%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET643+3 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:48:21 AM UTC 2026 % Result : Theorem 0.40s 0.63s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET643+3 : TPTP v9.2.1. Released v2.2.0. % 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 : n016.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 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 16:06:09 EDT 2026 % 0.18/0.35 % CPUTime : % 0.31/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.63 % SZS status Theorem % 0.40/0.63 % SZS output start Proof % 0.40/0.63 ( % 0.40/0.63 (declare-sort $$unsorted 0) % 0.40/0.63 (declare-const tptp.subset_type (-> $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.relation_like (-> $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.set_type $$unsorted) % 0.40/0.63 (declare-const tptp.member_type (-> $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.ilf_type (-> $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.relation_type (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.63 (define @t1 () (@var "D" $$unsorted)) % 0.40/0.63 (define @t2 () (@var "C" $$unsorted)) % 0.40/0.63 (define @t3 () (@var "B" $$unsorted)) % 0.40/0.63 (define @t4 () (tptp.ilf_type @t3 (tptp.relation_type @t2 @t1))) % 0.40/0.63 (define @t5 () (tptp.subset @t3 (tptp.cross_product @t2 @t1))) % 0.40/0.63 (define @t6 () (=> @t5 @t4)) % 0.40/0.63 (define @t7 () (tptp.ilf_type @t1 tptp.set_type)) % 0.40/0.63 (define @t8 () (@list @t1)) % 0.40/0.63 (define @t9 () (forall @t8 (=> @t7 @t6))) % 0.40/0.63 (define @t10 () (tptp.ilf_type @t2 tptp.set_type)) % 0.40/0.63 (define @t11 () (=> @t10 @t9)) % 0.40/0.63 (define @t12 () (@list @t2)) % 0.40/0.63 (define @t13 () (forall @t12 @t11)) % 0.40/0.63 (define @t14 () (tptp.ilf_type @t3 tptp.set_type)) % 0.40/0.63 (define @t15 () (=> @t14 @t13)) % 0.40/0.63 (define @t16 () (@list @t3)) % 0.40/0.63 (define @t17 () (forall @t16 @t15)) % 0.40/0.63 (define @t18 () (@var "F" $$unsorted)) % 0.40/0.63 (define @t19 () (@var "E" $$unsorted)) % 0.40/0.63 (define @t20 () (tptp.ilf_type @t19 tptp.set_type)) % 0.40/0.63 (define @t21 () (@list @t19)) % 0.40/0.63 (define @t22 () (tptp.cross_product @t3 @t2)) % 0.40/0.63 (define @t23 () (tptp.ilf_type @t22 tptp.set_type)) % 0.40/0.63 (define @t24 () (forall @t12 (=> @t10 @t23))) % 0.40/0.63 (define @t25 () (=> @t14 @t24)) % 0.40/0.63 (define @t26 () (forall @t16 @t25)) % 0.40/0.63 (define @t27 () (tptp.subset_type @t22)) % 0.40/0.63 (define @t28 () (tptp.relation_type @t3 @t2)) % 0.40/0.63 (define @t29 () (tptp.ilf_type @t1 @t27)) % 0.40/0.63 (define @t30 () (tptp.power_set @t3)) % 0.40/0.63 (define @t31 () (tptp.ilf_type @t2 (tptp.subset_type @t3))) % 0.40/0.63 (define @t32 () (tptp.member @t1 @t2)) % 0.40/0.63 (define @t33 () (tptp.member @t1 @t3)) % 0.40/0.63 (define @t34 () (=> @t33 @t32)) % 0.40/0.63 (define @t35 () (forall @t8 (=> @t7 @t34))) % 0.40/0.63 (define @t36 () (tptp.subset @t3 @t2)) % 0.40/0.63 (define @t37 () (= @t36 @t35)) % 0.40/0.63 (define @t38 () (=> @t10 @t37)) % 0.40/0.63 (define @t39 () (forall @t12 @t38)) % 0.40/0.63 (define @t40 () (=> @t14 @t39)) % 0.40/0.63 (define @t41 () (forall @t16 @t40)) % 0.40/0.63 (define @t42 () (tptp.empty @t3)) % 0.40/0.63 (define @t43 () (tptp.member @t2 @t3)) % 0.40/0.63 (define @t44 () (tptp.relation_like @t3)) % 0.40/0.63 (define @t45 () (tptp.ilf_type @t22 @t28)) % 0.40/0.63 (define @t46 () (forall @t12 (=> @t10 @t45))) % 0.40/0.63 (define @t47 () (=> @t14 @t46)) % 0.40/0.63 (define @t48 () (forall @t16 @t47)) % 0.40/0.63 (define @t49 () (not @t48)) % 0.40/0.63 (define @t50 () (@var "BOUND_VARIABLE_7908" $$unsorted)) % 0.40/0.63 (define @t51 () (not @t33)) % 0.40/0.63 (define @t52 () (not @t7)) % 0.40/0.63 (define @t53 () (= (tptp.subset @t3 @t50) (forall @t8 (or @t52 @t51 (tptp.member @t1 @t50))))) % 0.40/0.63 (define @t54 () (not (tptp.ilf_type @t50 tptp.set_type))) % 0.40/0.63 (define @t55 () (not @t14)) % 0.40/0.63 (define @t56 () (or @t55 @t54 @t53)) % 0.40/0.63 (define @t57 () (or @t54 @t53)) % 0.40/0.63 (define @t58 () (or @t55 @t57)) % 0.40/0.63 (define @t59 () (@list @t3 @t50)) % 0.40/0.63 (define @t60 () (forall @t59 @t58)) % 0.40/0.63 (define @t61 () (@list @t50)) % 0.40/0.63 (define @t62 () (forall @t61 @t58)) % 0.40/0.63 (define @t63 () (forall @t61 @t57)) % 0.40/0.63 (define @t64 () (@list @t2)) % 0.40/0.63 (define @t65 () (or @t55 @t63)) % 0.40/0.63 (define @t66 () (or @t52 @t51 @t32)) % 0.40/0.63 (define @t67 () (= @t36 (forall @t8 @t66))) % 0.40/0.63 (define @t68 () (not @t10)) % 0.40/0.63 (define @t69 () (forall @t12 (or @t68 @t67))) % 0.40/0.63 (define @t70 () (@var "BOUND_VARIABLE_7627" $$unsorted)) % 0.40/0.63 (define @t71 () (@var "BOUND_VARIABLE_7625" $$unsorted)) % 0.40/0.63 (define @t72 () (tptp.ilf_type @t3 (tptp.relation_type @t71 @t70))) % 0.40/0.63 (define @t73 () (not (tptp.subset @t3 (tptp.cross_product @t71 @t70)))) % 0.40/0.63 (define @t74 () (not (tptp.ilf_type @t70 tptp.set_type))) % 0.40/0.63 (define @t75 () (not (tptp.ilf_type @t71 tptp.set_type))) % 0.40/0.63 (define @t76 () (or @t75 @t74 @t73 @t72)) % 0.40/0.63 (define @t77 () (or @t55 @t76)) % 0.40/0.63 (define @t78 () (forall (@list @t3 @t71 @t70) @t77)) % 0.40/0.63 (define @t79 () (@list @t71 @t70)) % 0.40/0.63 (define @t80 () (forall @t79 @t77)) % 0.40/0.63 (define @t81 () (forall @t79 @t76)) % 0.40/0.63 (define @t82 () (@var "BOUND_VARIABLE_7605" $$unsorted)) % 0.40/0.63 (define @t83 () (or @t55 @t81)) % 0.40/0.63 (define @t84 () (tptp.ilf_type @t3 (tptp.relation_type @t2 @t82))) % 0.40/0.63 (define @t85 () (not (tptp.subset @t3 (tptp.cross_product @t2 @t82)))) % 0.40/0.63 (define @t86 () (not (tptp.ilf_type @t82 tptp.set_type))) % 0.40/0.63 (define @t87 () (or @t68 @t86 @t85 @t84)) % 0.40/0.63 (define @t88 () (@list @t2 @t82)) % 0.40/0.63 (define @t89 () (forall @t88 @t87)) % 0.40/0.63 (define @t90 () (or @t86 @t85 @t84)) % 0.40/0.63 (define @t91 () (or @t68 @t90)) % 0.40/0.63 (define @t92 () (forall @t88 @t91)) % 0.40/0.63 (define @t93 () (@list @t82)) % 0.40/0.63 (define @t94 () (forall @t93 @t91)) % 0.40/0.63 (define @t95 () (forall @t93 @t90)) % 0.40/0.63 (define @t96 () (or @t68 @t95)) % 0.40/0.63 (define @t97 () (not @t5)) % 0.40/0.63 (define @t98 () (or @t52 @t97 @t4)) % 0.40/0.63 (define @t99 () (forall @t8 @t98)) % 0.40/0.63 (define @t100 () (@var "BOUND_VARIABLE_8090" $$unsorted)) % 0.40/0.63 (define @t101 () (tptp.ilf_type (tptp.cross_product @t3 @t100) (tptp.relation_type @t3 @t100))) % 0.40/0.63 (define @t102 () (not (tptp.ilf_type @t100 tptp.set_type))) % 0.40/0.63 (define @t103 () (or @t55 @t102 @t101)) % 0.40/0.63 (define @t104 () (@list @t3 @t100)) % 0.40/0.63 (define @t105 () (forall @t104 @t103)) % 0.40/0.63 (define @t106 () (@quantifiers_skolemize @t105 1)) % 0.40/0.63 (define @t107 () (@quantifiers_skolemize @t105 0)) % 0.40/0.63 (define @t108 () (tptp.cross_product @t107 @t106)) % 0.40/0.63 (define @t109 () (@var "BOUND_VARIABLE_7750" $$unsorted)) % 0.40/0.63 (define @t110 () (tptp.ilf_type (tptp.cross_product @t3 @t109) tptp.set_type)) % 0.40/0.63 (define @t111 () (not (tptp.ilf_type @t109 tptp.set_type))) % 0.40/0.63 (define @t112 () (or @t111 @t110)) % 0.40/0.63 (define @t113 () (or @t55 @t112)) % 0.40/0.63 (define @t114 () (forall (@list @t3 @t109) @t113)) % 0.40/0.63 (define @t115 () (@list @t109)) % 0.40/0.63 (define @t116 () (forall @t115 @t113)) % 0.40/0.63 (define @t117 () (forall @t115 @t112)) % 0.40/0.63 (define @t118 () (or @t55 @t117)) % 0.40/0.63 (define @t119 () (forall @t12 (or @t68 @t23))) % 0.40/0.63 (define @t120 () (or @t102 @t101)) % 0.40/0.63 (define @t121 () (or @t55 @t120)) % 0.40/0.63 (define @t122 () (forall @t104 @t121)) % 0.40/0.63 (define @t123 () (@list @t100)) % 0.40/0.63 (define @t124 () (forall @t123 @t121)) % 0.40/0.63 (define @t125 () (forall @t123 @t120)) % 0.40/0.63 (define @t126 () (or @t55 @t125)) % 0.40/0.63 (define @t127 () (forall @t12 (or @t68 @t45))) % 0.40/0.63 (define @t128 () (tptp.ilf_type @t106 tptp.set_type)) % 0.40/0.63 (define @t129 () (tptp.ilf_type @t108 (tptp.relation_type @t107 @t106))) % 0.40/0.63 (define @t130 () (not @t128)) % 0.40/0.63 (define @t131 () (tptp.ilf_type @t107 tptp.set_type)) % 0.40/0.63 (define @t132 () (not @t131)) % 0.40/0.63 (define @t133 () (or @t132 @t130 @t129)) % 0.40/0.63 (define @t134 () (@list true)) % 0.40/0.63 (define @t135 () (@list @t133)) % 0.40/0.63 (define @t136 () (tptp.ilf_type @t108 tptp.set_type)) % 0.40/0.63 (define @t137 () (or @t132 @t130 @t136)) % 0.40/0.63 (define @t138 () (tptp.subset @t108 @t108)) % 0.40/0.63 (define @t139 () (not @t138)) % 0.40/0.63 (define @t140 () (not @t136)) % 0.40/0.63 (define @t141 () (or @t140 @t132 @t130 @t139 @t129)) % 0.40/0.63 (define @t142 () (or @t140 @t140 @t138)) % 0.40/0.63 (define @t143 () (not @t142)) % 0.40/0.63 (define @t144 () (tptp.member @t1 @t108)) % 0.40/0.63 (define @t145 () (forall @t8 (or @t52 (not @t144) @t144))) % 0.40/0.63 (define @t146 () (= @t138 @t145)) % 0.40/0.63 (define @t147 () (or @t140 @t140 @t146)) % 0.40/0.63 (define @t148 () (forall @t59 @t56)) % 0.40/0.63 (assume @p1 @t17) % 0.40/0.63 (assume @p2 (forall @t16 (=> @t14 (forall @t12 (=> @t10 (forall @t8 (=> @t7 (= (tptp.member @t1 @t22) (exists @t21 (and @t20 (exists (@list @t18) (and (tptp.ilf_type @t18 tptp.set_type) (tptp.member @t19 @t3) (tptp.member @t18 @t2) (= @t1 (tptp.ordered_pair @t19 @t18)))))))))))))) % 0.40/0.63 (assume @p3 @t26) % 0.40/0.63 (assume @p4 (forall @t16 (=> @t14 (forall @t12 (=> @t10 (and (forall @t8 (=> @t29 (tptp.ilf_type @t1 @t28))) (forall @t21 (=> (tptp.ilf_type @t19 @t28) (tptp.ilf_type @t19 @t27))))))))) % 0.40/0.63 (assume @p5 (forall @t16 (=> @t14 (forall @t12 (=> @t10 (exists @t8 (tptp.ilf_type @t1 (tptp.relation_type @t2 @t3)))))))) % 0.40/0.63 (assume @p6 (forall @t16 (=> @t14 (forall @t12 (=> @t10 (tptp.ilf_type (tptp.ordered_pair @t3 @t2) tptp.set_type)))))) % 0.40/0.63 (assume @p7 (forall @t16 (=> @t14 (forall @t12 (=> @t10 (= @t31 (tptp.ilf_type @t2 (tptp.member_type @t30)))))))) % 0.40/0.63 (assume @p8 (forall @t16 (=> @t14 (exists @t12 @t31)))) % 0.40/0.63 (assume @p9 @t41) % 0.40/0.63 (assume @p10 (forall @t16 (=> @t14 (tptp.subset @t3 @t3)))) % 0.40/0.63 (assume @p11 (forall @t16 (=> @t14 (forall @t12 (=> @t10 (= (tptp.member @t3 (tptp.power_set @t2)) @t35)))))) % 0.40/0.63 (assume @p12 (forall @t16 (=> @t14 (and (not (tptp.empty @t30)) (tptp.ilf_type @t30 tptp.set_type))))) % 0.40/0.63 (assume @p13 (forall @t16 (=> @t14 (forall @t12 (=> (and (not (tptp.empty @t2)) @t10) (= (tptp.ilf_type @t3 (tptp.member_type @t2)) (tptp.member @t3 @t2))))))) % 0.40/0.63 (assume @p14 (forall @t16 (=> (and (not @t42) @t14) (exists @t12 (tptp.ilf_type @t2 (tptp.member_type @t3)))))) % 0.40/0.63 (assume @p15 (forall @t16 (=> @t14 (= @t42 (forall @t12 (=> @t10 (not @t43))))))) % 0.40/0.63 (assume @p16 (forall @t16 (=> @t14 (= @t44 (forall @t12 (=> @t10 (=> @t43 (exists @t8 (and @t7 (exists @t21 (and @t20 (= @t2 (tptp.ordered_pair @t1 @t19))))))))))))) % 0.40/0.63 (assume @p17 (forall @t16 (=> (and @t42 @t14) @t44))) % 0.40/0.63 (assume @p18 (forall @t16 (=> @t14 (forall @t12 (=> @t10 (forall @t8 (=> @t29 (tptp.relation_like @t1)))))))) % 0.40/0.63 (assume @p19 (forall @t16 @t14)) % 0.40/0.63 (assume @p20 @t49) % 0.40/0.63 (assume @p21 true) % 0.40/0.63 (step @p22 :rule aci_norm :args ((= @t58 @t56))) % 0.40/0.63 (step @p23 :rule cong :premises (@p22) :args (@t60)) % 0.40/0.63 (step @p24 :rule quant-merge-prenex :args ((= (forall @t16 @t62) @t60))) % 0.40/0.63 (step @p25 :rule alpha_equiv :args (@t63 (@list @t50) @t64)) % 0.40/0.63 (step @p26 :rule refl :args (@t55)) % 0.40/0.63 (step @p27 :rule nary_cong :premises (@p26 @p25) :args (@t65)) % 0.40/0.63 (step @p28 :rule quant-miniscope-or :args ((= @t62 @t65))) % 0.40/0.63 (step @p29 :rule trans :premises (@p28 @p27)) % 0.40/0.63 (step @p30 :rule symm :premises (@p29)) % 0.40/0.63 (step @p31 :rule cong :premises (@p30) :args ((forall @t16 (or @t55 @t69)))) % 0.40/0.63 (step @p32 :rule trans :premises (@p31 @p24)) % 0.40/0.63 (step @p33 :rule trans :premises (@p32 @p23)) % 0.40/0.63 (step @p34 :rule bool-impl-elim :args (@t14 @t69)) % 0.40/0.63 (step @p35 :rule cong :premises (@p34) :args ((forall @t16 (=> @t14 @t69)))) % 0.40/0.63 (step @p36 :rule trans :premises (@p35 @p33)) % 0.40/0.63 (step @p37 :rule bool-impl-elim :args (@t10 @t67)) % 0.40/0.63 (step @p38 :rule cong :premises (@p37) :args ((forall @t12 (=> @t10 @t67)))) % 0.40/0.63 (step @p39 :rule aci_norm :args ((= (or @t52 (or @t51 @t32)) @t66))) % 0.40/0.63 (step @p40 :rule bool-impl-elim :args (@t33 @t32)) % 0.40/0.63 (step @p41 :rule refl :args (@t52)) % 0.40/0.63 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or @t52 @t34))) % 0.40/0.63 (step @p43 :rule trans :premises (@p42 @p39)) % 0.40/0.63 (step @p44 :rule bool-impl-elim :args (@t7 @t34)) % 0.40/0.63 (step @p45 :rule trans :premises (@p44 @p43)) % 0.40/0.63 (step @p46 :rule cong :premises (@p45) :args (@t35)) % 0.40/0.63 (step @p47 :rule refl :args (@t36)) % 0.40/0.63 (step @p48 :rule cong :premises (@p47 @p46) :args (@t37)) % 0.40/0.63 (step @p49 :rule refl :args (@t10)) % 0.40/0.63 (step @p50 :rule cong :premises (@p49 @p48) :args (@t38)) % 0.40/0.63 (step @p51 :rule cong :premises (@p50) :args (@t39)) % 0.40/0.63 (step @p52 :rule trans :premises (@p51 @p38)) % 0.40/0.63 (step @p53 :rule refl :args (@t14)) % 0.40/0.63 (step @p54 :rule cong :premises (@p53 @p52) :args (@t40)) % 0.40/0.63 (step @p55 :rule cong :premises (@p54) :args (@t41)) % 0.40/0.63 (step @p56 :rule trans :premises (@p55 @p36)) % 0.40/0.63 (step @p57 :rule eq_resolve :premises (@p9 @p56)) % 0.40/0.63 (step @p58 :rule aci_norm :args ((= @t77 (or @t55 @t75 @t74 @t73 @t72)))) % 0.40/0.63 (step @p59 :rule cong :premises (@p58) :args (@t78)) % 0.40/0.63 (step @p60 :rule quant-merge-prenex :args ((= (forall @t16 @t80) @t78))) % 0.40/0.63 (step @p61 :rule alpha_equiv :args (@t81 (@list @t71 @t70) (@list @t2 @t82))) % 0.40/0.63 (step @p62 :rule nary_cong :premises (@p26 @p61) :args (@t83)) % 0.40/0.63 (step @p63 :rule quant-miniscope-or :args ((= @t80 @t83))) % 0.40/0.63 (step @p64 :rule trans :premises (@p63 @p62)) % 0.40/0.63 (step @p65 :rule symm :premises (@p64)) % 0.40/0.63 (step @p66 :rule cong :premises (@p65) :args ((forall @t16 (or @t55 @t89)))) % 0.40/0.63 (step @p67 :rule trans :premises (@p66 @p60)) % 0.40/0.63 (step @p68 :rule trans :premises (@p67 @p59)) % 0.40/0.63 (step @p69 :rule bool-impl-elim :args (@t14 @t89)) % 0.40/0.63 (step @p70 :rule cong :premises (@p69) :args ((forall @t16 (=> @t14 @t89)))) % 0.40/0.63 (step @p71 :rule trans :premises (@p70 @p68)) % 0.40/0.63 (step @p72 :rule aci_norm :args ((= @t91 @t87))) % 0.40/0.63 (step @p73 :rule cong :premises (@p72) :args (@t92)) % 0.40/0.63 (step @p74 :rule quant-merge-prenex :args ((= (forall @t12 @t94) @t92))) % 0.40/0.63 (step @p75 :rule alpha_equiv :args (@t95 (@list @t82) (@list @t1))) % 0.40/0.63 (step @p76 :rule refl :args (@t68)) % 0.40/0.63 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t96)) % 0.40/0.63 (step @p78 :rule quant-miniscope-or :args ((= @t94 @t96))) % 0.40/0.63 (step @p79 :rule trans :premises (@p78 @p77)) % 0.40/0.63 (step @p80 :rule symm :premises (@p79)) % 0.40/0.63 (step @p81 :rule cong :premises (@p80) :args ((forall @t12 (or @t68 @t99)))) % 0.40/0.63 (step @p82 :rule trans :premises (@p81 @p74)) % 0.40/0.63 (step @p83 :rule trans :premises (@p82 @p73)) % 0.40/0.63 (step @p84 :rule bool-impl-elim :args (@t10 @t99)) % 0.40/0.63 (step @p85 :rule cong :premises (@p84) :args ((forall @t12 (=> @t10 @t99)))) % 0.40/0.63 (step @p86 :rule trans :premises (@p85 @p83)) % 0.40/0.63 (step @p87 :rule aci_norm :args ((= (or @t52 (or @t97 @t4)) @t98))) % 0.40/0.63 (step @p88 :rule bool-impl-elim :args (@t5 @t4)) % 0.40/0.63 (step @p89 :rule nary_cong :premises (@p41 @p88) :args ((or @t52 @t6))) % 0.40/0.63 (step @p90 :rule trans :premises (@p89 @p87)) % 0.40/0.63 (step @p91 :rule bool-impl-elim :args (@t7 @t6)) % 0.40/0.63 (step @p92 :rule trans :premises (@p91 @p90)) % 0.40/0.63 (step @p93 :rule cong :premises (@p92) :args (@t9)) % 0.40/0.63 (step @p94 :rule cong :premises (@p49 @p93) :args (@t11)) % 0.40/0.63 (step @p95 :rule cong :premises (@p94) :args (@t13)) % 0.40/0.63 (step @p96 :rule trans :premises (@p95 @p86)) % 0.40/0.63 (step @p97 :rule cong :premises (@p53 @p96) :args (@t15)) % 0.40/0.63 (step @p98 :rule cong :premises (@p97) :args (@t17)) % 0.40/0.63 (step @p99 :rule trans :premises (@p98 @p71)) % 0.40/0.63 (step @p100 :rule eq_resolve :premises (@p1 @p99)) % 0.40/0.63 (step @p101 :rule instantiate :premises (@p100) :args ((@list @t108 @t107 @t106))) % 0.40/0.63 (step @p102 :rule aci_norm :args ((= @t113 (or @t55 @t111 @t110)))) % 0.40/0.63 (step @p103 :rule cong :premises (@p102) :args (@t114)) % 0.40/0.63 (step @p104 :rule quant-merge-prenex :args ((= (forall @t16 @t116) @t114))) % 0.40/0.63 (step @p105 :rule alpha_equiv :args (@t117 (@list @t109) @t64)) % 0.40/0.63 (step @p106 :rule nary_cong :premises (@p26 @p105) :args (@t118)) % 0.40/0.63 (step @p107 :rule quant-miniscope-or :args ((= @t116 @t118))) % 0.40/0.63 (step @p108 :rule trans :premises (@p107 @p106)) % 0.40/0.63 (step @p109 :rule symm :premises (@p108)) % 0.40/0.63 (step @p110 :rule cong :premises (@p109) :args ((forall @t16 (or @t55 @t119)))) % 0.40/0.63 (step @p111 :rule trans :premises (@p110 @p104)) % 0.40/0.63 (step @p112 :rule trans :premises (@p111 @p103)) % 0.40/0.63 (step @p113 :rule bool-impl-elim :args (@t14 @t119)) % 0.40/0.63 (step @p114 :rule cong :premises (@p113) :args ((forall @t16 (=> @t14 @t119)))) % 0.40/0.63 (step @p115 :rule trans :premises (@p114 @p112)) % 0.40/0.63 (step @p116 :rule bool-impl-elim :args (@t10 @t23)) % 0.40/0.63 (step @p117 :rule cong :premises (@p116) :args (@t24)) % 0.40/0.63 (step @p118 :rule cong :premises (@p53 @p117) :args (@t25)) % 0.40/0.63 (step @p119 :rule cong :premises (@p118) :args (@t26)) % 0.40/0.63 (step @p120 :rule trans :premises (@p119 @p115)) % 0.40/0.63 (step @p121 :rule eq_resolve :premises (@p3 @p120)) % 0.40/0.63 (step @p122 :rule instantiate :premises (@p121) :args ((@list @t107 @t106))) % 0.40/0.63 (step @p123 :rule aci_norm :args ((= @t121 @t103))) % 0.40/0.63 (step @p124 :rule cong :premises (@p123) :args (@t122)) % 0.40/0.63 (step @p125 :rule quant-merge-prenex :args ((= (forall @t16 @t124) @t122))) % 0.40/0.63 (step @p126 :rule alpha_equiv :args (@t125 (@list @t100) @t64)) % 0.40/0.63 (step @p127 :rule nary_cong :premises (@p26 @p126) :args (@t126)) % 0.40/0.63 (step @p128 :rule quant-miniscope-or :args ((= @t124 @t126))) % 0.40/0.63 (step @p129 :rule trans :premises (@p128 @p127)) % 0.40/0.63 (step @p130 :rule symm :premises (@p129)) % 0.40/0.63 (step @p131 :rule cong :premises (@p130) :args ((forall @t16 (or @t55 @t127)))) % 0.40/0.63 (step @p132 :rule trans :premises (@p131 @p125)) % 0.40/0.63 (step @p133 :rule trans :premises (@p132 @p124)) % 0.40/0.63 (step @p134 :rule bool-impl-elim :args (@t14 @t127)) % 0.40/0.63 (step @p135 :rule cong :premises (@p134) :args ((forall @t16 (=> @t14 @t127)))) % 0.40/0.63 (step @p136 :rule trans :premises (@p135 @p133)) % 0.40/0.63 (step @p137 :rule bool-impl-elim :args (@t10 @t45)) % 0.40/0.63 (step @p138 :rule cong :premises (@p137) :args (@t46)) % 0.40/0.63 (step @p139 :rule cong :premises (@p53 @p138) :args (@t47)) % 0.40/0.63 (step @p140 :rule cong :premises (@p139) :args (@t48)) % 0.40/0.63 (step @p141 :rule trans :premises (@p140 @p136)) % 0.40/0.63 (step @p142 :rule cong :premises (@p141) :args (@t49)) % 0.40/0.63 (step @p143 :rule eq_resolve :premises (@p20 @p142)) % 0.40/0.63 (step @p144 :rule skolemize :premises (@p143)) % 0.40/0.63 (step @p145 :rule bool-double-not-elim :args (@t128)) % 0.40/0.63 (step @p146 :rule refl :args (@t133)) % 0.40/0.63 (step @p147 :rule nary_cong :premises (@p146 @p145) :args ((or @t133 (not @t130)))) % 0.40/0.63 (step @p148 :rule cnf_or_neg :args (@t133 1)) % 0.40/0.63 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 0.40/0.63 (step @p150 :rule reordering :premises (@p149) :args ((or @t128 @t133))) % 0.40/0.63 (step @p151 :rule chain_m_resolution :premises (@p150 @p144) :args (@t128 @t134 @t135)) % 0.37/0.64 (step @p152 :rule bool-double-not-elim :args (@t131)) % 0.37/0.64 (step @p153 :rule nary_cong :premises (@p146 @p152) :args ((or @t133 (not @t132)))) % 0.37/0.64 (step @p154 :rule cnf_or_neg :args (@t133 0)) % 0.37/0.64 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 0.37/0.64 (step @p156 :rule reordering :premises (@p155) :args ((or @t131 @t133))) % 0.37/0.64 (step @p157 :rule chain_m_resolution :premises (@p156 @p144) :args (@t131 @t134 @t135)) % 0.37/0.64 (step @p158 :rule cnf_or_pos :args (@t137)) % 0.37/0.64 (step @p159 :rule reordering :premises (@p158) :args ((or @t132 @t130 @t136 (not @t137)))) % 0.37/0.64 (step @p160 :rule chain_m_resolution :premises (@p159 @p157 @p151 @p122) :args (@t136 (@list false false false) (@list @t131 @t128 @t137))) % 0.37/0.64 (step @p161 :rule cnf_or_neg :args (@t133 2)) % 0.37/0.64 (step @p162 :rule chain_m_resolution :premises (@p161 @p144) :args ((not @t129) @t134 @t135)) % 0.37/0.64 (step @p163 :rule cnf_or_pos :args (@t141)) % 0.37/0.64 (step @p164 :rule reordering :premises (@p163) :args ((or @t132 @t130 @t129 @t140 @t139 (not @t141)))) % 0.37/0.64 (step @p165 :rule chain_m_resolution :premises (@p164 @p157 @p151 @p162 @p160 @p101) :args (@t139 (@list false false true false false) (@list @t131 @t128 @t129 @t136 @t141))) % 0.37/0.64 (step @p166 :rule cnf_or_pos :args (@t142)) % 0.37/0.64 (step @p167 :rule factoring :premises (@p166)) % 0.37/0.64 (step @p168 :rule reordering :premises (@p167) :args ((or @t140 @t138 @t143))) % 0.37/0.64 (step @p169 :rule chain_m_resolution :premises (@p168 @p160 @p165) :args (@t143 (@list false true) (@list @t136 @t138))) % 0.37/0.64 (step @p170 :rule bool-eq-true :args (@t138)) % 0.37/0.64 (step @p171 :rule quant-unused-vars :args ((= (forall @t8 true) true))) % 0.37/0.64 (step @p172 :rule bool-or-taut2 :args ((or @t52) @t144 false false)) % 0.37/0.64 (step @p173 :rule cong :premises (@p172) :args (@t145)) % 0.37/0.64 (step @p174 :rule trans :premises (@p173 @p171)) % 0.37/0.64 (step @p175 :rule refl :args (@t138)) % 0.37/0.64 (step @p176 :rule cong :premises (@p175 @p174) :args (@t146)) % 0.37/0.64 (step @p177 :rule trans :premises (@p176 @p170)) % 0.37/0.64 (step @p178 :rule refl :args (@t140)) % 0.37/0.64 (step @p179 :rule nary_cong :premises (@p178 @p178 @p177) :args (@t147)) % 0.37/0.64 (step @p180 :rule refl :args (@t148)) % 0.37/0.64 (step @p181 :rule cong :premises (@p180 @p179) :args ((=> @t148 @t147))) % 0.37/0.64 (assume-push @p189 @t148) % 0.37/0.64 (step @p183 :rule instantiate :premises (@p57) :args ((@list @t108 @t108))) % 0.37/0.64 (step-pop @p190 :rule scope :premises (@p183)) % 0.37/0.64 (step @p184 :rule process_scope :premises (@p190) :args (@t147)) % 0.37/0.64 (step @p186 :rule eq_resolve :premises (@p184 @p181)) % 0.37/0.64 (step @p187 :rule implies_elim :premises (@p186)) % 0.37/0.64 (step @p188 false :rule chain_m_resolution :premises (@p187 @p169 @p57) :args (false (@list true false) (@list @t142 @t148))) % 0.37/0.64 ) % 0.37/0.64 % SZS output end Proof % 0.37/0.64 % cvc5 exiting %------------------------------------------------------------------------------