%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET758+4 : TPTP v9.2.1. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n024.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 08:48:35 AM UTC 2026 % Result : Theorem 0.16s 0.40s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.07 % Problem : SET758+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.08/0.26 % Computer : n024.cluster.edu % 0.08/0.26 % Model : x86_64 x86_64 % 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.26 % Memory : 8042.1875MB % 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.26 % CPULimit : 300 % 0.08/0.26 % WCLimit : 300 % 0.08/0.26 % DateTime : Tue Jun 2 11:10:45 EDT 2026 % 0.08/0.26 % CPUTime : % 0.16/0.34 %----Proving TF0_NAR, FOF, or CNF % 0.16/0.40 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.16/0.40 % SZS status Theorem % 0.16/0.40 % SZS output start Proof % 0.16/0.40 ( % 0.16/0.40 (declare-sort $$unsorted 0) % 0.16/0.40 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.empty_set $$unsorted) % 0.16/0.40 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.40 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.40 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.40 (define @t1 () (@var "B" $$unsorted)) % 0.16/0.40 (define @t2 () (@var "X" $$unsorted)) % 0.16/0.40 (define @t3 () (tptp.member @t2 @t1)) % 0.16/0.40 (define @t4 () (@var "A" $$unsorted)) % 0.16/0.40 (define @t5 () (tptp.member @t2 @t4)) % 0.16/0.40 (define @t6 () (@list @t2)) % 0.16/0.40 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.16/0.40 (define @t8 () (tptp.subset @t4 @t1)) % 0.16/0.40 (define @t9 () (= @t8 @t7)) % 0.16/0.40 (define @t10 () (@list @t4 @t1)) % 0.16/0.40 (define @t11 () (forall @t10 @t9)) % 0.16/0.40 (define @t12 () (@list @t2 @t4)) % 0.16/0.40 (define @t13 () (@list @t2 @t4 @t1)) % 0.16/0.40 (define @t14 () (@var "E" $$unsorted)) % 0.16/0.40 (define @t15 () (= @t2 @t4)) % 0.16/0.40 (define @t16 () (@var "Y" $$unsorted)) % 0.16/0.40 (define @t17 () (tptp.member @t2 @t16)) % 0.16/0.40 (define @t18 () (tptp.member @t16 @t4)) % 0.16/0.40 (define @t19 () (@list @t16)) % 0.16/0.40 (define @t20 () (@var "Y2" $$unsorted)) % 0.16/0.40 (define @t21 () (@var "Y1" $$unsorted)) % 0.16/0.40 (define @t22 () (= @t21 @t20)) % 0.16/0.40 (define @t23 () (@var "F" $$unsorted)) % 0.16/0.40 (define @t24 () (tptp.apply @t23 @t2 @t20)) % 0.16/0.40 (define @t25 () (tptp.apply @t23 @t2 @t21)) % 0.16/0.40 (define @t26 () (and @t25 @t24)) % 0.16/0.40 (define @t27 () (=> @t26 @t22)) % 0.16/0.40 (define @t28 () (tptp.member @t20 @t1)) % 0.16/0.40 (define @t29 () (tptp.member @t21 @t1)) % 0.16/0.40 (define @t30 () (and @t5 @t29 @t28)) % 0.16/0.40 (define @t31 () (@list @t2 @t21 @t20)) % 0.16/0.40 (define @t32 () (forall @t31 (=> @t30 @t27))) % 0.16/0.40 (define @t33 () (tptp.apply @t23 @t2 @t16)) % 0.16/0.40 (define @t34 () (tptp.member @t16 @t1)) % 0.16/0.40 (define @t35 () (and @t34 @t33)) % 0.16/0.40 (define @t36 () (exists @t19 @t35)) % 0.16/0.40 (define @t37 () (=> @t5 @t36)) % 0.16/0.40 (define @t38 () (forall @t6 @t37)) % 0.16/0.40 (define @t39 () (and @t38 @t32)) % 0.16/0.40 (define @t40 () (tptp.maps @t23 @t4 @t1)) % 0.16/0.40 (define @t41 () (= @t40 @t39)) % 0.16/0.40 (define @t42 () (@list @t23 @t4 @t1)) % 0.16/0.40 (define @t43 () (forall @t42 @t41)) % 0.16/0.40 (define @t44 () (@var "Z" $$unsorted)) % 0.16/0.40 (define @t45 () (@var "G" $$unsorted)) % 0.16/0.40 (define @t46 () (exists @t19 (and @t34 @t33 (tptp.apply @t45 @t16 @t44)))) % 0.16/0.40 (define @t47 () (@var "H" $$unsorted)) % 0.16/0.40 (define @t48 () (@var "C" $$unsorted)) % 0.16/0.40 (define @t49 () (and @t5 (tptp.member @t44 @t48))) % 0.16/0.40 (define @t50 () (@var "X2" $$unsorted)) % 0.16/0.40 (define @t51 () (@var "X1" $$unsorted)) % 0.16/0.40 (define @t52 () (tptp.member @t50 @t4)) % 0.16/0.40 (define @t53 () (tptp.member @t51 @t4)) % 0.16/0.40 (define @t54 () (tptp.injective @t23 @t4 @t1)) % 0.16/0.40 (define @t55 () (tptp.surjective @t23 @t4 @t1)) % 0.16/0.40 (define @t56 () (tptp.one_to_one @t23 @t4 @t1)) % 0.16/0.40 (define @t57 () (and @t5 @t34)) % 0.16/0.40 (define @t58 () (and @t5 @t33)) % 0.16/0.40 (define @t59 () (exists @t6 @t58)) % 0.16/0.40 (define @t60 () (and @t34 @t59)) % 0.16/0.40 (define @t61 () (tptp.member @t16 (tptp.image3 @t23 @t4 @t1))) % 0.16/0.40 (define @t62 () (= @t61 @t60)) % 0.16/0.40 (define @t63 () (@list @t23 @t4 @t1 @t16)) % 0.16/0.40 (define @t64 () (forall @t63 @t62)) % 0.16/0.40 (define @t65 () (and @t5 @t36)) % 0.16/0.40 (define @t66 () (tptp.member @t2 (tptp.inverse_image3 @t23 @t1 @t4))) % 0.16/0.40 (define @t67 () (= @t66 @t65)) % 0.16/0.40 (define @t68 () (forall (@list @t23 @t1 @t4 @t2) @t67)) % 0.16/0.40 (define @t69 () (@var "S" $$unsorted)) % 0.16/0.40 (define @t70 () (tptp.apply @t69 @t21 @t20)) % 0.16/0.40 (define @t71 () (tptp.apply @t23 @t50 @t20)) % 0.16/0.40 (define @t72 () (tptp.apply @t23 @t51 @t21)) % 0.16/0.40 (define @t73 () (@var "R" $$unsorted)) % 0.16/0.40 (define @t74 () (tptp.apply @t73 @t51 @t50)) % 0.16/0.40 (define @t75 () (and @t53 @t29 @t52 @t28 @t74 @t72 @t71)) % 0.16/0.40 (define @t76 () (@list @t51 @t21 @t50 @t20)) % 0.16/0.40 (define @t77 () (@list @t23 @t4 @t73 @t1 @t69)) % 0.16/0.40 (define @t78 () (tptp.subset (tptp.image3 @t23 (tptp.inverse_image3 @t23 @t16 @t4) @t1) @t16)) % 0.16/0.40 (define @t79 () (tptp.subset @t16 @t1)) % 0.16/0.40 (define @t80 () (and @t40 @t79)) % 0.16/0.40 (define @t81 () (forall @t63 (=> @t80 @t78))) % 0.16/0.40 (define @t82 () (not @t81)) % 0.16/0.40 (define @t83 () (forall @t19 (not @t35))) % 0.16/0.40 (define @t84 () (not @t83)) % 0.16/0.40 (define @t85 () (not @t79)) % 0.16/0.40 (define @t86 () (not @t40)) % 0.16/0.40 (define @t87 () (or @t86 @t85 @t78)) % 0.16/0.40 (define @t88 () (forall @t63 @t87)) % 0.16/0.40 (define @t89 () (@quantifiers_skolemize @t88 3)) % 0.16/0.40 (define @t90 () (tptp.member @t2 @t89)) % 0.16/0.40 (define @t91 () (@quantifiers_skolemize @t88 2)) % 0.16/0.40 (define @t92 () (@quantifiers_skolemize @t88 1)) % 0.16/0.40 (define @t93 () (@quantifiers_skolemize @t88 0)) % 0.16/0.40 (define @t94 () (tptp.inverse_image3 @t93 @t89 @t92)) % 0.16/0.40 (define @t95 () (tptp.image3 @t93 @t94 @t91)) % 0.16/0.40 (define @t96 () (forall @t6 (or (not (tptp.member @t2 @t95)) @t90))) % 0.16/0.40 (define @t97 () (@quantifiers_skolemize @t96 0)) % 0.16/0.40 (define @t98 () (forall @t6 (or (not (tptp.member @t2 @t94)) (not (tptp.apply @t93 @t2 @t97))))) % 0.16/0.40 (define @t99 () (@quantifiers_skolemize @t98 0)) % 0.16/0.40 (define @t100 () (forall @t6 (not @t58))) % 0.16/0.40 (define @t101 () (not @t100)) % 0.16/0.40 (define @t102 () (tptp.subset @t95 @t89)) % 0.16/0.40 (define @t103 () (tptp.subset @t89 @t91)) % 0.16/0.40 (define @t104 () (not @t103)) % 0.16/0.40 (define @t105 () (tptp.maps @t93 @t92 @t91)) % 0.16/0.40 (define @t106 () (not @t105)) % 0.16/0.40 (define @t107 () (or @t106 @t104 @t102)) % 0.16/0.40 (define @t108 () (@list true)) % 0.16/0.40 (define @t109 () (@list @t107)) % 0.16/0.40 (define @t110 () (= @t102 @t96)) % 0.16/0.40 (define @t111 () (not @t96)) % 0.16/0.40 (define @t112 () (tptp.member @t97 @t95)) % 0.16/0.40 (define @t113 () (tptp.member @t97 @t89)) % 0.16/0.40 (define @t114 () (not @t112)) % 0.16/0.40 (define @t115 () (or @t114 @t113)) % 0.16/0.40 (define @t116 () (@list @t115)) % 0.16/0.40 (define @t117 () (not @t98)) % 0.16/0.40 (define @t118 () (tptp.member @t97 @t91)) % 0.16/0.40 (define @t119 () (and @t118 @t117)) % 0.16/0.40 (define @t120 () (= @t112 @t119)) % 0.16/0.40 (define @t121 () (@list false false)) % 0.16/0.40 (define @t122 () (not @t119)) % 0.16/0.40 (define @t123 () (@list false)) % 0.16/0.40 (define @t124 () (@list @t119)) % 0.16/0.40 (define @t125 () (tptp.member @t99 @t94)) % 0.16/0.40 (define @t126 () (tptp.apply @t93 @t99 @t97)) % 0.16/0.40 (define @t127 () (not @t126)) % 0.16/0.40 (define @t128 () (not @t125)) % 0.16/0.40 (define @t129 () (or @t128 @t127)) % 0.16/0.40 (define @t130 () (@list @t129)) % 0.16/0.40 (define @t131 () (forall @t19 (or (not (tptp.member @t16 @t89)) (not (tptp.apply @t93 @t99 @t16))))) % 0.16/0.40 (define @t132 () (not @t131)) % 0.16/0.40 (define @t133 () (tptp.member @t99 @t92)) % 0.16/0.40 (define @t134 () (and @t133 @t132)) % 0.16/0.40 (define @t135 () (= @t125 @t134)) % 0.16/0.40 (define @t136 () (not @t134)) % 0.16/0.40 (define @t137 () (@list @t134)) % 0.16/0.40 (define @t138 () (@quantifiers_skolemize @t131 0)) % 0.16/0.40 (define @t139 () (tptp.member @t138 @t89)) % 0.16/0.40 (define @t140 () (tptp.apply @t93 @t99 @t138)) % 0.16/0.40 (define @t141 () (not @t140)) % 0.16/0.40 (define @t142 () (not @t139)) % 0.16/0.40 (define @t143 () (or @t142 @t141)) % 0.16/0.40 (define @t144 () (@list @t143)) % 0.16/0.40 (define @t145 () (not @t24)) % 0.16/0.40 (define @t146 () (not @t25)) % 0.16/0.40 (define @t147 () (not @t28)) % 0.16/0.40 (define @t148 () (not @t29)) % 0.16/0.40 (define @t149 () (not @t5)) % 0.16/0.40 (define @t150 () (or @t146 @t145 @t22)) % 0.16/0.40 (define @t151 () (or @t149 @t148 @t147)) % 0.16/0.40 (define @t152 () (not (forall @t19 (or (not @t34) (not @t33))))) % 0.16/0.40 (define @t153 () (not (tptp.member @t2 @t92))) % 0.16/0.40 (define @t154 () (forall @t31 (or @t153 (not (tptp.member @t21 @t91)) (not (tptp.member @t20 @t91)) (not (tptp.apply @t93 @t2 @t21)) (not (tptp.apply @t93 @t2 @t20)) @t22))) % 0.16/0.40 (define @t155 () (and (forall @t6 (or @t153 (not (forall @t19 (or (not (tptp.member @t16 @t91)) (not (tptp.apply @t93 @t2 @t16))))))) @t154)) % 0.16/0.40 (define @t156 () (= @t105 @t155)) % 0.16/0.40 (define @t157 () (not @t118)) % 0.16/0.40 (define @t158 () (tptp.member @t138 @t91)) % 0.16/0.40 (define @t159 () (not @t158)) % 0.16/0.40 (define @t160 () (not @t133)) % 0.16/0.40 (define @t161 () (or @t160 @t159 @t157 @t141 @t127 (= @t138 @t97))) % 0.16/0.40 (define @t162 () (= @t97 @t138)) % 0.16/0.40 (define @t163 () (or @t160 @t159 @t157 @t141 @t127 @t162)) % 0.16/0.40 (define @t164 () (forall @t6 (or (not @t90) (tptp.member @t2 @t91)))) % 0.16/0.40 (define @t165 () (= @t103 @t164)) % 0.16/0.40 (define @t166 () (or @t142 @t158)) % 0.16/0.40 (assume @p1 @t11) % 0.16/0.40 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.16/0.40 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.16/0.40 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.16/0.40 (assume @p5 (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.16/0.40 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.16/0.40 (assume @p7 (forall (@list @t1 @t4 @t14) (= (tptp.member @t1 (tptp.difference @t14 @t4)) (and (tptp.member @t1 @t14) (not (tptp.member @t1 @t4)))))) % 0.16/0.40 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t15))) % 0.16/0.40 (assume @p9 (forall @t13 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t15 (= @t2 @t1))))) % 0.16/0.40 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t19 (and @t18 @t17))))) % 0.16/0.40 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t19 (=> @t18 @t17))))) % 0.16/0.40 (assume @p12 @t43) % 0.16/0.40 (assume @p13 (forall (@list @t47 @t45 @t23 @t4 @t1 @t48) (= (tptp.compose_predicate @t47 @t45 @t23 @t4 @t1 @t48) (forall (@list @t2 @t44) (=> @t49 (= (tptp.apply @t47 @t2 @t44) @t46)))))) % 0.16/0.40 (assume @p14 (forall (@list @t45 @t23 @t4 @t1 @t48 @t2 @t44) (=> @t49 (= (tptp.apply (tptp.compose_function @t45 @t23 @t4 @t1 @t48) @t2 @t44) @t46)))) % 0.16/0.40 (assume @p15 (forall (@list @t23 @t45 @t4 @t1) (= (tptp.equal_maps @t23 @t45 @t4 @t1) (forall @t31 (=> @t30 (=> (and @t25 (tptp.apply @t45 @t2 @t20)) @t22)))))) % 0.16/0.40 (assume @p16 (forall (@list @t23 @t4) (= (tptp.identity @t23 @t4) (forall @t6 (=> @t5 (tptp.apply @t23 @t2 @t2)))))) % 0.16/0.40 (assume @p17 (forall @t42 (= @t54 (forall (@list @t51 @t50 @t16) (=> (and @t53 @t52 @t34) (=> (and (tptp.apply @t23 @t51 @t16) (tptp.apply @t23 @t50 @t16)) (= @t51 @t50))))))) % 0.16/0.40 (assume @p18 (forall @t42 (= @t55 (forall @t19 (=> @t34 (exists (@list @t14) (and (tptp.member @t14 @t4) (tptp.apply @t23 @t14 @t16)))))))) % 0.16/0.40 (assume @p19 (forall @t42 (= @t56 (and @t54 @t55)))) % 0.16/0.40 (assume @p20 (forall (@list @t45 @t23 @t4 @t1) (= (tptp.inverse_predicate @t45 @t23 @t4 @t1) (forall (@list @t2 @t16) (=> @t57 (= @t33 (tptp.apply @t45 @t16 @t2))))))) % 0.16/0.40 (assume @p21 (forall (@list @t23 @t4 @t1 @t2 @t16) (=> @t57 (= @t33 (tptp.apply (tptp.inverse_function @t23 @t4 @t1) @t16 @t2))))) % 0.16/0.40 (assume @p22 (forall (@list @t23 @t4 @t16) (= (tptp.member @t16 (tptp.image2 @t23 @t4)) @t59))) % 0.16/0.40 (assume @p23 @t64) % 0.16/0.40 (assume @p24 (forall (@list @t23 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t23 @t1)) @t36))) % 0.16/0.40 (assume @p25 @t68) % 0.16/0.40 (assume @p26 (forall @t77 (= (tptp.increasing @t23 @t4 @t73 @t1 @t69) (forall @t76 (=> @t75 @t70))))) % 0.16/0.40 (assume @p27 (forall @t77 (= (tptp.decreasing @t23 @t4 @t73 @t1 @t69) (forall @t76 (=> @t75 (tptp.apply @t69 @t20 @t21)))))) % 0.16/0.40 (assume @p28 (forall @t77 (= (tptp.isomorphism @t23 @t4 @t73 @t1 @t69) (and @t40 @t56 (forall @t76 (=> (and @t53 @t29 @t52 @t28 @t72 @t71) (= @t74 @t70))))))) % 0.16/0.40 (assume @p29 @t82) % 0.16/0.40 (assume @p30 true) % 0.16/0.40 (step @p31 :rule evaluate :args ((= false true))) % 0.16/0.40 (step @p32 :rule bool-and-de-morgan :args (@t34 @t33 true)) % 0.16/0.40 (step @p33 :rule cong :premises (@p32) :args (@t83)) % 0.16/0.40 (step @p34 :rule cong :premises (@p33) :args (@t84)) % 0.16/0.40 (step @p35 :rule exists-elim :args ((= @t36 @t84))) % 0.16/0.40 (step @p36 :rule trans :premises (@p35 @p34)) % 0.16/0.40 (step @p37 :rule refl :args (@t5)) % 0.16/0.40 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t65)) % 0.16/0.40 (step @p39 :rule refl :args (@t66)) % 0.16/0.40 (step @p40 :rule cong :premises (@p39 @p38) :args (@t67)) % 0.16/0.40 (step @p41 :rule cong :premises (@p40) :args (@t68)) % 0.16/0.40 (step @p42 :rule eq_resolve :premises (@p25 @p41)) % 0.16/0.40 (step @p43 :rule instantiate :premises (@p42) :args ((@list @t93 @t89 @t92 @t99))) % 0.16/0.40 (step @p44 :rule bool-and-de-morgan :args (@t5 @t33 true)) % 0.16/0.40 (step @p45 :rule cong :premises (@p44) :args (@t100)) % 0.16/0.40 (step @p46 :rule cong :premises (@p45) :args (@t101)) % 0.16/0.40 (step @p47 :rule exists-elim :args ((= @t59 @t101))) % 0.16/0.40 (step @p48 :rule trans :premises (@p47 @p46)) % 0.16/0.40 (step @p49 :rule refl :args (@t34)) % 0.16/0.40 (step @p50 :rule nary_cong :premises (@p49 @p48) :args (@t60)) % 0.16/0.40 (step @p51 :rule refl :args (@t61)) % 0.16/0.40 (step @p52 :rule cong :premises (@p51 @p50) :args (@t62)) % 0.16/0.40 (step @p53 :rule cong :premises (@p52) :args (@t64)) % 0.16/0.40 (step @p54 :rule eq_resolve :premises (@p23 @p53)) % 0.16/0.40 (step @p55 :rule instantiate :premises (@p54) :args ((@list @t93 @t94 @t91 @t97))) % 0.16/0.40 (step @p56 :rule bool-impl-elim :args (@t5 @t3)) % 0.16/0.40 (step @p57 :rule cong :premises (@p56) :args (@t7)) % 0.16/0.40 (step @p58 :rule refl :args (@t8)) % 0.16/0.40 (step @p59 :rule cong :premises (@p58 @p57) :args (@t9)) % 0.16/0.40 (step @p60 :rule cong :premises (@p59) :args (@t11)) % 0.16/0.40 (step @p61 :rule eq_resolve :premises (@p1 @p60)) % 0.16/0.40 (step @p62 :rule instantiate :premises (@p61) :args ((@list @t95 @t89))) % 0.16/0.40 (step @p63 :rule aci_norm :args ((= (or (or @t86 @t85) @t78) @t87))) % 0.16/0.40 (step @p64 :rule refl :args (@t78)) % 0.16/0.40 (step @p65 :rule bool-and-de-morgan :args (@t40 @t79 true)) % 0.16/0.40 (step @p66 :rule nary_cong :premises (@p65 @p64) :args ((or (not @t80) @t78))) % 0.16/0.40 (step @p67 :rule trans :premises (@p66 @p63)) % 0.16/0.40 (step @p68 :rule bool-impl-elim :args (@t80 @t78)) % 0.16/0.40 (step @p69 :rule trans :premises (@p68 @p67)) % 0.16/0.40 (step @p70 :rule cong :premises (@p69) :args (@t81)) % 0.16/0.40 (step @p71 :rule cong :premises (@p70) :args (@t82)) % 0.16/0.40 (step @p72 :rule eq_resolve :premises (@p29 @p71)) % 0.16/0.40 (step @p73 :rule skolemize :premises (@p72)) % 0.16/0.40 (step @p74 :rule cnf_or_neg :args (@t107 2)) % 0.16/0.40 (step @p75 :rule chain_m_resolution :premises (@p74 @p73) :args ((not @t102) @t108 @t109)) % 0.16/0.40 (step @p76 :rule cnf_equiv_pos2 :args (@t110)) % 0.16/0.40 (step @p77 :rule reordering :premises (@p76) :args ((or @t102 @t111 (not @t110)))) % 0.16/0.40 (step @p78 :rule chain_m_resolution :premises (@p77 @p75 @p62) :args (@t111 (@list true false) (@list @t102 @t110))) % 0.16/0.40 (step @p79 :rule skolemize :premises (@p78)) % 0.16/0.40 (step @p80 :rule bool-double-not-elim :args (@t112)) % 0.16/0.40 (step @p81 :rule refl :args (@t115)) % 0.16/0.40 (step @p82 :rule nary_cong :premises (@p81 @p80) :args ((or @t115 (not @t114)))) % 0.16/0.40 (step @p83 :rule cnf_or_neg :args (@t115 0)) % 0.16/0.40 (step @p84 :rule eq_resolve :premises (@p83 @p82)) % 0.16/0.40 (step @p85 :rule reordering :premises (@p84) :args ((or @t112 @t115))) % 0.16/0.40 (step @p86 :rule chain_m_resolution :premises (@p85 @p79) :args (@t112 @t108 @t116)) % 0.16/0.40 (step @p87 :rule cnf_equiv_pos1 :args (@t120)) % 0.16/0.40 (step @p88 :rule reordering :premises (@p87) :args ((or @t114 @t119 (not @t120)))) % 0.16/0.40 (step @p89 :rule chain_m_resolution :premises (@p88 @p86 @p55) :args (@t119 @t121 (@list @t112 @t120))) % 0.16/0.40 (step @p90 :rule cnf_and_pos :args (@t119 1)) % 0.16/0.40 (step @p91 :rule reordering :premises (@p90) :args ((or @t117 @t122))) % 0.16/0.40 (step @p92 :rule chain_m_resolution :premises (@p91 @p89) :args (@t117 @t123 @t124)) % 0.16/0.40 (step @p93 :rule skolemize :premises (@p92)) % 0.16/0.40 (step @p94 :rule bool-double-not-elim :args (@t125)) % 0.16/0.40 (step @p95 :rule refl :args (@t129)) % 0.16/0.40 (step @p96 :rule nary_cong :premises (@p95 @p94) :args ((or @t129 (not @t128)))) % 0.16/0.40 (step @p97 :rule cnf_or_neg :args (@t129 0)) % 0.16/0.40 (step @p98 :rule eq_resolve :premises (@p97 @p96)) % 0.16/0.40 (step @p99 :rule reordering :premises (@p98) :args ((or @t125 @t129))) % 0.16/0.40 (step @p100 :rule chain_m_resolution :premises (@p99 @p93) :args (@t125 @t108 @t130)) % 0.16/0.40 (step @p101 :rule cnf_equiv_pos1 :args (@t135)) % 0.16/0.40 (step @p102 :rule reordering :premises (@p101) :args ((or @t128 @t134 (not @t135)))) % 0.16/0.40 (step @p103 :rule chain_m_resolution :premises (@p102 @p100 @p43) :args (@t134 @t121 (@list @t125 @t135))) % 0.16/0.40 (step @p104 :rule cnf_and_pos :args (@t134 1)) % 0.16/0.40 (step @p105 :rule reordering :premises (@p104) :args ((or @t132 @t136))) % 0.16/0.40 (step @p106 :rule chain_m_resolution :premises (@p105 @p103) :args (@t132 @t123 @t137)) % 0.16/0.40 (step @p107 :rule skolemize :premises (@p106)) % 0.16/0.40 (step @p108 :rule bool-double-not-elim :args (@t139)) % 0.16/0.40 (step @p109 :rule refl :args (@t143)) % 0.16/0.40 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or @t143 (not @t142)))) % 0.16/0.40 (step @p111 :rule cnf_or_neg :args (@t143 0)) % 0.16/0.40 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.16/0.40 (step @p113 :rule reordering :premises (@p112) :args ((or @t139 @t143))) % 0.16/0.40 (step @p114 :rule chain_m_resolution :premises (@p113 @p107) :args (@t139 @t108 @t144)) % 0.16/0.40 (step @p115 :rule true_intro :premises (@p114)) % 0.16/0.40 (step @p116 :rule refl :args (@t89)) % 0.16/0.40 (step @p117 :rule aci_norm :args ((= (or @t151 @t150) (or @t149 @t148 @t147 @t146 @t145 @t22)))) % 0.16/0.40 (step @p118 :rule aci_norm :args ((= (or (or @t146 @t145) @t22) @t150))) % 0.16/0.40 (step @p119 :rule refl :args (@t22)) % 0.16/0.40 (step @p120 :rule bool-and-de-morgan :args (@t25 @t24 true)) % 0.16/0.40 (step @p121 :rule nary_cong :premises (@p120 @p119) :args ((or (not @t26) @t22))) % 0.16/0.40 (step @p122 :rule trans :premises (@p121 @p118)) % 0.16/0.40 (step @p123 :rule bool-impl-elim :args (@t26 @t22)) % 0.16/0.40 (step @p124 :rule trans :premises (@p123 @p122)) % 0.16/0.40 (step @p125 :rule aci_norm :args ((= (or @t149 (or @t148 @t147)) @t151))) % 0.16/0.40 (step @p126 :rule bool-and-de-morgan :args (@t29 @t28 true)) % 0.16/0.40 (step @p127 :rule refl :args (@t149)) % 0.16/0.40 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or @t149 (not (and @t29 @t28))))) % 0.16/0.40 (step @p129 :rule bool-and-de-morgan :args (@t5 @t29 (and @t28))) % 0.16/0.40 (step @p130 :rule trans :premises (@p129 @p128)) % 0.16/0.40 (step @p131 :rule trans :premises (@p130 @p125)) % 0.16/0.40 (step @p132 :rule nary_cong :premises (@p131 @p124) :args ((or (not @t30) @t27))) % 0.16/0.40 (step @p133 :rule trans :premises (@p132 @p117)) % 0.16/0.40 (step @p134 :rule bool-impl-elim :args (@t30 @t27)) % 0.16/0.40 (step @p135 :rule trans :premises (@p134 @p133)) % 0.16/0.40 (step @p136 :rule cong :premises (@p135) :args (@t32)) % 0.16/0.40 (step @p137 :rule bool-impl-elim :args (@t5 @t152)) % 0.16/0.40 (step @p138 :rule cong :premises (@p137) :args ((forall @t6 (=> @t5 @t152)))) % 0.16/0.40 (step @p139 :rule cong :premises (@p37 @p36) :args (@t37)) % 0.16/0.40 (step @p140 :rule cong :premises (@p139) :args (@t38)) % 0.16/0.40 (step @p141 :rule trans :premises (@p140 @p138)) % 0.16/0.40 (step @p142 :rule nary_cong :premises (@p141 @p136) :args (@t39)) % 0.16/0.40 (step @p143 :rule refl :args (@t40)) % 0.16/0.40 (step @p144 :rule cong :premises (@p143 @p142) :args (@t41)) % 0.16/0.40 (step @p145 :rule cong :premises (@p144) :args (@t43)) % 0.16/0.40 (step @p146 :rule eq_resolve :premises (@p12 @p145)) % 0.16/0.40 (step @p147 :rule instantiate :premises (@p146) :args ((@list @t93 @t92 @t91))) % 0.16/0.40 (step @p148 :rule bool-double-not-elim :args (@t105)) % 0.16/0.40 (step @p149 :rule refl :args (@t107)) % 0.16/0.40 (step @p150 :rule nary_cong :premises (@p149 @p148) :args ((or @t107 (not @t106)))) % 0.16/0.40 (step @p151 :rule cnf_or_neg :args (@t107 0)) % 0.16/0.40 (step @p152 :rule eq_resolve :premises (@p151 @p150)) % 0.16/0.40 (step @p153 :rule reordering :premises (@p152) :args ((or @t105 @t107))) % 0.16/0.40 (step @p154 :rule chain_m_resolution :premises (@p153 @p73) :args (@t105 @t108 @t109)) % 0.16/0.40 (step @p155 :rule cnf_equiv_pos1 :args (@t156)) % 0.16/0.40 (step @p156 :rule reordering :premises (@p155) :args ((or @t106 @t155 (not @t156)))) % 0.16/0.40 (step @p157 :rule chain_m_resolution :premises (@p156 @p154 @p147) :args (@t155 @t121 (@list @t105 @t156))) % 0.16/0.40 (step @p158 :rule cnf_and_pos :args (@t155 1)) % 0.16/0.40 (step @p159 :rule reordering :premises (@p158) :args ((or @t154 (not @t155)))) % 0.16/0.40 (step @p160 :rule chain_m_resolution :premises (@p159 @p157) :args (@t154 @t123 (@list @t155))) % 0.16/0.40 (step @p161 :rule eq-symm :args (@t138 @t97)) % 0.16/0.40 (step @p162 :rule refl :args (@t127)) % 0.16/0.40 (step @p163 :rule refl :args (@t141)) % 0.16/0.40 (step @p164 :rule refl :args (@t157)) % 0.16/0.40 (step @p165 :rule refl :args (@t159)) % 0.16/0.40 (step @p166 :rule refl :args (@t160)) % 0.16/0.40 (step @p167 :rule nary_cong :premises (@p166 @p165 @p164 @p163 @p162 @p161) :args (@t161)) % 0.16/0.40 (step @p168 :rule refl :args (@t154)) % 0.16/0.40 (step @p169 :rule cong :premises (@p168 @p167) :args ((=> @t154 @t161))) % 0.16/0.40 (assume-push @p219 @t154) % 0.16/0.40 (step @p171 :rule instantiate :premises (@p160) :args ((@list @t99 @t138 @t97))) % 0.16/0.40 (step-pop @p220 :rule scope :premises (@p171)) % 0.16/0.40 (step @p172 :rule process_scope :premises (@p220) :args (@t161)) % 0.16/0.40 (step @p174 :rule eq_resolve :premises (@p172 @p169)) % 0.16/0.40 (step @p175 :rule implies_elim :premises (@p174)) % 0.16/0.40 (step @p176 :rule chain_m_resolution :premises (@p175 @p160) :args (@t163 @t123 (@list @t154))) % 0.16/0.40 (step @p177 :rule instantiate :premises (@p61) :args ((@list @t89 @t91))) % 0.16/0.40 (step @p178 :rule bool-double-not-elim :args (@t103)) % 0.16/0.40 (step @p179 :rule nary_cong :premises (@p149 @p178) :args ((or @t107 (not @t104)))) % 0.16/0.40 (step @p180 :rule cnf_or_neg :args (@t107 1)) % 0.16/0.40 (step @p181 :rule eq_resolve :premises (@p180 @p179)) % 0.16/0.40 (step @p182 :rule reordering :premises (@p181) :args ((or @t103 @t107))) % 0.16/0.40 (step @p183 :rule chain_m_resolution :premises (@p182 @p73) :args (@t103 @t108 @t109)) % 0.16/0.40 (step @p184 :rule cnf_equiv_pos1 :args (@t165)) % 0.16/0.40 (step @p185 :rule reordering :premises (@p184) :args ((or @t104 @t164 (not @t165)))) % 0.16/0.40 (step @p186 :rule chain_m_resolution :premises (@p185 @p183 @p177) :args (@t164 @t121 (@list @t103 @t165))) % 0.16/0.40 (step @p187 :rule instantiate :premises (@p186) :args ((@list @t138))) % 0.16/0.40 (step @p188 :rule cnf_or_pos :args (@t166)) % 0.16/0.40 (step @p189 :rule reordering :premises (@p188) :args ((or @t142 @t158 (not @t166)))) % 0.16/0.40 (step @p190 :rule chain_m_resolution :premises (@p189 @p114 @p187) :args (@t158 @t121 (@list @t139 @t166))) % 0.16/0.40 (step @p191 :rule bool-double-not-elim :args (@t140)) % 0.16/0.40 (step @p192 :rule nary_cong :premises (@p109 @p191) :args ((or @t143 (not @t141)))) % 0.16/0.40 (step @p193 :rule cnf_or_neg :args (@t143 1)) % 0.16/0.40 (step @p194 :rule eq_resolve :premises (@p193 @p192)) % 0.16/0.40 (step @p195 :rule reordering :premises (@p194) :args ((or @t140 @t143))) % 0.16/0.40 (step @p196 :rule chain_m_resolution :premises (@p195 @p107) :args (@t140 @t108 @t144)) % 0.16/0.40 (step @p197 :rule cnf_and_pos :args (@t134 0)) % 0.16/0.40 (step @p198 :rule reordering :premises (@p197) :args ((or @t133 @t136))) % 0.16/0.40 (step @p199 :rule chain_m_resolution :premises (@p198 @p103) :args (@t133 @t123 @t137)) % 0.16/0.40 (step @p200 :rule bool-double-not-elim :args (@t126)) % 0.16/0.40 (step @p201 :rule nary_cong :premises (@p95 @p200) :args ((or @t129 (not @t127)))) % 0.16/0.40 (step @p202 :rule cnf_or_neg :args (@t129 1)) % 0.16/0.40 (step @p203 :rule eq_resolve :premises (@p202 @p201)) % 0.16/0.40 (step @p204 :rule reordering :premises (@p203) :args ((or @t126 @t129))) % 0.16/0.40 (step @p205 :rule chain_m_resolution :premises (@p204 @p93) :args (@t126 @t108 @t130)) % 0.16/0.40 (step @p206 :rule cnf_and_pos :args (@t119 0)) % 0.16/0.40 (step @p207 :rule reordering :premises (@p206) :args ((or @t118 @t122))) % 0.16/0.40 (step @p208 :rule chain_m_resolution :premises (@p207 @p89) :args (@t118 @t123 @t124)) % 0.16/0.40 (step @p209 :rule cnf_or_pos :args (@t163)) % 0.16/0.40 (step @p210 :rule reordering :premises (@p209) :args ((or @t157 @t127 @t160 @t141 @t159 @t162 (not @t163)))) % 0.16/0.40 (step @p211 :rule chain_m_resolution :premises (@p210 @p208 @p205 @p199 @p196 @p190 @p176) :args (@t162 (@list false false false false false false) (@list @t118 @t126 @t133 @t140 @t158 @t163))) % 0.16/0.40 (step @p212 :rule cong :premises (@p211 @p116) :args (@t113)) % 0.16/0.40 (step @p213 :rule cnf_or_neg :args (@t115 1)) % 0.16/0.40 (step @p214 :rule chain_m_resolution :premises (@p213 @p79) :args ((not @t113) @t108 @t116)) % 0.16/0.40 (step @p215 :rule false_intro :premises (@p214)) % 0.16/0.40 (step @p216 :rule symm :premises (@p215)) % 0.16/0.40 (step @p217 :rule trans :premises (@p216 @p212 @p115)) % 0.16/0.40 (step @p218 false :rule eq_resolve :premises (@p217 @p31)) % 0.16/0.40 ) % 0.16/0.40 % SZS output end Proof % 0.16/0.40 % cvc5 exiting %------------------------------------------------------------------------------