%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET763+4 : TPTP v9.2.1. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:48:36 AM UTC 2026 % Result : Theorem 0.84s 1.04s % Output : Proof 0.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET763+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n017.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 16:09:31 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.84/1.04 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.84/1.04 % SZS status Theorem % 0.84/1.04 % SZS output start Proof % 0.84/1.04 ( % 0.84/1.04 (declare-sort $$unsorted 0) % 0.84/1.04 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.empty_set $$unsorted) % 0.84/1.04 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.84/1.04 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.84/1.04 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.84/1.04 (define @t1 () (@var "B" $$unsorted)) % 0.84/1.04 (define @t2 () (@var "X" $$unsorted)) % 0.84/1.04 (define @t3 () (tptp.member @t2 @t1)) % 0.84/1.04 (define @t4 () (@var "A" $$unsorted)) % 0.84/1.04 (define @t5 () (tptp.member @t2 @t4)) % 0.84/1.04 (define @t6 () (@list @t2)) % 0.84/1.04 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.84/1.04 (define @t8 () (tptp.subset @t4 @t1)) % 0.84/1.04 (define @t9 () (= @t8 @t7)) % 0.84/1.04 (define @t10 () (@list @t4 @t1)) % 0.84/1.04 (define @t11 () (forall @t10 @t9)) % 0.84/1.04 (define @t12 () (tptp.subset @t2 @t4)) % 0.84/1.04 (define @t13 () (@list @t2 @t4)) % 0.84/1.04 (define @t14 () (@list @t2 @t4 @t1)) % 0.84/1.04 (define @t15 () (tptp.member @t2 tptp.empty_set)) % 0.84/1.04 (define @t16 () (not @t15)) % 0.84/1.04 (define @t17 () (forall @t6 @t16)) % 0.84/1.04 (define @t18 () (@var "E" $$unsorted)) % 0.84/1.04 (define @t19 () (= @t2 @t4)) % 0.84/1.04 (define @t20 () (@var "Y" $$unsorted)) % 0.84/1.04 (define @t21 () (tptp.member @t2 @t20)) % 0.84/1.04 (define @t22 () (tptp.member @t20 @t4)) % 0.84/1.04 (define @t23 () (@list @t20)) % 0.84/1.04 (define @t24 () (@var "Y2" $$unsorted)) % 0.84/1.04 (define @t25 () (@var "Y1" $$unsorted)) % 0.84/1.04 (define @t26 () (= @t25 @t24)) % 0.84/1.04 (define @t27 () (@var "F" $$unsorted)) % 0.84/1.04 (define @t28 () (tptp.apply @t27 @t2 @t24)) % 0.84/1.04 (define @t29 () (tptp.apply @t27 @t2 @t25)) % 0.84/1.04 (define @t30 () (and @t29 @t28)) % 0.84/1.04 (define @t31 () (=> @t30 @t26)) % 0.84/1.04 (define @t32 () (tptp.member @t24 @t1)) % 0.84/1.04 (define @t33 () (tptp.member @t25 @t1)) % 0.84/1.04 (define @t34 () (and @t5 @t33 @t32)) % 0.84/1.04 (define @t35 () (@list @t2 @t25 @t24)) % 0.84/1.04 (define @t36 () (forall @t35 (=> @t34 @t31))) % 0.84/1.04 (define @t37 () (tptp.apply @t27 @t2 @t20)) % 0.84/1.04 (define @t38 () (tptp.member @t20 @t1)) % 0.84/1.04 (define @t39 () (and @t38 @t37)) % 0.84/1.04 (define @t40 () (exists @t23 @t39)) % 0.84/1.04 (define @t41 () (=> @t5 @t40)) % 0.84/1.04 (define @t42 () (forall @t6 @t41)) % 0.84/1.04 (define @t43 () (and @t42 @t36)) % 0.84/1.04 (define @t44 () (tptp.maps @t27 @t4 @t1)) % 0.84/1.04 (define @t45 () (= @t44 @t43)) % 0.84/1.04 (define @t46 () (@list @t27 @t4 @t1)) % 0.84/1.04 (define @t47 () (forall @t46 @t45)) % 0.84/1.04 (define @t48 () (@var "Z" $$unsorted)) % 0.84/1.04 (define @t49 () (@var "G" $$unsorted)) % 0.84/1.04 (define @t50 () (exists @t23 (and @t38 @t37 (tptp.apply @t49 @t20 @t48)))) % 0.84/1.04 (define @t51 () (@var "H" $$unsorted)) % 0.84/1.04 (define @t52 () (@var "C" $$unsorted)) % 0.84/1.04 (define @t53 () (and @t5 (tptp.member @t48 @t52))) % 0.84/1.04 (define @t54 () (@var "X2" $$unsorted)) % 0.84/1.04 (define @t55 () (@var "X1" $$unsorted)) % 0.84/1.04 (define @t56 () (tptp.member @t54 @t4)) % 0.84/1.04 (define @t57 () (tptp.member @t55 @t4)) % 0.84/1.04 (define @t58 () (tptp.injective @t27 @t4 @t1)) % 0.84/1.04 (define @t59 () (tptp.surjective @t27 @t4 @t1)) % 0.84/1.04 (define @t60 () (tptp.one_to_one @t27 @t4 @t1)) % 0.84/1.04 (define @t61 () (and @t5 @t38)) % 0.84/1.04 (define @t62 () (and @t5 @t37)) % 0.84/1.04 (define @t63 () (exists @t6 @t62)) % 0.84/1.04 (define @t64 () (tptp.member @t20 (tptp.image2 @t27 @t4))) % 0.84/1.04 (define @t65 () (= @t64 @t63)) % 0.84/1.04 (define @t66 () (forall (@list @t27 @t4 @t20) @t65)) % 0.84/1.04 (define @t67 () (@var "S" $$unsorted)) % 0.84/1.04 (define @t68 () (tptp.apply @t67 @t25 @t24)) % 0.84/1.04 (define @t69 () (tptp.apply @t27 @t54 @t24)) % 0.84/1.04 (define @t70 () (tptp.apply @t27 @t55 @t25)) % 0.84/1.04 (define @t71 () (@var "R" $$unsorted)) % 0.84/1.04 (define @t72 () (tptp.apply @t71 @t55 @t54)) % 0.84/1.04 (define @t73 () (and @t57 @t33 @t56 @t32 @t72 @t70 @t69)) % 0.84/1.04 (define @t74 () (@list @t55 @t25 @t54 @t24)) % 0.84/1.04 (define @t75 () (@list @t27 @t4 @t71 @t1 @t67)) % 0.84/1.04 (define @t76 () (tptp.equal_set @t2 tptp.empty_set)) % 0.84/1.04 (define @t77 () (tptp.equal_set (tptp.image2 @t27 @t2) tptp.empty_set)) % 0.84/1.04 (define @t78 () (and @t44 @t12 @t77)) % 0.84/1.04 (define @t79 () (@list @t27 @t4 @t1 @t2)) % 0.84/1.04 (define @t80 () (forall @t79 (=> @t78 @t76))) % 0.84/1.04 (define @t81 () (not @t80)) % 0.84/1.04 (define @t82 () (not @t77)) % 0.84/1.04 (define @t83 () (not @t12)) % 0.84/1.04 (define @t84 () (not @t44)) % 0.84/1.04 (define @t85 () (or @t84 @t83 @t82 @t76)) % 0.84/1.04 (define @t86 () (forall @t79 @t85)) % 0.84/1.04 (define @t87 () (@quantifiers_skolemize @t86 3)) % 0.84/1.04 (define @t88 () (@quantifiers_skolemize @t86 0)) % 0.84/1.04 (define @t89 () (tptp.image2 @t88 @t87)) % 0.84/1.04 (define @t90 () (@list @t89 tptp.empty_set)) % 0.84/1.04 (define @t91 () (or @t84 @t83 @t82)) % 0.84/1.04 (define @t92 () (tptp.equal_set @t89 tptp.empty_set)) % 0.84/1.04 (define @t93 () (tptp.equal_set @t87 tptp.empty_set)) % 0.84/1.04 (define @t94 () (not @t92)) % 0.84/1.04 (define @t95 () (@quantifiers_skolemize @t86 1)) % 0.84/1.04 (define @t96 () (tptp.subset @t87 @t95)) % 0.84/1.04 (define @t97 () (not @t96)) % 0.84/1.04 (define @t98 () (@quantifiers_skolemize @t86 2)) % 0.84/1.04 (define @t99 () (tptp.maps @t88 @t95 @t98)) % 0.84/1.04 (define @t100 () (not @t99)) % 0.84/1.04 (define @t101 () (or @t100 @t97 @t94 @t93)) % 0.84/1.04 (define @t102 () (@list true)) % 0.84/1.04 (define @t103 () (@list @t101)) % 0.84/1.04 (define @t104 () (tptp.subset @t89 tptp.empty_set)) % 0.84/1.04 (define @t105 () (and @t104 (tptp.subset tptp.empty_set @t89))) % 0.84/1.04 (define @t106 () (= @t92 @t105)) % 0.84/1.04 (define @t107 () (@list false false)) % 0.84/1.04 (define @t108 () (@list false)) % 0.84/1.04 (define @t109 () (forall @t6 (or (not (tptp.member @t2 @t89)) @t15))) % 0.84/1.04 (define @t110 () (= @t104 @t109)) % 0.84/1.04 (define @t111 () (tptp.member @t2 @t87)) % 0.84/1.04 (define @t112 () (not @t111)) % 0.84/1.04 (define @t113 () (forall @t6 (or @t112 @t15))) % 0.84/1.04 (define @t114 () (@quantifiers_skolemize @t113 0)) % 0.84/1.04 (define @t115 () (not (tptp.member @t20 @t98))) % 0.84/1.04 (define @t116 () (forall @t23 (or @t115 (not (tptp.apply @t88 @t114 @t20))))) % 0.84/1.04 (define @t117 () (@quantifiers_skolemize @t116 0)) % 0.84/1.04 (define @t118 () (@list @t117)) % 0.84/1.04 (define @t119 () (forall @t6 (not @t62))) % 0.84/1.04 (define @t120 () (not @t119)) % 0.84/1.04 (define @t121 () (not @t28)) % 0.84/1.04 (define @t122 () (not @t29)) % 0.84/1.04 (define @t123 () (not @t32)) % 0.84/1.04 (define @t124 () (not @t33)) % 0.84/1.04 (define @t125 () (not @t5)) % 0.84/1.04 (define @t126 () (or @t122 @t121 @t26)) % 0.84/1.04 (define @t127 () (or @t125 @t124 @t123)) % 0.84/1.04 (define @t128 () (not (forall @t23 (or (not @t38) (not @t37))))) % 0.84/1.04 (define @t129 () (forall @t23 (not @t39))) % 0.84/1.04 (define @t130 () (not @t129)) % 0.84/1.04 (define @t131 () (tptp.member @t2 @t95)) % 0.84/1.04 (define @t132 () (not @t131)) % 0.84/1.04 (define @t133 () (forall @t6 (or @t132 (not (forall @t23 (or @t115 (not (tptp.apply @t88 @t2 @t20)))))))) % 0.84/1.04 (define @t134 () (and @t133 (forall @t35 (or @t132 (not (tptp.member @t25 @t98)) (not (tptp.member @t24 @t98)) (not (tptp.apply @t88 @t2 @t25)) (not (tptp.apply @t88 @t2 @t24)) @t26)))) % 0.84/1.04 (define @t135 () (= @t99 @t134)) % 0.84/1.04 (define @t136 () (@list @t114)) % 0.84/1.04 (define @t137 () (forall @t6 (or @t112 @t131))) % 0.84/1.04 (define @t138 () (= @t96 @t137)) % 0.84/1.04 (define @t139 () (@list @t87 tptp.empty_set)) % 0.84/1.04 (define @t140 () (forall @t6 (or @t16 @t111))) % 0.84/1.04 (define @t141 () (@quantifiers_skolemize @t140 0)) % 0.84/1.04 (define @t142 () (tptp.member @t141 tptp.empty_set)) % 0.84/1.04 (define @t143 () (not @t142)) % 0.84/1.04 (define @t144 () (or @t143 (tptp.member @t141 @t87))) % 0.84/1.04 (define @t145 () (not @t144)) % 0.84/1.04 (define @t146 () (not @t140)) % 0.84/1.04 (define @t147 () (tptp.subset tptp.empty_set @t87)) % 0.84/1.04 (define @t148 () (= @t147 @t140)) % 0.84/1.04 (define @t149 () (tptp.subset @t87 tptp.empty_set)) % 0.84/1.04 (define @t150 () (and @t149 @t147)) % 0.84/1.04 (define @t151 () (= @t93 @t150)) % 0.84/1.04 (define @t152 () (not @t150)) % 0.84/1.04 (define @t153 () (@list true false)) % 0.84/1.04 (define @t154 () (= @t149 @t113)) % 0.84/1.04 (define @t155 () (not @t113)) % 0.84/1.04 (define @t156 () (tptp.member @t114 @t87)) % 0.84/1.04 (define @t157 () (not @t156)) % 0.84/1.04 (define @t158 () (or @t157 (tptp.member @t114 tptp.empty_set))) % 0.84/1.04 (define @t159 () (not @t158)) % 0.84/1.04 (define @t160 () (tptp.member @t114 @t95)) % 0.84/1.04 (define @t161 () (or @t157 @t160)) % 0.84/1.04 (define @t162 () (not @t116)) % 0.84/1.04 (define @t163 () (not @t160)) % 0.84/1.04 (define @t164 () (or @t163 @t162)) % 0.84/1.04 (define @t165 () (tptp.apply @t88 @t114 @t117)) % 0.84/1.04 (define @t166 () (not @t165)) % 0.84/1.04 (define @t167 () (or (not (tptp.member @t117 @t98)) @t166)) % 0.84/1.04 (define @t168 () (not @t167)) % 0.84/1.04 (define @t169 () (or @t157 @t166)) % 0.84/1.04 (define @t170 () (not @t169)) % 0.84/1.04 (define @t171 () (forall @t6 (or @t112 (not (tptp.apply @t88 @t2 @t117))))) % 0.84/1.04 (define @t172 () (not @t171)) % 0.84/1.04 (define @t173 () (tptp.member @t117 @t89)) % 0.84/1.04 (define @t174 () (= @t173 @t172)) % 0.84/1.04 (define @t175 () (not @t174)) % 0.84/1.04 (define @t176 () (tptp.member @t117 tptp.empty_set)) % 0.84/1.04 (define @t177 () (not @t173)) % 0.84/1.04 (define @t178 () (or @t177 @t176)) % 0.84/1.04 (assume @p1 @t11) % 0.84/1.04 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.84/1.04 (assume @p3 (forall @t13 (= (tptp.member @t2 (tptp.power_set @t4)) @t12))) % 0.84/1.04 (assume @p4 (forall @t14 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.84/1.04 (assume @p5 (forall @t14 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.84/1.04 (assume @p6 @t17) % 0.84/1.04 (assume @p7 (forall (@list @t1 @t4 @t18) (= (tptp.member @t1 (tptp.difference @t18 @t4)) (and (tptp.member @t1 @t18) (not (tptp.member @t1 @t4)))))) % 0.84/1.04 (assume @p8 (forall @t13 (= (tptp.member @t2 (tptp.singleton @t4)) @t19))) % 0.84/1.04 (assume @p9 (forall @t14 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t19 (= @t2 @t1))))) % 0.84/1.04 (assume @p10 (forall @t13 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t23 (and @t22 @t21))))) % 0.84/1.04 (assume @p11 (forall @t13 (= (tptp.member @t2 (tptp.product @t4)) (forall @t23 (=> @t22 @t21))))) % 0.84/1.04 (assume @p12 @t47) % 0.84/1.04 (assume @p13 (forall (@list @t51 @t49 @t27 @t4 @t1 @t52) (= (tptp.compose_predicate @t51 @t49 @t27 @t4 @t1 @t52) (forall (@list @t2 @t48) (=> @t53 (= (tptp.apply @t51 @t2 @t48) @t50)))))) % 0.84/1.04 (assume @p14 (forall (@list @t49 @t27 @t4 @t1 @t52 @t2 @t48) (=> @t53 (= (tptp.apply (tptp.compose_function @t49 @t27 @t4 @t1 @t52) @t2 @t48) @t50)))) % 0.84/1.04 (assume @p15 (forall (@list @t27 @t49 @t4 @t1) (= (tptp.equal_maps @t27 @t49 @t4 @t1) (forall @t35 (=> @t34 (=> (and @t29 (tptp.apply @t49 @t2 @t24)) @t26)))))) % 0.84/1.04 (assume @p16 (forall (@list @t27 @t4) (= (tptp.identity @t27 @t4) (forall @t6 (=> @t5 (tptp.apply @t27 @t2 @t2)))))) % 0.84/1.04 (assume @p17 (forall @t46 (= @t58 (forall (@list @t55 @t54 @t20) (=> (and @t57 @t56 @t38) (=> (and (tptp.apply @t27 @t55 @t20) (tptp.apply @t27 @t54 @t20)) (= @t55 @t54))))))) % 0.84/1.04 (assume @p18 (forall @t46 (= @t59 (forall @t23 (=> @t38 (exists (@list @t18) (and (tptp.member @t18 @t4) (tptp.apply @t27 @t18 @t20)))))))) % 0.84/1.04 (assume @p19 (forall @t46 (= @t60 (and @t58 @t59)))) % 0.84/1.04 (assume @p20 (forall (@list @t49 @t27 @t4 @t1) (= (tptp.inverse_predicate @t49 @t27 @t4 @t1) (forall (@list @t2 @t20) (=> @t61 (= @t37 (tptp.apply @t49 @t20 @t2))))))) % 0.84/1.04 (assume @p21 (forall (@list @t27 @t4 @t1 @t2 @t20) (=> @t61 (= @t37 (tptp.apply (tptp.inverse_function @t27 @t4 @t1) @t20 @t2))))) % 0.84/1.04 (assume @p22 @t66) % 0.84/1.04 (assume @p23 (forall (@list @t27 @t4 @t1 @t20) (= (tptp.member @t20 (tptp.image3 @t27 @t4 @t1)) (and @t38 @t63)))) % 0.84/1.04 (assume @p24 (forall (@list @t27 @t1 @t2) (= (tptp.member @t2 (tptp.inverse_image2 @t27 @t1)) @t40))) % 0.84/1.04 (assume @p25 (forall (@list @t27 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t27 @t1 @t4)) (and @t5 @t40)))) % 0.84/1.04 (assume @p26 (forall @t75 (= (tptp.increasing @t27 @t4 @t71 @t1 @t67) (forall @t74 (=> @t73 @t68))))) % 0.84/1.04 (assume @p27 (forall @t75 (= (tptp.decreasing @t27 @t4 @t71 @t1 @t67) (forall @t74 (=> @t73 (tptp.apply @t67 @t24 @t25)))))) % 0.84/1.04 (assume @p28 (forall @t75 (= (tptp.isomorphism @t27 @t4 @t71 @t1 @t67) (and @t44 @t60 (forall @t74 (=> (and @t57 @t33 @t56 @t32 @t70 @t69) (= @t72 @t68))))))) % 0.84/1.04 (assume @p29 @t81) % 0.84/1.04 (assume @p30 true) % 0.84/1.04 (step @p31 :rule bool-impl-elim :args (@t5 @t3)) % 0.84/1.04 (step @p32 :rule cong :premises (@p31) :args (@t7)) % 0.84/1.04 (step @p33 :rule refl :args (@t8)) % 0.84/1.04 (step @p34 :rule cong :premises (@p33 @p32) :args (@t9)) % 0.84/1.04 (step @p35 :rule cong :premises (@p34) :args (@t11)) % 0.84/1.04 (step @p36 :rule eq_resolve :premises (@p1 @p35)) % 0.84/1.04 (step @p37 :rule instantiate :premises (@p36) :args (@t90)) % 0.84/1.04 (step @p38 :rule instantiate :premises (@p2) :args (@t90)) % 0.84/1.04 (step @p39 :rule aci_norm :args ((= (or @t91 @t76) @t85))) % 0.84/1.04 (step @p40 :rule refl :args (@t76)) % 0.84/1.04 (step @p41 :rule aci_norm :args ((= (or @t84 (or @t83 @t82)) @t91))) % 0.84/1.04 (step @p42 :rule bool-and-de-morgan :args (@t12 @t77 true)) % 0.84/1.04 (step @p43 :rule refl :args (@t84)) % 0.84/1.04 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or @t84 (not (and @t12 @t77))))) % 0.84/1.04 (step @p45 :rule bool-and-de-morgan :args (@t44 @t12 (and @t77))) % 0.84/1.04 (step @p46 :rule trans :premises (@p45 @p44)) % 0.84/1.04 (step @p47 :rule trans :premises (@p46 @p41)) % 0.84/1.04 (step @p48 :rule nary_cong :premises (@p47 @p40) :args ((or (not @t78) @t76))) % 0.84/1.04 (step @p49 :rule trans :premises (@p48 @p39)) % 0.84/1.04 (step @p50 :rule bool-impl-elim :args (@t78 @t76)) % 0.84/1.04 (step @p51 :rule trans :premises (@p50 @p49)) % 0.84/1.04 (step @p52 :rule cong :premises (@p51) :args (@t80)) % 0.84/1.04 (step @p53 :rule cong :premises (@p52) :args (@t81)) % 0.84/1.04 (step @p54 :rule eq_resolve :premises (@p29 @p53)) % 0.84/1.04 (step @p55 :rule skolemize :premises (@p54)) % 0.84/1.04 (step @p56 :rule bool-double-not-elim :args (@t92)) % 0.84/1.04 (step @p57 :rule refl :args (@t101)) % 0.84/1.04 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or @t101 (not @t94)))) % 0.84/1.04 (step @p59 :rule cnf_or_neg :args (@t101 2)) % 0.84/1.04 (step @p60 :rule eq_resolve :premises (@p59 @p58)) % 0.84/1.04 (step @p61 :rule reordering :premises (@p60) :args ((or @t92 @t101))) % 0.84/1.04 (step @p62 :rule chain_m_resolution :premises (@p61 @p55) :args (@t92 @t102 @t103)) % 0.84/1.04 (step @p63 :rule cnf_equiv_pos1 :args (@t106)) % 0.84/1.04 (step @p64 :rule reordering :premises (@p63) :args ((or @t94 @t105 (not @t106)))) % 0.84/1.04 (step @p65 :rule chain_m_resolution :premises (@p64 @p62 @p38) :args (@t105 @t107 (@list @t92 @t106))) % 0.84/1.04 (step @p66 :rule cnf_and_pos :args (@t105 0)) % 0.84/1.04 (step @p67 :rule reordering :premises (@p66) :args ((or @t104 (not @t105)))) % 0.84/1.04 (step @p68 :rule chain_m_resolution :premises (@p67 @p65) :args (@t104 @t108 (@list @t105))) % 0.84/1.04 (step @p69 :rule cnf_equiv_pos1 :args (@t110)) % 0.84/1.04 (step @p70 :rule reordering :premises (@p69) :args ((or (not @t104) @t109 (not @t110)))) % 0.84/1.04 (step @p71 :rule chain_m_resolution :premises (@p70 @p68 @p37) :args (@t109 @t107 (@list @t104 @t110))) % 0.84/1.04 (step @p72 :rule instantiate :premises (@p71) :args (@t118)) % 0.84/1.04 (step @p73 :rule bool-and-de-morgan :args (@t5 @t37 true)) % 0.84/1.04 (step @p74 :rule cong :premises (@p73) :args (@t119)) % 0.84/1.04 (step @p75 :rule cong :premises (@p74) :args (@t120)) % 0.84/1.04 (step @p76 :rule exists-elim :args ((= @t63 @t120))) % 0.84/1.04 (step @p77 :rule trans :premises (@p76 @p75)) % 0.84/1.04 (step @p78 :rule refl :args (@t64)) % 0.84/1.04 (step @p79 :rule cong :premises (@p78 @p77) :args (@t65)) % 0.84/1.04 (step @p80 :rule cong :premises (@p79) :args (@t66)) % 0.84/1.04 (step @p81 :rule eq_resolve :premises (@p22 @p80)) % 0.84/1.04 (step @p82 :rule instantiate :premises (@p81) :args ((@list @t88 @t87 @t117))) % 0.84/1.04 (step @p83 :rule aci_norm :args ((= (or @t127 @t126) (or @t125 @t124 @t123 @t122 @t121 @t26)))) % 0.84/1.04 (step @p84 :rule aci_norm :args ((= (or (or @t122 @t121) @t26) @t126))) % 0.84/1.04 (step @p85 :rule refl :args (@t26)) % 0.84/1.04 (step @p86 :rule bool-and-de-morgan :args (@t29 @t28 true)) % 0.84/1.04 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or (not @t30) @t26))) % 0.84/1.04 (step @p88 :rule trans :premises (@p87 @p84)) % 0.84/1.04 (step @p89 :rule bool-impl-elim :args (@t30 @t26)) % 0.84/1.04 (step @p90 :rule trans :premises (@p89 @p88)) % 0.84/1.04 (step @p91 :rule aci_norm :args ((= (or @t125 (or @t124 @t123)) @t127))) % 0.84/1.04 (step @p92 :rule bool-and-de-morgan :args (@t33 @t32 true)) % 0.84/1.04 (step @p93 :rule refl :args (@t125)) % 0.84/1.04 (step @p94 :rule nary_cong :premises (@p93 @p92) :args ((or @t125 (not (and @t33 @t32))))) % 0.84/1.04 (step @p95 :rule bool-and-de-morgan :args (@t5 @t33 (and @t32))) % 0.84/1.04 (step @p96 :rule trans :premises (@p95 @p94)) % 0.84/1.04 (step @p97 :rule trans :premises (@p96 @p91)) % 0.84/1.04 (step @p98 :rule nary_cong :premises (@p97 @p90) :args ((or (not @t34) @t31))) % 0.84/1.04 (step @p99 :rule trans :premises (@p98 @p83)) % 0.84/1.04 (step @p100 :rule bool-impl-elim :args (@t34 @t31)) % 0.84/1.04 (step @p101 :rule trans :premises (@p100 @p99)) % 0.84/1.04 (step @p102 :rule cong :premises (@p101) :args (@t36)) % 0.84/1.04 (step @p103 :rule bool-impl-elim :args (@t5 @t128)) % 0.84/1.04 (step @p104 :rule cong :premises (@p103) :args ((forall @t6 (=> @t5 @t128)))) % 0.84/1.04 (step @p105 :rule bool-and-de-morgan :args (@t38 @t37 true)) % 0.84/1.04 (step @p106 :rule cong :premises (@p105) :args (@t129)) % 0.84/1.04 (step @p107 :rule cong :premises (@p106) :args (@t130)) % 0.84/1.04 (step @p108 :rule exists-elim :args ((= @t40 @t130))) % 0.84/1.04 (step @p109 :rule trans :premises (@p108 @p107)) % 0.84/1.04 (step @p110 :rule refl :args (@t5)) % 0.84/1.04 (step @p111 :rule cong :premises (@p110 @p109) :args (@t41)) % 0.84/1.04 (step @p112 :rule cong :premises (@p111) :args (@t42)) % 0.84/1.04 (step @p113 :rule trans :premises (@p112 @p104)) % 0.84/1.04 (step @p114 :rule nary_cong :premises (@p113 @p102) :args (@t43)) % 0.84/1.04 (step @p115 :rule refl :args (@t44)) % 0.84/1.04 (step @p116 :rule cong :premises (@p115 @p114) :args (@t45)) % 0.84/1.04 (step @p117 :rule cong :premises (@p116) :args (@t47)) % 0.84/1.04 (step @p118 :rule eq_resolve :premises (@p12 @p117)) % 0.84/1.04 (step @p119 :rule instantiate :premises (@p118) :args ((@list @t88 @t95 @t98))) % 0.84/1.04 (step @p120 :rule bool-double-not-elim :args (@t99)) % 0.84/1.04 (step @p121 :rule nary_cong :premises (@p57 @p120) :args ((or @t101 (not @t100)))) % 0.84/1.04 (step @p122 :rule cnf_or_neg :args (@t101 0)) % 0.84/1.04 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.84/1.04 (step @p124 :rule reordering :premises (@p123) :args ((or @t99 @t101))) % 0.84/1.04 (step @p125 :rule chain_m_resolution :premises (@p124 @p55) :args (@t99 @t102 @t103)) % 0.84/1.04 (step @p126 :rule cnf_equiv_pos1 :args (@t135)) % 0.84/1.04 (step @p127 :rule reordering :premises (@p126) :args ((or @t100 @t134 (not @t135)))) % 0.84/1.04 (step @p128 :rule chain_m_resolution :premises (@p127 @p125 @p119) :args (@t134 @t107 (@list @t99 @t135))) % 0.84/1.04 (step @p129 :rule cnf_and_pos :args (@t134 0)) % 0.84/1.04 (step @p130 :rule reordering :premises (@p129) :args ((or @t133 (not @t134)))) % 0.84/1.04 (step @p131 :rule chain_m_resolution :premises (@p130 @p128) :args (@t133 @t108 (@list @t134))) % 0.84/1.04 (step @p132 :rule instantiate :premises (@p131) :args (@t136)) % 0.84/1.04 (step @p133 :rule instantiate :premises (@p36) :args ((@list @t87 @t95))) % 0.84/1.04 (step @p134 :rule bool-double-not-elim :args (@t96)) % 0.84/1.04 (step @p135 :rule nary_cong :premises (@p57 @p134) :args ((or @t101 (not @t97)))) % 0.84/1.04 (step @p136 :rule cnf_or_neg :args (@t101 1)) % 0.84/1.04 (step @p137 :rule eq_resolve :premises (@p136 @p135)) % 0.84/1.04 (step @p138 :rule reordering :premises (@p137) :args ((or @t96 @t101))) % 0.84/1.04 (step @p139 :rule chain_m_resolution :premises (@p138 @p55) :args (@t96 @t102 @t103)) % 0.84/1.04 (step @p140 :rule cnf_equiv_pos1 :args (@t138)) % 0.84/1.04 (step @p141 :rule reordering :premises (@p140) :args ((or @t97 @t137 (not @t138)))) % 0.84/1.04 (step @p142 :rule chain_m_resolution :premises (@p141 @p139 @p133) :args (@t137 @t107 (@list @t96 @t138))) % 0.84/1.04 (step @p143 :rule instantiate :premises (@p142) :args (@t136)) % 0.84/1.04 (step @p144 :rule instantiate :premises (@p36) :args (@t139)) % 0.84/1.04 (step @p145 :rule instantiate :premises (@p36) :args ((@list tptp.empty_set @t87))) % 0.84/1.04 (step @p146 :rule instantiate :premises (@p6) :args ((@list @t141))) % 0.84/1.04 (step @p147 :rule bool-double-not-elim :args (@t142)) % 0.84/1.04 (step @p148 :rule refl :args (@t144)) % 0.84/1.04 (step @p149 :rule nary_cong :premises (@p148 @p147) :args ((or @t144 (not @t143)))) % 0.84/1.04 (step @p150 :rule cnf_or_neg :args (@t144 0)) % 0.84/1.04 (step @p151 :rule eq_resolve :premises (@p150 @p149)) % 0.84/1.04 (step @p152 :rule reordering :premises (@p151) :args ((or @t142 @t144))) % 0.84/1.04 (step @p153 :rule chain_m_resolution :premises (@p152 @p146) :args (@t144 @t102 (@list @t142))) % 0.84/1.04 (step @p154 :rule refl :args (@t145)) % 0.84/1.04 (step @p155 :rule bool-double-not-elim :args (@t140)) % 0.84/1.04 (step @p156 :rule nary_cong :premises (@p155 @p154) :args ((or (not @t146) @t145))) % 0.84/1.04 (assume-push @p244 @t146) % 0.84/1.04 (step @p158 :rule skolemize :premises (@p244)) % 0.84/1.04 (step-pop @p245 :rule scope :premises (@p158)) % 0.84/1.04 (step @p159 :rule process_scope :premises (@p245) :args (@t145)) % 0.84/1.04 (step @p161 :rule implies_elim :premises (@p159)) % 0.84/1.04 (step @p162 :rule eq_resolve :premises (@p161 @p156)) % 0.84/1.04 (step @p163 :rule chain_m_resolution :premises (@p162 @p153) :args (@t140 @t108 (@list @t144))) % 0.84/1.04 (step @p164 :rule cnf_equiv_pos2 :args (@t148)) % 0.84/1.04 (step @p165 :rule reordering :premises (@p164) :args ((or @t147 @t146 (not @t148)))) % 0.84/1.04 (step @p166 :rule chain_m_resolution :premises (@p165 @p163 @p145) :args (@t147 @t107 (@list @t140 @t148))) % 0.84/1.04 (step @p167 :rule instantiate :premises (@p2) :args (@t139)) % 0.84/1.04 (step @p168 :rule cnf_or_neg :args (@t101 3)) % 0.84/1.04 (step @p169 :rule chain_m_resolution :premises (@p168 @p55) :args ((not @t93) @t102 @t103)) % 0.84/1.04 (step @p170 :rule cnf_equiv_pos2 :args (@t151)) % 0.84/1.04 (step @p171 :rule reordering :premises (@p170) :args ((or @t93 @t152 (not @t151)))) % 0.84/1.04 (step @p172 :rule chain_m_resolution :premises (@p171 @p169 @p167) :args (@t152 @t153 (@list @t93 @t151))) % 0.84/1.04 (step @p173 :rule cnf_and_neg :args (@t150)) % 0.84/1.04 (step @p174 :rule chain_m_resolution :premises (@p173 @p172 @p166) :args ((not @t149) @t153 (@list @t150 @t147))) % 0.84/1.04 (step @p175 :rule cnf_equiv_pos2 :args (@t154)) % 0.84/1.04 (step @p176 :rule reordering :premises (@p175) :args ((or @t149 @t155 (not @t154)))) % 0.84/1.04 (step @p177 :rule chain_m_resolution :premises (@p176 @p174 @p144) :args (@t155 @t153 (@list @t149 @t154))) % 0.84/1.04 (step @p178 :rule refl :args (@t159)) % 0.84/1.04 (step @p179 :rule bool-double-not-elim :args (@t113)) % 0.84/1.04 (step @p180 :rule nary_cong :premises (@p179 @p178) :args ((or (not @t155) @t159))) % 0.84/1.04 (assume-push @p246 @t155) % 0.84/1.04 (step @p182 :rule skolemize :premises (@p246)) % 0.84/1.04 (step-pop @p247 :rule scope :premises (@p182)) % 0.84/1.04 (step @p183 :rule process_scope :premises (@p247) :args (@t159)) % 0.84/1.04 (step @p185 :rule implies_elim :premises (@p183)) % 0.84/1.04 (step @p186 :rule eq_resolve :premises (@p185 @p180)) % 0.84/1.04 (step @p187 :rule chain_m_resolution :premises (@p186 @p177) :args (@t159 @t102 (@list @t113))) % 0.84/1.04 (step @p188 :rule bool-double-not-elim :args (@t156)) % 0.84/1.04 (step @p189 :rule refl :args (@t158)) % 0.84/1.04 (step @p190 :rule nary_cong :premises (@p189 @p188) :args ((or @t158 (not @t157)))) % 0.84/1.04 (step @p191 :rule cnf_or_neg :args (@t158 0)) % 0.84/1.04 (step @p192 :rule eq_resolve :premises (@p191 @p190)) % 0.84/1.04 (step @p193 :rule reordering :premises (@p192) :args ((or @t156 @t158))) % 0.84/1.04 (step @p194 :rule chain_m_resolution :premises (@p193 @p187) :args (@t156 @t102 (@list @t158))) % 0.84/1.04 (step @p195 :rule cnf_or_pos :args (@t161)) % 0.84/1.04 (step @p196 :rule reordering :premises (@p195) :args ((or @t157 @t160 (not @t161)))) % 0.84/1.04 (step @p197 :rule chain_m_resolution :premises (@p196 @p194 @p143) :args (@t160 @t107 (@list @t156 @t161))) % 0.84/1.04 (step @p198 :rule cnf_or_pos :args (@t164)) % 0.84/1.04 (step @p199 :rule reordering :premises (@p198) :args ((or @t163 @t162 (not @t164)))) % 0.84/1.04 (step @p200 :rule chain_m_resolution :premises (@p199 @p197 @p132) :args (@t162 @t107 (@list @t160 @t164))) % 0.84/1.04 (step @p201 :rule refl :args (@t168)) % 0.84/1.04 (step @p202 :rule bool-double-not-elim :args (@t116)) % 0.84/1.04 (step @p203 :rule nary_cong :premises (@p202 @p201) :args ((or (not @t162) @t168))) % 0.84/1.04 (assume-push @p248 @t162) % 0.84/1.04 (step @p205 :rule skolemize :premises (@p248)) % 0.84/1.04 (step-pop @p249 :rule scope :premises (@p205)) % 0.84/1.04 (step @p206 :rule process_scope :premises (@p249) :args (@t168)) % 0.84/1.04 (step @p208 :rule implies_elim :premises (@p206)) % 0.84/1.04 (step @p209 :rule eq_resolve :premises (@p208 @p203)) % 0.84/1.04 (step @p210 :rule chain_m_resolution :premises (@p209 @p200) :args (@t168 @t102 (@list @t116))) % 0.84/1.04 (step @p211 :rule bool-double-not-elim :args (@t165)) % 0.84/1.04 (step @p212 :rule refl :args (@t167)) % 0.84/1.04 (step @p213 :rule nary_cong :premises (@p212 @p211) :args ((or @t167 (not @t166)))) % 0.84/1.04 (step @p214 :rule cnf_or_neg :args (@t167 1)) % 0.84/1.04 (step @p215 :rule eq_resolve :premises (@p214 @p213)) % 0.84/1.04 (step @p216 :rule reordering :premises (@p215) :args ((or @t165 @t167))) % 0.84/1.04 (step @p217 :rule chain_m_resolution :premises (@p216 @p210) :args (@t165 @t102 (@list @t167))) % 0.84/1.04 (step @p218 :rule cnf_or_pos :args (@t169)) % 0.84/1.04 (step @p219 :rule reordering :premises (@p218) :args ((or @t157 @t166 @t170))) % 0.84/1.04 (step @p220 :rule chain_m_resolution :premises (@p219 @p194 @p217) :args (@t170 @t107 (@list @t156 @t165))) % 0.84/1.04 (assume-push @p250 @t171) % 0.84/1.04 (step @p222 :rule instantiate :premises (@p250) :args (@t136)) % 0.84/1.04 (step-pop @p251 :rule scope :premises (@p222)) % 0.84/1.04 (step @p223 :rule process_scope :premises (@p251) :args (@t169)) % 0.84/1.04 (step @p225 :rule implies_elim :premises (@p223)) % 0.84/1.04 (step @p226 :rule chain_m_resolution :premises (@p225 @p220) :args (@t172 @t102 (@list @t169))) % 0.84/1.04 (step @p227 :rule bool-double-not-elim :args (@t171)) % 0.84/1.04 (step @p228 :rule refl :args (@t173)) % 0.84/1.04 (step @p229 :rule refl :args (@t175)) % 0.84/1.04 (step @p230 :rule nary_cong :premises (@p229 @p228 @p227) :args ((or @t175 @t173 (not @t172)))) % 0.84/1.04 (step @p231 :rule cnf_equiv_pos2 :args (@t174)) % 0.84/1.04 (step @p232 :rule eq_resolve :premises (@p231 @p230)) % 0.84/1.04 (step @p233 :rule reordering :premises (@p232) :args ((or @t173 @t171 @t175))) % 0.84/1.04 (step @p234 :rule chain_m_resolution :premises (@p233 @p226 @p82) :args (@t173 @t153 (@list @t171 @t174))) % 0.84/1.04 (step @p235 :rule cnf_or_pos :args (@t178)) % 0.84/1.04 (step @p236 :rule reordering :premises (@p235) :args ((or @t176 @t177 (not @t178)))) % 0.84/1.04 (step @p237 :rule chain_m_resolution :premises (@p236 @p234 @p72) :args (@t176 @t107 (@list @t173 @t178))) % 0.84/1.04 (assume-push @p252 @t17) % 0.84/1.04 (step @p239 :rule instantiate :premises (@p6) :args (@t118)) % 0.84/1.04 (step-pop @p253 :rule scope :premises (@p239)) % 0.84/1.04 (step @p240 :rule process_scope :premises (@p253) :args ((not @t176))) % 0.84/1.04 (step @p242 :rule implies_elim :premises (@p240)) % 0.84/1.04 (step @p243 false :rule chain_m_resolution :premises (@p242 @p237 @p6) :args (false @t107 (@list @t176 @t17))) % 0.84/1.04 ) % 0.84/1.04 % SZS output end Proof % 0.84/1.04 % cvc5 exiting %------------------------------------------------------------------------------