%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU321+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 08:51:22 AM UTC 2026 % Result : Theorem 0.43s 0.62s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU321+1 : TPTP v9.2.1. Released v3.3.0. % 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 : 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 16:56:33 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.43/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.43/0.62 % SZS status Theorem % 0.43/0.62 % SZS output start Proof % 0.43/0.62 ( % 0.43/0.62 (declare-sort $$unsorted 0) % 0.43/0.62 (declare-const tptp.empty_set $$unsorted) % 0.43/0.62 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.62 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.natural (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.v2_membered (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.the_carrier (-> $$unsorted $$unsorted)) % 0.43/0.62 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.43/0.62 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.v1_xcmplx_0 (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.one_sorted_str (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.v1_rat_1 (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.empty_carrier (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.v4_membered (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.v1_int_1 (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.v1_membered (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.v1_xreal_0 (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.v5_membered (-> $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.43/0.62 (declare-const tptp.v3_membered (-> $$unsorted Bool)) % 0.43/0.62 (define @t1 () (@var "A" $$unsorted)) % 0.43/0.62 (define @t2 () (@var "B" $$unsorted)) % 0.43/0.62 (define @t3 () (@list @t1 @t2)) % 0.43/0.62 (define @t4 () (tptp.empty @t2)) % 0.43/0.62 (define @t5 () (tptp.the_carrier @t1)) % 0.43/0.62 (define @t6 () (tptp.powerset @t5)) % 0.43/0.62 (define @t7 () (tptp.element @t2 @t6)) % 0.43/0.62 (define @t8 () (@list @t2)) % 0.43/0.62 (define @t9 () (tptp.one_sorted_str @t1)) % 0.43/0.62 (define @t10 () (tptp.empty_carrier @t1)) % 0.43/0.62 (define @t11 () (not @t10)) % 0.43/0.62 (define @t12 () (and @t11 @t9)) % 0.43/0.62 (define @t13 () (@list @t1)) % 0.43/0.62 (define @t14 () (tptp.v4_membered @t1)) % 0.43/0.62 (define @t15 () (tptp.v5_membered @t1)) % 0.43/0.62 (define @t16 () (tptp.v3_membered @t1)) % 0.43/0.62 (define @t17 () (tptp.v2_membered @t1)) % 0.43/0.62 (define @t18 () (tptp.v1_membered @t1)) % 0.43/0.62 (define @t19 () (tptp.empty @t1)) % 0.43/0.62 (define @t20 () (tptp.v1_xcmplx_0 @t2)) % 0.43/0.62 (define @t21 () (tptp.element @t2 @t1)) % 0.43/0.62 (define @t22 () (tptp.v1_xreal_0 @t2)) % 0.43/0.62 (define @t23 () (tptp.v1_rat_1 @t2)) % 0.43/0.62 (define @t24 () (tptp.v1_int_1 @t2)) % 0.43/0.62 (define @t25 () (tptp.v1_membered @t2)) % 0.43/0.62 (define @t26 () (tptp.powerset @t1)) % 0.43/0.62 (define @t27 () (tptp.element @t2 @t26)) % 0.43/0.62 (define @t28 () (tptp.v2_membered @t2)) % 0.43/0.62 (define @t29 () (tptp.v3_membered @t2)) % 0.43/0.62 (define @t30 () (tptp.v4_membered @t2)) % 0.43/0.62 (define @t31 () (tptp.in @t1 @t2)) % 0.43/0.62 (define @t32 () (tptp.element @t1 @t2)) % 0.43/0.62 (define @t33 () (@var "C" $$unsorted)) % 0.43/0.62 (define @t34 () (tptp.element @t2 (tptp.powerset @t33))) % 0.43/0.62 (define @t35 () (@list @t1 @t2 @t33)) % 0.43/0.62 (define @t36 () (tptp.subset_complement @t1 @t2)) % 0.43/0.62 (define @t37 () (not (tptp.empty @t5))) % 0.43/0.62 (define @t38 () (forall @t13 (=> @t12 @t37))) % 0.43/0.62 (define @t39 () (tptp.empty tptp.empty_set)) % 0.43/0.62 (define @t40 () (= @t1 tptp.empty_set)) % 0.43/0.62 (define @t41 () (tptp.in @t33 @t2)) % 0.43/0.62 (define @t42 () (not @t41)) % 0.43/0.62 (define @t43 () (tptp.subset_complement @t5 @t2)) % 0.43/0.62 (define @t44 () (= (tptp.in @t33 @t43) @t42)) % 0.43/0.62 (define @t45 () (tptp.element @t33 @t5)) % 0.43/0.62 (define @t46 () (@list @t33)) % 0.43/0.62 (define @t47 () (forall @t46 (=> @t45 @t44))) % 0.43/0.62 (define @t48 () (=> @t7 @t47)) % 0.43/0.62 (define @t49 () (forall @t8 @t48)) % 0.43/0.62 (define @t50 () (=> @t12 @t49)) % 0.43/0.62 (define @t51 () (forall @t13 @t50)) % 0.43/0.62 (define @t52 () (not @t51)) % 0.43/0.62 (define @t53 () (tptp.in @t33 @t36)) % 0.43/0.62 (define @t54 () (=> @t42 @t53)) % 0.43/0.62 (define @t55 () (tptp.element @t33 @t1)) % 0.43/0.62 (define @t56 () (forall @t46 (=> @t55 @t54))) % 0.43/0.62 (define @t57 () (=> @t27 @t56)) % 0.43/0.62 (define @t58 () (forall @t8 @t57)) % 0.43/0.62 (define @t59 () (not @t40)) % 0.43/0.62 (define @t60 () (=> @t59 @t58)) % 0.43/0.62 (define @t61 () (forall @t13 @t60)) % 0.43/0.62 (define @t62 () (tptp.in @t2 @t33)) % 0.43/0.62 (define @t63 () (tptp.in @t2 (tptp.subset_complement @t1 @t33))) % 0.43/0.62 (define @t64 () (not (and @t63 @t62))) % 0.43/0.62 (define @t65 () (tptp.element @t33 @t26)) % 0.43/0.62 (define @t66 () (forall @t35 (=> @t65 @t64))) % 0.43/0.62 (define @t67 () (not @t62)) % 0.43/0.62 (define @t68 () (not @t63)) % 0.43/0.62 (define @t69 () (not @t65)) % 0.43/0.62 (define @t70 () (or @t69 @t68 @t67)) % 0.43/0.62 (define @t71 () (@var "BOUND_VARIABLE_7965" $$unsorted)) % 0.43/0.62 (define @t72 () (@var "BOUND_VARIABLE_7967" $$unsorted)) % 0.43/0.62 (define @t73 () (= (tptp.in @t72 (tptp.subset_complement @t5 @t71)) (not (tptp.in @t72 @t71)))) % 0.43/0.62 (define @t74 () (not (tptp.element @t72 @t5))) % 0.43/0.62 (define @t75 () (not (tptp.element @t71 @t6))) % 0.43/0.62 (define @t76 () (not @t9)) % 0.43/0.62 (define @t77 () (or @t10 @t76 @t75 @t74 @t73)) % 0.43/0.62 (define @t78 () (or @t75 @t74 @t73)) % 0.43/0.62 (define @t79 () (or @t10 @t76 @t78)) % 0.43/0.62 (define @t80 () (@list @t1 @t71 @t72)) % 0.43/0.62 (define @t81 () (forall @t80 @t79)) % 0.43/0.62 (define @t82 () (@list @t71 @t72)) % 0.43/0.62 (define @t83 () (forall @t82 @t79)) % 0.43/0.62 (define @t84 () (forall @t82 @t78)) % 0.43/0.62 (define @t85 () (@var "BOUND_VARIABLE_7947" $$unsorted)) % 0.43/0.62 (define @t86 () (or @t10 @t76 @t84)) % 0.43/0.62 (define @t87 () (= (tptp.in @t85 @t43) (not (tptp.in @t85 @t2)))) % 0.43/0.62 (define @t88 () (not (tptp.element @t85 @t5))) % 0.43/0.62 (define @t89 () (not @t7)) % 0.43/0.62 (define @t90 () (or @t89 @t88 @t87)) % 0.43/0.62 (define @t91 () (@list @t2 @t85)) % 0.43/0.62 (define @t92 () (forall @t91 @t90)) % 0.43/0.62 (define @t93 () (or @t10 @t76 @t92)) % 0.43/0.62 (define @t94 () (or @t10 @t76)) % 0.43/0.62 (define @t95 () (not @t12)) % 0.43/0.62 (define @t96 () (or @t88 @t87)) % 0.43/0.62 (define @t97 () (or @t89 @t96)) % 0.43/0.62 (define @t98 () (forall @t91 @t97)) % 0.43/0.62 (define @t99 () (@list @t85)) % 0.43/0.62 (define @t100 () (forall @t99 @t97)) % 0.43/0.62 (define @t101 () (forall @t99 @t96)) % 0.43/0.62 (define @t102 () (@list @t33)) % 0.43/0.62 (define @t103 () (or @t89 @t101)) % 0.43/0.62 (define @t104 () (forall @t46 (or (not @t45) @t44))) % 0.43/0.62 (define @t105 () (forall @t80 @t77)) % 0.43/0.62 (define @t106 () (@quantifiers_skolemize @t105 1)) % 0.43/0.62 (define @t107 () (@quantifiers_skolemize @t105 2)) % 0.43/0.62 (define @t108 () (tptp.in @t107 @t106)) % 0.43/0.62 (define @t109 () (not @t108)) % 0.43/0.62 (define @t110 () (@quantifiers_skolemize @t105 0)) % 0.43/0.62 (define @t111 () (tptp.the_carrier @t110)) % 0.43/0.62 (define @t112 () (tptp.in @t107 (tptp.subset_complement @t111 @t106))) % 0.43/0.62 (define @t113 () (= @t112 @t109)) % 0.43/0.62 (define @t114 () (tptp.element @t107 @t111)) % 0.43/0.62 (define @t115 () (not @t114)) % 0.43/0.62 (define @t116 () (tptp.element @t106 (tptp.powerset @t111))) % 0.43/0.62 (define @t117 () (not @t116)) % 0.43/0.62 (define @t118 () (tptp.one_sorted_str @t110)) % 0.43/0.62 (define @t119 () (not @t118)) % 0.43/0.62 (define @t120 () (tptp.empty_carrier @t110)) % 0.43/0.62 (define @t121 () (or @t120 @t119 @t117 @t115 @t113)) % 0.43/0.62 (define @t122 () (@list true)) % 0.43/0.62 (define @t123 () (@list @t121)) % 0.43/0.62 (define @t124 () (not @t112)) % 0.43/0.62 (define @t125 () (tptp.empty @t111)) % 0.43/0.62 (define @t126 () (not @t125)) % 0.43/0.62 (define @t127 () (or @t120 @t119 @t126)) % 0.43/0.62 (define @t128 () (= tptp.empty_set @t111)) % 0.43/0.62 (define @t129 () (not @t128)) % 0.43/0.62 (define @t130 () (not @t39)) % 0.43/0.62 (define @t131 () (and @t39 @t128 @t126)) % 0.43/0.62 (define @t132 () (@list false true)) % 0.43/0.62 (define @t133 () (@var "BOUND_VARIABLE_8010" $$unsorted)) % 0.43/0.62 (define @t134 () (@var "BOUND_VARIABLE_8012" $$unsorted)) % 0.43/0.62 (define @t135 () (tptp.in @t134 (tptp.subset_complement @t1 @t133))) % 0.43/0.62 (define @t136 () (tptp.in @t134 @t133)) % 0.43/0.62 (define @t137 () (not (tptp.element @t134 @t1))) % 0.43/0.62 (define @t138 () (not (tptp.element @t133 @t26))) % 0.43/0.62 (define @t139 () (or @t40 @t138 @t137 @t136 @t135)) % 0.43/0.62 (define @t140 () (or @t138 @t137 @t136 @t135)) % 0.43/0.62 (define @t141 () (or @t40 @t140)) % 0.43/0.62 (define @t142 () (@list @t1 @t133 @t134)) % 0.43/0.62 (define @t143 () (forall @t142 @t141)) % 0.43/0.62 (define @t144 () (@list @t133 @t134)) % 0.43/0.62 (define @t145 () (forall @t144 @t141)) % 0.43/0.62 (define @t146 () (forall @t144 @t140)) % 0.43/0.62 (define @t147 () (@var "BOUND_VARIABLE_7994" $$unsorted)) % 0.43/0.62 (define @t148 () (or @t40 @t146)) % 0.43/0.62 (define @t149 () (tptp.in @t147 @t36)) % 0.43/0.62 (define @t150 () (tptp.in @t147 @t2)) % 0.43/0.62 (define @t151 () (not (tptp.element @t147 @t1))) % 0.43/0.62 (define @t152 () (not @t27)) % 0.43/0.62 (define @t153 () (or @t152 @t151 @t150 @t149)) % 0.43/0.62 (define @t154 () (@list @t2 @t147)) % 0.43/0.62 (define @t155 () (forall @t154 @t153)) % 0.43/0.62 (define @t156 () (or @t151 @t150 @t149)) % 0.43/0.62 (define @t157 () (or @t152 @t156)) % 0.43/0.62 (define @t158 () (forall @t154 @t157)) % 0.43/0.62 (define @t159 () (@list @t147)) % 0.43/0.62 (define @t160 () (forall @t159 @t157)) % 0.43/0.62 (define @t161 () (forall @t159 @t156)) % 0.43/0.62 (define @t162 () (or @t152 @t161)) % 0.43/0.62 (define @t163 () (not @t55)) % 0.43/0.62 (define @t164 () (or @t163 @t41 @t53)) % 0.43/0.62 (define @t165 () (forall @t46 @t164)) % 0.43/0.62 (define @t166 () (or (= @t111 tptp.empty_set) @t117 @t115 @t108 @t112)) % 0.43/0.62 (define @t167 () (forall @t142 @t139)) % 0.43/0.62 (define @t168 () (or @t128 @t117 @t115 @t108 @t112)) % 0.43/0.62 (define @t169 () (or @t117 @t124 @t109)) % 0.43/0.62 (define @t170 () (not @t169)) % 0.43/0.62 (define @t171 () (forall @t35 @t70)) % 0.43/0.62 (assume @p1 (forall @t3 (tptp.subset @t1 @t1))) % 0.43/0.62 (assume @p2 (forall @t13 (=> @t12 (exists @t8 (and @t7 (not @t4)))))) % 0.43/0.62 (assume @p3 (forall @t13 (=> @t15 @t14))) % 0.43/0.62 (assume @p4 (forall @t13 (=> @t14 @t16))) % 0.43/0.62 (assume @p5 (forall @t13 (=> @t16 @t17))) % 0.43/0.62 (assume @p6 (forall @t13 (=> @t17 @t18))) % 0.43/0.62 (assume @p7 (exists @t13 (and (not @t19) @t18 @t17 @t16 @t14 @t15))) % 0.43/0.62 (assume @p8 (forall @t13 (=> @t18 (forall @t8 (=> @t21 @t20))))) % 0.43/0.62 (assume @p9 (forall @t13 (=> @t17 (forall @t8 (=> @t21 (and @t20 @t22)))))) % 0.43/0.62 (assume @p10 (forall @t13 (=> @t16 (forall @t8 (=> @t21 (and @t20 @t22 @t23)))))) % 0.43/0.62 (assume @p11 (forall @t13 (=> @t14 (forall @t8 (=> @t21 (and @t20 @t22 @t24 @t23)))))) % 0.43/0.62 (assume @p12 (forall @t13 (=> @t15 (forall @t8 (=> @t21 (and @t20 (tptp.natural @t2) @t22 @t24 @t23)))))) % 0.43/0.62 (assume @p13 (forall @t13 (=> @t19 (and @t18 @t17 @t16 @t14 @t15)))) % 0.43/0.62 (assume @p14 (forall @t13 (=> @t18 (forall @t8 (=> @t27 @t25))))) % 0.43/0.62 (assume @p15 (forall @t13 (=> @t17 (forall @t8 (=> @t27 (and @t25 @t28)))))) % 0.43/0.62 (assume @p16 (forall @t13 (=> @t16 (forall @t8 (=> @t27 (and @t25 @t28 @t29)))))) % 0.43/0.62 (assume @p17 (forall @t13 (=> @t14 (forall @t8 (=> @t27 (and @t25 @t28 @t29 @t30)))))) % 0.43/0.62 (assume @p18 (forall @t13 (=> @t15 (forall @t8 (=> @t27 (and @t25 @t28 @t29 @t30 (tptp.v5_membered @t2))))))) % 0.43/0.62 (assume @p19 (forall @t3 (=> @t32 (or @t4 @t31)))) % 0.43/0.62 (assume @p20 (forall @t35 (not (and @t31 @t34 (tptp.empty @t33))))) % 0.43/0.62 (assume @p21 (forall @t3 (not (and @t19 (not (= @t1 @t2)) @t4)))) % 0.43/0.62 (assume @p22 (forall @t3 (=> @t27 (= (tptp.subset_complement @t1 @t36) @t2)))) % 0.43/0.62 (assume @p23 (forall @t3 (=> @t31 (not (tptp.in @t2 @t1))))) % 0.43/0.62 (assume @p24 (exists @t13 @t9)) % 0.43/0.62 (assume @p25 (forall @t13 (exists @t8 @t21))) % 0.43/0.62 (assume @p26 true) % 0.43/0.62 (assume @p27 (forall @t3 (=> @t27 (tptp.element @t36 @t26)))) % 0.43/0.62 (assume @p28 (exists @t13 (and @t9 @t11))) % 0.43/0.62 (assume @p29 @t38) % 0.43/0.62 (assume @p30 (and @t39 (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))) % 0.43/0.62 (assume @p31 (forall @t3 (=> @t31 @t32))) % 0.43/0.62 (assume @p32 (forall @t3 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2)))) % 0.43/0.62 (assume @p33 (forall @t35 (=> (and @t31 @t34) (tptp.element @t1 @t33)))) % 0.43/0.62 (assume @p34 (forall @t13 (=> @t19 @t40))) % 0.43/0.62 (assume @p35 (forall @t3 (not (and @t31 @t4)))) % 0.43/0.62 (assume @p36 @t52) % 0.43/0.62 (assume @p37 @t61) % 0.43/0.62 (assume @p38 @t66) % 0.43/0.62 (step @p39 :rule aci_norm :args ((= (or @t69 (or @t68 @t67)) @t70))) % 0.43/0.62 (step @p40 :rule bool-and-de-morgan :args (@t63 @t62 true)) % 0.43/0.62 (step @p41 :rule refl :args (@t69)) % 0.43/0.62 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or @t69 @t64))) % 0.43/0.62 (step @p43 :rule trans :premises (@p42 @p39)) % 0.43/0.62 (step @p44 :rule bool-impl-elim :args (@t65 @t64)) % 0.43/0.62 (step @p45 :rule trans :premises (@p44 @p43)) % 0.43/0.62 (step @p46 :rule cong :premises (@p45) :args (@t66)) % 0.43/0.62 (step @p47 :rule eq_resolve :premises (@p38 @p46)) % 0.43/0.62 (step @p48 :rule aci_norm :args ((= @t79 @t77))) % 0.43/0.62 (step @p49 :rule cong :premises (@p48) :args (@t81)) % 0.43/0.62 (step @p50 :rule quant-merge-prenex :args ((= (forall @t13 @t83) @t81))) % 0.43/0.62 (step @p51 :rule alpha_equiv :args (@t84 (@list @t71 @t72) (@list @t2 @t85))) % 0.43/0.62 (step @p52 :rule refl :args (@t76)) % 0.43/0.62 (step @p53 :rule refl :args (@t10)) % 0.43/0.62 (step @p54 :rule nary_cong :premises (@p53 @p52 @p51) :args (@t86)) % 0.43/0.62 (step @p55 :rule quant-miniscope-or :args ((= @t83 @t86))) % 0.43/0.62 (step @p56 :rule trans :premises (@p55 @p54)) % 0.43/0.62 (step @p57 :rule symm :premises (@p56)) % 0.43/0.62 (step @p58 :rule cong :premises (@p57) :args ((forall @t13 @t93))) % 0.43/0.62 (step @p59 :rule trans :premises (@p58 @p50)) % 0.43/0.62 (step @p60 :rule trans :premises (@p59 @p49)) % 0.43/0.62 (step @p61 :rule aci_norm :args ((= (or @t94 @t92) @t93))) % 0.43/0.62 (step @p62 :rule refl :args (@t92)) % 0.43/0.62 (step @p63 :rule bool-double-not-elim :args (@t10)) % 0.43/0.62 (step @p64 :rule nary_cong :premises (@p63 @p52) :args ((or (not @t11) @t76))) % 0.43/0.62 (step @p65 :rule bool-and-de-morgan :args (@t11 @t9 true)) % 0.43/0.62 (step @p66 :rule trans :premises (@p65 @p64)) % 0.43/0.62 (step @p67 :rule nary_cong :premises (@p66 @p62) :args ((or @t95 @t92))) % 0.43/0.62 (step @p68 :rule trans :premises (@p67 @p61)) % 0.43/0.62 (step @p69 :rule bool-impl-elim :args (@t12 @t92)) % 0.43/0.62 (step @p70 :rule trans :premises (@p69 @p68)) % 0.43/0.62 (step @p71 :rule cong :premises (@p70) :args ((forall @t13 (=> @t12 @t92)))) % 0.43/0.62 (step @p72 :rule trans :premises (@p71 @p60)) % 0.43/0.62 (step @p73 :rule aci_norm :args ((= @t97 @t90))) % 0.43/0.62 (step @p74 :rule cong :premises (@p73) :args (@t98)) % 0.43/0.62 (step @p75 :rule quant-merge-prenex :args ((= (forall @t8 @t100) @t98))) % 0.43/0.62 (step @p76 :rule alpha_equiv :args (@t101 (@list @t85) @t102)) % 0.43/0.62 (step @p77 :rule refl :args (@t89)) % 0.43/0.62 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t103)) % 0.43/0.62 (step @p79 :rule quant-miniscope-or :args ((= @t100 @t103))) % 0.43/0.62 (step @p80 :rule trans :premises (@p79 @p78)) % 0.43/0.62 (step @p81 :rule symm :premises (@p80)) % 0.43/0.62 (step @p82 :rule cong :premises (@p81) :args ((forall @t8 (or @t89 @t104)))) % 0.43/0.62 (step @p83 :rule trans :premises (@p82 @p75)) % 0.43/0.62 (step @p84 :rule trans :premises (@p83 @p74)) % 0.43/0.62 (step @p85 :rule bool-impl-elim :args (@t7 @t104)) % 0.43/0.62 (step @p86 :rule cong :premises (@p85) :args ((forall @t8 (=> @t7 @t104)))) % 0.43/0.62 (step @p87 :rule trans :premises (@p86 @p84)) % 0.43/0.62 (step @p88 :rule bool-impl-elim :args (@t45 @t44)) % 0.43/0.62 (step @p89 :rule cong :premises (@p88) :args (@t47)) % 0.43/0.62 (step @p90 :rule refl :args (@t7)) % 0.43/0.62 (step @p91 :rule cong :premises (@p90 @p89) :args (@t48)) % 0.43/0.62 (step @p92 :rule cong :premises (@p91) :args (@t49)) % 0.43/0.62 (step @p93 :rule trans :premises (@p92 @p87)) % 0.43/0.62 (step @p94 :rule refl :args (@t12)) % 0.43/0.62 (step @p95 :rule cong :premises (@p94 @p93) :args (@t50)) % 0.43/0.62 (step @p96 :rule cong :premises (@p95) :args (@t51)) % 0.43/0.62 (step @p97 :rule trans :premises (@p96 @p72)) % 0.43/0.62 (step @p98 :rule cong :premises (@p97) :args (@t52)) % 0.43/0.62 (step @p99 :rule eq_resolve :premises (@p36 @p98)) % 0.43/0.62 (step @p100 :rule skolemize :premises (@p99)) % 0.43/0.62 (step @p101 :rule cnf_or_neg :args (@t121 4)) % 0.43/0.62 (step @p102 :rule chain_m_resolution :premises (@p101 @p100) :args ((not @t113) @t122 @t123)) % 0.43/0.62 (step @p103 :rule bool-double-not-elim :args (@t108)) % 0.43/0.62 (step @p104 :rule refl :args (@t124)) % 0.43/0.62 (step @p105 :rule refl :args (@t113)) % 0.43/0.62 (step @p106 :rule nary_cong :premises (@p105 @p104 @p103) :args ((or @t113 @t124 (not @t109)))) % 0.43/0.62 (step @p107 :rule cnf_equiv_neg2 :args (@t113)) % 0.43/0.62 (step @p108 :rule eq_resolve :premises (@p107 @p106)) % 0.43/0.62 (step @p109 :rule reordering :premises (@p108) :args ((or @t108 @t113 @t124))) % 0.43/0.62 (step @p110 :rule bool-double-not-elim :args (@t116)) % 0.43/0.62 (step @p111 :rule refl :args (@t121)) % 0.43/0.62 (step @p112 :rule nary_cong :premises (@p111 @p110) :args ((or @t121 (not @t117)))) % 0.43/0.62 (step @p113 :rule cnf_or_neg :args (@t121 2)) % 0.43/0.62 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 0.43/0.62 (step @p115 :rule 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:rule trans :premises (@p127 @p126)) % 0.43/0.62 (step @p129 :rule cong :premises (@p128) :args (@t38)) % 0.43/0.62 (step @p130 :rule eq_resolve :premises (@p29 @p129)) % 0.43/0.62 (step @p131 :rule instantiate :premises (@p130) :args ((@list @t110))) % 0.43/0.62 (step @p132 :rule bool-double-not-elim :args (@t118)) % 0.43/0.62 (step @p133 :rule nary_cong :premises (@p111 @p132) :args ((or @t121 (not @t119)))) % 0.43/0.62 (step @p134 :rule cnf_or_neg :args (@t121 1)) % 0.43/0.62 (step @p135 :rule eq_resolve :premises (@p134 @p133)) % 0.43/0.62 (step @p136 :rule reordering :premises (@p135) :args ((or @t118 @t121))) % 0.43/0.62 (step @p137 :rule chain_m_resolution :premises (@p136 @p100) :args (@t118 @t122 @t123)) % 0.43/0.62 (step @p138 :rule cnf_or_neg :args (@t121 0)) % 0.43/0.62 (step @p139 :rule chain_m_resolution :premises (@p138 @p100) :args ((not @t120) @t122 @t123)) % 0.43/0.62 (step @p140 :rule cnf_or_pos :args (@t127)) % 0.43/0.62 (step @p141 :rule reordering :premises (@p140) :args ((or @t120 @t119 @t126 (not @t127)))) % 0.43/0.62 (step @p142 :rule chain_m_resolution :premises (@p141 @p139 @p137 @p131) :args (@t126 (@list true false false) (@list @t120 @t118 @t127))) % 0.43/0.62 (step @p143 :rule and_elim :premises (@p30) :args (0)) % 0.43/0.62 (step @p144 :rule refl :args (@t129)) % 0.43/0.62 (step @p145 :rule bool-double-not-elim :args (@t125)) % 0.43/0.62 (step @p146 :rule refl :args (@t130)) % 0.43/0.62 (step @p147 :rule nary_cong :premises (@p146 @p145 @p144) :args ((or @t130 (not @t126) @t129))) % 0.43/0.62 (assume-push @p261 @t39) % 0.43/0.62 (assume-push @p262 @t128) % 0.43/0.62 (assume-push @p263 @t126) % 0.43/0.62 (step @p151 :rule evaluate :args ((= false true))) % 0.43/0.62 (step @p152 :rule true_intro :premises (@p143)) % 0.43/0.62 (step @p153 :rule symm :premises (@p262)) % 0.43/0.62 (step @p154 :rule cong :premises (@p153) :args (@t125)) % 0.43/0.62 (step @p155 :rule false_intro :premises (@p142)) % 0.43/0.62 (step @p156 :rule symm :premises (@p155)) % 0.43/0.62 (step @p157 :rule trans :premises (@p156 @p154 @p152)) % 0.43/0.62 (step @p158 false :rule eq_resolve :premises (@p157 @p151)) % 0.43/0.62 (step-pop @p264 :rule scope :premises (@p158)) % 0.43/0.62 (step-pop @p265 :rule scope :premises (@p264)) % 0.43/0.62 (step-pop @p266 :rule scope :premises (@p265)) % 0.43/0.62 (step @p159 :rule process_scope :premises (@p266) :args (false)) % 0.43/0.62 (assume-push @p267 @t39) % 0.43/0.62 (assume-push @p268 @t126) % 0.43/0.62 (assume-push @p269 @t128) % 0.43/0.62 (step @p166 :rule and_intro :premises (@p143 @p269 @p142)) % 0.43/0.62 (step-pop @p270 :rule scope :premises (@p166)) % 0.43/0.62 (step-pop @p271 :rule scope :premises (@p270)) % 0.43/0.62 (step-pop @p272 :rule scope :premises (@p271)) % 0.43/0.62 (step @p167 :rule process_scope :premises (@p272) :args (@t131)) % 0.43/0.62 (step @p171 :rule implies_elim :premises (@p167)) % 0.43/0.62 (step @p172 :rule resolution :premises (@p171 @p159) :args (true @t131)) % 0.43/0.62 (step @p173 :rule not_and :premises (@p172)) % 0.43/0.62 (step @p174 :rule eq_resolve :premises (@p173 @p147)) % 0.43/0.62 (step @p175 :rule chain_m_resolution :premises (@p174 @p143 @p142) :args (@t129 @t132 (@list @t39 @t125))) % 0.43/0.62 (step @p176 :rule aci_norm :args ((= @t141 @t139))) % 0.43/0.62 (step @p177 :rule cong :premises (@p176) :args (@t143)) % 0.43/0.62 (step @p178 :rule quant-merge-prenex :args ((= (forall @t13 @t145) @t143))) % 0.43/0.62 (step @p179 :rule alpha_equiv :args (@t146 (@list @t133 @t134) (@list @t2 @t147))) % 0.43/0.62 (step @p180 :rule refl :args (@t40)) % 0.43/0.62 (step @p181 :rule nary_cong :premises (@p180 @p179) :args (@t148)) % 0.43/0.62 (step @p182 :rule quant-miniscope-or :args ((= @t145 @t148))) % 0.43/0.62 (step @p183 :rule trans :premises (@p182 @p181)) % 0.43/0.62 (step @p184 :rule symm :premises (@p183)) % 0.43/0.62 (step @p185 :rule cong :premises (@p184) :args ((forall @t13 (or @t40 @t155)))) % 0.43/0.62 (step @p186 :rule trans 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% 0.43/0.62 (step @p201 :rule quant-miniscope-or :args ((= @t160 @t162))) % 0.43/0.62 (step @p202 :rule trans :premises (@p201 @p200)) % 0.43/0.62 (step @p203 :rule symm :premises (@p202)) % 0.43/0.62 (step @p204 :rule cong :premises (@p203) :args ((forall @t8 (or @t152 @t165)))) % 0.43/0.62 (step @p205 :rule trans :premises (@p204 @p197)) % 0.43/0.62 (step @p206 :rule trans :premises (@p205 @p196)) % 0.43/0.62 (step @p207 :rule bool-impl-elim :args (@t27 @t165)) % 0.43/0.62 (step @p208 :rule cong :premises (@p207) :args ((forall @t8 (=> @t27 @t165)))) % 0.43/0.62 (step @p209 :rule trans :premises (@p208 @p206)) % 0.43/0.62 (step @p210 :rule aci_norm :args ((= (or @t163 (or @t41 @t53)) @t164))) % 0.43/0.62 (step @p211 :rule refl :args (@t53)) % 0.43/0.62 (step @p212 :rule bool-double-not-elim :args (@t41)) % 0.43/0.62 (step @p213 :rule nary_cong :premises (@p212 @p211) :args ((or (not @t42) @t53))) % 0.43/0.62 (step @p214 :rule bool-impl-elim :args (@t42 @t53)) % 0.43/0.62 (step @p215 :rule trans :premises (@p214 @p213)) % 0.43/0.62 (step @p216 :rule refl :args (@t163)) % 0.43/0.62 (step @p217 :rule nary_cong :premises (@p216 @p215) :args ((or @t163 @t54))) % 0.43/0.62 (step @p218 :rule trans :premises (@p217 @p210)) % 0.43/0.62 (step @p219 :rule bool-impl-elim :args (@t55 @t54)) % 0.43/0.62 (step @p220 :rule trans :premises (@p219 @p218)) % 0.43/0.62 (step @p221 :rule cong :premises (@p220) :args (@t56)) % 0.43/0.62 (step @p222 :rule refl :args (@t27)) % 0.43/0.62 (step @p223 :rule cong :premises (@p222 @p221) :args (@t57)) % 0.43/0.62 (step @p224 :rule cong :premises (@p223) :args (@t58)) % 0.43/0.62 (step @p225 :rule trans :premises (@p224 @p209)) % 0.43/0.62 (step @p226 :rule refl :args (@t59)) % 0.43/0.62 (step @p227 :rule cong :premises (@p226 @p225) :args (@t60)) % 0.43/0.62 (step @p228 :rule cong :premises (@p227) :args (@t61)) % 0.43/0.62 (step @p229 :rule trans :premises (@p228 @p194)) % 0.43/0.62 (step @p230 :rule eq_resolve :premises (@p37 @p229)) % 0.43/0.62 (step @p231 :rule refl :args (@t112)) % 0.43/0.62 (step @p232 :rule refl :args (@t108)) % 0.43/0.62 (step @p233 :rule refl :args (@t115)) % 0.43/0.62 (step @p234 :rule refl :args (@t117)) % 0.43/0.62 (step @p235 :rule eq-symm :args (@t111 tptp.empty_set)) % 0.43/0.62 (step @p236 :rule nary_cong :premises (@p235 @p234 @p233 @p232 @p231) :args (@t166)) % 0.43/0.62 (step @p237 :rule refl :args (@t167)) % 0.43/0.62 (step @p238 :rule cong :premises (@p237 @p236) :args ((=> @t167 @t166))) % 0.43/0.62 (assume-push @p273 @t167) % 0.43/0.62 (step @p240 :rule instantiate :premises (@p230) :args ((@list @t111 @t106 @t107))) % 0.43/0.62 (step-pop @p274 :rule scope :premises (@p240)) % 0.43/0.62 (step @p241 :rule process_scope :premises (@p274) :args (@t166)) % 0.43/0.62 (step @p243 :rule eq_resolve :premises (@p241 @p238)) % 0.43/0.62 (step @p244 :rule implies_elim :premises (@p243)) % 0.43/0.62 (step @p245 :rule chain_m_resolution :premises (@p244 @p230) :args (@t168 (@list false) (@list @t167))) % 0.43/0.62 (step @p246 :rule cnf_or_pos :args (@t168)) % 0.43/0.62 (step @p247 :rule reordering :premises (@p246) :args ((or @t117 @t115 @t112 @t108 @t128 (not @t168)))) % 0.43/0.62 (step @p248 :rule chain_m_resolution :premises (@p247 @p245 @p175 @p122 @p116 @p109 @p102) :args (@t108 (@list false true false false true true) (@list @t168 @t128 @t114 @t116 @t112 @t113))) % 0.43/0.62 (step @p249 :rule cnf_equiv_neg1 :args (@t113)) % 0.43/0.62 (step @p250 :rule reordering :premises (@p249) :args ((or @t112 @t109 @t113))) % 0.43/0.62 (step @p251 :rule chain_m_resolution :premises (@p250 @p248 @p102) :args (@t112 @t132 (@list @t108 @t113))) % 0.43/0.62 (step @p252 :rule cnf_or_pos :args (@t169)) % 0.43/0.62 (step @p253 :rule reordering :premises (@p252) :args ((or @t117 @t109 @t124 @t170))) % 0.43/0.62 (step @p254 :rule chain_m_resolution :premises (@p253 @p116 @p248 @p251) :args (@t170 (@list false false false) (@list @t116 @t108 @t112))) % 0.43/0.62 (assume-push @p275 @t171) % 0.43/0.62 (step @p256 :rule instantiate :premises (@p47) :args ((@list @t111 @t107 @t106))) % 0.43/0.62 (step-pop @p276 :rule scope :premises (@p256)) % 0.43/0.62 (step @p257 :rule process_scope :premises (@p276) :args (@t169)) % 0.43/0.62 (step @p259 :rule implies_elim :premises (@p257)) % 0.43/0.62 (step @p260 false :rule chain_m_resolution :premises (@p259 @p254 @p47) :args (false (@list true false) (@list @t169 @t171))) % 0.43/0.62 ) % 0.43/0.62 % SZS output end Proof % 0.43/0.62 % cvc5 exiting %------------------------------------------------------------------------------