%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET016-6 : TPTP v9.2.1. Bugfixed v2.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:46:57 AM UTC 2026 % Result : Unsatisfiable 33.70s 34.00s % Output : Proof 33.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SET016-6 : TPTP v9.2.1. Bugfixed v2.1.0. % 0.08/0.15 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.36 % Computer : n004.cluster.edu % 0.16/0.36 % Model : x86_64 x86_64 % 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.36 % Memory : 8042.1875MB % 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.36 % CPULimit : 300 % 0.16/0.36 % WCLimit : 300 % 0.16/0.36 % DateTime : Tue Jun 2 14:40:37 EDT 2026 % 0.16/0.36 % CPUTime : % 0.28/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.28/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.41/15.69 --- Run --no-e-matching --full-saturate-quant at 6... % 21.52/21.74 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 27.53/27.80 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.62/33.86 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 33.70/34.00 % SZS status Unsatisfiable % 33.70/34.00 % SZS output start Proof % 33.70/34.01 ( % 33.70/34.01 (declare-sort $$unsorted 0) % 33.70/34.01 (declare-const tptp.not_homomorphism2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.compatible (-> $$unsorted $$unsorted $$unsorted Bool)) % 33.70/34.01 (declare-const tptp.operation (-> $$unsorted Bool)) % 33.70/34.01 (declare-const tptp.cantor (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.diagonalise (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.regular (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.z $$unsorted) % 33.70/34.01 (declare-const tptp.function (-> $$unsorted Bool)) % 33.70/34.01 (declare-const tptp.single_valued_class (-> $$unsorted Bool)) % 33.70/34.01 (declare-const tptp.compose (-> $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.element_relation $$unsorted) % 33.70/34.01 (declare-const tptp.power_class (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.second (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.complement (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.not_homomorphism1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.universal_class $$unsorted) % 33.70/34.01 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 33.70/34.01 (declare-const tptp.restrict (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.subclass (-> $$unsorted $$unsorted Bool)) % 33.70/34.01 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 33.70/34.01 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.successor_relation $$unsorted) % 33.70/34.01 (declare-const tptp.choice $$unsorted) % 33.70/34.01 (declare-const tptp.symmetric_difference (-> $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.y $$unsorted) % 33.70/34.01 (declare-const tptp.domain_of (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.x $$unsorted) % 33.70/34.01 (declare-const tptp.subset_relation $$unsorted) % 33.70/34.01 (declare-const tptp.null_class $$unsorted) % 33.70/34.01 (declare-const tptp.w $$unsorted) % 33.70/34.01 (declare-const tptp.range_of (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.omega $$unsorted) % 33.70/34.01 (declare-const tptp.homomorphism (-> $$unsorted $$unsorted $$unsorted Bool)) % 33.70/34.01 (declare-const tptp.rotate (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.range (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.flip (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.identity_relation $$unsorted) % 33.70/34.01 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.sum_class (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.domain (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.not_subclass_element (-> $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.cross_product (-> $$unsorted $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.successor (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.first (-> $$unsorted $$unsorted)) % 33.70/34.01 (declare-const tptp.inductive (-> $$unsorted Bool)) % 33.70/34.01 (define @t1 () (@var "Y" $$unsorted)) % 33.70/34.01 (define @t2 () (@var "U" $$unsorted)) % 33.70/34.01 (define @t3 () (@var "X" $$unsorted)) % 33.70/34.01 (define @t4 () (tptp.member @t2 @t3)) % 33.70/34.01 (define @t5 () (not @t4)) % 33.70/34.01 (define @t6 () (tptp.subclass @t3 @t1)) % 33.70/34.01 (define @t7 () (not @t6)) % 33.70/34.01 (define @t8 () (tptp.not_subclass_element @t3 @t1)) % 33.70/34.01 (define @t9 () (@list @t3 @t1)) % 33.70/34.01 (define @t10 () (@list @t3)) % 33.70/34.01 (define @t11 () (= @t3 @t1)) % 33.70/34.01 (define @t12 () (not @t11)) % 33.70/34.01 (define @t13 () (tptp.subclass @t1 @t3)) % 33.70/34.01 (define @t14 () (tptp.unordered_pair @t3 @t1)) % 33.70/34.01 (define @t15 () (not (tptp.member @t2 @t14))) % 33.70/34.01 (define @t16 () (or @t15 (= @t2 @t3) (= @t2 @t1))) % 33.70/34.01 (define @t17 () (@list @t2 @t3 @t1)) % 33.70/34.01 (define @t18 () (forall @t17 @t16)) % 33.70/34.01 (define @t19 () (not (tptp.member @t3 tptp.universal_class))) % 33.70/34.01 (define @t20 () (not (tptp.member @t1 tptp.universal_class))) % 33.70/34.01 (define @t21 () (tptp.singleton @t3)) % 33.70/34.01 (define @t22 () (forall @t10 (= (tptp.unordered_pair @t3 @t3) @t21))) % 33.70/34.01 (define @t23 () (tptp.ordered_pair @t3 @t1)) % 33.70/34.01 (define @t24 () (tptp.singleton @t1)) % 33.70/34.01 (define @t25 () (forall @t9 (= (tptp.unordered_pair @t21 (tptp.unordered_pair @t3 @t24)) @t23))) % 33.70/34.01 (define @t26 () (tptp.cross_product @t3 @t1)) % 33.70/34.01 (define @t27 () (@var "V" $$unsorted)) % 33.70/34.01 (define @t28 () (tptp.ordered_pair @t2 @t27)) % 33.70/34.01 (define @t29 () (tptp.member @t28 @t26)) % 33.70/34.01 (define @t30 () (not @t29)) % 33.70/34.01 (define @t31 () (@list @t2 @t27 @t3 @t1)) % 33.70/34.01 (define @t32 () (tptp.member @t27 @t1)) % 33.70/34.01 (define @t33 () (@var "Z" $$unsorted)) % 33.70/34.01 (define @t34 () (@list @t33 @t3 @t1)) % 33.70/34.01 (define @t35 () (tptp.cross_product tptp.universal_class tptp.universal_class)) % 33.70/34.01 (define @t36 () (tptp.member @t3 @t1)) % 33.70/34.01 (define @t37 () (tptp.member @t23 tptp.element_relation)) % 33.70/34.01 (define @t38 () (not (tptp.member @t23 @t35))) % 33.70/34.01 (define @t39 () (tptp.member @t33 @t3)) % 33.70/34.01 (define @t40 () (tptp.intersection @t3 @t1)) % 33.70/34.01 (define @t41 () (tptp.member @t33 @t40)) % 33.70/34.01 (define @t42 () (not @t41)) % 33.70/34.01 (define @t43 () (tptp.member @t33 @t1)) % 33.70/34.01 (define @t44 () (not @t39)) % 33.70/34.01 (define @t45 () (tptp.complement @t3)) % 33.70/34.01 (define @t46 () (tptp.member @t33 @t45)) % 33.70/34.01 (define @t47 () (@list @t33 @t3)) % 33.70/34.01 (define @t48 () (not (tptp.member @t33 tptp.universal_class))) % 33.70/34.01 (define @t49 () (tptp.complement (tptp.intersection @t45 (tptp.complement @t1)))) % 33.70/34.01 (define @t50 () (@var "Xr" $$unsorted)) % 33.70/34.01 (define @t51 () (tptp.restrict @t50 @t3 @t1)) % 33.70/34.01 (define @t52 () (tptp.domain_of @t3)) % 33.70/34.01 (define @t53 () (tptp.member @t33 @t52)) % 33.70/34.01 (define @t54 () (= (tptp.restrict @t3 (tptp.singleton @t33) tptp.universal_class) tptp.null_class)) % 33.70/34.01 (define @t55 () (tptp.cross_product @t35 tptp.universal_class)) % 33.70/34.01 (define @t56 () (tptp.rotate @t3)) % 33.70/34.01 (define @t57 () (@var "W" $$unsorted)) % 33.70/34.01 (define @t58 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t27 @t57) @t2) @t3)) % 33.70/34.01 (define @t59 () (tptp.ordered_pair @t28 @t57)) % 33.70/34.01 (define @t60 () (tptp.member @t59 @t56)) % 33.70/34.01 (define @t61 () (@list @t2 @t27 @t57 @t3)) % 33.70/34.01 (define @t62 () (not (tptp.member @t59 @t55))) % 33.70/34.01 (define @t63 () (tptp.flip @t3)) % 33.70/34.01 (define @t64 () (tptp.member (tptp.ordered_pair (tptp.ordered_pair @t27 @t2) @t57) @t3)) % 33.70/34.01 (define @t65 () (tptp.member @t59 @t63)) % 33.70/34.01 (define @t66 () (@list @t1)) % 33.70/34.01 (define @t67 () (tptp.successor @t3)) % 33.70/34.01 (define @t68 () (= @t67 @t1)) % 33.70/34.01 (define @t69 () (tptp.member @t23 tptp.successor_relation)) % 33.70/34.01 (define @t70 () (tptp.member tptp.null_class @t3)) % 33.70/34.01 (define @t71 () (tptp.inductive @t3)) % 33.70/34.01 (define @t72 () (not @t71)) % 33.70/34.01 (define @t73 () (tptp.subclass (tptp.image tptp.successor_relation @t3) @t3)) % 33.70/34.01 (define @t74 () (tptp.sum_class @t3)) % 33.70/34.01 (define @t75 () (@var "Yr" $$unsorted)) % 33.70/34.01 (define @t76 () (tptp.compose @t75 @t50)) % 33.70/34.01 (define @t77 () (tptp.member @t33 (tptp.image @t75 (tptp.image @t50 @t24)))) % 33.70/34.01 (define @t78 () (tptp.ordered_pair @t1 @t33)) % 33.70/34.01 (define @t79 () (tptp.member @t78 @t76)) % 33.70/34.01 (define @t80 () (tptp.subclass (tptp.compose @t3 (tptp.inverse @t3)) tptp.identity_relation)) % 33.70/34.01 (define @t81 () (tptp.single_valued_class @t3)) % 33.70/34.01 (define @t82 () (@var "Xf" $$unsorted)) % 33.70/34.01 (define @t83 () (tptp.subclass @t82 @t35)) % 33.70/34.01 (define @t84 () (tptp.function @t82)) % 33.70/34.01 (define @t85 () (not @t84)) % 33.70/34.01 (define @t86 () (@list @t82)) % 33.70/34.01 (define @t87 () (tptp.inverse @t82)) % 33.70/34.01 (define @t88 () (tptp.subclass (tptp.compose @t82 @t87) tptp.identity_relation)) % 33.70/34.01 (define @t89 () (tptp.regular @t3)) % 33.70/34.01 (define @t90 () (= @t3 tptp.null_class)) % 33.70/34.01 (define @t91 () (tptp.one_to_one @t82)) % 33.70/34.01 (define @t92 () (not @t91)) % 33.70/34.01 (define @t93 () (tptp.function @t87)) % 33.70/34.01 (define @t94 () (tptp.inverse tptp.element_relation)) % 33.70/34.01 (define @t95 () (tptp.operation @t82)) % 33.70/34.01 (define @t96 () (not @t95)) % 33.70/34.01 (define @t97 () (tptp.domain_of @t82)) % 33.70/34.01 (define @t98 () (tptp.domain_of @t97)) % 33.70/34.01 (define @t99 () (= (tptp.cross_product @t98 @t98) @t97)) % 33.70/34.01 (define @t100 () (tptp.subclass (tptp.range_of @t82) @t98)) % 33.70/34.01 (define @t101 () (@var "Xh" $$unsorted)) % 33.70/34.01 (define @t102 () (tptp.function @t101)) % 33.70/34.01 (define @t103 () (@var "Xf2" $$unsorted)) % 33.70/34.01 (define @t104 () (@var "Xf1" $$unsorted)) % 33.70/34.01 (define @t105 () (tptp.compatible @t101 @t104 @t103)) % 33.70/34.01 (define @t106 () (not @t105)) % 33.70/34.01 (define @t107 () (@list @t101 @t104 @t103)) % 33.70/34.01 (define @t108 () (tptp.domain_of @t104)) % 33.70/34.01 (define @t109 () (= (tptp.domain_of @t108) (tptp.domain_of @t101))) % 33.70/34.01 (define @t110 () (tptp.subclass (tptp.range_of @t101) (tptp.domain_of (tptp.domain_of @t103)))) % 33.70/34.01 (define @t111 () (tptp.operation @t104)) % 33.70/34.01 (define @t112 () (tptp.homomorphism @t101 @t104 @t103)) % 33.70/34.01 (define @t113 () (not @t112)) % 33.70/34.01 (define @t114 () (tptp.operation @t103)) % 33.70/34.01 (define @t115 () (tptp.not_homomorphism2 @t101 @t104 @t103)) % 33.70/34.01 (define @t116 () (tptp.not_homomorphism1 @t101 @t104 @t103)) % 33.70/34.01 (define @t117 () (tptp.ordered_pair @t116 @t115)) % 33.70/34.01 (define @t118 () (not @t114)) % 33.70/34.01 (define @t119 () (not @t111)) % 33.70/34.01 (define @t120 () (@list @t104 @t103 @t101)) % 33.70/34.01 (define @t121 () (tptp.ordered_pair tptp.y tptp.z)) % 33.70/34.01 (define @t122 () (tptp.member tptp.w tptp.universal_class)) % 33.70/34.01 (define @t123 () (= tptp.w tptp.y)) % 33.70/34.01 (define @t124 () (tptp.unordered_pair tptp.w tptp.w)) % 33.70/34.01 (define @t125 () (tptp.singleton tptp.w)) % 33.70/34.01 (define @t126 () (= @t124 @t125)) % 33.70/34.01 (define @t127 () (= @t125 @t124)) % 33.70/34.01 (define @t128 () (@list false)) % 33.70/34.01 (define @t129 () (@list @t22)) % 33.70/34.01 (define @t130 () (tptp.unordered_pair tptp.y tptp.y)) % 33.70/34.01 (define @t131 () (tptp.singleton tptp.y)) % 33.70/34.01 (define @t132 () (= @t130 @t131)) % 33.70/34.01 (define @t133 () (@list tptp.y)) % 33.70/34.01 (define @t134 () (= @t131 @t130)) % 33.70/34.01 (define @t135 () (tptp.member tptp.w @t130)) % 33.70/34.01 (define @t136 () (not @t135)) % 33.70/34.01 (define @t137 () (= tptp.y tptp.w)) % 33.70/34.01 (define @t138 () (or @t136 @t137 @t137)) % 33.70/34.01 (define @t139 () (forall @t17 (or @t15 (= @t3 @t2) (= @t1 @t2)))) % 33.70/34.01 (define @t140 () (or @t136 @t123 @t123)) % 33.70/34.01 (define @t141 () (tptp.singleton tptp.x)) % 33.70/34.01 (define @t142 () (tptp.unordered_pair tptp.w @t141)) % 33.70/34.01 (define @t143 () (tptp.unordered_pair tptp.y (tptp.singleton tptp.z))) % 33.70/34.01 (define @t144 () (tptp.member @t131 tptp.universal_class)) % 33.70/34.01 (define @t145 () (tptp.unordered_pair @t131 @t143)) % 33.70/34.01 (define @t146 () (tptp.member @t131 @t145)) % 33.70/34.01 (define @t147 () (not @t144)) % 33.70/34.01 (define @t148 () (or @t147 @t146)) % 33.70/34.01 (define @t149 () (@list false false)) % 33.70/34.01 (define @t150 () (= @t145 @t121)) % 33.70/34.01 (define @t151 () (tptp.member @t131 (tptp.unordered_pair @t125 @t142))) % 33.70/34.01 (define @t152 () (tptp.member tptp.w @t142)) % 33.70/34.01 (define @t153 () (not @t122)) % 33.70/34.01 (define @t154 () (or @t153 @t152)) % 33.70/34.01 (define @t155 () (= @t142 @t131)) % 33.70/34.01 (define @t156 () (not @t155)) % 33.70/34.01 (define @t157 () (not @t134)) % 33.70/34.01 (define @t158 () (not @t152)) % 33.70/34.01 (define @t159 () (not @t136)) % 33.70/34.01 (define @t160 () (and @t136 @t134 @t155 @t152)) % 33.70/34.01 (define @t161 () (= @t125 @t131)) % 33.70/34.01 (define @t162 () (not @t151)) % 33.70/34.01 (define @t163 () (or @t162 @t161 @t155)) % 33.70/34.01 (define @t164 () (tptp.member tptp.w @t124)) % 33.70/34.01 (define @t165 () (or @t153 @t164)) % 33.70/34.01 (define @t166 () (not @t164)) % 33.70/34.01 (define @t167 () (not @t161)) % 33.70/34.01 (define @t168 () (not @t127)) % 33.70/34.01 (define @t169 () (and @t164 @t127 @t161 @t134 @t136)) % 33.70/34.01 (assume @p1 (forall (@list @t3 @t1 @t2) (or @t7 @t5 (tptp.member @t2 @t1)))) % 33.70/34.01 (assume @p2 (forall @t9 (or (tptp.member @t8 @t3) @t6))) % 33.70/34.01 (assume @p3 (forall @t9 (or (not (tptp.member @t8 @t1)) @t6))) % 33.70/34.01 (assume @p4 (forall @t10 (tptp.subclass @t3 tptp.universal_class))) % 33.70/34.01 (assume @p5 (forall @t9 (or @t12 @t6))) % 33.70/34.01 (assume @p6 (forall @t9 (or @t12 @t13))) % 33.70/34.01 (assume @p7 (forall @t9 (or @t7 (not @t13) @t11))) % 33.70/34.01 (assume @p8 @t18) % 33.70/34.01 (assume @p9 (forall @t9 (or @t19 (tptp.member @t3 @t14)))) % 33.70/34.01 (assume @p10 (forall (@list @t1 @t3) (or @t20 (tptp.member @t1 @t14)))) % 33.70/34.01 (assume @p11 (forall @t9 (tptp.member @t14 tptp.universal_class))) % 33.70/34.01 (assume @p12 @t22) % 33.70/34.01 (assume @p13 @t25) % 33.70/34.01 (assume @p14 (forall @t31 (or @t30 @t4))) % 33.70/34.01 (assume @p15 (forall @t31 (or @t30 @t32))) % 33.70/34.01 (assume @p16 (forall (@list @t2 @t3 @t27 @t1) (or @t5 (not @t32) @t29))) % 33.70/34.01 (assume @p17 (forall @t34 (or (not (tptp.member @t33 @t26)) (= (tptp.ordered_pair (tptp.first @t33) (tptp.second @t33)) @t33)))) % 33.70/34.01 (assume @p18 (tptp.subclass tptp.element_relation @t35)) % 33.70/34.01 (assume @p19 (forall @t9 (or (not @t37) @t36))) % 33.70/34.01 (assume @p20 (forall @t9 (or @t38 (not @t36) @t37))) % 33.70/34.01 (assume @p21 (forall @t34 (or @t42 @t39))) % 33.70/34.01 (assume @p22 (forall @t34 (or @t42 @t43))) % 33.70/34.01 (assume @p23 (forall @t34 (or @t44 (not @t43) @t41))) % 33.70/34.01 (assume @p24 (forall @t47 (or (not @t46) @t44))) % 33.70/34.01 (assume @p25 (forall @t47 (or @t48 @t46 @t39))) % 33.70/34.01 (assume @p26 (forall @t9 (= @t49 (tptp.union @t3 @t1)))) % 33.70/34.01 (assume @p27 (forall @t9 (= (tptp.intersection (tptp.complement @t40) @t49) (tptp.symmetric_difference @t3 @t1)))) % 33.70/34.01 (assume @p28 (forall (@list @t50 @t3 @t1) (= (tptp.intersection @t50 @t26) @t51))) % 33.70/34.01 (assume @p29 (forall (@list @t3 @t1 @t50) (= (tptp.intersection @t26 @t50) @t51))) % 33.70/34.01 (assume @p30 (forall (@list @t3 @t33) (or (not @t54) (not @t53)))) % 33.70/34.01 (assume @p31 (forall @t47 (or @t48 @t54 @t53))) % 33.70/34.01 (assume @p32 (forall @t10 (tptp.subclass @t56 @t55))) % 33.70/34.01 (assume @p33 (forall @t61 (or (not @t60) @t58))) % 33.70/34.01 (assume @p34 (forall (@list @t27 @t57 @t2 @t3) (or (not @t58) @t62 @t60))) % 33.70/34.01 (assume @p35 (forall @t10 (tptp.subclass @t63 @t55))) % 33.70/34.01 (assume @p36 (forall @t61 (or (not @t65) @t64))) % 33.70/34.01 (assume @p37 (forall (@list @t27 @t2 @t57 @t3) (or (not @t64) @t62 @t65))) % 33.70/34.01 (assume @p38 (forall @t66 (= (tptp.domain_of (tptp.flip (tptp.cross_product @t1 tptp.universal_class))) (tptp.inverse @t1)))) % 33.70/34.01 (assume @p39 (forall (@list @t33) (= (tptp.domain_of (tptp.inverse @t33)) (tptp.range_of @t33)))) % 33.70/34.01 (assume @p40 (forall @t34 (= (tptp.first (tptp.not_subclass_element (tptp.restrict @t33 @t3 @t24) tptp.null_class)) (tptp.domain @t33 @t3 @t1)))) % 33.70/34.01 (assume @p41 (forall @t34 (= (tptp.second (tptp.not_subclass_element (tptp.restrict @t33 @t21 @t1) tptp.null_class)) (tptp.range @t33 @t3 @t1)))) % 33.70/34.01 (assume @p42 (forall (@list @t50 @t3) (= (tptp.range_of (tptp.restrict @t50 @t3 tptp.universal_class)) (tptp.image @t50 @t3)))) % 33.70/34.01 (assume @p43 (forall @t10 (= (tptp.union @t3 @t21) @t67))) % 33.70/34.01 (assume @p44 (tptp.subclass tptp.successor_relation @t35)) % 33.70/34.01 (assume @p45 (forall @t9 (or (not @t69) @t68))) % 33.70/34.01 (assume @p46 (forall @t9 (or (not @t68) @t38 @t69))) % 33.70/34.01 (assume @p47 (forall @t10 (or @t72 @t70))) % 33.70/34.01 (assume @p48 (forall @t10 (or @t72 @t73))) % 33.70/34.01 (assume @p49 (forall @t10 (or (not @t70) (not @t73) @t71))) % 33.70/34.01 (assume @p50 (tptp.inductive tptp.omega)) % 33.70/34.01 (assume @p51 (forall @t66 (or (not (tptp.inductive @t1)) (tptp.subclass tptp.omega @t1)))) % 33.70/34.01 (assume @p52 (tptp.member tptp.omega tptp.universal_class)) % 33.70/34.01 (assume @p53 (forall @t10 (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class @t3)) @t74))) % 33.70/34.01 (assume @p54 (forall @t10 (or @t19 (tptp.member @t74 tptp.universal_class)))) % 33.70/34.01 (assume @p55 (forall @t10 (= (tptp.complement (tptp.image tptp.element_relation @t45)) (tptp.power_class @t3)))) % 33.70/34.01 (assume @p56 (forall (@list @t2) (or (not (tptp.member @t2 tptp.universal_class)) (tptp.member (tptp.power_class @t2) tptp.universal_class)))) % 33.70/34.01 (assume @p57 (forall (@list @t75 @t50) (tptp.subclass @t76 @t35))) % 33.70/34.01 (assume @p58 (forall (@list @t1 @t33 @t75 @t50) (or (not @t79) @t77))) % 33.70/34.01 (assume @p59 (forall (@list @t33 @t75 @t50 @t1) (or (not @t77) (not (tptp.member @t78 @t35)) @t79))) % 33.70/34.01 (assume @p60 (forall @t10 (or (not @t81) @t80))) % 33.70/34.01 (assume @p61 (forall @t10 (or (not @t80) @t81))) % 33.70/34.01 (assume @p62 (forall @t86 (or @t85 @t83))) % 33.70/34.01 (assume @p63 (forall @t86 (or @t85 @t88))) % 33.70/34.01 (assume @p64 (forall @t86 (or (not @t83) (not @t88) @t84))) % 33.70/34.01 (assume @p65 (forall (@list @t82 @t3) (or @t85 @t19 (tptp.member (tptp.image @t82 @t3) tptp.universal_class)))) % 33.70/34.01 (assume @p66 (forall @t10 (or @t90 (tptp.member @t89 @t3)))) % 33.70/34.01 (assume @p67 (forall @t10 (or @t90 (= (tptp.intersection @t3 @t89) tptp.null_class)))) % 33.70/34.01 (assume @p68 (forall (@list @t82 @t1) (= (tptp.sum_class (tptp.image @t82 @t24)) (tptp.apply @t82 @t1)))) % 33.70/34.01 (assume @p69 (tptp.function tptp.choice)) % 33.70/34.01 (assume @p70 (forall @t66 (or @t20 (= @t1 tptp.null_class) (tptp.member (tptp.apply tptp.choice @t1) @t1)))) % 33.70/34.01 (assume @p71 (forall @t86 (or @t92 @t84))) % 33.70/34.01 (assume @p72 (forall @t86 (or @t92 @t93))) % 33.70/34.01 (assume @p73 (forall @t86 (or (not @t93) @t85 @t91))) % 33.70/34.01 (assume @p74 (= (tptp.intersection @t35 (tptp.intersection @t35 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) @t94)))) tptp.subset_relation)) % 33.70/34.01 (assume @p75 (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation)) % 33.70/34.01 (assume @p76 (forall (@list @t50) (= (tptp.complement (tptp.domain_of (tptp.intersection @t50 tptp.identity_relation))) (tptp.diagonalise @t50)))) % 33.70/34.01 (assume @p77 (forall @t10 (= (tptp.intersection @t52 (tptp.diagonalise (tptp.compose @t94 @t3))) (tptp.cantor @t3)))) % 33.70/34.01 (assume @p78 (forall @t86 (or @t96 @t84))) % 33.70/34.01 (assume @p79 (forall @t86 (or @t96 @t99))) % 33.70/34.01 (assume @p80 (forall @t86 (or @t96 @t100))) % 33.70/34.01 (assume @p81 (forall @t86 (or @t85 (not @t99) (not @t100) @t95))) % 33.70/34.01 (assume @p82 (forall @t107 (or @t106 @t102))) % 33.70/34.01 (assume @p83 (forall @t107 (or @t106 @t109))) % 33.70/34.01 (assume @p84 (forall @t107 (or @t106 @t110))) % 33.70/34.01 (assume @p85 (forall @t107 (or (not @t102) (not @t109) (not @t110) @t105))) % 33.70/34.01 (assume @p86 (forall @t107 (or @t113 @t111))) % 33.70/34.01 (assume @p87 (forall @t107 (or @t113 @t114))) % 33.70/34.01 (assume @p88 (forall @t107 (or @t113 @t105))) % 33.70/34.01 (assume @p89 (forall (@list @t101 @t104 @t103 @t3 @t1) (or @t113 (not (tptp.member @t23 @t108)) (= (tptp.apply @t103 (tptp.ordered_pair (tptp.apply @t101 @t3) (tptp.apply @t101 @t1))) (tptp.apply @t101 (tptp.apply @t104 @t23)))))) % 33.70/34.01 (assume @p90 (forall @t120 (or @t119 @t118 @t106 (tptp.member @t117 @t108) @t112))) % 33.70/34.01 (assume @p91 (forall @t120 (or @t119 @t118 @t106 (not (= (tptp.apply @t103 (tptp.ordered_pair (tptp.apply @t101 @t116) (tptp.apply @t101 @t115))) (tptp.apply @t101 (tptp.apply @t104 @t117)))) @t112))) % 33.70/34.01 (assume @p92 (= (tptp.ordered_pair tptp.w tptp.x) @t121)) % 33.70/34.01 (assume @p93 @t122) % 33.70/34.01 (assume @p94 (not @t123)) % 33.70/34.01 (step @p95 :rule eq-symm :args (@t124 @t125)) % 33.70/34.01 (step @p96 :rule refl :args (@t22)) % 33.70/34.01 (step @p97 :rule cong :premises (@p96 @p95) :args ((=> @t22 @t126))) % 33.70/34.01 (assume-push @p253 @t22) % 33.70/34.01 (step @p99 :rule instantiate :premises (@p12) :args ((@list tptp.w))) % 33.70/34.01 (step-pop @p254 :rule scope :premises (@p99)) % 33.70/34.01 (step @p100 :rule process_scope :premises (@p254) :args (@t126)) % 33.70/34.01 (step @p102 :rule eq_resolve :premises (@p100 @p97)) % 33.70/34.01 (step @p103 :rule implies_elim :premises (@p102)) % 33.70/34.01 (step @p104 :rule chain_m_resolution :premises (@p103 @p12) :args (@t127 @t128 @t129)) % 33.70/34.01 (step @p105 :rule eq-symm :args (@t130 @t131)) % 33.70/34.01 (step @p106 :rule cong :premises (@p96 @p105) :args ((=> @t22 @t132))) % 33.70/34.01 (assume-push @p255 @t22) % 33.70/34.01 (step @p108 :rule instantiate :premises (@p12) :args (@t133)) % 33.70/34.01 (step-pop @p256 :rule scope :premises (@p108)) % 33.70/34.01 (step @p109 :rule process_scope :premises (@p256) :args (@t132)) % 33.70/34.01 (step @p111 :rule eq_resolve :premises (@p109 @p106)) % 33.70/34.01 (step @p112 :rule implies_elim :premises (@p111)) % 33.70/34.01 (step @p113 :rule chain_m_resolution :premises (@p112 @p12) :args (@t134 @t128 @t129)) % 33.70/34.01 (step @p114 :rule eq-symm :args (@t2 @t1)) % 33.70/34.01 (step @p115 :rule eq-symm :args (@t2 @t3)) % 33.70/34.01 (step @p116 :rule refl :args (@t15)) % 33.70/34.01 (step @p117 :rule nary_cong :premises (@p116 @p115 @p114) :args (@t16)) % 33.70/34.01 (step @p118 :rule cong :premises (@p117) :args (@t18)) % 33.70/34.01 (step @p119 :rule eq_resolve :premises (@p8 @p118)) % 33.70/34.01 (step @p120 :rule eq-symm :args (tptp.y tptp.w)) % 33.70/34.01 (step @p121 :rule refl :args (@t136)) % 33.70/34.01 (step @p122 :rule nary_cong :premises (@p121 @p120 @p120) :args (@t138)) % 33.70/34.01 (step @p123 :rule refl :args (@t139)) % 33.70/34.01 (step @p124 :rule cong :premises (@p123 @p122) :args ((=> @t139 @t138))) % 33.70/34.01 (assume-push @p257 @t139) % 33.70/34.01 (step @p126 :rule instantiate :premises (@p119) :args ((@list tptp.w tptp.y tptp.y))) % 33.70/34.01 (step-pop @p258 :rule scope :premises (@p126)) % 33.70/34.01 (step @p127 :rule process_scope :premises (@p258) :args (@t138)) % 33.70/34.01 (step @p129 :rule eq_resolve :premises (@p127 @p124)) % 33.70/34.01 (step @p130 :rule implies_elim :premises (@p129)) % 33.70/34.01 (step @p131 :rule chain_m_resolution :premises (@p130 @p119) :args (@t140 @t128 (@list @t139))) % 33.70/34.01 (step @p132 :rule cnf_or_pos :args (@t140)) % 33.70/34.01 (step @p133 :rule factoring :premises (@p132)) % 33.70/34.01 (step @p134 :rule reordering :premises (@p133) :args ((or @t123 @t136 (not @t140)))) % 33.70/34.01 (step @p135 :rule chain_m_resolution :premises (@p134 @p94 @p131) :args (@t136 (@list true false) (@list @t123 @t140))) % 33.70/34.01 (step @p136 :rule instantiate :premises (@p119) :args ((@list @t131 @t125 @t142))) % 33.70/34.01 (step @p137 :rule instantiate :premises (@p9) :args ((@list @t131 @t143))) % 33.70/34.01 (step @p138 :rule instantiate :premises (@p11) :args ((@list tptp.y tptp.y))) % 33.70/34.01 (step @p139 :rule true_intro :premises (@p138)) % 33.70/34.01 (step @p140 :rule refl :args (tptp.universal_class)) % 33.70/34.01 (step @p141 :rule cong :premises (@p113 @p140) :args (@t144)) % 33.70/34.01 (step @p142 :rule trans :premises (@p141 @p139)) % 33.70/34.01 (step @p143 :rule true_elim :premises (@p142)) % 33.70/34.01 (step @p144 :rule cnf_or_pos :args (@t148)) % 33.70/34.01 (step @p145 :rule reordering :premises (@p144) :args ((or @t147 @t146 (not @t148)))) % 33.70/34.01 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p137) :args (@t146 @t149 (@list @t144 @t148))) % 33.70/34.01 (step @p147 :rule true_intro :premises (@p146)) % 33.70/34.01 (step @p148 :rule eq-symm :args (@t145 @t121)) % 33.70/34.01 (step @p149 :rule refl :args (@t25)) % 33.70/34.01 (step @p150 :rule cong :premises (@p149 @p148) :args ((=> @t25 @t150))) % 33.70/34.01 (assume-push @p259 @t25) % 33.70/34.01 (step @p152 :rule instantiate :premises (@p13) :args ((@list tptp.y tptp.z))) % 33.70/34.01 (step-pop @p260 :rule scope :premises (@p152)) % 33.70/34.01 (step @p153 :rule process_scope :premises (@p260) :args (@t150)) % 33.70/34.01 (step @p155 :rule eq_resolve :premises (@p153 @p150)) % 33.70/34.01 (step @p156 :rule implies_elim :premises (@p155)) % 33.70/34.01 (step @p157 :rule chain_m_resolution :premises (@p156 @p13) :args ((= @t121 @t145) @t128 (@list @t25))) % 33.70/34.01 (step @p158 :rule instantiate :premises (@p13) :args ((@list tptp.w tptp.x))) % 33.70/34.01 (step @p159 :rule trans :premises (@p158 @p92 @p157)) % 33.70/34.01 (step @p160 :rule refl :args (@t131)) % 33.70/34.01 (step @p161 :rule cong :premises (@p160 @p159) :args (@t151)) % 33.70/34.01 (step @p162 :rule trans :premises (@p161 @p147)) % 33.70/34.01 (step @p163 :rule true_elim :premises (@p162)) % 33.70/34.01 (step @p164 :rule instantiate :premises (@p9) :args ((@list tptp.w @t141))) % 33.70/34.01 (step @p165 :rule cnf_or_pos :args (@t154)) % 33.70/34.01 (step @p166 :rule reordering :premises (@p165) :args ((or @t153 @t152 (not @t154)))) % 33.70/34.01 (step @p167 :rule chain_m_resolution :premises (@p166 @p93 @p164) :args (@t152 @t149 (@list @t122 @t154))) % 33.70/34.01 (step @p168 :rule bool-double-not-elim :args (@t135)) % 33.70/34.01 (step @p169 :rule refl :args (@t156)) % 33.70/34.01 (step @p170 :rule refl :args (@t157)) % 33.70/34.01 (step @p171 :rule refl :args (@t158)) % 33.70/34.01 (step @p172 :rule nary_cong :premises (@p171 @p170 @p169 @p168) :args ((or @t158 @t157 @t156 @t159))) % 33.70/34.01 (assume-push @p261 @t136) % 33.70/34.01 (assume-push @p262 @t134) % 33.70/34.01 (assume-push @p263 @t155) % 33.70/34.01 (assume-push @p264 @t152) % 33.70/34.01 (step @p177 :rule evaluate :args ((= true false))) % 33.70/34.01 (step @p178 :rule false_intro :premises (@p135)) % 33.70/34.01 (step @p179 :rule trans :premises (@p263 @p113)) % 33.70/34.01 (step @p180 :rule refl :args (tptp.w)) % 33.70/34.01 (step @p181 :rule cong :premises (@p180 @p179) :args (@t152)) % 33.70/34.01 (step @p182 :rule true_intro :premises (@p167)) % 33.70/34.01 (step @p183 :rule symm :premises (@p182)) % 33.70/34.01 (step @p184 :rule trans :premises (@p183 @p181 @p178)) % 33.70/34.01 (step @p185 false :rule eq_resolve :premises (@p184 @p177)) % 33.70/34.01 (step-pop @p265 :rule scope :premises (@p185)) % 33.70/34.01 (step-pop @p266 :rule scope :premises (@p265)) % 33.70/34.01 (step-pop @p267 :rule scope :premises (@p266)) % 33.70/34.01 (step-pop @p268 :rule scope :premises (@p267)) % 33.70/34.01 (step @p186 :rule process_scope :premises (@p268) :args (false)) % 33.70/34.01 (assume-push @p269 @t152) % 33.70/34.01 (assume-push @p270 @t134) % 33.70/34.01 (assume-push @p271 @t155) % 33.70/34.01 (assume-push @p272 @t136) % 33.70/34.01 (step @p195 :rule and_intro :premises (@p135 @p113 @p271 @p167)) % 33.70/34.01 (step-pop @p273 :rule scope :premises (@p195)) % 33.70/34.01 (step-pop @p274 :rule scope :premises (@p273)) % 33.70/34.01 (step-pop @p275 :rule scope :premises (@p274)) % 33.70/34.01 (step-pop @p276 :rule scope :premises (@p275)) % 33.70/34.01 (step @p196 :rule process_scope :premises (@p276) :args (@t160)) % 33.70/34.01 (step @p201 :rule implies_elim :premises (@p196)) % 33.70/34.01 (step @p202 :rule resolution :premises (@p201 @p186) :args (true @t160)) % 33.70/34.01 (step @p203 :rule not_and :premises (@p202)) % 33.70/34.01 (step @p204 :rule eq_resolve :premises (@p203 @p172)) % 33.70/34.01 (step @p205 :rule chain_m_resolution :premises (@p204 @p167 @p113 @p135) :args (@t156 (@list false false true) (@list @t152 @t134 @t135))) % 33.70/34.01 (step @p206 :rule cnf_or_pos :args (@t163)) % 33.70/34.01 (step @p207 :rule reordering :premises (@p206) :args ((or @t161 @t155 @t162 (not @t163)))) % 33.70/34.01 (step @p208 :rule chain_m_resolution :premises (@p207 @p205 @p163 @p136) :args (@t161 (@list true false false) (@list @t155 @t151 @t163))) % 33.70/34.01 (step @p209 :rule instantiate :premises (@p9) :args ((@list tptp.w tptp.w))) % 33.70/34.01 (step @p210 :rule cnf_or_pos :args (@t165)) % 33.70/34.01 (step @p211 :rule reordering :premises (@p210) :args ((or @t153 @t164 (not @t165)))) % 33.70/34.01 (step @p212 :rule chain_m_resolution :premises (@p211 @p93 @p209) :args (@t164 @t149 (@list @t122 @t165))) % 33.70/34.01 (step @p213 :rule refl :args (@t166)) % 33.70/34.01 (step @p214 :rule refl :args (@t167)) % 33.70/34.01 (step @p215 :rule refl :args (@t168)) % 33.70/34.01 (step @p216 :rule nary_cong :premises (@p215 @p170 @p214 @p168 @p213) :args ((or @t168 @t157 @t167 @t159 @t166))) % 33.70/34.01 (assume-push @p277 @t164) % 33.70/34.01 (assume-push @p278 @t127) % 33.70/34.01 (assume-push @p279 @t161) % 33.70/34.01 (assume-push @p280 @t134) % 33.70/34.01 (assume-push @p281 @t136) % 33.70/34.01 (step @p222 :rule evaluate :args ((= false true))) % 33.70/34.01 (step @p223 :rule true_intro :premises (@p212)) % 33.70/34.01 (step @p224 :rule symm :premises (@p279)) % 33.70/34.01 (step @p108 :rule instantiate :premises (@p12) :args (@t133)) % 33.70/34.01 (step @p225 :rule trans :premises (@p108 @p224 @p104)) % 33.70/34.01 (step @p180 :rule refl :args (tptp.w)) % 33.70/34.01 (step @p226 :rule cong :premises (@p180 @p225) :args (@t135)) % 33.70/34.01 (step @p178 :rule false_intro :premises (@p135)) % 33.70/34.01 (step @p227 :rule symm :premises (@p178)) % 33.70/34.01 (step @p228 :rule trans :premises (@p227 @p226 @p223)) % 33.70/34.01 (step @p229 false :rule eq_resolve :premises (@p228 @p222)) % 33.70/34.01 (step-pop @p282 :rule scope :premises (@p229)) % 33.70/34.01 (step-pop @p283 :rule scope :premises (@p282)) % 33.70/34.01 (step-pop @p284 :rule scope :premises (@p283)) % 33.70/34.01 (step-pop @p285 :rule scope :premises (@p284)) % 33.70/34.01 (step-pop @p286 :rule scope :premises (@p285)) % 33.70/34.01 (step @p230 :rule process_scope :premises (@p286) :args (false)) % 33.70/34.01 (assume-push @p287 @t127) % 33.70/34.01 (assume-push @p288 @t134) % 33.70/34.01 (assume-push @p289 @t161) % 33.70/34.01 (assume-push @p290 @t136) % 33.70/34.01 (assume-push @p291 @t164) % 33.70/34.01 (step @p241 :rule and_intro :premises (@p212 @p104 @p289 @p113 @p135)) % 33.70/34.01 (step-pop @p292 :rule scope :premises (@p241)) % 33.70/34.01 (step-pop @p293 :rule scope :premises (@p292)) % 33.70/34.01 (step-pop @p294 :rule scope :premises (@p293)) % 33.70/34.01 (step-pop @p295 :rule scope :premises (@p294)) % 33.70/34.01 (step-pop @p296 :rule scope :premises (@p295)) % 33.70/34.01 (step @p242 :rule process_scope :premises (@p296) :args (@t169)) % 33.70/34.01 (step @p248 :rule implies_elim :premises (@p242)) % 33.70/34.01 (step @p249 :rule resolution :premises (@p248 @p230) :args (true @t169)) % 33.70/34.01 (step @p250 :rule not_and :premises (@p249)) % 33.70/34.01 (step @p251 :rule eq_resolve :premises (@p250 @p216)) % 33.70/34.01 (step @p252 false :rule chain_m_resolution :premises (@p251 @p212 @p208 @p135 @p113 @p104) :args (false (@list false false true false false) (@list @t164 @t161 @t135 @t134 @t127))) % 33.70/34.01 ) % 33.70/34.01 % SZS output end Proof % 33.70/34.01 % cvc5 exiting %------------------------------------------------------------------------------