 % cvc5 exiting %------------------------------------------------------------------------------