%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET776+4 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n019.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 08:48:37 AM UTC 2026 % Result : Theorem 0.38s 0.60s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SET776+4 : TPTP v9.2.1. Released v2.2.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n019.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 16:11:49 EDT 2026 % 0.19/0.35 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.60 % SZS status Theorem % 0.38/0.60 % SZS output start Proof % 0.38/0.60 ( % 0.38/0.60 (declare-sort $$unsorted 0) % 0.38/0.60 (declare-const tptp.pre_order (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.equivalence (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.equivalence_class (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.empty_set $$unsorted) % 0.38/0.60 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.partition (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.60 (define @t1 () (@var "B" $$unsorted)) % 0.38/0.60 (define @t2 () (@var "X" $$unsorted)) % 0.38/0.60 (define @t3 () (tptp.member @t2 @t1)) % 0.38/0.60 (define @t4 () (@var "A" $$unsorted)) % 0.38/0.60 (define @t5 () (tptp.member @t2 @t4)) % 0.38/0.60 (define @t6 () (@list @t2)) % 0.38/0.60 (define @t7 () (tptp.subset @t4 @t1)) % 0.38/0.60 (define @t8 () (@list @t4 @t1)) % 0.38/0.60 (define @t9 () (@list @t2 @t4)) % 0.38/0.60 (define @t10 () (and @t5 @t3)) % 0.38/0.60 (define @t11 () (@list @t2 @t4 @t1)) % 0.38/0.60 (define @t12 () (@var "E" $$unsorted)) % 0.38/0.60 (define @t13 () (tptp.member @t1 @t12)) % 0.38/0.60 (define @t14 () (= @t2 @t4)) % 0.38/0.60 (define @t15 () (@var "Y" $$unsorted)) % 0.38/0.60 (define @t16 () (tptp.member @t2 @t15)) % 0.38/0.60 (define @t17 () (tptp.member @t15 @t4)) % 0.38/0.60 (define @t18 () (@list @t15)) % 0.38/0.60 (define @t19 () (exists @t18 (and @t17 @t16))) % 0.38/0.60 (define @t20 () (@var "Z" $$unsorted)) % 0.38/0.60 (define @t21 () (and @t5 @t17)) % 0.38/0.60 (define @t22 () (@list @t2 @t15)) % 0.38/0.60 (define @t23 () (tptp.member @t2 @t12)) % 0.38/0.60 (define @t24 () (@var "R" $$unsorted)) % 0.38/0.60 (define @t25 () (tptp.apply @t24 @t2 @t20)) % 0.38/0.60 (define @t26 () (tptp.apply @t24 @t15 @t20)) % 0.38/0.60 (define @t27 () (tptp.apply @t24 @t2 @t15)) % 0.38/0.60 (define @t28 () (and @t27 @t26)) % 0.38/0.60 (define @t29 () (=> @t28 @t25)) % 0.38/0.60 (define @t30 () (@list @t2 @t15 @t20)) % 0.38/0.60 (define @t31 () (tptp.apply @t24 @t2 @t2)) % 0.38/0.60 (define @t32 () (tptp.member @t20 @t12)) % 0.38/0.60 (define @t33 () (tptp.member @t15 @t12)) % 0.38/0.60 (define @t34 () (and @t23 @t33 @t32)) % 0.38/0.60 (define @t35 () (forall @t30 (=> @t34 @t29))) % 0.38/0.60 (define @t36 () (forall @t6 (=> @t23 @t31))) % 0.38/0.60 (define @t37 () (and @t36 @t35)) % 0.38/0.60 (define @t38 () (tptp.pre_order @t24 @t12)) % 0.38/0.60 (define @t39 () (= @t38 @t37)) % 0.38/0.60 (define @t40 () (forall (@list @t24 @t12) @t39)) % 0.38/0.60 (define @t41 () (@var "Y2" $$unsorted)) % 0.38/0.60 (define @t42 () (@var "Y1" $$unsorted)) % 0.38/0.60 (define @t43 () (@var "P" $$unsorted)) % 0.38/0.60 (define @t44 () (tptp.apply @t43 @t42 @t41)) % 0.38/0.60 (define @t45 () (@var "X2" $$unsorted)) % 0.38/0.60 (define @t46 () (@var "X1" $$unsorted)) % 0.38/0.60 (define @t47 () (tptp.apply @t43 @t46 @t45)) % 0.38/0.60 (define @t48 () (tptp.apply @t24 @t45 @t41)) % 0.38/0.60 (define @t49 () (tptp.apply @t24 @t46 @t42)) % 0.38/0.60 (define @t50 () (and @t49 @t48 @t47)) % 0.38/0.60 (define @t51 () (=> @t50 @t44)) % 0.38/0.60 (define @t52 () (tptp.member @t41 @t12)) % 0.38/0.60 (define @t53 () (tptp.member @t42 @t12)) % 0.38/0.60 (define @t54 () (tptp.member @t45 @t12)) % 0.38/0.60 (define @t55 () (tptp.member @t46 @t12)) % 0.38/0.60 (define @t56 () (and @t55 @t54 @t53 @t52)) % 0.38/0.60 (define @t57 () (@list @t46 @t45 @t42 @t41)) % 0.38/0.60 (define @t58 () (forall @t57 (=> @t56 @t51))) % 0.38/0.60 (define @t59 () (= (tptp.apply @t24 @t4 @t1) (and (tptp.apply @t43 @t4 @t1) (tptp.apply @t43 @t1 @t4)))) % 0.38/0.60 (define @t60 () (tptp.member @t4 @t12)) % 0.38/0.60 (define @t61 () (and @t60 @t13)) % 0.38/0.60 (define @t62 () (forall @t8 (=> @t61 @t59))) % 0.38/0.60 (define @t63 () (tptp.pre_order @t43 @t12)) % 0.38/0.60 (define @t64 () (and @t63 @t62)) % 0.38/0.60 (define @t65 () (=> @t64 @t58)) % 0.38/0.60 (define @t66 () (@list @t12 @t43 @t24)) % 0.38/0.60 (define @t67 () (forall @t66 @t65)) % 0.38/0.60 (define @t68 () (not @t67)) % 0.38/0.60 (define @t69 () (not @t26)) % 0.38/0.60 (define @t70 () (not @t27)) % 0.38/0.60 (define @t71 () (not @t32)) % 0.38/0.60 (define @t72 () (not @t33)) % 0.38/0.60 (define @t73 () (not @t23)) % 0.38/0.60 (define @t74 () (or @t70 @t69 @t25)) % 0.38/0.60 (define @t75 () (or @t73 @t72 @t71)) % 0.38/0.60 (define @t76 () (@var "BOUND_VARIABLE_7755" $$unsorted)) % 0.38/0.60 (define @t77 () (@var "BOUND_VARIABLE_7753" $$unsorted)) % 0.38/0.60 (define @t78 () (tptp.apply @t43 @t77 @t76)) % 0.38/0.60 (define @t79 () (@var "BOUND_VARIABLE_7751" $$unsorted)) % 0.38/0.60 (define @t80 () (@var "BOUND_VARIABLE_7749" $$unsorted)) % 0.38/0.60 (define @t81 () (not (tptp.apply @t43 @t80 @t79))) % 0.38/0.60 (define @t82 () (not (tptp.apply @t24 @t79 @t76))) % 0.38/0.60 (define @t83 () (not (tptp.apply @t24 @t80 @t77))) % 0.38/0.60 (define @t84 () (not (tptp.member @t76 @t12))) % 0.38/0.60 (define @t85 () (not (tptp.member @t77 @t12))) % 0.38/0.60 (define @t86 () (not (tptp.member @t79 @t12))) % 0.38/0.60 (define @t87 () (not (tptp.member @t80 @t12))) % 0.38/0.60 (define @t88 () (not @t13)) % 0.38/0.60 (define @t89 () (not @t60)) % 0.38/0.60 (define @t90 () (or @t89 @t88 @t59)) % 0.38/0.60 (define @t91 () (forall @t8 @t90)) % 0.38/0.60 (define @t92 () (not @t91)) % 0.38/0.60 (define @t93 () (not @t63)) % 0.38/0.60 (define @t94 () (or @t93 @t92 @t87 @t86 @t85 @t84 @t83 @t82 @t81 @t78)) % 0.38/0.60 (define @t95 () (@list @t12 @t43 @t24 @t80 @t79 @t77 @t76)) % 0.38/0.60 (define @t96 () (forall @t95 @t94)) % 0.38/0.60 (define @t97 () (@quantifiers_skolemize @t96 0)) % 0.38/0.60 (define @t98 () (@quantifiers_skolemize @t96 1)) % 0.38/0.60 (define @t99 () (or @t87 @t86 @t85 @t84 @t83 @t82 @t81 @t78)) % 0.38/0.60 (define @t100 () (or @t93 @t92 @t99)) % 0.38/0.60 (define @t101 () (forall @t95 @t100)) % 0.38/0.60 (define @t102 () (@list @t80 @t79 @t77 @t76)) % 0.38/0.60 (define @t103 () (forall @t102 @t100)) % 0.38/0.60 (define @t104 () (forall @t102 @t99)) % 0.38/0.60 (define @t105 () (or @t93 @t92 @t104)) % 0.38/0.60 (define @t106 () (not @t47)) % 0.38/0.60 (define @t107 () (not @t48)) % 0.38/0.60 (define @t108 () (not @t49)) % 0.38/0.60 (define @t109 () (not @t52)) % 0.38/0.60 (define @t110 () (not @t53)) % 0.38/0.60 (define @t111 () (not @t54)) % 0.38/0.60 (define @t112 () (not @t55)) % 0.38/0.60 (define @t113 () (or @t112 @t111 @t110 @t109 @t108 @t107 @t106 @t44)) % 0.38/0.60 (define @t114 () (forall @t57 @t113)) % 0.38/0.60 (define @t115 () (or @t93 @t92 @t114)) % 0.38/0.60 (define @t116 () (and @t63 @t91)) % 0.38/0.60 (define @t117 () (or @t108 @t107 @t106 @t44)) % 0.38/0.60 (define @t118 () (or @t112 @t111 @t110 @t109)) % 0.38/0.60 (define @t119 () (or @t108 @t107 @t106)) % 0.38/0.60 (define @t120 () (tptp.pre_order @t98 @t97)) % 0.38/0.60 (define @t121 () (@quantifiers_skolemize @t96 6)) % 0.38/0.60 (define @t122 () (@quantifiers_skolemize @t96 5)) % 0.38/0.60 (define @t123 () (tptp.apply @t98 @t122 @t121)) % 0.38/0.60 (define @t124 () (@quantifiers_skolemize @t96 4)) % 0.38/0.60 (define @t125 () (@quantifiers_skolemize @t96 3)) % 0.38/0.60 (define @t126 () (tptp.apply @t98 @t125 @t124)) % 0.38/0.60 (define @t127 () (not @t126)) % 0.38/0.60 (define @t128 () (@quantifiers_skolemize @t96 2)) % 0.38/0.60 (define @t129 () (tptp.apply @t128 @t124 @t121)) % 0.38/0.60 (define @t130 () (not @t129)) % 0.38/0.60 (define @t131 () (tptp.apply @t128 @t125 @t122)) % 0.38/0.60 (define @t132 () (not @t131)) % 0.38/0.60 (define @t133 () (tptp.member @t121 @t97)) % 0.38/0.60 (define @t134 () (not @t133)) % 0.38/0.60 (define @t135 () (tptp.member @t122 @t97)) % 0.38/0.60 (define @t136 () (not @t135)) % 0.38/0.60 (define @t137 () (tptp.member @t124 @t97)) % 0.38/0.60 (define @t138 () (not @t137)) % 0.38/0.60 (define @t139 () (tptp.member @t125 @t97)) % 0.38/0.60 (define @t140 () (not @t139)) % 0.38/0.60 (define @t141 () (forall @t8 (or (not (tptp.member @t4 @t97)) (not (tptp.member @t1 @t97)) (= (tptp.apply @t128 @t4 @t1) (and (tptp.apply @t98 @t4 @t1) (tptp.apply @t98 @t1 @t4)))))) % 0.38/0.60 (define @t142 () (not @t141)) % 0.38/0.60 (define @t143 () (not @t120)) % 0.38/0.60 (define @t144 () (or @t143 @t142 @t140 @t138 @t136 @t134 @t132 @t130 @t127 @t123)) % 0.38/0.60 (define @t145 () (@list true)) % 0.38/0.60 (define @t146 () (@list @t144)) % 0.38/0.60 (define @t147 () (not (tptp.member @t2 @t97))) % 0.38/0.60 (define @t148 () (forall @t30 (or @t147 (not (tptp.member @t15 @t97)) (not (tptp.member @t20 @t97)) (not (tptp.apply @t98 @t2 @t15)) (not (tptp.apply @t98 @t15 @t20)) (tptp.apply @t98 @t2 @t20)))) % 0.38/0.60 (define @t149 () (and (forall @t6 (or @t147 (tptp.apply @t98 @t2 @t2))) @t148)) % 0.38/0.60 (define @t150 () (= @t120 @t149)) % 0.38/0.60 (define @t151 () (@list false false)) % 0.38/0.60 (define @t152 () (@list false)) % 0.38/0.60 (define @t153 () (tptp.apply @t98 @t124 @t121)) % 0.38/0.60 (define @t154 () (and @t153 (tptp.apply @t98 @t121 @t124))) % 0.38/0.60 (define @t155 () (= @t129 @t154)) % 0.38/0.60 (define @t156 () (or @t138 @t134 @t155)) % 0.38/0.60 (define @t157 () (@list false false false)) % 0.38/0.60 (define @t158 () (tptp.apply @t98 @t125 @t121)) % 0.38/0.60 (define @t159 () (not @t153)) % 0.38/0.60 (define @t160 () (or @t140 @t138 @t134 @t127 @t159 @t158)) % 0.38/0.60 (define @t161 () (tptp.apply @t98 @t122 @t125)) % 0.38/0.60 (define @t162 () (and (tptp.apply @t98 @t125 @t122) @t161)) % 0.38/0.60 (define @t163 () (= @t131 @t162)) % 0.38/0.60 (define @t164 () (or @t140 @t136 @t163)) % 0.38/0.60 (define @t165 () (not @t158)) % 0.38/0.60 (define @t166 () (not @t161)) % 0.38/0.60 (define @t167 () (or @t136 @t140 @t134 @t166 @t165 @t123)) % 0.38/0.60 (define @t168 () (not @t167)) % 0.38/0.60 (assume @p1 (forall @t8 (= @t7 (forall @t6 (=> @t5 @t3))))) % 0.38/0.60 (assume @p2 (forall @t8 (= (tptp.equal_set @t4 @t1) (and @t7 (tptp.subset @t1 @t4))))) % 0.38/0.60 (assume @p3 (forall @t9 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.38/0.60 (assume @p4 (forall @t11 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) @t10))) % 0.38/0.60 (assume @p5 (forall @t11 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.38/0.60 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.38/0.60 (assume @p7 (forall (@list @t1 @t4 @t12) (= (tptp.member @t1 (tptp.difference @t12 @t4)) (and @t13 (not (tptp.member @t1 @t4)))))) % 0.38/0.60 (assume @p8 (forall @t9 (= (tptp.member @t2 (tptp.singleton @t4)) @t14))) % 0.38/0.60 (assume @p9 (forall @t11 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t14 (= @t2 @t1))))) % 0.38/0.60 (assume @p10 (forall @t9 (= (tptp.member @t2 (tptp.sum @t4)) @t19))) % 0.38/0.60 (assume @p11 (forall @t9 (= (tptp.member @t2 (tptp.product @t4)) (forall @t18 (=> @t17 @t16))))) % 0.38/0.60 (assume @p12 (forall @t8 (= (tptp.disjoint @t4 @t1) (not (exists @t6 @t10))))) % 0.38/0.60 (assume @p13 (forall (@list @t4 @t12) (= (tptp.partition @t4 @t12) (and (forall @t6 (=> @t5 (tptp.subset @t2 @t12))) (forall @t6 (=> @t23 @t19)) (forall @t22 (=> @t21 (=> (exists (@list @t20) (and (tptp.member @t20 @t2) (tptp.member @t20 @t15))) (= @t2 @t15)))))))) % 0.38/0.60 (assume @p14 (forall (@list @t4 @t24) (= (tptp.equivalence @t24 @t4) (and (forall @t6 (=> @t5 @t31)) (forall @t22 (=> @t21 (=> @t27 (tptp.apply @t24 @t15 @t2)))) (forall @t30 (=> (and @t5 @t17 (tptp.member @t20 @t4)) @t29)))))) % 0.38/0.60 (assume @p15 (forall (@list @t24 @t12 @t4 @t2) (= (tptp.member @t2 (tptp.equivalence_class @t4 @t12 @t24)) (and @t23 (tptp.apply @t24 @t4 @t2))))) % 0.38/0.60 (assume @p16 @t40) % 0.38/0.60 (assume @p17 @t68) % 0.38/0.60 (assume @p18 true) % 0.38/0.60 (step @p19 :rule aci_norm :args ((= (or @t75 @t74) (or @t73 @t72 @t71 @t70 @t69 @t25)))) % 0.38/0.60 (step @p20 :rule aci_norm :args ((= (or (or @t70 @t69) @t25) @t74))) % 0.38/0.60 (step @p21 :rule refl :args (@t25)) % 0.38/0.60 (step @p22 :rule bool-and-de-morgan :args (@t27 @t26 true)) % 0.38/0.60 (step @p23 :rule nary_cong :premises (@p22 @p21) :args ((or (not @t28) @t25))) % 0.38/0.60 (step @p24 :rule trans :premises (@p23 @p20)) % 0.38/0.60 (step @p25 :rule bool-impl-elim :args (@t28 @t25)) % 0.38/0.60 (step @p26 :rule trans :premises (@p25 @p24)) % 0.38/0.60 (step @p27 :rule aci_norm :args ((= (or @t73 (or @t72 @t71)) @t75))) % 0.38/0.60 (step @p28 :rule bool-and-de-morgan :args (@t33 @t32 true)) % 0.38/0.60 (step @p29 :rule refl :args (@t73)) % 0.38/0.60 (step @p30 :rule nary_cong :premises (@p29 @p28) :args ((or @t73 (not (and @t33 @t32))))) % 0.38/0.60 (step @p31 :rule bool-and-de-morgan :args (@t23 @t33 (and @t32))) % 0.38/0.60 (step @p32 :rule trans :premises (@p31 @p30)) % 0.38/0.60 (step @p33 :rule trans :premises (@p32 @p27)) % 0.38/0.60 (step @p34 :rule nary_cong :premises (@p33 @p26) :args ((or (not @t34) @t29))) % 0.38/0.60 (step @p35 :rule trans :premises (@p34 @p19)) % 0.38/0.60 (step @p36 :rule bool-impl-elim :args (@t34 @t29)) % 0.38/0.60 (step @p37 :rule trans :premises (@p36 @p35)) % 0.38/0.60 (step @p38 :rule cong :premises (@p37) :args (@t35)) % 0.38/0.60 (step @p39 :rule bool-impl-elim :args (@t23 @t31)) % 0.38/0.60 (step @p40 :rule cong :premises (@p39) :args (@t36)) % 0.38/0.60 (step @p41 :rule nary_cong :premises (@p40 @p38) :args (@t37)) % 0.38/0.60 (step @p42 :rule refl :args (@t38)) % 0.38/0.60 (step @p43 :rule cong :premises (@p42 @p41) :args (@t39)) % 0.38/0.60 (step @p44 :rule cong :premises (@p43) :args (@t40)) % 0.38/0.60 (step @p45 :rule eq_resolve :premises (@p16 @p44)) % 0.38/0.60 (step @p46 :rule instantiate :premises (@p45) :args ((@list @t98 @t97))) % 0.38/0.60 (step @p47 :rule aci_norm :args ((= @t100 @t94))) % 0.38/0.60 (step @p48 :rule cong :premises (@p47) :args (@t101)) % 0.38/0.60 (step @p49 :rule quant-merge-prenex :args ((= (forall @t66 @t103) @t101))) % 0.38/0.60 (step @p50 :rule alpha_equiv :args (@t104 (@list @t80 @t79 @t77 @t76) (@list @t46 @t45 @t42 @t41))) % 0.38/0.60 (step @p51 :rule refl :args (@t92)) % 0.38/0.60 (step @p52 :rule refl :args (@t93)) % 0.38/0.60 (step @p53 :rule nary_cong :premises (@p52 @p51 @p50) :args (@t105)) % 0.38/0.60 (step @p54 :rule quant-miniscope-or :args ((= @t103 @t105))) % 0.38/0.60 (step @p55 :rule trans :premises (@p54 @p53)) % 0.38/0.60 (step @p56 :rule symm :premises (@p55)) % 0.38/0.60 (step @p57 :rule cong :premises (@p56) :args ((forall @t66 @t115))) % 0.38/0.60 (step @p58 :rule trans :premises (@p57 @p49)) % 0.38/0.60 (step @p59 :rule trans :premises (@p58 @p48)) % 0.38/0.60 (step @p60 :rule aci_norm :args ((= (or (or @t93 @t92) @t114) @t115))) % 0.38/0.60 (step @p61 :rule refl :args (@t114)) % 0.38/0.60 (step @p62 :rule bool-and-de-morgan :args (@t63 @t91 true)) % 0.38/0.60 (step @p63 :rule nary_cong :premises (@p62 @p61) :args ((or (not @t116) @t114))) % 0.38/0.60 (step @p64 :rule trans :premises (@p63 @p60)) % 0.38/0.60 (step @p65 :rule bool-impl-elim :args (@t116 @t114)) % 0.38/0.60 (step @p66 :rule trans :premises (@p65 @p64)) % 0.38/0.60 (step @p67 :rule cong :premises (@p66) :args ((forall @t66 (=> @t116 @t114)))) % 0.38/0.60 (step @p68 :rule trans :premises (@p67 @p59)) % 0.38/0.60 (step @p69 :rule aci_norm :args ((= (or @t118 @t117) @t113))) % 0.38/0.60 (step @p70 :rule aci_norm :args ((= (or @t119 @t44) @t117))) % 0.38/0.60 (step @p71 :rule refl :args (@t44)) % 0.38/0.60 (step @p72 :rule aci_norm :args ((= (or @t108 (or @t107 @t106)) @t119))) % 0.38/0.60 (step @p73 :rule bool-and-de-morgan :args (@t48 @t47 true)) % 0.38/0.60 (step @p74 :rule refl :args (@t108)) % 0.38/0.60 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or @t108 (not (and @t48 @t47))))) % 0.38/0.60 (step @p76 :rule bool-and-de-morgan :args (@t49 @t48 (and @t47))) % 0.38/0.60 (step @p77 :rule trans :premises (@p76 @p75)) % 0.38/0.60 (step @p78 :rule trans :premises (@p77 @p72)) % 0.38/0.60 (step @p79 :rule nary_cong :premises (@p78 @p71) :args ((or (not @t50) @t44))) % 0.38/0.60 (step @p80 :rule trans :premises (@p79 @p70)) % 0.38/0.60 (step @p81 :rule bool-impl-elim :args (@t50 @t44)) % 0.38/0.60 (step @p82 :rule trans :premises (@p81 @p80)) % 0.38/0.60 (step @p83 :rule aci_norm :args ((= (or @t112 (or @t111 (or @t110 @t109))) @t118))) % 0.38/0.60 (step @p84 :rule bool-and-de-morgan :args (@t53 @t52 true)) % 0.38/0.60 (step @p85 :rule refl :args (@t111)) % 0.38/0.60 (step @p86 :rule nary_cong :premises (@p85 @p84) :args ((or @t111 (not (and @t53 @t52))))) % 0.38/0.60 (step @p87 :rule bool-and-de-morgan :args (@t54 @t53 (and @t52))) % 0.38/0.60 (step @p88 :rule trans :premises (@p87 @p86)) % 0.38/0.60 (step @p89 :rule refl :args (@t112)) % 0.38/0.60 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or @t112 (not (and @t54 @t53 @t52))))) % 0.38/0.60 (step @p91 :rule bool-and-de-morgan :args (@t55 @t54 (and @t53 @t52))) % 0.38/0.60 (step @p92 :rule trans :premises (@p91 @p90)) % 0.38/0.60 (step @p93 :rule trans :premises (@p92 @p83)) % 0.38/0.60 (step @p94 :rule nary_cong :premises (@p93 @p82) :args ((or (not @t56) @t51))) % 0.38/0.60 (step @p95 :rule trans :premises (@p94 @p69)) % 0.38/0.60 (step @p96 :rule bool-impl-elim :args (@t56 @t51)) % 0.38/0.60 (step @p97 :rule trans :premises (@p96 @p95)) % 0.38/0.60 (step @p98 :rule cong :premises (@p97) :args (@t58)) % 0.38/0.60 (step @p99 :rule aci_norm :args ((= (or (or @t89 @t88) @t59) @t90))) % 0.38/0.60 (step @p100 :rule refl :args (@t59)) % 0.38/0.60 (step @p101 :rule bool-and-de-morgan :args (@t60 @t13 true)) % 0.38/0.60 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or (not @t61) @t59))) % 0.38/0.60 (step @p103 :rule trans :premises (@p102 @p99)) % 0.38/0.60 (step @p104 :rule bool-impl-elim :args (@t61 @t59)) % 0.38/0.60 (step @p105 :rule trans :premises (@p104 @p103)) % 0.38/0.60 (step @p106 :rule cong :premises (@p105) :args (@t62)) % 0.38/0.60 (step @p107 :rule refl :args (@t63)) % 0.38/0.60 (step @p108 :rule nary_cong :premises (@p107 @p106) :args (@t64)) % 0.38/0.60 (step @p109 :rule cong :premises (@p108 @p98) :args (@t65)) % 0.38/0.60 (step @p110 :rule cong :premises (@p109) :args (@t67)) % 0.38/0.60 (step @p111 :rule trans :premises (@p110 @p68)) % 0.38/0.60 (step @p112 :rule cong :premises (@p111) :args (@t68)) % 0.38/0.60 (step @p113 :rule eq_resolve :premises (@p17 @p112)) % 0.38/0.60 (step @p114 :rule skolemize :premises (@p113)) % 0.38/0.60 (step @p115 :rule bool-double-not-elim :args (@t120)) % 0.38/0.60 (step @p116 :rule refl :args (@t144)) % 0.38/0.60 (step @p117 :rule nary_cong :premises (@p116 @p115) :args ((or @t144 (not @t143)))) % 0.38/0.60 (step @p118 :rule cnf_or_neg :args (@t144 0)) % 0.38/0.60 (step @p119 :rule eq_resolve :premises (@p118 @p117)) % 0.38/0.60 (step @p120 :rule reordering :premises (@p119) :args ((or @t120 @t144))) % 0.38/0.60 (step @p121 :rule chain_m_resolution :premises (@p120 @p114) :args (@t120 @t145 @t146)) % 0.38/0.60 (step @p122 :rule cnf_equiv_pos1 :args (@t150)) % 0.38/0.60 (step @p123 :rule reordering :premises (@p122) :args ((or @t143 @t149 (not @t150)))) % 0.38/0.60 (step @p124 :rule chain_m_resolution :premises (@p123 @p121 @p46) :args (@t149 @t151 (@list @t120 @t150))) % 0.38/0.60 (step @p125 :rule cnf_and_pos :args (@t149 1)) % 0.38/0.60 (step @p126 :rule reordering :premises (@p125) :args ((or @t148 (not @t149)))) % 0.38/0.60 (step @p127 :rule chain_m_resolution :premises (@p126 @p124) :args (@t148 @t152 (@list @t149))) % 0.38/0.60 (step @p128 :rule instantiate :premises (@p127) :args ((@list @t125 @t124 @t121))) % 0.38/0.60 (step @p129 :rule bool-double-not-elim :args (@t141)) % 0.38/0.60 (step @p130 :rule nary_cong :premises (@p116 @p129) :args ((or @t144 (not @t142)))) % 0.38/0.60 (step @p131 :rule cnf_or_neg :args (@t144 1)) % 0.38/0.60 (step @p132 :rule eq_resolve :premises (@p131 @p130)) % 0.38/0.60 (step @p133 :rule reordering :premises (@p132) :args ((or @t141 @t144))) % 0.38/0.60 (step @p134 :rule chain_m_resolution :premises (@p133 @p114) :args (@t141 @t145 @t146)) % 0.38/0.60 (step @p135 :rule instantiate :premises (@p134) :args ((@list @t124 @t121))) % 0.38/0.60 (step @p136 :rule bool-double-not-elim :args (@t133)) % 0.38/0.60 (step @p137 :rule nary_cong :premises (@p116 @p136) :args ((or @t144 (not @t134)))) % 0.38/0.60 (step @p138 :rule cnf_or_neg :args (@t144 5)) % 0.38/0.60 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.38/0.60 (step @p140 :rule reordering :premises (@p139) :args ((or @t133 @t144))) % 0.38/0.60 (step @p141 :rule chain_m_resolution :premises (@p140 @p114) :args (@t133 @t145 @t146)) % 0.38/0.60 (step @p142 :rule bool-double-not-elim :args (@t137)) % 0.38/0.60 (step @p143 :rule nary_cong :premises (@p116 @p142) :args ((or @t144 (not @t138)))) % 0.38/0.60 (step @p144 :rule cnf_or_neg :args (@t144 3)) % 0.38/0.60 (step @p145 :rule eq_resolve :premises (@p144 @p143)) % 0.38/0.60 (step @p146 :rule reordering :premises (@p145) :args ((or @t137 @t144))) % 0.38/0.60 (step @p147 :rule chain_m_resolution :premises (@p146 @p114) :args (@t137 @t145 @t146)) % 0.38/0.60 (step @p148 :rule cnf_or_pos :args (@t156)) % 0.38/0.60 (step @p149 :rule reordering :premises (@p148) :args ((or @t138 @t134 @t155 (not @t156)))) % 0.38/0.60 (step @p150 :rule chain_m_resolution :premises (@p149 @p147 @p141 @p135) :args (@t155 @t157 (@list @t137 @t133 @t156))) % 0.38/0.60 (step @p151 :rule bool-double-not-elim :args (@t129)) % 0.38/0.60 (step @p152 :rule nary_cong :premises (@p116 @p151) :args ((or @t144 (not @t130)))) % 0.38/0.60 (step @p153 :rule cnf_or_neg :args (@t144 7)) % 0.38/0.60 (step @p154 :rule eq_resolve :premises (@p153 @p152)) % 0.38/0.60 (step @p155 :rule reordering :premises (@p154) :args ((or @t129 @t144))) % 0.38/0.60 (step @p156 :rule chain_m_resolution :premises (@p155 @p114) :args (@t129 @t145 @t146)) % 0.38/0.60 (step @p157 :rule cnf_equiv_pos1 :args (@t155)) % 0.38/0.60 (step @p158 :rule reordering :premises (@p157) :args ((or @t130 @t154 (not @t155)))) % 0.38/0.60 (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p150) :args (@t154 @t151 (@list @t129 @t155))) % 0.38/0.60 (step @p160 :rule cnf_and_pos :args (@t154 0)) % 0.38/0.60 (step @p161 :rule reordering :premises (@p160) :args ((or @t153 (not @t154)))) % 0.38/0.60 (step @p162 :rule chain_m_resolution :premises (@p161 @p159) :args (@t153 @t152 (@list @t154))) % 0.38/0.60 (step @p163 :rule bool-double-not-elim :args (@t126)) % 0.38/0.60 (step @p164 :rule nary_cong :premises (@p116 @p163) :args ((or @t144 (not @t127)))) % 0.38/0.60 (step @p165 :rule cnf_or_neg :args (@t144 8)) % 0.38/0.60 (step @p166 :rule eq_resolve :premises (@p165 @p164)) % 0.38/0.60 (step @p167 :rule reordering :premises (@p166) :args ((or @t126 @t144))) % 0.38/0.60 (step @p168 :rule chain_m_resolution :premises (@p167 @p114) :args (@t126 @t145 @t146)) % 0.38/0.60 (step @p169 :rule bool-double-not-elim :args (@t139)) % 0.38/0.60 (step @p170 :rule nary_cong :premises (@p116 @p169) :args ((or @t144 (not @t140)))) % 0.38/0.60 (step @p171 :rule cnf_or_neg :args (@t144 2)) % 0.38/0.60 (step @p172 :rule eq_resolve :premises (@p171 @p170)) % 0.38/0.60 (step @p173 :rule reordering :premises (@p172) :args ((or @t139 @t144))) % 0.38/0.60 (step @p174 :rule chain_m_resolution :premises (@p173 @p114) :args (@t139 @t145 @t146)) % 0.38/0.60 (step @p175 :rule cnf_or_pos :args (@t160)) % 0.38/0.60 (step @p176 :rule reordering :premises (@p175) :args ((or @t140 @t138 @t134 @t127 @t159 @t158 (not @t160)))) % 0.38/0.60 (step @p177 :rule chain_m_resolution :premises (@p176 @p174 @p147 @p141 @p168 @p162 @p128) :args (@t158 (@list false false false false false false) (@list @t139 @t137 @t133 @t126 @t153 @t160))) % 0.38/0.60 (step @p178 :rule instantiate :premises (@p134) :args ((@list @t125 @t122))) % 0.38/0.60 (step @p179 :rule bool-double-not-elim :args (@t135)) % 0.38/0.60 (step @p180 :rule nary_cong :premises (@p116 @p179) :args ((or @t144 (not @t136)))) % 0.38/0.60 (step @p181 :rule cnf_or_neg :args (@t144 4)) % 0.38/0.61 (step @p182 :rule eq_resolve :premises (@p181 @p180)) % 0.38/0.61 (step @p183 :rule reordering :premises (@p182) :args ((or @t135 @t144))) % 0.38/0.61 (step @p184 :rule chain_m_resolution :premises (@p183 @p114) :args (@t135 @t145 @t146)) % 0.38/0.61 (step @p185 :rule cnf_or_pos :args (@t164)) % 0.38/0.61 (step @p186 :rule reordering :premises (@p185) :args ((or @t140 @t136 @t163 (not @t164)))) % 0.38/0.61 (step @p187 :rule chain_m_resolution :premises (@p186 @p174 @p184 @p178) :args (@t163 @t157 (@list @t139 @t135 @t164))) % 0.38/0.61 (step @p188 :rule bool-double-not-elim :args (@t131)) % 0.38/0.61 (step @p189 :rule nary_cong :premises (@p116 @p188) :args ((or @t144 (not @t132)))) % 0.38/0.61 (step @p190 :rule cnf_or_neg :args (@t144 6)) % 0.38/0.61 (step @p191 :rule eq_resolve :premises (@p190 @p189)) % 0.38/0.61 (step @p192 :rule reordering :premises (@p191) :args ((or @t131 @t144))) % 0.38/0.61 (step @p193 :rule chain_m_resolution :premises (@p192 @p114) :args (@t131 @t145 @t146)) % 0.38/0.61 (step @p194 :rule cnf_equiv_pos1 :args (@t163)) % 0.38/0.61 (step @p195 :rule reordering :premises (@p194) :args ((or @t132 @t162 (not @t163)))) % 0.38/0.61 (step @p196 :rule chain_m_resolution :premises (@p195 @p193 @p187) :args (@t162 @t151 (@list @t131 @t163))) % 0.38/0.61 (step @p197 :rule cnf_and_pos :args (@t162 1)) % 0.38/0.61 (step @p198 :rule reordering :premises (@p197) :args ((or @t161 (not @t162)))) % 0.38/0.61 (step @p199 :rule chain_m_resolution :premises (@p198 @p196) :args (@t161 @t152 (@list @t162))) % 0.38/0.61 (step @p200 :rule cnf_or_neg :args (@t144 9)) % 0.38/0.61 (step @p201 :rule chain_m_resolution :premises (@p200 @p114) :args ((not @t123) @t145 @t146)) % 0.38/0.61 (step @p202 :rule cnf_or_pos :args (@t167)) % 0.38/0.61 (step @p203 :rule reordering :premises (@p202) :args ((or @t140 @t136 @t134 @t123 @t166 @t165 @t168))) % 0.38/0.61 (step @p204 :rule chain_m_resolution :premises (@p203 @p174 @p184 @p141 @p201 @p199 @p177) :args (@t168 (@list false false false true false false) (@list @t139 @t135 @t133 @t123 @t161 @t158))) % 0.38/0.61 (assume-push @p211 @t148) % 0.38/0.61 (step @p206 :rule instantiate :premises (@p127) :args ((@list @t122 @t125 @t121))) % 0.38/0.61 (step-pop @p212 :rule scope :premises (@p206)) % 0.38/0.61 (step @p207 :rule process_scope :premises (@p212) :args (@t167)) % 0.38/0.61 (step @p209 :rule implies_elim :premises (@p207)) % 0.38/0.61 (step @p210 false :rule chain_m_resolution :premises (@p209 @p204 @p127) :args (false (@list true false) (@list @t167 @t148))) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------