%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET055^12 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:47:09 AM UTC 2026 % Result : Theorem 0.37s 0.76s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET055^12 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n008.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 14:48:33 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.52 %----Proving TH0 % 0.37/0.76 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.76 % SZS status Theorem % 0.37/0.76 % SZS output start Proof % 0.37/0.76 ( % 0.37/0.76 (declare-sort $$unsorted 0) % 0.37/0.76 (declare-sort tptp.mworld 0) % 0.37/0.76 (declare-const tptp.mactual tptp.mworld) % 0.37/0.76 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.37/0.76 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.37/0.76 (declare-const tptp.identity_relation $$unsorted) % 0.37/0.76 (declare-const tptp.successor_relation $$unsorted) % 0.37/0.76 (declare-const tptp.null_class $$unsorted) % 0.37/0.76 (declare-const tptp.element_relation $$unsorted) % 0.37/0.76 (declare-const tptp.universal_class $$unsorted) % 0.37/0.76 (declare-const tptp.member (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.76 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.qmltpeq (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.76 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.subclass (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.76 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.76 (declare-const tptp.disjoint (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.37/0.76 (declare-const tptp.function (-> $$unsorted tptp.mworld Bool)) % 0.37/0.76 (declare-const tptp.inductive (-> $$unsorted tptp.mworld Bool)) % 0.37/0.76 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.37/0.76 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.76 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.76 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.76 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.76 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.76 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.76 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (and (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.76 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.76 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.76 (define @t1 () (@var "V" tptp.mworld)) % 0.37/0.76 (define @t2 () (@var "W" tptp.mworld)) % 0.37/0.76 (define @t3 () (_ (_ tptp.mrel @t2) @t1)) % 0.37/0.76 (define @t4 () (@var "X" $$unsorted)) % 0.37/0.76 (define @t5 () (_ (_ tptp.eiw_di @t4) @t2)) % 0.37/0.76 (define @t6 () (@list @t4)) % 0.37/0.76 (define @t7 () (@list @t2)) % 0.37/0.76 (define @t8 () (@var "__flatten_var_0" tptp.mworld)) % 0.37/0.76 (define @t9 () (_ tptp.qmltpeq @t4)) % 0.37/0.76 (define @t10 () (_ @t9 @t4)) % 0.37/0.76 (define @t11 () (@list @t4 @t8)) % 0.37/0.76 (define @t12 () (lambda @t11 (_ @t10 @t8))) % 0.37/0.76 (define @t13 () (_ tptp.mlocal (_ tptp.mforall_di @t12))) % 0.37/0.76 (define @t14 () (@var "Y" $$unsorted)) % 0.37/0.76 (define @t15 () (_ tptp.qmltpeq @t14)) % 0.37/0.76 (define @t16 () (_ @t9 @t14)) % 0.37/0.76 (define @t17 () (@list @t14 @t8)) % 0.37/0.76 (define @t18 () (@var "Z" $$unsorted)) % 0.37/0.76 (define @t19 () (@list @t18 @t8)) % 0.37/0.76 (define @t20 () (@var "C" $$unsorted)) % 0.37/0.76 (define @t21 () (@var "B" $$unsorted)) % 0.37/0.76 (define @t22 () (@var "A" $$unsorted)) % 0.37/0.76 (define @t23 () (_ (_ tptp.qmltpeq @t22) @t21)) % 0.37/0.76 (define @t24 () (_ tptp.mimplies @t23)) % 0.37/0.76 (define @t25 () (@list @t20 @t8)) % 0.37/0.76 (define @t26 () (@list @t21 @t8)) % 0.37/0.76 (define @t27 () (@list @t22 @t8)) % 0.37/0.76 (define @t28 () (_ tptp.apply @t20)) % 0.37/0.76 (define @t29 () (_ tptp.compose @t20)) % 0.37/0.76 (define @t30 () (_ tptp.cross_product @t20)) % 0.37/0.76 (define @t31 () (_ tptp.image @t20)) % 0.37/0.76 (define @t32 () (_ tptp.intersection @t20)) % 0.37/0.76 (define @t33 () (_ tptp.ordered_pair @t20)) % 0.37/0.76 (define @t34 () (@var "D" $$unsorted)) % 0.37/0.76 (define @t35 () (@list @t34 @t8)) % 0.37/0.76 (define @t36 () (_ tptp.restrict @t20)) % 0.37/0.76 (define @t37 () (_ @t36 @t34)) % 0.37/0.76 (define @t38 () (_ tptp.union @t20)) % 0.37/0.76 (define @t39 () (_ tptp.unordered_pair @t20)) % 0.37/0.76 (define @t40 () (_ tptp.mand @t23)) % 0.37/0.76 (define @t41 () (_ tptp.disjoint @t20)) % 0.37/0.76 (define @t42 () (_ tptp.member @t20)) % 0.37/0.76 (define @t43 () (_ tptp.subclass @t20)) % 0.37/0.76 (define @t44 () (@var "U" $$unsorted)) % 0.37/0.76 (define @t45 () (_ tptp.member @t44)) % 0.37/0.76 (define @t46 () (_ @t45 @t14)) % 0.37/0.76 (define @t47 () (_ @t45 @t4)) % 0.37/0.76 (define @t48 () (@list @t44 @t8)) % 0.37/0.76 (define @t49 () (_ tptp.subclass @t4)) % 0.37/0.76 (define @t50 () (_ @t49 @t14)) % 0.37/0.76 (define @t51 () (_ tptp.qmltpeq @t44)) % 0.37/0.76 (define @t52 () (_ @t45 tptp.universal_class)) % 0.37/0.76 (define @t53 () (_ tptp.mand @t52)) % 0.37/0.76 (define @t54 () (_ tptp.unordered_pair @t4)) % 0.37/0.76 (define @t55 () (_ @t54 @t14)) % 0.37/0.76 (define @t56 () (_ tptp.singleton @t4)) % 0.37/0.76 (define @t57 () (_ tptp.singleton @t14)) % 0.37/0.76 (define @t58 () (_ (_ tptp.ordered_pair @t4) @t14)) % 0.37/0.76 (define @t59 () (@var "V" $$unsorted)) % 0.37/0.76 (define @t60 () (_ tptp.member @t59)) % 0.37/0.76 (define @t61 () (_ tptp.mand @t47)) % 0.37/0.76 (define @t62 () (_ (_ tptp.cross_product @t4) @t14)) % 0.37/0.76 (define @t63 () (_ (_ tptp.ordered_pair @t44) @t59)) % 0.37/0.76 (define @t64 () (_ tptp.member @t63)) % 0.37/0.76 (define @t65 () (@list @t59 @t8)) % 0.37/0.76 (define @t66 () (_ tptp.member @t18)) % 0.37/0.76 (define @t67 () (_ tptp.member @t4)) % 0.37/0.76 (define @t68 () (_ tptp.member @t14)) % 0.37/0.76 (define @t69 () (_ @t68 tptp.universal_class)) % 0.37/0.76 (define @t70 () (_ tptp.mand @t69)) % 0.37/0.76 (define @t71 () (_ tptp.member @t58)) % 0.37/0.76 (define @t72 () (_ (_ tptp.cross_product tptp.universal_class) tptp.universal_class)) % 0.37/0.76 (define @t73 () (_ @t66 @t14)) % 0.37/0.76 (define @t74 () (_ @t66 @t4)) % 0.37/0.76 (define @t75 () (_ tptp.mand (_ @t66 tptp.universal_class))) % 0.37/0.76 (define @t76 () (@var "XR" $$unsorted)) % 0.37/0.76 (define @t77 () (_ (_ tptp.restrict @t76) @t4)) % 0.37/0.76 (define @t78 () (@list @t76 @t8)) % 0.37/0.76 (define @t79 () (@var "W" $$unsorted)) % 0.37/0.76 (define @t80 () (_ tptp.ordered_pair @t59)) % 0.37/0.76 (define @t81 () (_ (_ tptp.cross_product @t72) tptp.universal_class)) % 0.37/0.76 (define @t82 () (_ tptp.member (_ (_ tptp.ordered_pair @t63) @t79))) % 0.37/0.76 (define @t83 () (_ tptp.mand (_ @t82 @t81))) % 0.37/0.76 (define @t84 () (_ tptp.rotate @t4)) % 0.37/0.76 (define @t85 () (@list @t79 @t8)) % 0.37/0.76 (define @t86 () (_ tptp.flip @t4)) % 0.37/0.76 (define @t87 () (_ tptp.union @t4)) % 0.37/0.76 (define @t88 () (_ tptp.qmltpeq (_ tptp.successor @t4))) % 0.37/0.76 (define @t89 () (_ @t67 tptp.universal_class)) % 0.37/0.76 (define @t90 () (_ tptp.mand @t89)) % 0.37/0.76 (define @t91 () (_ tptp.inductive @t4)) % 0.37/0.76 (define @t92 () (_ tptp.sum_class @t4)) % 0.37/0.76 (define @t93 () (@var "YR" $$unsorted)) % 0.37/0.76 (define @t94 () (_ (_ tptp.compose @t93) @t76)) % 0.37/0.76 (define @t95 () (@list @t93 @t8)) % 0.37/0.76 (define @t96 () (_ tptp.image @t93)) % 0.37/0.76 (define @t97 () (@var "XF" $$unsorted)) % 0.37/0.76 (define @t98 () (_ tptp.function @t97)) % 0.37/0.76 (define @t99 () (@list @t97 @t8)) % 0.37/0.76 (define @t100 () (_ tptp.image @t97)) % 0.37/0.76 (define @t101 () (_ (_ tptp.apply @t97) @t14)) % 0.37/0.76 (define @t102 () (not @t13)) % 0.37/0.76 (define @t103 () (@var "Phi" (-> tptp.mworld Bool))) % 0.37/0.76 (define @t104 () (lambda (@list @t103) (_ @t103 tptp.mactual))) % 0.37/0.76 (define @t105 () (@var "A" (-> tptp.mworld Bool))) % 0.37/0.76 (define @t106 () (_ @t105 @t2)) % 0.37/0.76 (define @t107 () (lambda (@list @t105 @t2) (not @t106))) % 0.37/0.76 (define @t108 () (@var "B" (-> tptp.mworld Bool))) % 0.37/0.76 (define @t109 () (_ @t108 @t2)) % 0.37/0.76 (define @t110 () (@list @t105 @t108 @t2)) % 0.37/0.76 (define @t111 () (lambda @t110 (and @t106 @t109))) % 0.37/0.76 (define @t112 () (lambda @t110 (or @t106 @t109))) % 0.37/0.76 (define @t113 () (lambda @t110 (=> @t106 @t109))) % 0.37/0.76 (define @t114 () (lambda @t110 (= @t106 @t109))) % 0.37/0.76 (define @t115 () (_ @t103 @t1)) % 0.37/0.76 (define @t116 () (@list @t1)) % 0.37/0.76 (define @t117 () (@list @t103 @t2)) % 0.37/0.76 (define @t118 () (lambda @t117 (forall @t116 (=> @t3 @t115)))) % 0.37/0.76 (define @t119 () (lambda @t117 (exists @t116 (and @t3 @t115)))) % 0.37/0.76 (define @t120 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.37/0.76 (define @t121 () (_ (_ @t120 @t4) @t2)) % 0.37/0.76 (define @t122 () (forall @t6 (=> @t5 @t121))) % 0.37/0.76 (define @t123 () (@list @t120 @t2)) % 0.37/0.76 (define @t124 () (lambda @t123 @t122)) % 0.37/0.76 (define @t125 () (lambda @t123 (exists @t6 (and @t5 @t121)))) % 0.37/0.76 (define @t126 () (tptp.qmltpeq @t4 @t4 @t2)) % 0.37/0.76 (define @t127 () (tptp.eiw_di @t4 @t2)) % 0.37/0.76 (define @t128 () (not @t127)) % 0.37/0.76 (define @t129 () (lambda @t7 (forall @t6 (or @t128 @t126)))) % 0.37/0.76 (define @t130 () (_ @t129 tptp.mactual)) % 0.37/0.76 (define @t131 () (_ @t10 @t2)) % 0.37/0.76 (define @t132 () (or @t128 @t131)) % 0.37/0.76 (define @t133 () (_ @t12 @t4 @t2)) % 0.37/0.76 (define @t134 () (or @t128 @t133)) % 0.37/0.76 (define @t135 () (forall @t6 @t134)) % 0.37/0.76 (define @t136 () (lambda @t7 @t135)) % 0.37/0.76 (define @t137 () (_ @t120 @t4 @t2)) % 0.37/0.76 (define @t138 () (_ (lambda @t123 (forall @t6 (or @t128 @t137))) @t12)) % 0.37/0.76 (define @t139 () (not @t5)) % 0.37/0.76 (define @t140 () (or @t139 @t121)) % 0.37/0.76 (assume @p1 (forall (@list @t2 @t1) @t3)) % 0.37/0.76 (assume @p2 (forall @t7 (exists @t6 @t5))) % 0.37/0.76 (assume @p3 @t13) % 0.37/0.76 (assume @p4 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.mimplies @t16) (_ @t15 @t4)) @t8))) @t8))))) % 0.37/0.76 (assume @p5 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t19 (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t16) (_ @t15 @t18))) (_ @t9 @t18)) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p6 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ (_ tptp.apply @t22) @t20)) (_ (_ tptp.apply @t21) @t20))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p7 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ @t28 @t22)) (_ @t28 @t21))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p8 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.complement @t22)) (_ tptp.complement @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p9 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ (_ tptp.compose @t22) @t20)) (_ (_ tptp.compose @t21) @t20))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p10 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ @t29 @t22)) (_ @t29 @t21))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p11 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ (_ tptp.cross_product @t22) @t20)) (_ (_ tptp.cross_product @t21) @t20))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p12 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ @t30 @t22)) (_ @t30 @t21))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p13 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.domain_of @t22)) (_ tptp.domain_of @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p14 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.first @t22)) (_ tptp.first @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p15 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.flip @t22)) (_ tptp.flip @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p16 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ (_ tptp.image @t22) @t20)) (_ (_ tptp.image @t21) @t20))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p17 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ @t31 @t22)) (_ @t31 @t21))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p18 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ (_ tptp.intersection @t22) @t20)) (_ (_ tptp.intersection @t21) @t20))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p19 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ @t32 @t22)) (_ @t32 @t21))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p20 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.inverse @t22)) (_ tptp.inverse @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p21 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ (_ tptp.ordered_pair @t22) @t20)) (_ (_ tptp.ordered_pair @t21) @t20))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p22 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ @t33 @t22)) (_ @t33 @t21))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p23 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.power_class @t22)) (_ tptp.power_class @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p24 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.range_of @t22)) (_ tptp.range_of @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p25 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mforall_di (lambda @t35 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ (_ (_ tptp.restrict @t22) @t20) @t34)) (_ (_ (_ tptp.restrict @t21) @t20) @t34))) @t8))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p26 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mforall_di (lambda @t35 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ (_ @t36 @t22) @t34)) (_ (_ @t36 @t21) @t34))) @t8))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p27 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ tptp.mforall_di (lambda @t35 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ @t37 @t22)) (_ @t37 @t21))) @t8))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p28 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.rotate @t22)) (_ tptp.rotate @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p29 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.second @t22)) (_ tptp.second @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p30 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.singleton @t22)) (_ tptp.singleton @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p31 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.successor @t22)) (_ tptp.successor @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p32 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ tptp.sum_class @t22)) (_ tptp.sum_class @t21))) @t8))) @t8))))) % 0.37/0.76 (assume @p33 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ (_ tptp.union @t22) @t20)) (_ (_ tptp.union @t21) @t20))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p34 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ @t38 @t22)) (_ @t38 @t21))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p35 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ (_ tptp.unordered_pair @t22) @t20)) (_ (_ tptp.unordered_pair @t21) @t20))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p36 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ @t24 (_ (_ tptp.qmltpeq (_ @t39 @t22)) (_ @t39 @t21))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p37 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ (_ tptp.mimplies (_ @t40 (_ (_ tptp.disjoint @t22) @t20))) (_ (_ tptp.disjoint @t21) @t20)) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p38 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ (_ tptp.mimplies (_ @t40 (_ @t41 @t22))) (_ @t41 @t21)) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p39 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ (_ tptp.mimplies (_ @t40 (_ tptp.function @t22))) (_ tptp.function @t21)) @t8))) @t8))))) % 0.37/0.76 (assume @p40 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ (_ tptp.mimplies (_ @t40 (_ tptp.inductive @t22))) (_ tptp.inductive @t21)) @t8))) @t8))))) % 0.37/0.76 (assume @p41 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ (_ tptp.mimplies (_ @t40 (_ (_ tptp.member @t22) @t20))) (_ (_ tptp.member @t21) @t20)) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p42 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ (_ tptp.mimplies (_ @t40 (_ @t42 @t22))) (_ @t42 @t21)) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p43 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ (_ tptp.mimplies (_ @t40 (_ (_ tptp.subclass @t22) @t20))) (_ (_ tptp.subclass @t21) @t20)) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p44 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t27 (_ (_ tptp.mforall_di (lambda @t26 (_ (_ tptp.mforall_di (lambda @t25 (_ (_ (_ tptp.mimplies (_ @t40 (_ @t43 @t22))) (_ @t43 @t21)) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p45 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.mequiv @t50) (_ tptp.mforall_di (lambda @t48 (_ (_ (_ tptp.mimplies @t47) @t46) @t8)))) @t8))) @t8))))) % 0.37/0.76 (assume @p46 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ @t49 tptp.universal_class) @t8))))) % 0.37/0.76 (assume @p47 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.mequiv @t16) (_ (_ tptp.mand @t50) (_ (_ tptp.subclass @t14) @t4))) @t8))) @t8))))) % 0.37/0.76 (assume @p48 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t48 (_ (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.mequiv (_ @t45 @t55)) (_ @t53 (_ (_ tptp.mor (_ @t51 @t4)) (_ @t51 @t14)))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p49 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.member @t55) tptp.universal_class) @t8))) @t8))))) % 0.37/0.76 (assume @p50 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ (_ tptp.qmltpeq @t56) (_ @t54 @t4)) @t8))))) % 0.37/0.76 (assume @p51 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.qmltpeq @t58) (_ (_ tptp.unordered_pair @t56) (_ @t54 @t57))) @t8))) @t8))))) % 0.37/0.76 (assume @p52 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t48 (_ (_ tptp.mforall_di (lambda @t65 (_ (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.mequiv (_ @t64 @t62)) (_ @t61 (_ @t60 @t14))) @t8))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p53 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t19 (_ (_ (_ tptp.mimplies (_ @t66 @t62)) (_ (_ tptp.qmltpeq @t18) (_ (_ tptp.ordered_pair (_ tptp.first @t18)) (_ tptp.second @t18)))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p54 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.mequiv (_ @t71 tptp.element_relation)) (_ @t70 (_ @t67 @t14))) @t8))) @t8))))) % 0.37/0.76 (assume @p55 (_ tptp.mlocal (_ (_ tptp.subclass tptp.element_relation) @t72))) % 0.37/0.76 (assume @p56 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t19 (_ (_ (_ tptp.mequiv (_ @t66 (_ (_ tptp.intersection @t4) @t14))) (_ (_ tptp.mand @t74) @t73)) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p57 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t19 (_ (_ (_ tptp.mequiv (_ @t66 (_ tptp.complement @t4))) (_ @t75 (_ tptp.mnot @t74))) @t8))) @t8))))) % 0.37/0.76 (assume @p58 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t78 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.qmltpeq (_ @t77 @t14)) (_ (_ tptp.intersection @t76) @t62)) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p59 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mnot (_ @t67 tptp.null_class)) @t8))))) % 0.37/0.76 (assume @p60 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t19 (_ (_ (_ tptp.mequiv (_ @t66 (_ tptp.domain_of @t4))) (_ @t75 (_ tptp.mnot (_ (_ tptp.qmltpeq (_ (_ (_ tptp.restrict @t4) (_ tptp.singleton @t18)) tptp.universal_class)) tptp.null_class)))) @t8))) @t8))))) % 0.37/0.76 (assume @p61 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t48 (_ (_ tptp.mforall_di (lambda @t65 (_ (_ tptp.mforall_di (lambda @t85 (_ (_ (_ tptp.mequiv (_ @t82 @t84)) (_ @t83 (_ (_ tptp.member (_ (_ tptp.ordered_pair (_ @t80 @t79)) @t44)) @t4))) @t8))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p62 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ (_ tptp.subclass @t84) @t81) @t8))))) % 0.37/0.76 (assume @p63 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t48 (_ (_ tptp.mforall_di (lambda @t65 (_ (_ tptp.mforall_di (lambda @t85 (_ (_ tptp.mforall_di (lambda @t11 (_ (_ (_ tptp.mequiv (_ @t82 @t86)) (_ @t83 (_ (_ tptp.member (_ (_ tptp.ordered_pair (_ @t80 @t44)) @t79)) @t4))) @t8))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p64 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ (_ tptp.subclass @t86) @t81) @t8))))) % 0.37/0.76 (assume @p65 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ tptp.mforall_di (lambda @t19 (_ (_ (_ tptp.mequiv (_ @t66 (_ @t87 @t14))) (_ (_ tptp.mor @t74) @t73)) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p66 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ @t88 (_ @t87 @t56)) @t8))))) % 0.37/0.76 (assume @p67 (_ tptp.mlocal (_ (_ tptp.subclass tptp.successor_relation) @t72))) % 0.37/0.76 (assume @p68 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.mequiv (_ @t71 tptp.successor_relation)) (_ @t90 (_ @t70 (_ @t88 @t14)))) @t8))) @t8))))) % 0.37/0.76 (assume @p69 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.qmltpeq (_ tptp.inverse @t14)) (_ tptp.domain_of (_ tptp.flip (_ (_ tptp.cross_product @t14) tptp.universal_class)))) @t8))))) % 0.37/0.76 (assume @p70 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t19 (_ (_ (_ tptp.qmltpeq (_ tptp.range_of @t18)) (_ tptp.domain_of (_ tptp.inverse @t18))) @t8))))) % 0.37/0.76 (assume @p71 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t78 (_ (_ (_ tptp.qmltpeq (_ (_ tptp.image @t76) @t4)) (_ tptp.range_of (_ @t77 tptp.universal_class))) @t8))) @t8))))) % 0.37/0.76 (assume @p72 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ (_ tptp.mequiv @t91) (_ (_ tptp.mand (_ (_ tptp.member tptp.null_class) @t4)) (_ (_ tptp.subclass (_ (_ tptp.image tptp.successor_relation) @t4)) @t4))) @t8))))) % 0.37/0.76 (assume @p73 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t11 (_ (_ @t90 (_ (_ tptp.mand @t91) (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.mimplies (_ tptp.inductive @t14)) @t50) @t8))))) @t8))))) % 0.37/0.76 (assume @p74 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t48 (_ (_ tptp.mforall_di (lambda @t11 (_ (_ (_ tptp.mequiv (_ @t45 @t92)) (_ tptp.mexists_di (lambda @t17 (_ (_ (_ tptp.mand @t46) (_ @t68 @t4)) @t8)))) @t8))) @t8))))) % 0.37/0.76 (assume @p75 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ (_ tptp.mimplies @t89) (_ (_ tptp.member @t92) tptp.universal_class)) @t8))))) % 0.37/0.76 (assume @p76 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t48 (_ (_ tptp.mforall_di (lambda @t11 (_ (_ (_ tptp.mequiv (_ @t45 (_ tptp.power_class @t4))) (_ @t53 (_ (_ tptp.subclass @t44) @t4))) @t8))) @t8))))) % 0.37/0.76 (assume @p77 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t48 (_ (_ (_ tptp.mimplies @t52) (_ (_ tptp.member (_ tptp.power_class @t44)) tptp.universal_class)) @t8))))) % 0.37/0.76 (assume @p78 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t78 (_ (_ tptp.mforall_di (lambda @t95 (_ (_ (_ tptp.subclass @t94) @t72) @t8))) @t8))))) % 0.37/0.76 (assume @p79 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t78 (_ (_ tptp.mforall_di (lambda @t95 (_ (_ tptp.mforall_di (lambda @t48 (_ (_ tptp.mforall_di (lambda @t65 (_ (_ (_ tptp.mequiv (_ @t64 @t94)) (_ @t53 (_ @t60 (_ @t96 (_ @t96 (_ tptp.singleton @t44)))))) @t8))) @t8))) @t8))) @t8))))) % 0.37/0.76 (assume @p80 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t99 (_ (_ (_ tptp.mequiv @t98) (_ (_ tptp.mand (_ (_ tptp.subclass @t97) @t72)) (_ (_ tptp.subclass (_ (_ tptp.compose @t97) (_ tptp.inverse @t97))) tptp.identity_relation))) @t8))))) % 0.37/0.76 (assume @p81 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t99 (_ (_ (_ tptp.mimplies (_ @t90 @t98)) (_ (_ tptp.member (_ @t100 @t4)) tptp.universal_class)) @t8))) @t8))))) % 0.37/0.76 (assume @p82 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.mequiv (_ (_ tptp.disjoint @t4) @t14)) (_ tptp.mforall_di (lambda @t48 (_ (_ tptp.mnot (_ @t61 @t46)) @t8)))) @t8))) @t8))))) % 0.37/0.76 (assume @p83 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t11 (_ (_ (_ tptp.mimplies (_ tptp.mnot (_ @t9 tptp.null_class))) (_ tptp.mexists_di (lambda @t48 (_ (_ @t53 (_ @t61 (_ (_ tptp.disjoint @t44) @t4))) @t8)))) @t8))))) % 0.37/0.76 (assume @p84 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t99 (_ (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.qmltpeq @t101) (_ tptp.sum_class (_ @t100 @t57))) @t8))) @t8))))) % 0.37/0.76 (assume @p85 (_ tptp.mlocal (_ tptp.mexists_di (lambda @t99 (_ (_ (_ tptp.mand @t98) (_ tptp.mforall_di (lambda @t17 (_ (_ (_ tptp.mimplies @t69) (_ (_ tptp.mor (_ @t15 tptp.null_class)) (_ (_ tptp.member @t101) @t14))) @t8)))) @t8))))) % 0.37/0.76 (assume @p86 @t102) % 0.37/0.76 (assume @p87 true) % 0.37/0.76 (step @p88 (= tptp.mlocal @t104) :rule refl :args (@t104)) % 0.37/0.76 (step @p89 (= tptp.mnot @t107) :rule refl :args (@t107)) % 0.37/0.76 (step @p90 (= tptp.mand @t111) :rule refl :args (@t111)) % 0.37/0.76 (step @p91 (= tptp.mor @t112) :rule refl :args (@t112)) % 0.37/0.76 (step @p92 (= tptp.mimplies @t113) :rule refl :args (@t113)) % 0.37/0.76 (step @p93 (= tptp.mequiv @t114) :rule refl :args (@t114)) % 0.37/0.76 (step @p94 (= tptp.mbox @t118) :rule refl :args (@t118)) % 0.37/0.76 (step @p95 (= tptp.mdia @t119) :rule refl :args (@t119)) % 0.37/0.76 (step @p96 (= tptp.mforall_di @t124) :rule refl :args (@t124)) % 0.37/0.76 (step @p97 (= tptp.mexists_di @t125) :rule refl :args (@t125)) % 0.37/0.76 (step @p98 :rule beta-reduce :args ((= @t130 (forall @t6 (or (not (tptp.eiw_di @t4 tptp.mactual)) (tptp.qmltpeq @t4 @t4 tptp.mactual)))))) % 0.37/0.76 (step @p99 :rule beta-reduce :args ((= (_ @t104 @t129) @t130))) % 0.37/0.76 (step @p100 :rule trans :premises (@p99 @p98)) % 0.37/0.76 (step @p101 :rule refl :args (@t126)) % 0.37/0.76 (step @p102 :rule refl :args (@t131)) % 0.37/0.76 (step @p103 :rule cong :premises (@p102 @p101) :args ((= @t131 @t126))) % 0.37/0.76 (step @p104 :rule symm :premises (@p103)) % 0.37/0.76 (step @p105 :rule eq_resolve :premises (@p102 @p104)) % 0.37/0.76 (step @p106 :rule refl :args (@t128)) % 0.37/0.76 (step @p107 :rule nary_cong :premises (@p106 @p105) :args (@t132)) % 0.37/0.76 (step @p108 :rule cong :premises (@p107) :args ((forall @t6 @t132))) % 0.37/0.76 (step @p109 :rule beta-reduce :args ((= @t133 @t131))) % 0.37/0.76 (step @p110 :rule refl :args (@t128)) % 0.37/0.76 (step @p111 :rule nary_cong :premises (@p110 @p109) :args (@t134)) % 0.37/0.76 (step @p112 :rule cong :premises (@p111) :args (@t135)) % 0.37/0.76 (step @p113 :rule trans :premises (@p112 @p108)) % 0.37/0.76 (step @p114 :rule cong :premises (@p113) :args (@t136)) % 0.37/0.76 (step @p115 :rule beta-reduce :args ((= @t138 @t136))) % 0.37/0.76 (step @p116 :rule trans :premises (@p115 @p114)) % 0.37/0.76 (step @p117 :rule refl :args (@t104)) % 0.37/0.76 (step @p118 :rule ho_cong :premises (@p117 @p116)) % 0.37/0.76 (step @p119 :rule trans :premises (@p118 @p100)) % 0.37/0.76 (step @p120 :rule cong :premises (@p119) :args ((not (_ @t104 @t138)))) % 0.37/0.76 (step @p121 :rule refl :args (@t12)) % 0.37/0.76 (step @p122 :rule refl :args (@t137)) % 0.37/0.76 (step @p123 :rule refl :args (@t121)) % 0.37/0.76 (step @p124 :rule cong :premises (@p123 @p122) :args ((= @t121 @t137))) % 0.37/0.76 (step @p125 :rule symm :premises (@p124)) % 0.37/0.76 (step @p126 :rule eq_resolve :premises (@p123 @p125)) % 0.37/0.76 (step @p127 :rule refl :args (@t127)) % 0.37/0.76 (step @p128 :rule refl :args (@t5)) % 0.37/0.76 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t5 @t127))) % 0.37/0.76 (step @p130 :rule symm :premises (@p129)) % 0.37/0.76 (step @p131 :rule eq_resolve :premises (@p128 @p130)) % 0.37/0.76 (step @p132 :rule cong :premises (@p131) :args (@t139)) % 0.37/0.76 (step @p133 :rule nary_cong :premises (@p132 @p126) :args (@t140)) % 0.37/0.76 (step @p134 :rule cong :premises (@p133) :args ((forall @t6 @t140))) % 0.37/0.76 (step @p135 :rule bool-impl-elim :args (@t5 @t121)) % 0.37/0.76 (step @p136 :rule cong :premises (@p135) :args (@t122)) % 0.37/0.76 (step @p137 :rule trans :premises (@p136 @p134)) % 0.37/0.76 (step @p138 :rule cong :premises (@p137) :args (@t124)) % 0.37/0.76 (step @p139 :rule trans :premises (@p96 @p138)) % 0.37/0.76 (step @p140 :rule ho_cong :premises (@p139 @p121)) % 0.37/0.76 (step @p141 :rule ho_cong :premises (@p88 @p140)) % 0.37/0.76 (step @p142 :rule cong :premises (@p141) :args (@t102)) % 0.37/0.76 (step @p143 :rule trans :premises (@p142 @p120)) % 0.37/0.76 (step @p144 :rule eq_resolve :premises (@p86 @p143)) % 0.37/0.76 (step @p145 :rule trans :premises (@p141 @p119)) % 0.37/0.76 (step @p146 :rule eq_resolve :premises (@p3 @p145)) % 0.37/0.76 (step @p147 false :rule contra :premises (@p146 @p144)) % 0.37/0.76 ) % 0.37/0.76 % SZS output end Proof % 0.37/0.76 % cvc5 exiting %------------------------------------------------------------------------------