%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU317+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n018.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 08:51:21 AM UTC 2026 % Result : Theorem 0.54s 0.72s % Output : Proof 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU317+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n018.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:56:05 EDT 2026 % 0.18/0.35 % CPUTime : % 0.34/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.54/0.72 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.54/0.72 % SZS status Theorem % 0.54/0.72 % SZS output start Proof % 0.54/0.72 ( % 0.54/0.72 (declare-sort $$unsorted 0) % 0.54/0.72 (declare-const tptp.closed_subset (-> $$unsorted $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.top_str (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.topstr_closure (-> $$unsorted $$unsorted $$unsorted)) % 0.54/0.72 (declare-const tptp.the_carrier (-> $$unsorted $$unsorted)) % 0.54/0.72 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.54/0.72 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.v3_membered (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.natural (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.v1_membered (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.v1_xreal_0 (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.v5_membered (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.empty_set $$unsorted) % 0.54/0.72 (declare-const tptp.v2_membered (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.v1_rat_1 (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.v1_xcmplx_0 (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.v1_int_1 (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.one_sorted_str (-> $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.54/0.72 (declare-const tptp.v4_membered (-> $$unsorted Bool)) % 0.54/0.72 (define @t1 () (@var "A" $$unsorted)) % 0.54/0.72 (define @t2 () (@var "B" $$unsorted)) % 0.54/0.72 (define @t3 () (tptp.in @t1 @t2)) % 0.54/0.72 (define @t4 () (@list @t1 @t2)) % 0.54/0.72 (define @t5 () (tptp.v1_xcmplx_0 @t2)) % 0.54/0.72 (define @t6 () (tptp.element @t2 @t1)) % 0.54/0.72 (define @t7 () (@list @t2)) % 0.54/0.72 (define @t8 () (tptp.v1_membered @t1)) % 0.54/0.72 (define @t9 () (@list @t1)) % 0.54/0.72 (define @t10 () (tptp.v1_xreal_0 @t2)) % 0.54/0.72 (define @t11 () (tptp.v2_membered @t1)) % 0.54/0.72 (define @t12 () (tptp.v1_rat_1 @t2)) % 0.54/0.72 (define @t13 () (tptp.v3_membered @t1)) % 0.54/0.72 (define @t14 () (tptp.v1_int_1 @t2)) % 0.54/0.72 (define @t15 () (tptp.v4_membered @t1)) % 0.54/0.72 (define @t16 () (tptp.v5_membered @t1)) % 0.54/0.72 (define @t17 () (tptp.empty @t1)) % 0.54/0.72 (define @t18 () (tptp.v1_membered @t2)) % 0.54/0.72 (define @t19 () (tptp.powerset @t1)) % 0.54/0.72 (define @t20 () (tptp.element @t2 @t19)) % 0.54/0.72 (define @t21 () (tptp.v2_membered @t2)) % 0.54/0.72 (define @t22 () (tptp.v3_membered @t2)) % 0.54/0.72 (define @t23 () (tptp.v4_membered @t2)) % 0.54/0.72 (define @t24 () (@var "C" $$unsorted)) % 0.54/0.72 (define @t25 () (tptp.in @t24 @t2)) % 0.54/0.72 (define @t26 () (tptp.in @t24 @t1)) % 0.54/0.72 (define @t27 () (@list @t24)) % 0.54/0.72 (define @t28 () (forall @t27 (=> @t26 @t25))) % 0.54/0.72 (define @t29 () (tptp.subset @t1 @t2)) % 0.54/0.72 (define @t30 () (= @t29 @t28)) % 0.54/0.72 (define @t31 () (forall @t4 @t30)) % 0.54/0.72 (define @t32 () (tptp.the_carrier @t1)) % 0.54/0.72 (define @t33 () (tptp.powerset @t32)) % 0.54/0.72 (define @t34 () (tptp.topstr_closure @t1 @t2)) % 0.54/0.72 (define @t35 () (tptp.element @t2 @t33)) % 0.54/0.72 (define @t36 () (tptp.top_str @t1)) % 0.54/0.72 (define @t37 () (tptp.one_sorted_str @t1)) % 0.54/0.72 (define @t38 () (not @t17)) % 0.54/0.72 (define @t39 () (tptp.empty @t2)) % 0.54/0.72 (define @t40 () (tptp.element @t1 @t2)) % 0.54/0.72 (define @t41 () (tptp.element @t1 (tptp.powerset @t2))) % 0.54/0.72 (define @t42 () (forall @t4 (= @t41 @t29))) % 0.54/0.72 (define @t43 () (@var "D" $$unsorted)) % 0.54/0.72 (define @t44 () (tptp.in @t24 @t43)) % 0.54/0.72 (define @t45 () (tptp.subset @t2 @t43)) % 0.54/0.72 (define @t46 () (tptp.closed_subset @t43 @t1)) % 0.54/0.72 (define @t47 () (and @t46 @t45)) % 0.54/0.72 (define @t48 () (=> @t47 @t44)) % 0.54/0.72 (define @t49 () (tptp.element @t43 @t33)) % 0.54/0.72 (define @t50 () (@list @t43)) % 0.54/0.72 (define @t51 () (forall @t50 (=> @t49 @t48))) % 0.54/0.72 (define @t52 () (tptp.in @t24 @t34)) % 0.54/0.72 (define @t53 () (= @t52 @t51)) % 0.54/0.72 (define @t54 () (tptp.in @t24 @t32)) % 0.54/0.72 (define @t55 () (=> @t54 @t53)) % 0.54/0.72 (define @t56 () (forall @t27 @t55)) % 0.54/0.72 (define @t57 () (=> @t35 @t56)) % 0.54/0.72 (define @t58 () (forall @t7 @t57)) % 0.54/0.72 (define @t59 () (=> @t36 @t58)) % 0.54/0.72 (define @t60 () (forall @t9 @t59)) % 0.54/0.72 (define @t61 () (tptp.subset @t2 @t34)) % 0.54/0.72 (define @t62 () (forall @t7 (=> @t35 @t61))) % 0.54/0.72 (define @t63 () (=> @t36 @t62)) % 0.54/0.72 (define @t64 () (forall @t9 @t63)) % 0.54/0.72 (define @t65 () (not @t64)) % 0.54/0.72 (define @t66 () (tptp.element @t2 (tptp.powerset @t24))) % 0.54/0.72 (define @t67 () (@list @t1 @t2 @t24)) % 0.54/0.72 (define @t68 () (@var "BOUND_VARIABLE_7994" $$unsorted)) % 0.54/0.72 (define @t69 () (tptp.subset @t68 (tptp.topstr_closure @t1 @t68))) % 0.54/0.72 (define @t70 () (not (tptp.element @t68 @t33))) % 0.54/0.72 (define @t71 () (not @t36)) % 0.54/0.72 (define @t72 () (or @t71 @t70 @t69)) % 0.54/0.72 (define @t73 () (@list @t1 @t68)) % 0.54/0.72 (define @t74 () (forall @t73 @t72)) % 0.54/0.72 (define @t75 () (@quantifiers_skolemize @t74 1)) % 0.54/0.72 (define @t76 () (@quantifiers_skolemize @t74 0)) % 0.54/0.72 (define @t77 () (tptp.topstr_closure @t76 @t75)) % 0.54/0.72 (define @t78 () (not (tptp.in @t24 @t75))) % 0.54/0.72 (define @t79 () (forall @t27 (or @t78 (tptp.in @t24 @t77)))) % 0.54/0.72 (define @t80 () (@quantifiers_skolemize @t79 0)) % 0.54/0.72 (define @t81 () (tptp.the_carrier @t76)) % 0.54/0.72 (define @t82 () (tptp.powerset @t81)) % 0.54/0.72 (define @t83 () (forall @t50 (or (not (tptp.element @t43 @t82)) (not (tptp.closed_subset @t43 @t76)) (not (tptp.subset @t75 @t43)) (tptp.in @t80 @t43)))) % 0.54/0.72 (define @t84 () (@quantifiers_skolemize @t83 0)) % 0.54/0.72 (define @t85 () (@var "BOUND_VARIABLE_7967" $$unsorted)) % 0.54/0.72 (define @t86 () (@var "BOUND_VARIABLE_7965" $$unsorted)) % 0.54/0.72 (define @t87 () (not @t46)) % 0.54/0.72 (define @t88 () (not @t49)) % 0.54/0.72 (define @t89 () (= (tptp.in @t85 (tptp.topstr_closure @t1 @t86)) (forall @t50 (or @t88 @t87 (not (tptp.subset @t86 @t43)) (tptp.in @t85 @t43))))) % 0.54/0.72 (define @t90 () (not (tptp.in @t85 @t32))) % 0.54/0.72 (define @t91 () (not (tptp.element @t86 @t33))) % 0.54/0.72 (define @t92 () (or @t91 @t90 @t89)) % 0.54/0.72 (define @t93 () (or @t71 @t92)) % 0.54/0.72 (define @t94 () (forall (@list @t1 @t86 @t85) @t93)) % 0.54/0.72 (define @t95 () (@list @t86 @t85)) % 0.54/0.72 (define @t96 () (forall @t95 @t93)) % 0.54/0.72 (define @t97 () (forall @t95 @t92)) % 0.54/0.72 (define @t98 () (@var "BOUND_VARIABLE_7946" $$unsorted)) % 0.54/0.72 (define @t99 () (or @t71 @t97)) % 0.54/0.72 (define @t100 () (not @t45)) % 0.54/0.72 (define @t101 () (= (tptp.in @t98 @t34) (forall @t50 (or @t88 @t87 @t100 (tptp.in @t98 @t43))))) % 0.54/0.72 (define @t102 () (not (tptp.in @t98 @t32))) % 0.54/0.72 (define @t103 () (not @t35)) % 0.54/0.72 (define @t104 () (or @t103 @t102 @t101)) % 0.54/0.72 (define @t105 () (@list @t2 @t98)) % 0.54/0.72 (define @t106 () (forall @t105 @t104)) % 0.54/0.72 (define @t107 () (or @t102 @t101)) % 0.54/0.72 (define @t108 () (or @t103 @t107)) % 0.54/0.72 (define @t109 () (forall @t105 @t108)) % 0.54/0.72 (define @t110 () (@list @t98)) % 0.54/0.72 (define @t111 () (forall @t110 @t108)) % 0.54/0.72 (define @t112 () (forall @t110 @t107)) % 0.54/0.72 (define @t113 () (or @t103 @t112)) % 0.54/0.72 (define @t114 () (or @t88 @t87 @t100 @t44)) % 0.54/0.72 (define @t115 () (= @t52 (forall @t50 @t114))) % 0.54/0.72 (define @t116 () (forall @t27 (or (not @t54) @t115))) % 0.54/0.72 (define @t117 () (or @t87 @t100 @t44)) % 0.54/0.72 (define @t118 () (@list @t75 @t81)) % 0.54/0.72 (define @t119 () (tptp.subset @t75 @t81)) % 0.54/0.72 (define @t120 () (tptp.element @t75 @t82)) % 0.54/0.72 (define @t121 () (forall @t4 (= @t29 @t41))) % 0.54/0.72 (define @t122 () (= @t119 @t120)) % 0.54/0.72 (define @t123 () (= @t120 @t119)) % 0.54/0.72 (define @t124 () (or @t70 @t69)) % 0.54/0.72 (define @t125 () (or @t71 @t124)) % 0.54/0.72 (define @t126 () (forall @t73 @t125)) % 0.54/0.72 (define @t127 () (@list @t68)) % 0.54/0.72 (define @t128 () (forall @t127 @t125)) % 0.54/0.72 (define @t129 () (forall @t127 @t124)) % 0.54/0.72 (define @t130 () (or @t71 @t129)) % 0.54/0.72 (define @t131 () (forall @t7 (or @t103 @t61))) % 0.54/0.72 (define @t132 () (tptp.subset @t75 @t77)) % 0.54/0.72 (define @t133 () (not @t120)) % 0.54/0.72 (define @t134 () (tptp.top_str @t76)) % 0.54/0.72 (define @t135 () (not @t134)) % 0.54/0.72 (define @t136 () (or @t135 @t133 @t132)) % 0.54/0.72 (define @t137 () (@list true)) % 0.54/0.72 (define @t138 () (@list @t136)) % 0.54/0.72 (define @t139 () (@list false false)) % 0.54/0.72 (define @t140 () (forall @t27 (or @t78 (tptp.in @t24 @t81)))) % 0.54/0.72 (define @t141 () (= @t119 @t140)) % 0.54/0.72 (define @t142 () (@list @t80)) % 0.54/0.72 (define @t143 () (= @t132 @t79)) % 0.54/0.72 (define @t144 () (not @t79)) % 0.54/0.72 (define @t145 () (@list true false)) % 0.54/0.72 (define @t146 () (tptp.in @t80 @t75)) % 0.54/0.72 (define @t147 () (tptp.in @t80 @t77)) % 0.54/0.72 (define @t148 () (not @t146)) % 0.54/0.72 (define @t149 () (or @t148 @t147)) % 0.54/0.72 (define @t150 () (@list @t149)) % 0.54/0.72 (define @t151 () (tptp.in @t80 @t81)) % 0.54/0.72 (define @t152 () (or @t148 @t151)) % 0.54/0.72 (define @t153 () (= @t147 @t83)) % 0.54/0.72 (define @t154 () (not @t151)) % 0.54/0.72 (define @t155 () (or @t135 @t133 @t154 @t153)) % 0.54/0.72 (define @t156 () (not @t83)) % 0.54/0.72 (define @t157 () (tptp.subset @t75 @t84)) % 0.54/0.72 (define @t158 () (tptp.in @t80 @t84)) % 0.54/0.72 (define @t159 () (not @t157)) % 0.54/0.72 (define @t160 () (or (not (tptp.element @t84 @t82)) (not (tptp.closed_subset @t84 @t76)) @t159 @t158)) % 0.54/0.72 (define @t161 () (@list @t160)) % 0.54/0.72 (define @t162 () (forall @t27 (or @t78 (tptp.in @t24 @t84)))) % 0.54/0.72 (define @t163 () (= @t157 @t162)) % 0.54/0.72 (define @t164 () (or @t148 @t158)) % 0.54/0.72 (define @t165 () (not @t164)) % 0.54/0.72 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 0.54/0.72 (assume @p2 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.54/0.72 (assume @p3 (forall @t9 (=> @t11 (forall @t7 (=> @t6 (and @t5 @t10)))))) % 0.54/0.72 (assume @p4 (forall @t9 (=> @t13 (forall @t7 (=> @t6 (and @t5 @t10 @t12)))))) % 0.54/0.72 (assume @p5 (forall @t9 (=> @t15 (forall @t7 (=> @t6 (and @t5 @t10 @t14 @t12)))))) % 0.54/0.72 (assume @p6 (forall @t9 (=> @t16 (forall @t7 (=> @t6 (and @t5 (tptp.natural @t2) @t10 @t14 @t12)))))) % 0.54/0.72 (assume @p7 (forall @t9 (=> @t17 (and @t8 @t11 @t13 @t15 @t16)))) % 0.54/0.72 (assume @p8 (forall @t9 (=> @t8 (forall @t7 (=> @t20 @t18))))) % 0.54/0.72 (assume @p9 (forall @t9 (=> @t11 (forall @t7 (=> @t20 (and @t18 @t21)))))) % 0.54/0.72 (assume @p10 (forall @t9 (=> @t13 (forall @t7 (=> @t20 (and @t18 @t21 @t22)))))) % 0.54/0.72 (assume @p11 (forall @t9 (=> @t15 (forall @t7 (=> @t20 (and @t18 @t21 @t22 @t23)))))) % 0.54/0.72 (assume @p12 (forall @t9 (=> @t16 @t15))) % 0.54/0.72 (assume @p13 (forall @t9 (=> @t16 (forall @t7 (=> @t20 (and @t18 @t21 @t22 @t23 (tptp.v5_membered @t2))))))) % 0.54/0.72 (assume @p14 (forall @t9 (=> @t15 @t13))) % 0.54/0.72 (assume @p15 (forall @t9 (=> @t13 @t11))) % 0.54/0.72 (assume @p16 (forall @t9 (=> @t11 @t8))) % 0.54/0.72 (assume @p17 @t31) % 0.54/0.72 (assume @p18 true) % 0.54/0.72 (assume @p19 (forall @t4 (=> (and @t36 @t35) (tptp.element @t34 @t33)))) % 0.54/0.72 (assume @p20 (forall @t9 (=> @t36 @t37))) % 0.54/0.72 (assume @p21 (exists @t9 @t36)) % 0.54/0.72 (assume @p22 (exists @t9 @t37)) % 0.54/0.72 (assume @p23 (forall @t9 (exists @t7 @t6))) % 0.54/0.72 (assume @p24 (forall @t9 (not (tptp.empty @t19)))) % 0.54/0.72 (assume @p25 (and (tptp.empty tptp.empty_set) (tptp.v1_membered tptp.empty_set) (tptp.v2_membered tptp.empty_set) (tptp.v3_membered tptp.empty_set) (tptp.v4_membered tptp.empty_set) (tptp.v5_membered tptp.empty_set))) % 0.54/0.72 (assume @p26 (exists @t9 (and @t38 @t8 @t11 @t13 @t15 @t16))) % 0.54/0.72 (assume @p27 (forall @t9 (=> @t38 (exists @t7 (and @t20 (not @t39)))))) % 0.54/0.72 (assume @p28 (forall @t9 (exists @t7 (and @t20 @t39)))) % 0.54/0.72 (assume @p29 (forall @t4 (tptp.subset @t1 @t1))) % 0.54/0.72 (assume @p30 (forall @t4 (=> @t3 @t40))) % 0.54/0.72 (assume @p31 (forall @t4 (=> @t40 (or @t39 @t3)))) % 0.54/0.72 (assume @p32 @t42) % 0.54/0.72 (assume @p33 @t60) % 0.54/0.72 (assume @p34 @t65) % 0.54/0.72 (assume @p35 (forall @t67 (=> (and @t3 @t66) (tptp.element @t1 @t24)))) % 0.54/0.72 (assume @p36 (forall @t67 (not (and @t3 @t66 (tptp.empty @t24))))) % 0.54/0.72 (assume @p37 (forall @t9 (=> @t17 (= @t1 tptp.empty_set)))) % 0.54/0.72 (assume @p38 (forall @t4 (not (and @t3 @t39)))) % 0.54/0.72 (assume @p39 (forall @t4 (not (and @t17 (not (= @t1 @t2)) @t39)))) % 0.54/0.72 (step @p40 :rule bool-impl-elim :args (@t26 @t25)) % 0.54/0.72 (step @p41 :rule cong :premises (@p40) :args (@t28)) % 0.54/0.72 (step @p42 :rule refl :args (@t29)) % 0.54/0.72 (step @p43 :rule cong :premises (@p42 @p41) :args (@t30)) % 0.54/0.72 (step @p44 :rule cong :premises (@p43) :args (@t31)) % 0.54/0.72 (step @p45 :rule eq_resolve :premises (@p17 @p44)) % 0.54/0.72 (step @p46 :rule instantiate :premises (@p45) :args ((@list @t75 @t84))) % 0.54/0.72 (step @p47 :rule aci_norm :args ((= @t93 (or @t71 @t91 @t90 @t89)))) % 0.54/0.72 (step @p48 :rule cong :premises (@p47) :args (@t94)) % 0.54/0.72 (step @p49 :rule quant-merge-prenex :args ((= (forall @t9 @t96) @t94))) % 0.54/0.72 (step @p50 :rule alpha_equiv :args (@t97 (@list @t86 @t85) (@list @t2 @t98))) % 0.54/0.72 (step @p51 :rule refl :args (@t71)) % 0.54/0.72 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t99)) % 0.54/0.72 (step @p53 :rule quant-miniscope-or :args ((= @t96 @t99))) % 0.54/0.72 (step @p54 :rule trans :premises (@p53 @p52)) % 0.54/0.72 (step @p55 :rule symm :premises (@p54)) % 0.54/0.72 (step @p56 :rule cong :premises (@p55) :args ((forall @t9 (or @t71 @t106)))) % 0.54/0.72 (step @p57 :rule trans :premises (@p56 @p49)) % 0.54/0.72 (step @p58 :rule trans :premises (@p57 @p48)) % 0.54/0.72 (step @p59 :rule bool-impl-elim :args (@t36 @t106)) % 0.54/0.72 (step @p60 :rule cong :premises (@p59) :args ((forall @t9 (=> @t36 @t106)))) % 0.54/0.72 (step @p61 :rule trans :premises (@p60 @p58)) % 0.54/0.72 (step @p62 :rule aci_norm :args ((= @t108 @t104))) % 0.54/0.72 (step @p63 :rule cong :premises (@p62) :args (@t109)) % 0.54/0.72 (step @p64 :rule quant-merge-prenex :args ((= (forall @t7 @t111) @t109))) % 0.54/0.72 (step @p65 :rule alpha_equiv :args (@t112 (@list @t98) (@list @t24))) % 0.54/0.72 (step @p66 :rule refl :args (@t103)) % 0.54/0.72 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t113)) % 0.54/0.72 (step @p68 :rule quant-miniscope-or :args ((= @t111 @t113))) % 0.54/0.72 (step @p69 :rule trans :premises (@p68 @p67)) % 0.54/0.72 (step @p70 :rule symm :premises (@p69)) % 0.54/0.72 (step @p71 :rule cong :premises (@p70) :args ((forall @t7 (or @t103 @t116)))) % 0.54/0.72 (step @p72 :rule trans :premises (@p71 @p64)) % 0.54/0.72 (step @p73 :rule trans :premises (@p72 @p63)) % 0.54/0.72 (step @p74 :rule bool-impl-elim :args (@t35 @t116)) % 0.54/0.72 (step @p75 :rule cong :premises (@p74) :args ((forall @t7 (=> @t35 @t116)))) % 0.54/0.72 (step @p76 :rule trans :premises (@p75 @p73)) % 0.54/0.72 (step @p77 :rule bool-impl-elim :args (@t54 @t115)) % 0.54/0.72 (step @p78 :rule cong :premises (@p77) :args ((forall @t27 (=> @t54 @t115)))) % 0.54/0.72 (step @p79 :rule aci_norm :args ((= (or @t88 @t117) @t114))) % 0.54/0.72 (step @p80 :rule aci_norm :args ((= (or (or @t87 @t100) @t44) @t117))) % 0.54/0.72 (step @p81 :rule refl :args (@t44)) % 0.54/0.72 (step @p82 :rule bool-and-de-morgan :args (@t46 @t45 true)) % 0.54/0.72 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or (not @t47) @t44))) % 0.54/0.72 (step @p84 :rule trans :premises (@p83 @p80)) % 0.54/0.72 (step @p85 :rule bool-impl-elim :args (@t47 @t44)) % 0.54/0.72 (step @p86 :rule trans :premises (@p85 @p84)) % 0.54/0.72 (step @p87 :rule refl :args (@t88)) % 0.54/0.72 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((or @t88 @t48))) % 0.54/0.72 (step @p89 :rule trans :premises (@p88 @p79)) % 0.54/0.72 (step @p90 :rule bool-impl-elim :args (@t49 @t48)) % 0.54/0.72 (step @p91 :rule trans :premises (@p90 @p89)) % 0.54/0.72 (step @p92 :rule cong :premises (@p91) :args (@t51)) % 0.54/0.72 (step @p93 :rule refl :args (@t52)) % 0.54/0.72 (step @p94 :rule cong :premises (@p93 @p92) :args (@t53)) % 0.54/0.72 (step @p95 :rule refl :args (@t54)) % 0.54/0.72 (step @p96 :rule cong :premises (@p95 @p94) :args (@t55)) % 0.54/0.72 (step @p97 :rule cong :premises (@p96) :args (@t56)) % 0.54/0.72 (step @p98 :rule trans :premises (@p97 @p78)) % 0.54/0.72 (step @p99 :rule refl :args (@t35)) % 0.54/0.72 (step @p100 :rule cong :premises (@p99 @p98) :args (@t57)) % 0.54/0.72 (step @p101 :rule cong :premises (@p100) :args (@t58)) % 0.54/0.72 (step @p102 :rule trans :premises (@p101 @p76)) % 0.54/0.72 (step @p103 :rule refl :args (@t36)) % 0.54/0.72 (step @p104 :rule cong :premises (@p103 @p102) :args (@t59)) % 0.54/0.72 (step @p105 :rule cong :premises (@p104) :args (@t60)) % 0.54/0.72 (step @p106 :rule trans :premises (@p105 @p61)) % 0.54/0.72 (step @p107 :rule eq_resolve :premises (@p33 @p106)) % 0.54/0.72 (step @p108 :rule instantiate :premises (@p107) :args ((@list @t76 @t75 @t80))) % 0.54/0.72 (step @p109 :rule instantiate :premises (@p45) :args (@t118)) % 0.54/0.72 (step @p110 :rule eq-symm :args (@t41 @t29)) % 0.54/0.72 (step @p111 :rule cong :premises (@p110) :args (@t42)) % 0.54/0.72 (step @p112 :rule eq_resolve :premises (@p32 @p111)) % 0.54/0.72 (step @p113 :rule eq-symm :args (@t119 @t120)) % 0.54/0.72 (step @p114 :rule refl :args (@t121)) % 0.54/0.72 (step @p115 :rule cong :premises (@p114 @p113) :args ((=> @t121 @t122))) % 0.54/0.72 (assume-push @p212 @t121) % 0.54/0.72 (step @p117 :rule instantiate :premises (@p112) :args (@t118)) % 0.54/0.72 (step-pop @p213 :rule scope :premises (@p117)) % 0.54/0.72 (step @p118 :rule process_scope :premises (@p213) :args (@t122)) % 0.54/0.72 (step @p120 :rule eq_resolve :premises (@p118 @p115)) % 0.54/0.72 (step @p121 :rule implies_elim :premises (@p120)) % 0.54/0.72 (step @p122 :rule chain_m_resolution :premises (@p121 @p112) :args (@t123 (@list false) (@list @t121))) % 0.54/0.72 (step @p123 :rule aci_norm :args ((= @t125 @t72))) % 0.54/0.72 (step @p124 :rule cong :premises (@p123) :args (@t126)) % 0.54/0.72 (step @p125 :rule quant-merge-prenex :args ((= (forall @t9 @t128) @t126))) % 0.54/0.72 (step @p126 :rule alpha_equiv :args (@t129 (@list @t68) (@list @t2))) % 0.54/0.72 (step @p127 :rule nary_cong :premises (@p51 @p126) :args (@t130)) % 0.54/0.72 (step @p128 :rule quant-miniscope-or :args ((= @t128 @t130))) % 0.54/0.72 (step @p129 :rule trans :premises (@p128 @p127)) % 0.54/0.72 (step @p130 :rule symm :premises (@p129)) % 0.54/0.72 (step @p131 :rule cong :premises (@p130) :args ((forall @t9 (or @t71 @t131)))) % 0.54/0.72 (step @p132 :rule trans :premises (@p131 @p125)) % 0.54/0.72 (step @p133 :rule trans :premises (@p132 @p124)) % 0.54/0.72 (step @p134 :rule bool-impl-elim :args (@t36 @t131)) % 0.54/0.72 (step @p135 :rule cong :premises (@p134) :args ((forall @t9 (=> @t36 @t131)))) % 0.54/0.72 (step @p136 :rule trans :premises (@p135 @p133)) % 0.54/0.72 (step @p137 :rule bool-impl-elim :args (@t35 @t61)) % 0.54/0.72 (step @p138 :rule cong :premises (@p137) :args (@t62)) % 0.54/0.72 (step @p139 :rule cong :premises (@p103 @p138) :args (@t63)) % 0.54/0.72 (step @p140 :rule cong :premises (@p139) :args (@t64)) % 0.54/0.72 (step @p141 :rule trans :premises (@p140 @p136)) % 0.54/0.72 (step @p142 :rule cong :premises (@p141) :args (@t65)) % 0.54/0.72 (step @p143 :rule eq_resolve :premises (@p34 @p142)) % 0.54/0.72 (step @p144 :rule skolemize :premises (@p143)) % 0.54/0.72 (step @p145 :rule bool-double-not-elim :args (@t120)) % 0.54/0.72 (step @p146 :rule refl :args (@t136)) % 0.54/0.72 (step @p147 :rule nary_cong :premises (@p146 @p145) :args ((or @t136 (not @t133)))) % 0.54/0.72 (step @p148 :rule cnf_or_neg :args (@t136 1)) % 0.54/0.72 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 0.54/0.72 (step @p150 :rule reordering :premises (@p149) :args ((or @t120 @t136))) % 0.54/0.72 (step @p151 :rule chain_m_resolution :premises (@p150 @p144) :args (@t120 @t137 @t138)) % 0.54/0.72 (step @p152 :rule cnf_equiv_pos1 :args (@t123)) % 0.54/0.72 (step @p153 :rule reordering :premises (@p152) :args ((or @t133 @t119 (not @t123)))) % 0.54/0.72 (step @p154 :rule chain_m_resolution :premises (@p153 @p151 @p122) :args (@t119 @t139 (@list @t120 @t123))) % 0.54/0.72 (step @p155 :rule cnf_equiv_pos1 :args (@t141)) % 0.54/0.72 (step @p156 :rule reordering :premises (@p155) :args ((or (not @t119) @t140 (not @t141)))) % 0.54/0.72 (step @p157 :rule chain_m_resolution :premises (@p156 @p154 @p109) :args (@t140 @t139 (@list @t119 @t141))) % 0.54/0.72 (step @p158 :rule instantiate :premises (@p157) :args (@t142)) % 0.54/0.72 (step @p159 :rule instantiate :premises (@p45) :args ((@list @t75 @t77))) % 0.54/0.72 (step @p160 :rule cnf_or_neg :args (@t136 2)) % 0.54/0.72 (step @p161 :rule chain_m_resolution :premises (@p160 @p144) :args ((not @t132) @t137 @t138)) % 0.54/0.72 (step @p162 :rule cnf_equiv_pos2 :args (@t143)) % 0.54/0.72 (step @p163 :rule reordering :premises (@p162) :args ((or @t132 @t144 (not @t143)))) % 0.54/0.72 (step @p164 :rule chain_m_resolution :premises (@p163 @p161 @p159) :args (@t144 @t145 (@list @t132 @t143))) % 0.54/0.72 (step @p165 :rule skolemize :premises (@p164)) % 0.54/0.72 (step @p166 :rule bool-double-not-elim :args (@t146)) % 0.54/0.72 (step @p167 :rule refl :args (@t149)) % 0.54/0.72 (step @p168 :rule nary_cong :premises (@p167 @p166) :args ((or @t149 (not @t148)))) % 0.54/0.72 (step @p169 :rule cnf_or_neg :args (@t149 0)) % 0.54/0.72 (step @p170 :rule eq_resolve :premises (@p169 @p168)) % 0.54/0.72 (step @p171 :rule reordering :premises (@p170) :args ((or @t146 @t149))) % 0.54/0.72 (step @p172 :rule chain_m_resolution :premises (@p171 @p165) :args (@t146 @t137 @t150)) % 0.54/0.72 (step @p173 :rule cnf_or_pos :args (@t152)) % 0.54/0.72 (step @p174 :rule reordering :premises (@p173) :args ((or @t148 @t151 (not @t152)))) % 0.54/0.72 (step @p175 :rule chain_m_resolution :premises (@p174 @p172 @p158) :args (@t151 @t139 (@list @t146 @t152))) % 0.54/0.72 (step @p176 :rule bool-double-not-elim :args (@t134)) % 0.54/0.72 (step @p177 :rule nary_cong :premises (@p146 @p176) :args ((or @t136 (not @t135)))) % 0.54/0.72 (step @p178 :rule cnf_or_neg :args (@t136 0)) % 0.54/0.72 (step @p179 :rule eq_resolve :premises (@p178 @p177)) % 0.54/0.72 (step @p180 :rule reordering :premises (@p179) :args ((or @t134 @t136))) % 0.54/0.72 (step @p181 :rule chain_m_resolution :premises (@p180 @p144) :args (@t134 @t137 @t138)) % 0.54/0.72 (step @p182 :rule cnf_or_pos :args (@t155)) % 0.54/0.72 (step @p183 :rule reordering :premises (@p182) :args ((or @t135 @t133 @t154 @t153 (not @t155)))) % 0.54/0.72 (step @p184 :rule chain_m_resolution :premises (@p183 @p181 @p151 @p175 @p108) :args (@t153 (@list false false false false) (@list @t134 @t120 @t151 @t155))) % 0.54/0.72 (step @p185 :rule cnf_or_neg :args (@t149 1)) % 0.54/0.72 (step @p186 :rule chain_m_resolution :premises (@p185 @p165) :args ((not @t147) @t137 @t150)) % 0.54/0.72 (step @p187 :rule cnf_equiv_pos2 :args (@t153)) % 0.54/0.72 (step @p188 :rule reordering :premises (@p187) :args ((or @t147 @t156 (not @t153)))) % 0.54/0.72 (step @p189 :rule chain_m_resolution :premises (@p188 @p186 @p184) :args (@t156 @t145 (@list @t147 @t153))) % 0.54/0.72 (step @p190 :rule skolemize :premises (@p189)) % 0.54/0.72 (step @p191 :rule bool-double-not-elim :args (@t157)) % 0.54/0.72 (step @p192 :rule refl :args (@t160)) % 0.54/0.72 (step @p193 :rule nary_cong :premises (@p192 @p191) :args ((or @t160 (not @t159)))) % 0.54/0.72 (step @p194 :rule cnf_or_neg :args (@t160 2)) % 0.54/0.72 (step @p195 :rule eq_resolve :premises (@p194 @p193)) % 0.54/0.72 (step @p196 :rule reordering :premises (@p195) :args ((or @t157 @t160))) % 0.54/0.72 (step @p197 :rule chain_m_resolution :premises (@p196 @p190) :args (@t157 @t137 @t161)) % 0.54/0.72 (step @p198 :rule cnf_equiv_pos1 :args (@t163)) % 0.54/0.72 (step @p199 :rule reordering :premises (@p198) :args ((or @t159 @t162 (not @t163)))) % 0.54/0.72 (step @p200 :rule chain_m_resolution :premises (@p199 @p197 @p46) :args (@t162 @t139 (@list @t157 @t163))) % 0.54/0.72 (step @p201 :rule cnf_or_neg :args (@t160 3)) % 0.54/0.72 (step @p202 :rule chain_m_resolution :premises (@p201 @p190) :args ((not @t158) @t137 @t161)) % 0.54/0.72 (step @p203 :rule cnf_or_pos :args (@t164)) % 0.54/0.72 (step @p204 :rule reordering :premises (@p203) :args ((or @t148 @t158 @t165))) % 0.54/0.72 (step @p205 :rule chain_m_resolution :premises (@p204 @p172 @p202) :args (@t165 (@list false true) (@list @t146 @t158))) % 0.54/0.72 (assume-push @p214 @t162) % 0.54/0.72 (step @p207 :rule instantiate :premises (@p200) :args (@t142)) % 0.54/0.72 (step-pop @p215 :rule scope :premises (@p207)) % 0.54/0.72 (step @p208 :rule process_scope :premises (@p215) :args (@t164)) % 0.54/0.72 (step @p210 :rule implies_elim :premises (@p208)) % 0.54/0.72 (step @p211 false :rule chain_m_resolution :premises (@p210 @p205 @p200) :args (false @t145 (@list @t164 @t162))) % 0.54/0.72 ) % 0.54/0.72 % SZS output end Proof % 0.54/0.73 % cvc5 exiting %------------------------------------------------------------------------------