%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU236+3 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:51:04 AM UTC 2026 % Result : Theorem 34.00s 34.20s % Output : Proof 34.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU236+3 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n002.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 16:45:48 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 34.00/34.20 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 34.00/34.20 --- Run --no-e-matching --full-saturate-quant at 6... % 34.00/34.20 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 34.00/34.20 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 34.00/34.20 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 34.00/34.20 % SZS status Theorem % 34.00/34.20 % SZS output start Proof % 34.00/34.20 ( % 34.00/34.20 (declare-sort $$unsorted 0) % 34.00/34.20 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 34.00/34.20 (declare-const tptp.relation_non_empty (-> $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.empty_set $$unsorted) % 34.00/34.20 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.succ (-> $$unsorted $$unsorted)) % 34.00/34.20 (declare-const tptp.function (-> $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.empty (-> $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 34.00/34.20 (declare-const tptp.relation (-> $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 34.00/34.20 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.ordinal_subset (-> $$unsorted $$unsorted Bool)) % 34.00/34.20 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 34.00/34.20 (define @t1 () (@var "A" $$unsorted)) % 34.00/34.20 (define @t2 () (@var "B" $$unsorted)) % 34.00/34.20 (define @t3 () (tptp.in @t2 @t1)) % 34.00/34.20 (define @t4 () (tptp.in @t1 @t2)) % 34.00/34.20 (define @t5 () (@list @t1 @t2)) % 34.00/34.20 (define @t6 () (tptp.function @t1)) % 34.00/34.20 (define @t7 () (tptp.empty @t1)) % 34.00/34.20 (define @t8 () (@list @t1)) % 34.00/34.20 (define @t9 () (tptp.epsilon_connected @t1)) % 34.00/34.20 (define @t10 () (tptp.epsilon_transitive @t1)) % 34.00/34.20 (define @t11 () (and @t10 @t9)) % 34.00/34.20 (define @t12 () (tptp.ordinal @t1)) % 34.00/34.20 (define @t13 () (forall @t8 (=> @t12 @t11))) % 34.00/34.20 (define @t14 () (tptp.relation @t1)) % 34.00/34.20 (define @t15 () (tptp.one_to_one @t1)) % 34.00/34.20 (define @t16 () (and @t14 @t6 @t15)) % 34.00/34.20 (define @t17 () (and @t14 @t7 @t6)) % 34.00/34.20 (define @t18 () (and @t10 @t9 @t12)) % 34.00/34.20 (define @t19 () (tptp.set_union2 @t2 @t1)) % 34.00/34.20 (define @t20 () (tptp.set_union2 @t1 @t2)) % 34.00/34.20 (define @t21 () (tptp.ordinal_subset @t1 @t2)) % 34.00/34.20 (define @t22 () (tptp.ordinal @t2)) % 34.00/34.20 (define @t23 () (and @t12 @t22)) % 34.00/34.20 (define @t24 () (tptp.singleton @t1)) % 34.00/34.20 (define @t25 () (tptp.succ @t1)) % 34.00/34.20 (define @t26 () (@var "C" $$unsorted)) % 34.00/34.20 (define @t27 () (tptp.in @t26 @t2)) % 34.00/34.20 (define @t28 () (= @t27 (= @t26 @t1))) % 34.00/34.20 (define @t29 () (@list @t26)) % 34.00/34.20 (define @t30 () (forall @t29 @t28)) % 34.00/34.20 (define @t31 () (= @t2 @t24)) % 34.00/34.20 (define @t32 () (= @t31 @t30)) % 34.00/34.20 (define @t33 () (forall @t5 @t32)) % 34.00/34.20 (define @t34 () (tptp.subset @t2 @t1)) % 34.00/34.20 (define @t35 () (@list @t2)) % 34.00/34.20 (define @t36 () (forall @t35 (=> @t3 @t34))) % 34.00/34.20 (define @t37 () (= @t10 @t36)) % 34.00/34.20 (define @t38 () (forall @t8 @t37)) % 34.00/34.20 (define @t39 () (tptp.in @t26 @t1)) % 34.00/34.20 (define @t40 () (forall @t29 (=> @t39 @t27))) % 34.00/34.20 (define @t41 () (tptp.subset @t1 @t2)) % 34.00/34.20 (define @t42 () (= @t41 @t40)) % 34.00/34.20 (define @t43 () (forall @t5 @t42)) % 34.00/34.20 (define @t44 () (tptp.relation_empty_yielding tptp.empty_set)) % 34.00/34.20 (define @t45 () (tptp.relation tptp.empty_set)) % 34.00/34.20 (define @t46 () (tptp.empty tptp.empty_set)) % 34.00/34.20 (define @t47 () (not (tptp.empty @t25))) % 34.00/34.20 (define @t48 () (not @t7)) % 34.00/34.20 (define @t49 () (and @t47 (tptp.epsilon_transitive @t25) (tptp.epsilon_connected @t25) (tptp.ordinal @t25))) % 34.00/34.20 (define @t50 () (forall @t8 (=> @t12 @t49))) % 34.00/34.20 (define @t51 () (tptp.relation_empty_yielding @t1)) % 34.00/34.20 (define @t52 () (= @t21 @t41)) % 34.00/34.20 (define @t53 () (forall @t5 (=> @t23 @t52))) % 34.00/34.20 (define @t54 () (tptp.element @t1 @t2)) % 34.00/34.20 (define @t55 () (tptp.empty @t2)) % 34.00/34.20 (define @t56 () (= @t4 (tptp.ordinal_subset @t25 @t2))) % 34.00/34.20 (define @t57 () (forall @t35 (=> @t22 @t56))) % 34.00/34.20 (define @t58 () (=> @t12 @t57)) % 34.00/34.20 (define @t59 () (forall @t8 @t58)) % 34.00/34.20 (define @t60 () (not @t59)) % 34.00/34.20 (define @t61 () (tptp.element @t2 (tptp.powerset @t26))) % 34.00/34.20 (define @t62 () (@list @t1 @t2 @t26)) % 34.00/34.20 (define @t63 () (tptp.subset (tptp.set_union2 @t1 @t26) @t2)) % 34.00/34.20 (define @t64 () (tptp.subset @t26 @t2)) % 34.00/34.20 (define @t65 () (and @t41 @t64)) % 34.00/34.20 (define @t66 () (forall @t62 (=> @t65 @t63))) % 34.00/34.20 (define @t67 () (@var "BOUND_VARIABLE_7817" $$unsorted)) % 34.00/34.20 (define @t68 () (= (tptp.in @t1 @t67) (tptp.ordinal_subset @t25 @t67))) % 34.00/34.20 (define @t69 () (not (tptp.ordinal @t67))) % 34.00/34.20 (define @t70 () (not @t12)) % 34.00/34.20 (define @t71 () (or @t70 @t69 @t68)) % 34.00/34.20 (define @t72 () (@list @t1 @t67)) % 34.00/34.20 (define @t73 () (forall @t72 @t71)) % 34.00/34.20 (define @t74 () (@quantifiers_skolemize @t73 1)) % 34.00/34.20 (define @t75 () (@quantifiers_skolemize @t73 0)) % 34.00/34.20 (define @t76 () (tptp.succ @t75)) % 34.00/34.20 (define @t77 () (@list @t76 @t74)) % 34.00/34.20 (define @t78 () (not @t22)) % 34.00/34.20 (define @t79 () (@list @t75)) % 34.00/34.20 (define @t80 () (or @t69 @t68)) % 34.00/34.20 (define @t81 () (or @t70 @t80)) % 34.00/34.20 (define @t82 () (forall @t72 @t81)) % 34.00/34.20 (define @t83 () (@list @t67)) % 34.00/34.20 (define @t84 () (forall @t83 @t81)) % 34.00/34.20 (define @t85 () (forall @t83 @t80)) % 34.00/34.20 (define @t86 () (or @t70 @t85)) % 34.00/34.20 (define @t87 () (forall @t35 (or @t78 @t56))) % 34.00/34.20 (define @t88 () (tptp.ordinal @t75)) % 34.00/34.20 (define @t89 () (tptp.ordinal_subset @t76 @t74)) % 34.00/34.20 (define @t90 () (tptp.in @t75 @t74)) % 34.00/34.20 (define @t91 () (= @t90 @t89)) % 34.00/34.20 (define @t92 () (tptp.ordinal @t74)) % 34.00/34.20 (define @t93 () (not @t92)) % 34.00/34.20 (define @t94 () (not @t88)) % 34.00/34.20 (define @t95 () (or @t94 @t93 @t91)) % 34.00/34.20 (define @t96 () (@list true)) % 34.00/34.20 (define @t97 () (@list @t95)) % 34.00/34.20 (define @t98 () (tptp.ordinal @t76)) % 34.00/34.20 (define @t99 () (and (not (tptp.empty @t76)) (tptp.epsilon_transitive @t76) (tptp.epsilon_connected @t76) @t98)) % 34.00/34.20 (define @t100 () (or @t94 @t99)) % 34.00/34.20 (define @t101 () (@list false false)) % 34.00/34.20 (define @t102 () (@list false)) % 34.00/34.20 (define @t103 () (tptp.subset @t76 @t74)) % 34.00/34.20 (define @t104 () (= @t89 @t103)) % 34.00/34.20 (define @t105 () (not @t98)) % 34.00/34.20 (define @t106 () (or @t105 @t93 @t104)) % 34.00/34.20 (define @t107 () (@list @t74)) % 34.00/34.20 (define @t108 () (tptp.epsilon_transitive @t74)) % 34.00/34.20 (define @t109 () (and @t108 (tptp.epsilon_connected @t74))) % 34.00/34.20 (define @t110 () (or @t93 @t109)) % 34.00/34.20 (define @t111 () (forall @t35 (or (not (tptp.in @t2 @t74)) (tptp.subset @t2 @t74)))) % 34.00/34.20 (define @t112 () (= @t108 @t111)) % 34.00/34.20 (define @t113 () (tptp.subset @t75 @t74)) % 34.00/34.20 (define @t114 () (not @t90)) % 34.00/34.20 (define @t115 () (or @t114 @t113)) % 34.00/34.20 (define @t116 () (not @t104)) % 34.00/34.20 (define @t117 () (not @t103)) % 34.00/34.20 (define @t118 () (tptp.singleton @t75)) % 34.00/34.20 (define @t119 () (tptp.set_union2 @t75 @t118)) % 34.00/34.20 (define @t120 () (tptp.subset @t119 @t74)) % 34.00/34.20 (define @t121 () (not @t120)) % 34.00/34.20 (define @t122 () (= @t76 @t119)) % 34.00/34.20 (define @t123 () (not @t122)) % 34.00/34.20 (define @t124 () (and @t122 @t117)) % 34.00/34.20 (define @t125 () (not @t64)) % 34.00/34.20 (define @t126 () (not @t41)) % 34.00/34.20 (define @t127 () (tptp.subset @t118 @t74)) % 34.00/34.20 (define @t128 () (not @t127)) % 34.00/34.20 (define @t129 () (not @t113)) % 34.00/34.20 (define @t130 () (or @t129 @t128 @t120)) % 34.00/34.20 (define @t131 () (tptp.in @t26 @t74)) % 34.00/34.20 (define @t132 () (tptp.in @t26 @t118)) % 34.00/34.20 (define @t133 () (forall @t29 (or (not @t132) @t131))) % 34.00/34.20 (define @t134 () (= @t127 @t133)) % 34.00/34.20 (define @t135 () (not @t133)) % 34.00/34.20 (define @t136 () (@quantifiers_skolemize @t133 0)) % 34.00/34.20 (define @t137 () (tptp.in @t136 @t74)) % 34.00/34.20 (define @t138 () (tptp.in @t136 @t118)) % 34.00/34.20 (define @t139 () (not @t138)) % 34.00/34.20 (define @t140 () (or @t139 @t137)) % 34.00/34.20 (define @t141 () (not @t140)) % 34.00/34.20 (define @t142 () (forall @t29 (= @t132 (= @t26 @t75)))) % 34.00/34.20 (define @t143 () (= @t132 (= @t75 @t26))) % 34.00/34.20 (define @t144 () (forall @t29 @t143)) % 34.00/34.20 (define @t145 () (= (= @t118 @t118) @t144)) % 34.00/34.20 (define @t146 () (forall @t5 (= @t31 (forall @t29 (= @t27 (= @t1 @t26)))))) % 34.00/34.20 (define @t147 () (= @t138 (= @t136 @t75))) % 34.00/34.20 (define @t148 () (= @t75 @t136)) % 34.00/34.20 (define @t149 () (= @t138 @t148)) % 34.00/34.20 (define @t150 () (not @t148)) % 34.00/34.20 (define @t151 () (not @t137)) % 34.00/34.20 (define @t152 () (and @t90 @t148 @t151)) % 34.00/34.20 (define @t153 () (forall @t29 (or (not (tptp.in @t26 @t76)) @t131))) % 34.00/34.20 (define @t154 () (= @t103 @t153)) % 34.00/34.20 (define @t155 () (tptp.in @t75 @t76)) % 34.00/34.20 (define @t156 () (not @t155)) % 34.00/34.20 (define @t157 () (or @t156 @t90)) % 34.00/34.20 (define @t158 () (not @t157)) % 34.00/34.20 (define @t159 () (@list true false)) % 34.00/34.20 (assume @p1 (forall @t5 (=> @t4 (not @t3)))) % 34.00/34.20 (assume @p2 (forall @t8 (=> @t7 @t6))) % 34.00/34.20 (assume @p3 @t13) % 34.00/34.20 (assume @p4 (forall @t8 (=> @t7 @t14))) % 34.00/34.20 (assume @p5 (forall @t8 (=> @t17 @t16))) % 34.00/34.20 (assume @p6 (forall @t8 (=> @t11 @t12))) % 34.00/34.20 (assume @p7 (forall @t8 (=> @t7 @t18))) % 34.00/34.20 (assume @p8 (forall @t5 (= @t20 @t19))) % 34.00/34.20 (assume @p9 (forall @t5 (=> @t23 (or @t21 (tptp.ordinal_subset @t2 @t1))))) % 34.00/34.20 (assume @p10 (forall @t8 (= @t25 (tptp.set_union2 @t1 @t24)))) % 34.00/34.20 (assume @p11 @t33) % 34.00/34.20 (assume @p12 @t38) % 34.00/34.20 (assume @p13 @t43) % 34.00/34.20 (assume @p14 (forall @t8 (exists @t35 (tptp.element @t2 @t1)))) % 34.00/34.20 (assume @p15 (and @t46 @t45 @t44)) % 34.00/34.20 (assume @p16 (forall @t8 @t47)) % 34.00/34.20 (assume @p17 @t46) % 34.00/34.20 (assume @p18 (and @t45 @t44 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) @t46 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set))) % 34.00/34.20 (assume @p19 (forall @t5 (=> (and @t14 (tptp.relation @t2)) (tptp.relation @t20)))) % 34.00/34.20 (assume @p20 (forall @t5 (=> @t48 (not (tptp.empty @t20))))) % 34.00/34.20 (assume @p21 @t50) % 34.00/34.20 (assume @p22 (forall @t5 (=> @t48 (not (tptp.empty @t19))))) % 34.00/34.20 (assume @p23 (and @t46 @t45)) % 34.00/34.20 (assume @p24 (forall @t5 (= (tptp.set_union2 @t1 @t1) @t1))) % 34.00/34.20 (assume @p25 (exists @t8 (and @t14 @t6))) % 34.00/34.20 (assume @p26 (exists @t8 @t18)) % 34.00/34.20 (assume @p27 (exists @t8 (and @t7 @t14))) % 34.00/34.20 (assume @p28 (exists @t8 @t7)) % 34.00/34.20 (assume @p29 (exists @t8 @t17)) % 34.00/34.20 (assume @p30 (exists @t8 (and @t14 @t6 @t15 @t7 @t10 @t9 @t12))) % 34.00/34.20 (assume @p31 (exists @t8 (and @t48 @t14))) % 34.00/34.20 (assume @p32 (exists @t8 @t48)) % 34.00/34.20 (assume @p33 (exists @t8 @t16)) % 34.00/34.20 (assume @p34 (exists @t8 (and @t48 @t10 @t9 @t12))) % 34.00/34.20 (assume @p35 (exists @t8 (and @t14 @t51))) % 34.00/34.20 (assume @p36 (exists @t8 (and @t14 @t51 @t6))) % 34.00/34.20 (assume @p37 (exists @t8 (and @t14 (tptp.relation_non_empty @t1) @t6))) % 34.00/34.20 (assume @p38 @t53) % 34.00/34.20 (assume @p39 (forall @t5 (=> @t23 (tptp.ordinal_subset @t1 @t1)))) % 34.00/34.20 (assume @p40 (forall @t5 (tptp.subset @t1 @t1))) % 34.00/34.20 (assume @p41 (forall @t8 (tptp.in @t1 @t25))) % 34.00/34.20 (assume @p42 (forall @t8 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 34.00/34.20 (assume @p43 (forall @t5 (=> @t4 @t54))) % 34.00/34.20 (assume @p44 (forall @t5 (=> @t54 (or @t55 @t4)))) % 34.00/34.20 (assume @p45 @t60) % 34.00/34.20 (assume @p46 (forall @t5 (= (tptp.element @t1 (tptp.powerset @t2)) @t41))) % 34.00/34.20 (assume @p47 (forall @t62 (=> (and @t4 @t61) (tptp.element @t1 @t26)))) % 34.00/34.20 (assume @p48 (forall @t62 (not (and @t4 @t61 (tptp.empty @t26))))) % 34.00/34.20 (assume @p49 (forall @t8 (=> @t7 (= @t1 tptp.empty_set)))) % 34.00/34.20 (assume @p50 (forall @t5 (not (and @t4 @t55)))) % 34.00/34.20 (assume @p51 (forall @t5 (not (and @t7 (not (= @t1 @t2)) @t55)))) % 34.00/34.20 (assume @p52 @t66) % 34.00/34.20 (assume @p53 true) % 34.00/34.20 (step @p54 :rule bool-impl-elim :args (@t39 @t27)) % 34.00/34.20 (step @p55 :rule cong :premises (@p54) :args (@t40)) % 34.00/34.20 (step @p56 :rule refl :args (@t41)) % 34.00/34.20 (step @p57 :rule cong :premises (@p56 @p55) :args (@t42)) % 34.00/34.20 (step @p58 :rule cong :premises (@p57) :args (@t43)) % 34.00/34.20 (step @p59 :rule eq_resolve :premises (@p13 @p58)) % 34.00/34.20 (step @p60 :rule instantiate :premises (@p59) :args (@t77)) % 34.00/34.20 (step @p61 :rule aci_norm :args ((= (or (or @t70 @t78) @t52) (or @t70 @t78 @t52)))) % 34.00/34.20 (step @p62 :rule refl :args (@t52)) % 34.00/34.20 (step @p63 :rule bool-and-de-morgan :args (@t12 @t22 true)) % 34.00/34.20 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((or (not @t23) @t52))) % 34.00/34.20 (step @p65 :rule trans :premises (@p64 @p61)) % 34.00/34.20 (step @p66 :rule bool-impl-elim :args (@t23 @t52)) % 34.00/34.20 (step @p67 :rule trans :premises (@p66 @p65)) % 34.00/34.20 (step @p68 :rule cong :premises (@p67) :args (@t53)) % 34.00/34.20 (step @p69 :rule eq_resolve :premises (@p38 @p68)) % 34.00/34.20 (step @p70 :rule instantiate :premises (@p69) :args (@t77)) % 34.00/34.20 (step @p71 :rule bool-impl-elim :args (@t12 @t49)) % 34.00/34.20 (step @p72 :rule cong :premises (@p71) :args (@t50)) % 34.00/34.20 (step @p73 :rule eq_resolve :premises (@p21 @p72)) % 34.00/34.20 (step @p74 :rule instantiate :premises (@p73) :args (@t79)) % 34.00/34.20 (step @p75 :rule aci_norm :args ((= @t81 @t71))) % 34.00/34.20 (step @p76 :rule cong :premises (@p75) :args (@t82)) % 34.00/34.20 (step @p77 :rule quant-merge-prenex :args ((= (forall @t8 @t84) @t82))) % 34.00/34.20 (step @p78 :rule alpha_equiv :args (@t85 (@list @t67) (@list @t2))) % 34.00/34.20 (step @p79 :rule refl :args (@t70)) % 34.00/34.20 (step @p80 :rule nary_cong :premises (@p79 @p78) :args (@t86)) % 34.00/34.20 (step @p81 :rule quant-miniscope-or :args ((= @t84 @t86))) % 34.00/34.20 (step @p82 :rule trans :premises (@p81 @p80)) % 34.00/34.20 (step @p83 :rule symm :premises (@p82)) % 34.00/34.20 (step @p84 :rule cong :premises (@p83) :args ((forall @t8 (or @t70 @t87)))) % 34.00/34.20 (step @p85 :rule trans :premises (@p84 @p77)) % 34.00/34.20 (step @p86 :rule trans :premises (@p85 @p76)) % 34.00/34.20 (step @p87 :rule bool-impl-elim :args (@t12 @t87)) % 34.00/34.20 (step @p88 :rule cong :premises (@p87) :args ((forall @t8 (=> @t12 @t87)))) % 34.00/34.20 (step @p89 :rule trans :premises (@p88 @p86)) % 34.00/34.20 (step @p90 :rule bool-impl-elim :args (@t22 @t56)) % 34.00/34.20 (step @p91 :rule cong :premises (@p90) :args (@t57)) % 34.00/34.20 (step @p92 :rule refl :args (@t12)) % 34.00/34.20 (step @p93 :rule cong :premises (@p92 @p91) :args (@t58)) % 34.00/34.20 (step @p94 :rule cong :premises (@p93) :args (@t59)) % 34.00/34.20 (step @p95 :rule trans :premises (@p94 @p89)) % 34.00/34.20 (step @p96 :rule cong :premises (@p95) :args (@t60)) % 34.00/34.20 (step @p97 :rule eq_resolve :premises (@p45 @p96)) % 34.00/34.20 (step @p98 :rule skolemize :premises (@p97)) % 34.00/34.20 (step @p99 :rule bool-double-not-elim :args (@t88)) % 34.00/34.20 (step @p100 :rule refl :args (@t95)) % 34.00/34.20 (step @p101 :rule nary_cong :premises (@p100 @p99) :args ((or @t95 (not @t94)))) % 34.00/34.20 (step @p102 :rule cnf_or_neg :args (@t95 0)) % 34.00/34.20 (step @p103 :rule eq_resolve :premises (@p102 @p101)) % 34.00/34.20 (step @p104 :rule reordering :premises (@p103) :args ((or @t88 @t95))) % 34.00/34.20 (step @p105 :rule chain_m_resolution :premises (@p104 @p98) :args (@t88 @t96 @t97)) % 34.00/34.20 (step @p106 :rule cnf_or_pos :args (@t100)) % 34.00/34.20 (step @p107 :rule reordering :premises (@p106) :args ((or @t94 @t99 (not @t100)))) % 34.00/34.20 (step @p108 :rule chain_m_resolution :premises (@p107 @p105 @p74) :args (@t99 @t101 (@list @t88 @t100))) % 34.00/34.20 (step @p109 :rule cnf_and_pos :args (@t99 3)) % 34.00/34.20 (step @p110 :rule reordering :premises (@p109) :args ((or @t98 (not @t99)))) % 34.00/34.20 (step @p111 :rule chain_m_resolution :premises (@p110 @p108) :args (@t98 @t102 (@list @t99))) % 34.00/34.20 (step @p112 :rule bool-double-not-elim :args (@t92)) % 34.00/34.20 (step @p113 :rule nary_cong :premises (@p100 @p112) :args ((or @t95 (not @t93)))) % 34.00/34.20 (step @p114 :rule cnf_or_neg :args (@t95 1)) % 34.00/34.20 (step @p115 :rule eq_resolve :premises (@p114 @p113)) % 34.00/34.20 (step @p116 :rule reordering :premises (@p115) :args ((or @t92 @t95))) % 34.00/34.20 (step @p117 :rule chain_m_resolution :premises (@p116 @p98) :args (@t92 @t96 @t97)) % 34.00/34.20 (step @p118 :rule cnf_or_pos :args (@t106)) % 34.00/34.20 (step @p119 :rule reordering :premises (@p118) :args ((or @t93 @t105 @t104 (not @t106)))) % 34.00/34.20 (step @p120 :rule chain_m_resolution :premises (@p119 @p117 @p111 @p70) :args (@t104 (@list false false false) (@list @t92 @t98 @t106))) % 34.00/34.20 (step @p121 :rule cnf_or_neg :args (@t95 2)) % 34.00/34.20 (step @p122 :rule chain_m_resolution :premises (@p121 @p98) :args ((not @t91) @t96 @t97)) % 34.00/34.20 (step @p123 :rule cnf_equiv_neg2 :args (@t91)) % 34.00/34.20 (step @p124 :rule bool-impl-elim :args (@t3 @t34)) % 34.00/34.20 (step @p125 :rule cong :premises (@p124) :args (@t36)) % 34.00/34.20 (step @p126 :rule refl :args (@t10)) % 34.00/34.20 (step @p127 :rule cong :premises (@p126 @p125) :args (@t37)) % 34.00/34.20 (step @p128 :rule cong :premises (@p127) :args (@t38)) % 34.00/34.20 (step @p129 :rule eq_resolve :premises (@p12 @p128)) % 34.00/34.20 (step @p130 :rule instantiate :premises (@p129) :args (@t107)) % 34.00/34.20 (step @p131 :rule bool-impl-elim :args (@t12 @t11)) % 34.00/34.20 (step @p132 :rule cong :premises (@p131) :args (@t13)) % 34.00/34.20 (step @p133 :rule eq_resolve :premises (@p3 @p132)) % 34.00/34.20 (step @p134 :rule instantiate :premises (@p133) :args (@t107)) % 34.00/34.20 (step @p135 :rule cnf_or_pos :args (@t110)) % 34.00/34.20 (step @p136 :rule reordering :premises (@p135) :args ((or @t93 @t109 (not @t110)))) % 34.00/34.20 (step @p137 :rule chain_m_resolution :premises (@p136 @p117 @p134) :args (@t109 @t101 (@list @t92 @t110))) % 34.00/34.20 (step @p138 :rule cnf_and_pos :args (@t109 0)) % 34.00/34.20 (step @p139 :rule reordering :premises (@p138) :args ((or @t108 (not @t109)))) % 34.00/34.20 (step @p140 :rule chain_m_resolution :premises (@p139 @p137) :args (@t108 @t102 (@list @t109))) % 34.00/34.20 (step @p141 :rule cnf_equiv_pos1 :args (@t112)) % 34.00/34.20 (step @p142 :rule reordering :premises (@p141) :args ((or (not @t108) @t111 (not @t112)))) % 34.00/34.20 (step @p143 :rule chain_m_resolution :premises (@p142 @p140 @p130) :args (@t111 @t101 (@list @t108 @t112))) % 34.00/34.20 (step @p144 :rule instantiate :premises (@p143) :args (@t79)) % 34.00/34.20 (step @p145 :rule cnf_or_pos :args (@t115)) % 34.00/34.20 (step @p146 :rule reordering :premises (@p145) :args ((or @t114 @t113 (not @t115)))) % 34.00/34.20 (step @p147 :rule cnf_equiv_pos2 :args (@t104)) % 34.00/34.20 (step @p148 :rule reordering :premises (@p147) :args ((or @t89 @t117 @t116))) % 34.00/34.20 (step @p149 :rule instantiate :premises (@p10) :args (@t79)) % 34.00/34.20 (step @p150 :rule refl :args (@t121)) % 34.00/34.20 (step @p151 :rule bool-double-not-elim :args (@t103)) % 34.00/34.20 (step @p152 :rule refl :args (@t123)) % 34.00/34.20 (step @p153 :rule nary_cong :premises (@p152 @p151 @p150) :args ((or @t123 (not @t117) @t121))) % 34.00/34.20 (assume-push @p300 @t122) % 34.00/34.20 (assume-push @p301 @t117) % 34.00/34.20 (assume-push @p302 @t117) % 34.00/34.20 (assume-push @p303 @t122) % 34.00/34.20 (step @p158 :rule false_intro :premises (@p301)) % 34.00/34.20 (step @p159 :rule refl :args (@t74)) % 34.00/34.20 (step @p160 :rule symm :premises (@p149)) % 34.00/34.20 (step @p161 :rule cong :premises (@p160 @p159) :args (@t120)) % 34.00/34.20 (step @p162 :rule trans :premises (@p161 @p158)) % 34.00/34.20 (step @p163 :rule false_elim :premises (@p162)) % 34.00/34.20 (step-pop @p304 :rule scope :premises (@p163)) % 34.00/34.20 (step-pop @p305 :rule scope :premises (@p304)) % 34.00/34.20 (step @p164 :rule process_scope :premises (@p305) :args (@t121)) % 34.00/34.20 (step @p167 :rule and_intro :premises (@p301 @p149)) % 34.00/34.20 (step @p168 :rule modus_ponens :premises (@p167 @p164)) % 34.00/34.20 (step-pop @p306 :rule scope :premises (@p168)) % 34.00/34.20 (step-pop @p307 :rule scope :premises (@p306)) % 34.00/34.20 (step @p169 :rule process_scope :premises (@p307) :args (@t121)) % 34.00/34.20 (step @p172 :rule implies_elim :premises (@p169)) % 34.00/34.20 (step @p173 :rule cnf_and_neg :args (@t124)) % 34.00/34.20 (step @p174 :rule resolution :premises (@p173 @p172) :args (true @t124)) % 34.00/34.20 (step @p175 :rule eq_resolve :premises (@p174 @p153)) % 34.00/34.20 (step @p176 :rule reordering :premises (@p175) :args ((or @t103 @t123 @t121))) % 34.00/34.20 (step @p177 :rule aci_norm :args ((= (or (or @t126 @t125) @t63) (or @t126 @t125 @t63)))) % 34.00/34.20 (step @p178 :rule refl :args (@t63)) % 34.00/34.20 (step @p179 :rule bool-and-de-morgan :args (@t41 @t64 true)) % 34.00/34.20 (step @p180 :rule nary_cong :premises (@p179 @p178) :args ((or (not @t65) @t63))) % 34.00/34.20 (step @p181 :rule trans :premises (@p180 @p177)) % 34.00/34.20 (step @p182 :rule bool-impl-elim :args (@t65 @t63)) % 34.00/34.20 (step @p183 :rule trans :premises (@p182 @p181)) % 34.00/34.20 (step @p184 :rule cong :premises (@p183) :args (@t66)) % 34.00/34.20 (step @p185 :rule eq_resolve :premises (@p52 @p184)) % 34.00/34.20 (step @p186 :rule instantiate :premises (@p185) :args ((@list @t75 @t74 @t118))) % 34.00/34.20 (step @p187 :rule cnf_or_pos :args (@t130)) % 34.00/34.20 (step @p188 :rule reordering :premises (@p187) :args ((or @t129 @t128 @t120 (not @t130)))) % 34.00/34.20 (step @p189 :rule instantiate :premises (@p59) :args ((@list @t118 @t74))) % 34.00/34.20 (step @p190 :rule cnf_equiv_pos2 :args (@t134)) % 34.00/34.20 (step @p191 :rule reordering :premises (@p190) :args ((or @t127 @t135 (not @t134)))) % 34.00/34.20 (step @p192 :rule refl :args (@t141)) % 34.00/34.20 (step @p193 :rule bool-double-not-elim :args (@t133)) % 34.00/34.20 (step @p194 :rule nary_cong :premises (@p193 @p192) :args ((or (not @t135) @t141))) % 34.00/34.20 (assume-push @p308 @t135) % 34.00/34.20 (step @p196 :rule skolemize :premises (@p308)) % 34.00/34.20 (step-pop @p309 :rule scope :premises (@p196)) % 34.00/34.20 (step @p197 :rule process_scope :premises (@p309) :args (@t141)) % 34.00/34.20 (step @p199 :rule implies_elim :premises (@p197)) % 34.00/34.20 (step @p200 :rule eq_resolve :premises (@p199 @p194)) % 34.00/34.20 (step @p201 :rule bool-double-not-elim :args (@t138)) % 34.00/34.20 (step @p202 :rule refl :args (@t140)) % 34.00/34.20 (step @p203 :rule nary_cong :premises (@p202 @p201) :args ((or @t140 (not @t139)))) % 34.00/34.20 (step @p204 :rule cnf_or_neg :args (@t140 0)) % 34.00/34.20 (step @p205 :rule eq_resolve :premises (@p204 @p203)) % 34.00/34.20 (step @p206 :rule reordering :premises (@p205) :args ((or @t138 @t140))) % 34.00/34.20 (step @p207 :rule cnf_or_neg :args (@t140 1)) % 34.00/34.20 (step @p208 :rule eq-symm :args (@t26 @t1)) % 34.00/34.20 (step @p209 :rule refl :args (@t27)) % 34.00/34.20 (step @p210 :rule cong :premises (@p209 @p208) :args (@t28)) % 34.00/34.20 (step @p211 :rule cong :premises (@p210) :args (@t30)) % 34.00/34.20 (step @p212 :rule refl :args (@t31)) % 34.00/34.20 (step @p213 :rule cong :premises (@p212 @p211) :args (@t32)) % 34.00/34.20 (step @p214 :rule cong :premises (@p213) :args (@t33)) % 34.00/34.20 (step @p215 :rule eq_resolve :premises (@p11 @p214)) % 34.00/34.20 (step @p216 :rule bool-eq-true :args (@t142)) % 34.00/34.20 (step @p217 :rule eq-symm :args (true @t142)) % 34.00/34.20 (step @p218 :rule trans :premises (@p217 @p216)) % 34.00/34.20 (step @p219 :rule eq-symm :args (@t75 @t26)) % 34.00/34.20 (step @p220 :rule refl :args (@t132)) % 34.00/34.20 (step @p221 :rule cong :premises (@p220 @p219) :args (@t143)) % 34.00/34.20 (step @p222 :rule cong :premises (@p221) :args (@t144)) % 34.00/34.20 (step @p223 :rule eq-refl :args (@t118)) % 34.00/34.20 (step @p224 :rule cong :premises (@p223 @p222) :args (@t145)) % 34.00/34.20 (step @p225 :rule trans :premises (@p224 @p218)) % 34.00/34.20 (step @p226 :rule refl :args (@t146)) % 34.00/34.20 (step @p227 :rule cong :premises (@p226 @p225) :args ((=> @t146 @t145))) % 34.00/34.20 (assume-push @p310 @t146) % 34.00/34.20 (step @p229 :rule instantiate :premises (@p215) :args ((@list @t75 @t118))) % 34.00/34.20 (step-pop @p311 :rule scope :premises (@p229)) % 34.00/34.20 (step @p230 :rule process_scope :premises (@p311) :args (@t145)) % 34.00/34.20 (step @p232 :rule eq_resolve :premises (@p230 @p227)) % 34.00/34.20 (step @p233 :rule implies_elim :premises (@p232)) % 34.00/34.20 (step @p234 :rule chain_m_resolution :premises (@p233 @p215) :args (@t142 @t102 (@list @t146))) % 34.00/34.20 (step @p235 :rule eq-symm :args (@t136 @t75)) % 34.00/34.20 (step @p236 :rule refl :args (@t138)) % 34.00/34.20 (step @p237 :rule cong :premises (@p236 @p235) :args (@t147)) % 34.00/34.20 (step @p238 :rule refl :args (@t142)) % 34.00/34.20 (step @p239 :rule cong :premises (@p238 @p237) :args ((=> @t142 @t147))) % 34.00/34.20 (assume-push @p312 @t142) % 34.00/34.20 (step @p241 :rule instantiate :premises (@p234) :args ((@list @t136))) % 34.00/34.20 (step-pop @p313 :rule scope :premises (@p241)) % 34.00/34.20 (step @p242 :rule process_scope :premises (@p313) :args (@t147)) % 34.00/34.20 (step @p244 :rule eq_resolve :premises (@p242 @p239)) % 34.00/34.20 (step @p245 :rule implies_elim :premises (@p244)) % 34.00/34.20 (step @p246 :rule chain_m_resolution :premises (@p245 @p234) :args (@t149 @t102 (@list @t142))) % 34.00/34.20 (step @p247 :rule cnf_equiv_pos1 :args (@t149)) % 34.00/34.20 (step @p248 :rule reordering :premises (@p247) :args ((or @t139 @t148 (not @t149)))) % 34.00/34.20 (step @p249 :rule refl :args (@t150)) % 34.00/34.20 (step @p250 :rule bool-double-not-elim :args (@t137)) % 34.00/34.20 (step @p251 :rule refl :args (@t114)) % 34.00/34.20 (step @p252 :rule nary_cong :premises (@p251 @p250 @p249) :args ((or @t114 (not @t151) @t150))) % 34.00/34.20 (assume-push @p314 @t90) % 34.00/34.20 (assume-push @p315 @t148) % 34.00/34.20 (assume-push @p316 @t151) % 34.00/34.20 (step @p256 :rule evaluate :args ((= false true))) % 34.00/34.20 (step @p257 :rule true_intro :premises (@p314)) % 34.00/34.20 (step @p159 :rule refl :args (@t74)) % 34.00/34.20 (step @p258 :rule symm :premises (@p315)) % 34.00/34.20 (step @p259 :rule cong :premises (@p258 @p159) :args (@t137)) % 34.00/34.20 (step @p260 :rule false_intro :premises (@p316)) % 34.00/34.20 (step @p261 :rule symm :premises (@p260)) % 34.00/34.20 (step @p262 :rule trans :premises (@p261 @p259 @p257)) % 34.00/34.20 (step @p263 false :rule eq_resolve :premises (@p262 @p256)) % 34.00/34.20 (step-pop @p317 :rule scope :premises (@p263)) % 34.00/34.20 (step-pop @p318 :rule scope :premises (@p317)) % 34.00/34.20 (step-pop @p319 :rule scope :premises (@p318)) % 34.00/34.20 (step @p264 :rule process_scope :premises (@p319) :args (false)) % 34.00/34.20 (assume-push @p320 @t90) % 34.00/34.20 (assume-push @p321 @t151) % 34.00/34.20 (assume-push @p322 @t148) % 34.00/34.20 (step @p271 :rule and_intro :premises (@p320 @p322 @p321)) % 34.00/34.20 (step-pop @p323 :rule scope :premises (@p271)) % 34.00/34.20 (step-pop @p324 :rule scope :premises (@p323)) % 34.00/34.20 (step-pop @p325 :rule scope :premises (@p324)) % 34.00/34.20 (step @p272 :rule process_scope :premises (@p325) :args (@t152)) % 34.00/34.20 (step @p276 :rule implies_elim :premises (@p272)) % 34.00/34.20 (step @p277 :rule resolution :premises (@p276 @p264) :args (true @t152)) % 34.00/34.20 (step @p278 :rule not_and :premises (@p277)) % 34.00/34.20 (step @p279 :rule eq_resolve :premises (@p278 @p252)) % 34.00/34.20 (step @p280 :rule chain_m_resolution :premises (@p279 @p248 @p246 @p207 @p206 @p200 @p191 @p189 @p188 @p186 @p176 @p149 @p148 @p120 @p146 @p144 @p123 @p122) :args (@t114 (@list false false true false true true false true false true false true false false false true true) (@list @t148 @t149 @t137 @t138 @t140 @t133 @t134 @t127 @t130 @t120 @t122 @t103 @t104 @t113 @t115 @t89 @t91))) % 34.00/34.20 (step @p281 :rule cnf_equiv_neg1 :args (@t91)) % 34.00/34.20 (step @p282 :rule reordering :premises (@p281) :args ((or @t90 @t89 @t91))) % 34.00/34.20 (step @p283 :rule chain_m_resolution :premises (@p282 @p280 @p122) :args (@t89 (@list true true) (@list @t90 @t91))) % 34.00/34.20 (step @p284 :rule cnf_equiv_pos1 :args (@t104)) % 34.00/34.20 (step @p285 :rule reordering :premises (@p284) :args ((or (not @t89) @t103 @t116))) % 34.00/34.20 (step @p286 :rule chain_m_resolution :premises (@p285 @p283 @p120) :args (@t103 @t101 (@list @t89 @t104))) % 34.00/34.20 (step @p287 :rule cnf_equiv_pos1 :args (@t154)) % 34.00/34.20 (step @p288 :rule reordering :premises (@p287) :args ((or @t117 @t153 (not @t154)))) % 34.00/34.20 (step @p289 :rule chain_m_resolution :premises (@p288 @p286 @p60) :args (@t153 @t101 (@list @t103 @t154))) % 34.00/34.20 (step @p290 :rule instantiate :premises (@p41) :args (@t79)) % 34.00/34.20 (step @p291 :rule cnf_or_pos :args (@t157)) % 34.00/34.20 (step @p292 :rule reordering :premises (@p291) :args ((or @t90 @t156 @t158))) % 34.00/34.20 (step @p293 :rule chain_m_resolution :premises (@p292 @p280 @p290) :args (@t158 @t159 (@list @t90 @t155))) % 34.00/34.20 (assume-push @p326 @t153) % 34.00/34.20 (step @p295 :rule instantiate :premises (@p326) :args (@t79)) % 34.00/34.20 (step-pop @p327 :rule scope :premises (@p295)) % 34.00/34.20 (step @p296 :rule process_scope :premises (@p327) :args (@t157)) % 34.00/34.20 (step @p298 :rule implies_elim :premises (@p296)) % 34.00/34.20 (step @p299 false :rule chain_m_resolution :premises (@p298 @p293 @p289) :args (false @t159 (@list @t157 @t153))) % 34.00/34.20 ) % 34.00/34.20 % SZS output end Proof % 34.00/34.20 % cvc5 exiting %------------------------------------------------------------------------------