%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET754+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 : 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 08:48:35 AM UTC 2026 % Result : Theorem 0.41s 0.63s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET754+4 : TPTP v9.2.1. Bugfixed v2.2.1. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n017.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:09:31 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.41/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.41/0.63 % SZS status Theorem % 0.41/0.63 % SZS output start Proof % 0.41/0.63 ( % 0.41/0.63 (declare-sort $$unsorted 0) % 0.41/0.63 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.inverse_function (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.empty_set $$unsorted) % 0.41/0.63 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.equal_maps (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.one_to_one (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.increasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.surjective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.isomorphism (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.maps (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.compose_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.identity (-> $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.injective (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.compose_function (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.inverse_predicate (-> $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.inverse_image2 (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.63 (declare-const tptp.decreasing (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.63 (declare-const tptp.inverse_image3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.41/0.63 (define @t1 () (@var "B" $$unsorted)) % 0.41/0.63 (define @t2 () (@var "X" $$unsorted)) % 0.41/0.63 (define @t3 () (tptp.member @t2 @t1)) % 0.41/0.63 (define @t4 () (@var "A" $$unsorted)) % 0.41/0.63 (define @t5 () (tptp.member @t2 @t4)) % 0.41/0.63 (define @t6 () (@list @t2)) % 0.41/0.63 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.41/0.63 (define @t8 () (tptp.subset @t4 @t1)) % 0.41/0.63 (define @t9 () (= @t8 @t7)) % 0.41/0.63 (define @t10 () (@list @t4 @t1)) % 0.41/0.63 (define @t11 () (forall @t10 @t9)) % 0.41/0.63 (define @t12 () (@list @t2 @t4)) % 0.41/0.63 (define @t13 () (@list @t2 @t4 @t1)) % 0.41/0.63 (define @t14 () (@var "E" $$unsorted)) % 0.41/0.63 (define @t15 () (= @t2 @t4)) % 0.41/0.63 (define @t16 () (@var "Y" $$unsorted)) % 0.41/0.63 (define @t17 () (tptp.member @t2 @t16)) % 0.41/0.63 (define @t18 () (tptp.member @t16 @t4)) % 0.41/0.63 (define @t19 () (@list @t16)) % 0.41/0.63 (define @t20 () (@var "Y2" $$unsorted)) % 0.41/0.63 (define @t21 () (@var "Y1" $$unsorted)) % 0.41/0.63 (define @t22 () (= @t21 @t20)) % 0.41/0.63 (define @t23 () (@var "F" $$unsorted)) % 0.41/0.63 (define @t24 () (tptp.apply @t23 @t2 @t20)) % 0.41/0.63 (define @t25 () (tptp.apply @t23 @t2 @t21)) % 0.41/0.63 (define @t26 () (and @t25 @t24)) % 0.41/0.63 (define @t27 () (=> @t26 @t22)) % 0.41/0.63 (define @t28 () (tptp.member @t20 @t1)) % 0.41/0.63 (define @t29 () (tptp.member @t21 @t1)) % 0.41/0.63 (define @t30 () (and @t5 @t29 @t28)) % 0.41/0.63 (define @t31 () (@list @t2 @t21 @t20)) % 0.41/0.63 (define @t32 () (forall @t31 (=> @t30 @t27))) % 0.41/0.63 (define @t33 () (tptp.apply @t23 @t2 @t16)) % 0.41/0.63 (define @t34 () (tptp.member @t16 @t1)) % 0.41/0.63 (define @t35 () (and @t34 @t33)) % 0.41/0.63 (define @t36 () (exists @t19 @t35)) % 0.41/0.63 (define @t37 () (=> @t5 @t36)) % 0.41/0.63 (define @t38 () (forall @t6 @t37)) % 0.41/0.63 (define @t39 () (and @t38 @t32)) % 0.41/0.63 (define @t40 () (tptp.maps @t23 @t4 @t1)) % 0.41/0.63 (define @t41 () (= @t40 @t39)) % 0.41/0.63 (define @t42 () (@list @t23 @t4 @t1)) % 0.41/0.63 (define @t43 () (forall @t42 @t41)) % 0.41/0.63 (define @t44 () (@var "Z" $$unsorted)) % 0.41/0.63 (define @t45 () (@var "G" $$unsorted)) % 0.41/0.63 (define @t46 () (exists @t19 (and @t34 @t33 (tptp.apply @t45 @t16 @t44)))) % 0.41/0.63 (define @t47 () (@var "H" $$unsorted)) % 0.41/0.63 (define @t48 () (@var "C" $$unsorted)) % 0.41/0.63 (define @t49 () (and @t5 (tptp.member @t44 @t48))) % 0.41/0.63 (define @t50 () (@var "X2" $$unsorted)) % 0.41/0.63 (define @t51 () (@var "X1" $$unsorted)) % 0.41/0.63 (define @t52 () (tptp.member @t50 @t4)) % 0.41/0.63 (define @t53 () (tptp.member @t51 @t4)) % 0.41/0.63 (define @t54 () (tptp.injective @t23 @t4 @t1)) % 0.41/0.63 (define @t55 () (tptp.surjective @t23 @t4 @t1)) % 0.41/0.63 (define @t56 () (tptp.one_to_one @t23 @t4 @t1)) % 0.41/0.63 (define @t57 () (and @t5 @t34)) % 0.41/0.63 (define @t58 () (and @t5 @t33)) % 0.41/0.63 (define @t59 () (exists @t6 @t58)) % 0.41/0.63 (define @t60 () (tptp.member @t16 (tptp.image2 @t23 @t4))) % 0.41/0.63 (define @t61 () (= @t60 @t59)) % 0.41/0.63 (define @t62 () (forall (@list @t23 @t4 @t16) @t61)) % 0.41/0.63 (define @t63 () (tptp.member @t2 (tptp.inverse_image2 @t23 @t1))) % 0.41/0.63 (define @t64 () (forall (@list @t23 @t1 @t2) (= @t63 @t36))) % 0.41/0.63 (define @t65 () (@var "S" $$unsorted)) % 0.41/0.63 (define @t66 () (tptp.apply @t65 @t21 @t20)) % 0.41/0.63 (define @t67 () (tptp.apply @t23 @t50 @t20)) % 0.41/0.63 (define @t68 () (tptp.apply @t23 @t51 @t21)) % 0.41/0.63 (define @t69 () (@var "R" $$unsorted)) % 0.41/0.63 (define @t70 () (tptp.apply @t69 @t51 @t50)) % 0.41/0.63 (define @t71 () (and @t53 @t29 @t52 @t28 @t70 @t68 @t67)) % 0.41/0.63 (define @t72 () (@list @t51 @t21 @t50 @t20)) % 0.41/0.63 (define @t73 () (@list @t23 @t4 @t69 @t1 @t65)) % 0.41/0.63 (define @t74 () (tptp.subset @t48 (tptp.inverse_image2 @t23 (tptp.image2 @t23 @t48)))) % 0.41/0.63 (define @t75 () (tptp.subset @t48 @t4)) % 0.41/0.63 (define @t76 () (and @t40 @t75)) % 0.41/0.63 (define @t77 () (@list @t23 @t4 @t1 @t48)) % 0.41/0.63 (define @t78 () (forall @t77 (=> @t76 @t74))) % 0.41/0.63 (define @t79 () (not @t78)) % 0.41/0.63 (define @t80 () (forall @t6 (not @t58))) % 0.41/0.63 (define @t81 () (not @t80)) % 0.41/0.63 (define @t82 () (not @t75)) % 0.41/0.63 (define @t83 () (not @t40)) % 0.41/0.63 (define @t84 () (or @t83 @t82 @t74)) % 0.41/0.63 (define @t85 () (forall @t77 @t84)) % 0.41/0.63 (define @t86 () (@quantifiers_skolemize @t85 3)) % 0.41/0.63 (define @t87 () (@quantifiers_skolemize @t85 0)) % 0.41/0.63 (define @t88 () (tptp.image2 @t87 @t86)) % 0.41/0.63 (define @t89 () (tptp.inverse_image2 @t87 @t88)) % 0.41/0.63 (define @t90 () (not (tptp.member @t2 @t86))) % 0.41/0.63 (define @t91 () (forall @t6 (or @t90 (tptp.member @t2 @t89)))) % 0.41/0.63 (define @t92 () (@quantifiers_skolemize @t91 0)) % 0.41/0.63 (define @t93 () (not (tptp.apply @t87 @t92 @t16))) % 0.41/0.63 (define @t94 () (@quantifiers_skolemize @t85 2)) % 0.41/0.63 (define @t95 () (not (tptp.member @t16 @t94))) % 0.41/0.63 (define @t96 () (forall @t19 (or @t95 @t93))) % 0.41/0.63 (define @t97 () (@quantifiers_skolemize @t96 0)) % 0.41/0.63 (define @t98 () (not (forall @t19 (or (not @t34) (not @t33))))) % 0.41/0.63 (define @t99 () (forall @t19 (not @t35))) % 0.41/0.63 (define @t100 () (not @t99)) % 0.41/0.63 (define @t101 () (tptp.subset @t86 @t89)) % 0.41/0.63 (define @t102 () (@quantifiers_skolemize @t85 1)) % 0.41/0.63 (define @t103 () (tptp.subset @t86 @t102)) % 0.41/0.63 (define @t104 () (not @t103)) % 0.41/0.63 (define @t105 () (tptp.maps @t87 @t102 @t94)) % 0.41/0.63 (define @t106 () (not @t105)) % 0.41/0.63 (define @t107 () (or @t106 @t104 @t101)) % 0.41/0.63 (define @t108 () (@list true)) % 0.41/0.63 (define @t109 () (@list @t107)) % 0.41/0.63 (define @t110 () (= @t101 @t91)) % 0.41/0.63 (define @t111 () (not @t91)) % 0.41/0.63 (define @t112 () (@list true false)) % 0.41/0.63 (define @t113 () (tptp.member @t92 @t89)) % 0.41/0.63 (define @t114 () (tptp.member @t92 @t86)) % 0.41/0.63 (define @t115 () (not @t114)) % 0.41/0.63 (define @t116 () (or @t115 @t113)) % 0.41/0.63 (define @t117 () (@list @t116)) % 0.41/0.63 (define @t118 () (forall @t19 (or (not (tptp.member @t16 @t88)) @t93))) % 0.41/0.63 (define @t119 () (not @t118)) % 0.41/0.63 (define @t120 () (= @t113 @t119)) % 0.41/0.63 (define @t121 () (not @t120)) % 0.41/0.63 (define @t122 () (not @t24)) % 0.41/0.63 (define @t123 () (not @t25)) % 0.41/0.63 (define @t124 () (not @t28)) % 0.41/0.63 (define @t125 () (not @t29)) % 0.41/0.63 (define @t126 () (not @t5)) % 0.41/0.63 (define @t127 () (or @t123 @t122 @t22)) % 0.41/0.63 (define @t128 () (or @t126 @t125 @t124)) % 0.41/0.63 (define @t129 () (tptp.member @t2 @t102)) % 0.41/0.63 (define @t130 () (not @t129)) % 0.41/0.63 (define @t131 () (forall @t6 (or @t130 (not (forall @t19 (or @t95 (not (tptp.apply @t87 @t2 @t16)))))))) % 0.41/0.63 (define @t132 () (and @t131 (forall @t31 (or @t130 (not (tptp.member @t21 @t94)) (not (tptp.member @t20 @t94)) (not (tptp.apply @t87 @t2 @t21)) (not (tptp.apply @t87 @t2 @t20)) @t22)))) % 0.41/0.63 (define @t133 () (= @t105 @t132)) % 0.41/0.63 (define @t134 () (@list false false)) % 0.41/0.63 (define @t135 () (@list @t92)) % 0.41/0.63 (define @t136 () (forall @t6 (or @t90 @t129))) % 0.41/0.63 (define @t137 () (= @t103 @t136)) % 0.41/0.63 (define @t138 () (tptp.member @t92 @t102)) % 0.41/0.63 (define @t139 () (or @t115 @t138)) % 0.41/0.63 (define @t140 () (not @t96)) % 0.41/0.63 (define @t141 () (not @t138)) % 0.41/0.63 (define @t142 () (or @t141 @t140)) % 0.41/0.63 (define @t143 () (tptp.apply @t87 @t92 @t97)) % 0.41/0.63 (define @t144 () (not @t143)) % 0.41/0.63 (define @t145 () (or (not (tptp.member @t97 @t94)) @t144)) % 0.41/0.63 (define @t146 () (tptp.member @t97 @t88)) % 0.41/0.63 (define @t147 () (not @t146)) % 0.41/0.63 (define @t148 () (or @t147 @t144)) % 0.41/0.63 (define @t149 () (forall @t6 (or @t90 (not (tptp.apply @t87 @t2 @t97))))) % 0.41/0.63 (define @t150 () (not @t149)) % 0.41/0.63 (define @t151 () (= @t146 @t150)) % 0.41/0.63 (define @t152 () (not @t151)) % 0.41/0.63 (define @t153 () (or @t115 @t144)) % 0.41/0.63 (define @t154 () (not @t153)) % 0.41/0.63 (assume @p1 @t11) % 0.41/0.63 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.41/0.63 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.41/0.63 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.41/0.63 (assume @p5 (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.41/0.63 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.41/0.63 (assume @p7 (forall (@list @t1 @t4 @t14) (= (tptp.member @t1 (tptp.difference @t14 @t4)) (and (tptp.member @t1 @t14) (not (tptp.member @t1 @t4)))))) % 0.41/0.63 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t15))) % 0.41/0.63 (assume @p9 (forall @t13 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t15 (= @t2 @t1))))) % 0.41/0.63 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t19 (and @t18 @t17))))) % 0.41/0.63 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t19 (=> @t18 @t17))))) % 0.41/0.63 (assume @p12 @t43) % 0.41/0.63 (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)))))) % 0.41/0.63 (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)))) % 0.41/0.63 (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)))))) % 0.41/0.63 (assume @p16 (forall (@list @t23 @t4) (= (tptp.identity @t23 @t4) (forall @t6 (=> @t5 (tptp.apply @t23 @t2 @t2)))))) % 0.41/0.63 (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))))))) % 0.41/0.63 (assume @p18 (forall @t42 (= @t55 (forall @t19 (=> @t34 (exists (@list @t14) (and (tptp.member @t14 @t4) (tptp.apply @t23 @t14 @t16)))))))) % 0.41/0.63 (assume @p19 (forall @t42 (= @t56 (and @t54 @t55)))) % 0.41/0.63 (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))))))) % 0.41/0.63 (assume @p21 (forall (@list @t23 @t4 @t1 @t2 @t16) (=> @t57 (= @t33 (tptp.apply (tptp.inverse_function @t23 @t4 @t1) @t16 @t2))))) % 0.41/0.63 (assume @p22 @t62) % 0.41/0.63 (assume @p23 (forall (@list @t23 @t4 @t1 @t16) (= (tptp.member @t16 (tptp.image3 @t23 @t4 @t1)) (and @t34 @t59)))) % 0.41/0.63 (assume @p24 @t64) % 0.41/0.63 (assume @p25 (forall (@list @t23 @t1 @t4 @t2) (= (tptp.member @t2 (tptp.inverse_image3 @t23 @t1 @t4)) (and @t5 @t36)))) % 0.41/0.63 (assume @p26 (forall @t73 (= (tptp.increasing @t23 @t4 @t69 @t1 @t65) (forall @t72 (=> @t71 @t66))))) % 0.41/0.63 (assume @p27 (forall @t73 (= (tptp.decreasing @t23 @t4 @t69 @t1 @t65) (forall @t72 (=> @t71 (tptp.apply @t65 @t20 @t21)))))) % 0.41/0.63 (assume @p28 (forall @t73 (= (tptp.isomorphism @t23 @t4 @t69 @t1 @t65) (and @t40 @t56 (forall @t72 (=> (and @t53 @t29 @t52 @t28 @t68 @t67) (= @t70 @t66))))))) % 0.41/0.63 (assume @p29 @t79) % 0.41/0.63 (assume @p30 true) % 0.41/0.63 (step @p31 :rule bool-and-de-morgan :args (@t5 @t33 true)) % 0.41/0.63 (step @p32 :rule cong :premises (@p31) :args (@t80)) % 0.41/0.63 (step @p33 :rule cong :premises (@p32) :args (@t81)) % 0.41/0.63 (step @p34 :rule exists-elim :args ((= @t59 @t81))) % 0.41/0.63 (step @p35 :rule trans :premises (@p34 @p33)) % 0.41/0.63 (step @p36 :rule refl :args (@t60)) % 0.41/0.63 (step @p37 :rule cong :premises (@p36 @p35) :args (@t61)) % 0.41/0.63 (step @p38 :rule cong :premises (@p37) :args (@t62)) % 0.41/0.63 (step @p39 :rule eq_resolve :premises (@p22 @p38)) % 0.41/0.63 (step @p40 :rule instantiate :premises (@p39) :args ((@list @t87 @t86 @t97))) % 0.41/0.63 (step @p41 :rule eq-symm :args (@t98 @t63)) % 0.41/0.63 (step @p42 :rule refl :args (@t63)) % 0.41/0.63 (step @p43 :rule bool-and-de-morgan :args (@t34 @t33 true)) % 0.41/0.63 (step @p44 :rule cong :premises (@p43) :args (@t99)) % 0.41/0.63 (step @p45 :rule cong :premises (@p44) :args (@t100)) % 0.41/0.63 (step @p46 :rule exists-elim :args ((= @t36 @t100))) % 0.41/0.63 (step @p47 :rule trans :premises (@p46 @p45)) % 0.41/0.63 (step @p48 :rule cong :premises (@p47 @p42) :args ((= @t36 @t63))) % 0.41/0.63 (step @p49 :rule trans :premises (@p48 @p41)) % 0.41/0.63 (step @p50 :rule eq-symm :args (@t63 @t36)) % 0.41/0.63 (step @p51 :rule trans :premises (@p50 @p49)) % 0.41/0.63 (step @p52 :rule cong :premises (@p51) :args (@t64)) % 0.41/0.63 (step @p53 :rule eq_resolve :premises (@p24 @p52)) % 0.41/0.63 (step @p54 :rule instantiate :premises (@p53) :args ((@list @t87 @t88 @t92))) % 0.41/0.63 (step @p55 :rule bool-impl-elim :args (@t5 @t3)) % 0.41/0.63 (step @p56 :rule cong :premises (@p55) :args (@t7)) % 0.41/0.63 (step @p57 :rule refl :args (@t8)) % 0.41/0.63 (step @p58 :rule cong :premises (@p57 @p56) :args (@t9)) % 0.41/0.63 (step @p59 :rule cong :premises (@p58) :args (@t11)) % 0.41/0.63 (step @p60 :rule eq_resolve :premises (@p1 @p59)) % 0.41/0.63 (step @p61 :rule instantiate :premises (@p60) :args ((@list @t86 @t89))) % 0.41/0.63 (step @p62 :rule aci_norm :args ((= (or (or @t83 @t82) @t74) @t84))) % 0.41/0.63 (step @p63 :rule refl :args (@t74)) % 0.41/0.63 (step @p64 :rule bool-and-de-morgan :args (@t40 @t75 true)) % 0.41/0.63 (step @p65 :rule nary_cong :premises (@p64 @p63) :args ((or (not @t76) @t74))) % 0.41/0.63 (step @p66 :rule trans :premises (@p65 @p62)) % 0.41/0.63 (step @p67 :rule bool-impl-elim :args (@t76 @t74)) % 0.41/0.63 (step @p68 :rule trans :premises (@p67 @p66)) % 0.41/0.63 (step @p69 :rule cong :premises (@p68) :args (@t78)) % 0.41/0.63 (step @p70 :rule cong :premises (@p69) :args (@t79)) % 0.41/0.63 (step @p71 :rule eq_resolve :premises (@p29 @p70)) % 0.41/0.63 (step @p72 :rule skolemize :premises (@p71)) % 0.41/0.63 (step @p73 :rule cnf_or_neg :args (@t107 2)) % 0.41/0.63 (step @p74 :rule chain_m_resolution :premises (@p73 @p72) :args ((not @t101) @t108 @t109)) % 0.41/0.63 (step @p75 :rule cnf_equiv_pos2 :args (@t110)) % 0.41/0.63 (step @p76 :rule reordering :premises (@p75) :args ((or @t101 @t111 (not @t110)))) % 0.41/0.63 (step @p77 :rule chain_m_resolution :premises (@p76 @p74 @p61) :args (@t111 @t112 (@list @t101 @t110))) % 0.41/0.63 (step @p78 :rule skolemize :premises (@p77)) % 0.41/0.63 (step @p79 :rule cnf_or_neg :args (@t116 1)) % 0.41/0.63 (step @p80 :rule chain_m_resolution :premises (@p79 @p78) :args ((not @t113) @t108 @t117)) % 0.41/0.63 (step @p81 :rule bool-double-not-elim :args (@t118)) % 0.41/0.63 (step @p82 :rule refl :args (@t113)) % 0.41/0.63 (step @p83 :rule refl :args (@t121)) % 0.41/0.63 (step @p84 :rule nary_cong :premises (@p83 @p82 @p81) :args ((or @t121 @t113 (not @t119)))) % 0.41/0.63 (step @p85 :rule cnf_equiv_pos2 :args (@t120)) % 0.41/0.63 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.41/0.63 (step @p87 :rule reordering :premises (@p86) :args ((or @t113 @t118 @t121))) % 0.41/0.63 (step @p88 :rule chain_m_resolution :premises (@p87 @p80 @p54) :args (@t118 @t112 (@list @t113 @t120))) % 0.41/0.63 (step @p89 :rule instantiate :premises (@p88) :args ((@list @t97))) % 0.41/0.63 (step @p90 :rule aci_norm :args ((= (or @t128 @t127) (or @t126 @t125 @t124 @t123 @t122 @t22)))) % 0.41/0.63 (step @p91 :rule aci_norm :args ((= (or (or @t123 @t122) @t22) @t127))) % 0.41/0.63 (step @p92 :rule refl :args (@t22)) % 0.41/0.63 (step @p93 :rule bool-and-de-morgan :args (@t25 @t24 true)) % 0.41/0.63 (step @p94 :rule nary_cong :premises (@p93 @p92) :args ((or (not @t26) @t22))) % 0.41/0.63 (step @p95 :rule trans :premises (@p94 @p91)) % 0.41/0.63 (step @p96 :rule bool-impl-elim :args (@t26 @t22)) % 0.41/0.63 (step @p97 :rule trans :premises (@p96 @p95)) % 0.41/0.63 (step @p98 :rule aci_norm :args ((= (or @t126 (or @t125 @t124)) @t128))) % 0.41/0.63 (step @p99 :rule bool-and-de-morgan :args (@t29 @t28 true)) % 0.41/0.63 (step @p100 :rule refl :args (@t126)) % 0.41/0.63 (step @p101 :rule nary_cong :premises (@p100 @p99) :args ((or @t126 (not (and @t29 @t28))))) % 0.41/0.63 (step @p102 :rule bool-and-de-morgan :args (@t5 @t29 (and @t28))) % 0.41/0.63 (step @p103 :rule trans :premises (@p102 @p101)) % 0.41/0.63 (step @p104 :rule trans :premises (@p103 @p98)) % 0.41/0.63 (step @p105 :rule nary_cong :premises (@p104 @p97) :args ((or (not @t30) @t27))) % 0.41/0.63 (step @p106 :rule trans :premises (@p105 @p90)) % 0.41/0.63 (step @p107 :rule bool-impl-elim :args (@t30 @t27)) % 0.41/0.63 (step @p108 :rule trans :premises (@p107 @p106)) % 0.41/0.63 (step @p109 :rule cong :premises (@p108) :args (@t32)) % 0.41/0.63 (step @p110 :rule bool-impl-elim :args (@t5 @t98)) % 0.41/0.63 (step @p111 :rule cong :premises (@p110) :args ((forall @t6 (=> @t5 @t98)))) % 0.41/0.63 (step @p112 :rule refl :args (@t5)) % 0.41/0.63 (step @p113 :rule cong :premises (@p112 @p47) :args (@t37)) % 0.41/0.63 (step @p114 :rule cong :premises (@p113) :args (@t38)) % 0.41/0.63 (step @p115 :rule trans :premises (@p114 @p111)) % 0.41/0.63 (step @p116 :rule nary_cong :premises (@p115 @p109) :args (@t39)) % 0.41/0.63 (step @p117 :rule refl :args (@t40)) % 0.41/0.63 (step @p118 :rule cong :premises (@p117 @p116) :args (@t41)) % 0.41/0.63 (step @p119 :rule cong :premises (@p118) :args (@t43)) % 0.41/0.63 (step @p120 :rule eq_resolve :premises (@p12 @p119)) % 0.41/0.63 (step @p121 :rule instantiate :premises (@p120) :args ((@list @t87 @t102 @t94))) % 0.41/0.63 (step @p122 :rule bool-double-not-elim :args (@t105)) % 0.41/0.63 (step @p123 :rule refl :args (@t107)) % 0.41/0.63 (step @p124 :rule nary_cong :premises (@p123 @p122) :args ((or @t107 (not @t106)))) % 0.41/0.63 (step @p125 :rule cnf_or_neg :args (@t107 0)) % 0.41/0.63 (step @p126 :rule eq_resolve :premises (@p125 @p124)) % 0.41/0.63 (step @p127 :rule reordering :premises (@p126) :args ((or @t105 @t107))) % 0.41/0.63 (step @p128 :rule chain_m_resolution :premises (@p127 @p72) :args (@t105 @t108 @t109)) % 0.41/0.63 (step @p129 :rule cnf_equiv_pos1 :args (@t133)) % 0.41/0.63 (step @p130 :rule reordering :premises (@p129) :args ((or @t106 @t132 (not @t133)))) % 0.41/0.63 (step @p131 :rule chain_m_resolution :premises (@p130 @p128 @p121) :args (@t132 @t134 (@list @t105 @t133))) % 0.41/0.63 (step @p132 :rule cnf_and_pos :args (@t132 0)) % 0.41/0.63 (step @p133 :rule reordering :premises (@p132) :args ((or @t131 (not @t132)))) % 0.41/0.63 (step @p134 :rule chain_m_resolution :premises (@p133 @p131) :args (@t131 (@list false) (@list @t132))) % 0.41/0.63 (step @p135 :rule instantiate :premises (@p134) :args (@t135)) % 0.41/0.63 (step @p136 :rule instantiate :premises (@p60) :args ((@list @t86 @t102))) % 0.41/0.63 (step @p137 :rule bool-double-not-elim :args (@t103)) % 0.41/0.63 (step @p138 :rule nary_cong :premises (@p123 @p137) :args ((or @t107 (not @t104)))) % 0.41/0.63 (step @p139 :rule cnf_or_neg :args (@t107 1)) % 0.41/0.63 (step @p140 :rule eq_resolve :premises (@p139 @p138)) % 0.41/0.63 (step @p141 :rule reordering :premises (@p140) :args ((or @t103 @t107))) % 0.41/0.63 (step @p142 :rule chain_m_resolution :premises (@p141 @p72) :args (@t103 @t108 @t109)) % 0.41/0.63 (step @p143 :rule cnf_equiv_pos1 :args (@t137)) % 0.41/0.63 (step @p144 :rule reordering :premises (@p143) :args ((or @t104 @t136 (not @t137)))) % 0.41/0.63 (step @p145 :rule chain_m_resolution :premises (@p144 @p142 @p136) :args (@t136 @t134 (@list @t103 @t137))) % 0.41/0.63 (step @p146 :rule instantiate :premises (@p145) :args (@t135)) % 0.41/0.63 (step @p147 :rule bool-double-not-elim :args (@t114)) % 0.41/0.63 (step @p148 :rule refl :args (@t116)) % 0.41/0.63 (step @p149 :rule nary_cong :premises (@p148 @p147) :args ((or @t116 (not @t115)))) % 0.41/0.63 (step @p150 :rule cnf_or_neg :args (@t116 0)) % 0.41/0.63 (step @p151 :rule eq_resolve :premises (@p150 @p149)) % 0.41/0.63 (step @p152 :rule reordering :premises (@p151) :args ((or @t114 @t116))) % 0.41/0.63 (step @p153 :rule chain_m_resolution :premises (@p152 @p78) :args (@t114 @t108 @t117)) % 0.41/0.63 (step @p154 :rule cnf_or_pos :args (@t139)) % 0.41/0.63 (step @p155 :rule reordering :premises (@p154) :args ((or @t115 @t138 (not @t139)))) % 0.41/0.63 (step @p156 :rule chain_m_resolution :premises (@p155 @p153 @p146) :args (@t138 @t134 (@list @t114 @t139))) % 0.41/0.63 (step @p157 :rule cnf_or_pos :args (@t142)) % 0.41/0.63 (step @p158 :rule reordering :premises (@p157) :args ((or @t141 @t140 (not @t142)))) % 0.41/0.63 (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p135) :args (@t140 @t134 (@list @t138 @t142))) % 0.41/0.63 (step @p160 :rule skolemize :premises (@p159)) % 0.41/0.63 (step @p161 :rule bool-double-not-elim :args (@t143)) % 0.41/0.63 (step @p162 :rule refl :args (@t145)) % 0.41/0.63 (step @p163 :rule nary_cong :premises (@p162 @p161) :args ((or @t145 (not @t144)))) % 0.41/0.63 (step @p164 :rule cnf_or_neg :args (@t145 1)) % 0.41/0.63 (step @p165 :rule eq_resolve :premises (@p164 @p163)) % 0.41/0.63 (step @p166 :rule reordering :premises (@p165) :args ((or @t143 @t145))) % 0.41/0.63 (step @p167 :rule chain_m_resolution :premises (@p166 @p160) :args (@t143 @t108 (@list @t145))) % 0.41/0.63 (step @p168 :rule cnf_or_pos :args (@t148)) % 0.41/0.63 (step @p169 :rule reordering :premises (@p168) :args ((or @t144 @t147 (not @t148)))) % 0.41/0.63 (step @p170 :rule chain_m_resolution :premises (@p169 @p167 @p89) :args (@t147 @t134 (@list @t143 @t148))) % 0.41/0.63 (step @p171 :rule bool-double-not-elim :args (@t149)) % 0.41/0.63 (step @p172 :rule refl :args (@t146)) % 0.41/0.63 (step @p173 :rule refl :args (@t152)) % 0.41/0.63 (step @p174 :rule nary_cong :premises (@p173 @p172 @p171) :args ((or @t152 @t146 (not @t150)))) % 0.41/0.63 (step @p175 :rule cnf_equiv_pos2 :args (@t151)) % 0.41/0.63 (step @p176 :rule eq_resolve :premises (@p175 @p174)) % 0.41/0.63 (step @p177 :rule reordering :premises (@p176) :args ((or @t146 @t149 @t152))) % 0.41/0.63 (step @p178 :rule chain_m_resolution :premises (@p177 @p170 @p40) :args (@t149 @t112 (@list @t146 @t151))) % 0.41/0.63 (step @p179 :rule cnf_or_pos :args (@t153)) % 0.41/0.63 (step @p180 :rule reordering :premises (@p179) :args ((or @t115 @t144 @t154))) % 0.41/0.63 (step @p181 :rule chain_m_resolution :premises (@p180 @p153 @p167) :args (@t154 @t134 (@list @t114 @t143))) % 0.41/0.63 (assume-push @p188 @t149) % 0.41/0.63 (step @p183 :rule instantiate :premises (@p178) :args (@t135)) % 0.41/0.63 (step-pop @p189 :rule scope :premises (@p183)) % 0.41/0.63 (step @p184 :rule process_scope :premises (@p189) :args (@t153)) % 0.41/0.63 (step @p186 :rule implies_elim :premises (@p184)) % 0.41/0.63 (step @p187 false :rule chain_m_resolution :premises (@p186 @p181 @p178) :args (false @t112 (@list @t153 @t149))) % 0.41/0.63 ) % 0.41/0.63 % SZS output end Proof % 0.41/0.63 % cvc5 exiting %------------------------------------------------------------------------------