%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU157+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:50:46 AM UTC 2026 % Result : Theorem 127.65s 158.18s % Output : Proof 127.65s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU157+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n019.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:33:04 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 127.65/158.18 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 127.65/158.18 --- Run --no-e-matching --full-saturate-quant at 6... % 127.65/158.18 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 127.65/158.18 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 127.65/158.18 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 127.65/158.18 --- Run --trigger-sel=max --full-saturate-quant at 15... % 127.65/158.18 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 127.65/158.18 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 127.65/158.18 --- Run --prenex-quant=none --full-saturate-quant at 30... % 127.65/158.18 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 127.65/158.18 % SZS status Theorem % 127.65/158.18 % SZS output start Proof % 127.65/158.18 ( % 127.65/158.18 (declare-sort $$unsorted 0) % 127.65/158.18 (declare-const tptp.empty (-> $$unsorted Bool)) % 127.65/158.18 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 127.65/158.18 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 127.65/158.18 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 127.65/158.18 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 127.65/158.18 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 127.65/158.18 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 127.65/158.18 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 127.65/158.18 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 127.65/158.18 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 127.65/158.18 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 127.65/158.18 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 127.65/158.18 (declare-const tptp.empty_set $$unsorted) % 127.65/158.18 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 127.65/158.18 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 127.65/158.18 (define @t1 () (@var "A" $$unsorted)) % 127.65/158.18 (define @t2 () (@var "B" $$unsorted)) % 127.65/158.18 (define @t3 () (not (tptp.in @t2 @t1))) % 127.65/158.18 (define @t4 () (tptp.in @t1 @t2)) % 127.65/158.18 (define @t5 () (@list @t1 @t2)) % 127.65/158.18 (define @t6 () (tptp.proper_subset @t2 @t1)) % 127.65/158.18 (define @t7 () (tptp.proper_subset @t1 @t2)) % 127.65/158.18 (define @t8 () (tptp.unordered_pair @t1 @t2)) % 127.65/158.18 (define @t9 () (tptp.set_union2 @t2 @t1)) % 127.65/158.18 (define @t10 () (tptp.set_union2 @t1 @t2)) % 127.65/158.18 (define @t11 () (tptp.set_intersection2 @t1 @t2)) % 127.65/158.18 (define @t12 () (tptp.subset @t1 @t2)) % 127.65/158.18 (define @t13 () (= @t1 @t2)) % 127.65/158.18 (define @t14 () (@var "C" $$unsorted)) % 127.65/158.18 (define @t15 () (tptp.in @t14 @t2)) % 127.65/158.18 (define @t16 () (@list @t14)) % 127.65/158.18 (define @t17 () (tptp.singleton @t1)) % 127.65/158.18 (define @t18 () (= @t1 tptp.empty_set)) % 127.65/158.18 (define @t19 () (@list @t1)) % 127.65/158.18 (define @t20 () (@var "D" $$unsorted)) % 127.65/158.18 (define @t21 () (tptp.in @t20 @t14)) % 127.65/158.18 (define @t22 () (@list @t20)) % 127.65/158.18 (define @t23 () (@list @t1 @t2 @t14)) % 127.65/158.18 (define @t24 () (tptp.in @t20 @t2)) % 127.65/158.18 (define @t25 () (tptp.in @t20 @t1)) % 127.65/158.18 (define @t26 () (@var "F" $$unsorted)) % 127.65/158.18 (define @t27 () (@var "E" $$unsorted)) % 127.65/158.18 (define @t28 () (tptp.ordered_pair @t27 @t26)) % 127.65/158.18 (define @t29 () (= @t20 @t28)) % 127.65/158.18 (define @t30 () (tptp.in @t26 @t2)) % 127.65/158.18 (define @t31 () (tptp.in @t27 @t1)) % 127.65/158.18 (define @t32 () (and @t31 @t30 @t29)) % 127.65/158.18 (define @t33 () (@list @t27 @t26)) % 127.65/158.18 (define @t34 () (exists @t33 @t32)) % 127.65/158.18 (define @t35 () (= @t21 @t34)) % 127.65/158.18 (define @t36 () (forall @t22 @t35)) % 127.65/158.18 (define @t37 () (= @t14 (tptp.cartesian_product2 @t1 @t2))) % 127.65/158.18 (define @t38 () (= @t37 @t36)) % 127.65/158.18 (define @t39 () (forall @t23 @t38)) % 127.65/158.18 (define @t40 () (tptp.in @t14 @t1)) % 127.65/158.18 (define @t41 () (tptp.set_difference @t1 @t2)) % 127.65/158.18 (define @t42 () (tptp.ordered_pair @t1 @t2)) % 127.65/158.18 (define @t43 () (tptp.disjoint @t1 @t2)) % 127.65/158.18 (define @t44 () (not @t13)) % 127.65/158.18 (define @t45 () (tptp.empty @t1)) % 127.65/158.18 (define @t46 () (not @t45)) % 127.65/158.18 (define @t47 () (tptp.disjoint @t17 @t2)) % 127.65/158.18 (define @t48 () (tptp.singleton @t2)) % 127.65/158.18 (define @t49 () (@list @t1 @t2 @t14 @t20)) % 127.65/158.18 (define @t50 () (forall @t49 (= (tptp.in @t42 (tptp.cartesian_product2 @t14 @t20)) (and (tptp.in @t1 @t14) (tptp.in @t2 @t20))))) % 127.65/158.18 (define @t51 () (= @t1 @t14)) % 127.65/158.18 (define @t52 () (tptp.set_intersection2 @t2 @t14)) % 127.65/158.18 (define @t53 () (tptp.subset @t1 @t14)) % 127.65/158.18 (define @t54 () (and @t51 (= @t2 @t20))) % 127.65/158.18 (define @t55 () (= @t42 (tptp.ordered_pair @t14 @t20))) % 127.65/158.18 (define @t56 () (forall @t49 (=> @t55 @t54))) % 127.65/158.18 (define @t57 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 127.65/158.18 (define @t58 () (and @t40 @t15)) % 127.65/158.18 (define @t59 () (not @t43)) % 127.65/158.19 (define @t60 () (tptp.in @t14 @t11)) % 127.65/158.19 (define @t61 () (tptp.empty @t2)) % 127.65/158.19 (define @t62 () (= @t17 (tptp.unordered_pair @t2 @t14))) % 127.65/158.19 (define @t63 () (not @t29)) % 127.65/158.19 (define @t64 () (not @t30)) % 127.65/158.19 (define @t65 () (not @t31)) % 127.65/158.19 (define @t66 () (or @t65 @t64 @t63)) % 127.65/158.19 (define @t67 () (forall @t33 (not @t32))) % 127.65/158.19 (define @t68 () (not @t67)) % 127.65/158.19 (define @t69 () (@quantifiers_skolemize @t50 3)) % 127.65/158.19 (define @t70 () (not (tptp.in @t26 @t69))) % 127.65/158.19 (define @t71 () (@quantifiers_skolemize @t50 2)) % 127.65/158.19 (define @t72 () (not (tptp.in @t27 @t71))) % 127.65/158.19 (define @t73 () (tptp.cartesian_product2 @t71 @t69)) % 127.65/158.19 (define @t74 () (forall @t22 (= (tptp.in @t20 @t73) (not (forall @t33 (or @t72 @t70 @t63)))))) % 127.65/158.19 (define @t75 () (= (= @t73 @t73) @t74)) % 127.65/158.19 (define @t76 () (forall @t23 (= @t37 (forall @t22 (= @t21 (not (forall @t33 @t66))))))) % 127.65/158.19 (define @t77 () (@list false)) % 127.65/158.19 (define @t78 () (@quantifiers_skolemize @t50 1)) % 127.65/158.19 (define @t79 () (@quantifiers_skolemize @t50 0)) % 127.65/158.19 (define @t80 () (tptp.ordered_pair @t79 @t78)) % 127.65/158.19 (define @t81 () (not (= @t80 @t28))) % 127.65/158.19 (define @t82 () (or @t72 @t70 @t81)) % 127.65/158.19 (define @t83 () (forall @t33 @t82)) % 127.65/158.19 (define @t84 () (not @t83)) % 127.65/158.19 (define @t85 () (tptp.in @t80 @t73)) % 127.65/158.19 (define @t86 () (= @t85 @t84)) % 127.65/158.19 (define @t87 () (forall @t33 (or @t72 @t70 (not (= @t28 @t80))))) % 127.65/158.19 (define @t88 () (not @t87)) % 127.65/158.19 (define @t89 () (= @t85 @t88)) % 127.65/158.19 (define @t90 () (not @t89)) % 127.65/158.19 (define @t91 () (tptp.in @t78 @t69)) % 127.65/158.19 (define @t92 () (tptp.in @t79 @t71)) % 127.65/158.19 (define @t93 () (and @t92 @t91)) % 127.65/158.19 (define @t94 () (= @t85 @t93)) % 127.65/158.19 (define @t95 () (not @t93)) % 127.65/158.19 (define @t96 () (not @t91)) % 127.65/158.19 (define @t97 () (not @t92)) % 127.65/158.19 (define @t98 () (or @t97 @t96)) % 127.65/158.19 (define @t99 () (not (= @t80 @t80))) % 127.65/158.19 (define @t100 () (or @t97 @t96 @t99)) % 127.65/158.19 (define @t101 () (not @t88)) % 127.65/158.19 (define @t102 () (@list true false)) % 127.65/158.19 (define @t103 () (@quantifiers_skolemize @t87 1)) % 127.65/158.19 (define @t104 () (@quantifiers_skolemize @t87 0)) % 127.65/158.19 (define @t105 () (tptp.ordered_pair @t104 @t103)) % 127.65/158.19 (define @t106 () (= @t80 @t105)) % 127.65/158.19 (define @t107 () (not @t106)) % 127.65/158.19 (define @t108 () (tptp.in @t103 @t69)) % 127.65/158.19 (define @t109 () (not @t108)) % 127.65/158.19 (define @t110 () (tptp.in @t104 @t71)) % 127.65/158.19 (define @t111 () (not @t110)) % 127.65/158.19 (define @t112 () (or @t111 @t109 @t107)) % 127.65/158.19 (define @t113 () (not @t112)) % 127.65/158.19 (define @t114 () (not (= @t105 @t80))) % 127.65/158.19 (define @t115 () (or @t111 @t109 @t114)) % 127.65/158.19 (define @t116 () (not @t115)) % 127.65/158.19 (define @t117 () (@list true)) % 127.65/158.19 (define @t118 () (@list @t112)) % 127.65/158.19 (define @t119 () (= @t78 @t103)) % 127.65/158.19 (define @t120 () (= @t79 @t104)) % 127.65/158.19 (define @t121 () (and @t120 @t119)) % 127.65/158.19 (define @t122 () (or @t107 @t121)) % 127.65/158.19 (define @t123 () (@list false false)) % 127.65/158.19 (define @t124 () (not @t121)) % 127.65/158.19 (define @t125 () (@list @t121)) % 127.65/158.19 (define @t126 () (and @t110 @t120)) % 127.65/158.19 (define @t127 () (and @t108 @t119)) % 127.65/158.19 (assume @p1 (forall @t5 (=> @t4 @t3))) % 127.65/158.19 (assume @p2 (forall @t5 (=> @t7 (not @t6)))) % 127.65/158.19 (assume @p3 (forall @t5 (= @t8 (tptp.unordered_pair @t2 @t1)))) % 127.65/158.19 (assume @p4 (forall @t5 (= @t10 @t9))) % 127.65/158.19 (assume @p5 (forall @t5 (= @t11 (tptp.set_intersection2 @t2 @t1)))) % 127.65/158.19 (assume @p6 (forall @t5 (= @t13 (and @t12 (tptp.subset @t2 @t1))))) % 127.65/158.19 (assume @p7 (forall @t5 (= (= @t2 @t17) (forall @t16 (= @t15 (= @t14 @t1)))))) % 127.65/158.19 (assume @p8 (forall @t19 (= @t18 (forall (@list @t2) @t3)))) % 127.65/158.19 (assume @p9 (forall @t5 (= (= @t2 (tptp.powerset @t1)) (forall @t16 (= @t15 (tptp.subset @t14 @t1)))))) % 127.65/158.19 (assume @p10 (forall @t23 (= (= @t14 @t8) (forall @t22 (= @t21 (or (= @t20 @t1) (= @t20 @t2))))))) % 127.65/158.19 (assume @p11 (forall @t23 (= (= @t14 @t10) (forall @t22 (= @t21 (or @t25 @t24)))))) % 127.65/158.19 (assume @p12 @t39) % 127.65/158.19 (assume @p13 (forall @t5 (= @t12 (forall @t16 (=> @t40 @t15))))) % 127.65/158.19 (assume @p14 (forall @t23 (= (= @t14 @t11) (forall @t22 (= @t21 (and @t25 @t24)))))) % 127.65/158.19 (assume @p15 (forall @t5 (= (= @t2 (tptp.union @t1)) (forall @t16 (= @t15 (exists @t22 (and (tptp.in @t14 @t20) @t25))))))) % 127.65/158.19 (assume @p16 (forall @t23 (= (= @t14 @t41) (forall @t22 (= @t21 (and @t25 (not @t24))))))) % 127.65/158.19 (assume @p17 (forall @t5 (= @t42 (tptp.unordered_pair @t8 @t17)))) % 127.65/158.19 (assume @p18 (forall @t5 (= @t43 (= @t11 tptp.empty_set)))) % 127.65/158.19 (assume @p19 (forall @t5 (= @t7 (and @t12 @t44)))) % 127.65/158.19 (assume @p20 true) % 127.65/158.19 (assume @p21 (tptp.empty tptp.empty_set)) % 127.65/158.19 (assume @p22 (forall @t5 (not (tptp.empty @t42)))) % 127.65/158.19 (assume @p23 (forall @t5 (=> @t46 (not (tptp.empty @t10))))) % 127.65/158.19 (assume @p24 (forall @t5 (=> @t46 (not (tptp.empty @t9))))) % 127.65/158.19 (assume @p25 (forall @t5 (= (tptp.set_union2 @t1 @t1) @t1))) % 127.65/158.19 (assume @p26 (forall @t5 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 127.65/158.19 (assume @p27 (forall @t5 (not (tptp.proper_subset @t1 @t1)))) % 127.65/158.19 (assume @p28 (forall @t19 (not (= @t17 tptp.empty_set)))) % 127.65/158.19 (assume @p29 (forall @t5 (=> @t4 (= (tptp.set_union2 @t17 @t2) @t2)))) % 127.65/158.19 (assume @p30 (forall @t5 (not (and @t47 @t4)))) % 127.65/158.19 (assume @p31 (forall @t5 (=> (not @t4) @t47))) % 127.65/158.19 (assume @p32 (forall @t5 (= (tptp.subset @t17 @t2) @t4))) % 127.65/158.19 (assume @p33 (forall @t5 (= (= @t41 tptp.empty_set) @t12))) % 127.65/158.19 (assume @p34 (forall @t23 (=> @t12 (or @t40 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t14))))))) % 127.65/158.19 (assume @p35 (forall @t5 (= (tptp.subset @t1 @t48) (or @t18 (= @t1 @t48))))) % 127.65/158.19 (assume @p36 (forall @t5 (=> @t4 (tptp.subset @t1 (tptp.union @t2))))) % 127.65/158.19 (assume @p37 (not @t50)) % 127.65/158.19 (assume @p38 (exists @t19 @t45)) % 127.65/158.19 (assume @p39 (exists @t19 @t46)) % 127.65/158.19 (assume @p40 (forall @t5 (tptp.subset @t1 @t1))) % 127.65/158.19 (assume @p41 (forall @t5 (=> @t43 (tptp.disjoint @t2 @t1)))) % 127.65/158.19 (assume @p42 (forall @t49 (not (and (= @t8 (tptp.unordered_pair @t14 @t20)) (not @t51) (not (= @t1 @t20)))))) % 127.65/158.19 (assume @p43 (forall @t5 (=> @t12 (= @t10 @t2)))) % 127.65/158.19 (assume @p44 (forall @t5 (tptp.subset @t11 @t1))) % 127.65/158.19 (assume @p45 (forall @t23 (=> (and @t12 @t53) (tptp.subset @t1 @t52)))) % 127.65/158.19 (assume @p46 (forall @t19 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 127.65/158.19 (assume @p47 (forall @t23 (=> (and @t12 (tptp.subset @t2 @t14)) @t53))) % 127.65/158.19 (assume @p48 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 127.65/158.19 (assume @p49 (forall @t23 (=> @t12 (tptp.subset (tptp.set_intersection2 @t1 @t14) @t52)))) % 127.65/158.19 (assume @p50 (forall @t5 (=> @t12 (= @t11 @t1)))) % 127.65/158.19 (assume @p51 (forall @t19 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 127.65/158.19 (assume @p52 (forall @t5 (=> (forall @t16 (= @t40 @t15)) @t13))) % 127.65/158.19 (assume @p53 (forall @t19 (tptp.subset tptp.empty_set @t1))) % 127.65/158.19 (assume @p54 (forall @t23 (=> @t12 (tptp.subset (tptp.set_difference @t1 @t14) (tptp.set_difference @t2 @t14))))) % 127.65/158.19 (assume @p55 @t56) % 127.65/158.19 (assume @p56 (forall @t5 (tptp.subset @t41 @t1))) % 127.65/158.19 (assume @p57 (forall @t5 (= @t57 @t10))) % 127.65/158.19 (assume @p58 (forall @t19 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 127.65/158.19 (assume @p59 (forall @t5 (and (not (and @t59 (forall @t16 (not @t58)))) (not (and (exists @t16 @t58) @t43))))) % 127.65/158.19 (assume @p60 (forall @t19 (=> (tptp.subset @t1 tptp.empty_set) @t18))) % 127.65/158.19 (assume @p61 (forall @t5 (= (tptp.set_difference @t10 @t2) @t41))) % 127.65/158.19 (assume @p62 (forall @t5 (=> @t12 (= @t2 @t57)))) % 127.65/158.19 (assume @p63 (forall @t5 (= (tptp.set_difference @t1 @t41) @t11))) % 127.65/158.19 (assume @p64 (forall @t19 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 127.65/158.19 (assume @p65 (forall @t5 (and (not (and @t59 (forall @t16 (not @t60)))) (not (and (exists @t16 @t60) @t43))))) % 127.65/158.19 (assume @p66 (forall @t5 (not (and @t12 @t6)))) % 127.65/158.19 (assume @p67 (forall @t23 (=> (and @t12 (tptp.disjoint @t2 @t14)) (tptp.disjoint @t1 @t14)))) % 127.65/158.19 (assume @p68 (forall @t19 (= (tptp.unordered_pair @t1 @t1) @t17))) % 127.65/158.19 (assume @p69 (forall @t19 (=> @t45 @t18))) % 127.65/158.19 (assume @p70 (forall @t5 (=> (tptp.subset @t17 @t48) @t13))) % 127.65/158.19 (assume @p71 (forall @t5 (not (and @t4 @t61)))) % 127.65/158.19 (assume @p72 (forall @t5 (tptp.subset @t1 @t10))) % 127.65/158.19 (assume @p73 (forall @t5 (= @t43 (= @t41 @t1)))) % 127.65/158.19 (assume @p74 (forall @t5 (not (and @t45 @t44 @t61)))) % 127.65/158.19 (assume @p75 (forall @t23 (=> (and @t12 (tptp.subset @t14 @t2)) (tptp.subset (tptp.set_union2 @t1 @t14) @t2)))) % 127.65/158.19 (assume @p76 (forall @t23 (=> @t62 @t13))) % 127.65/158.19 (assume @p77 (forall @t23 (=> @t62 (= @t2 @t14)))) % 127.65/158.19 (step @p78 :rule aci_norm :args ((= (or @t65 (or @t64 @t63)) @t66))) % 127.65/158.19 (step @p79 :rule bool-and-de-morgan :args (@t30 @t29 true)) % 127.65/158.19 (step @p80 :rule refl :args (@t65)) % 127.65/158.19 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or @t65 (not (and @t30 @t29))))) % 127.65/158.19 (step @p82 :rule bool-and-de-morgan :args (@t31 @t30 (and @t29))) % 127.65/158.19 (step @p83 :rule trans :premises (@p82 @p81)) % 127.65/158.19 (step @p84 :rule trans :premises (@p83 @p78)) % 127.65/158.19 (step @p85 :rule cong :premises (@p84) :args (@t67)) % 127.65/158.19 (step @p86 :rule cong :premises (@p85) :args (@t68)) % 127.65/158.19 (step @p87 :rule exists-elim :args ((= @t34 @t68))) % 127.65/158.19 (step @p88 :rule trans :premises (@p87 @p86)) % 127.65/158.19 (step @p89 :rule refl :args (@t21)) % 127.65/158.19 (step @p90 :rule cong :premises (@p89 @p88) :args (@t35)) % 127.65/158.19 (step @p91 :rule cong :premises (@p90) :args (@t36)) % 127.65/158.19 (step @p92 :rule refl :args (@t37)) % 127.65/158.19 (step @p93 :rule cong :premises (@p92 @p91) :args (@t38)) % 127.65/158.19 (step @p94 :rule cong :premises (@p93) :args (@t39)) % 127.65/158.19 (step @p95 :rule eq_resolve :premises (@p12 @p94)) % 127.65/158.19 (step @p96 :rule bool-eq-true :args (@t74)) % 127.65/158.19 (step @p97 :rule eq-symm :args (true @t74)) % 127.65/158.19 (step @p98 :rule trans :premises (@p97 @p96)) % 127.65/158.19 (step @p99 :rule refl :args (@t74)) % 127.65/158.19 (step @p100 :rule eq-refl :args (@t73)) % 127.65/158.19 (step @p101 :rule cong :premises (@p100 @p99) :args (@t75)) % 127.65/158.19 (step @p102 :rule trans :premises (@p101 @p98)) % 127.65/158.19 (step @p103 :rule refl :args (@t76)) % 127.65/158.19 (step @p104 :rule cong :premises (@p103 @p102) :args ((=> @t76 @t75))) % 127.65/158.19 (assume-push @p263 @t76) % 127.65/158.19 (step @p106 :rule instantiate :premises (@p95) :args ((@list @t71 @t69 @t73))) % 127.65/158.19 (step-pop @p264 :rule scope :premises (@p106)) % 127.65/158.19 (step @p107 :rule process_scope :premises (@p264) :args (@t75)) % 127.65/158.19 (step @p109 :rule eq_resolve :premises (@p107 @p104)) % 127.65/158.19 (step @p110 :rule implies_elim :premises (@p109)) % 127.65/158.19 (step @p111 :rule chain_m_resolution :premises (@p110 @p95) :args (@t74 @t77 (@list @t76))) % 127.65/158.19 (step @p112 :rule eq-symm :args (@t80 @t28)) % 127.65/158.19 (step @p113 :rule cong :premises (@p112) :args (@t81)) % 127.65/158.19 (step @p114 :rule refl :args (@t70)) % 127.65/158.19 (step @p115 :rule refl :args (@t72)) % 127.65/158.19 (step @p116 :rule nary_cong :premises (@p115 @p114 @p113) :args (@t82)) % 127.65/158.19 (step @p117 :rule cong :premises (@p116) :args (@t83)) % 127.65/158.19 (step @p118 :rule cong :premises (@p117) :args (@t84)) % 127.65/158.19 (step @p119 :rule refl :args (@t85)) % 127.65/158.19 (step @p120 :rule cong :premises (@p119 @p118) :args (@t86)) % 127.65/158.19 (step @p121 :rule cong :premises (@p99 @p120) :args ((=> @t74 @t86))) % 127.65/158.19 (assume-push @p265 @t74) % 127.65/158.19 (step @p123 :rule instantiate :premises (@p111) :args ((@list @t80))) % 127.65/158.19 (step-pop @p266 :rule scope :premises (@p123)) % 127.65/158.19 (step @p124 :rule process_scope :premises (@p266) :args (@t86)) % 127.65/158.19 (step @p126 :rule eq_resolve :premises (@p124 @p121)) % 127.65/158.19 (step @p127 :rule implies_elim :premises (@p126)) % 127.65/158.19 (step @p128 :rule chain_m_resolution :premises (@p127 @p111) :args (@t89 @t77 (@list @t74))) % 127.65/158.19 (step @p129 :rule cnf_equiv_pos1 :args (@t89)) % 127.65/158.19 (step @p130 :rule reordering :premises (@p129) :args ((or (not @t85) @t88 @t90))) % 127.65/158.19 (step @p131 :rule skolemize :premises (@p37)) % 127.65/158.19 (step @p132 :rule cnf_equiv_neg1 :args (@t94)) % 127.65/158.19 (step @p133 :rule reordering :premises (@p132) :args ((or @t85 @t93 @t94))) % 127.65/158.19 (step @p134 :rule cnf_and_pos :args (@t93 0)) % 127.65/158.19 (step @p135 :rule reordering :premises (@p134) :args ((or @t92 @t95))) % 127.65/158.19 (step @p136 :rule cnf_and_pos :args (@t93 1)) % 127.65/158.19 (step @p137 :rule reordering :premises (@p136) :args ((or @t91 @t95))) % 127.65/158.19 (step @p138 :rule cnf_or_pos :args (@t98)) % 127.65/158.19 (step @p139 :rule reordering :premises (@p138) :args ((or @t97 @t96 (not @t98)))) % 127.65/158.19 (step @p140 :rule aci_norm :args ((= (or @t97 @t96 false) @t98))) % 127.65/158.19 (step @p141 :rule evaluate :args ((not true))) % 127.65/158.19 (step @p142 :rule eq-refl :args (@t80)) % 127.65/158.19 (step @p143 :rule cong :premises (@p142) :args (@t99)) % 127.65/158.19 (step @p144 :rule trans :premises (@p143 @p141)) % 127.65/158.19 (step @p145 :rule refl :args (@t96)) % 127.65/158.19 (step @p146 :rule refl :args (@t97)) % 127.65/158.19 (step @p147 :rule nary_cong :premises (@p146 @p145 @p144) :args (@t100)) % 127.65/158.19 (step @p148 :rule trans :premises (@p147 @p140)) % 127.65/158.19 (step @p149 :rule refl :args (@t87)) % 127.65/158.19 (step @p150 :rule cong :premises (@p149 @p148) :args ((=> @t87 @t100))) % 127.65/158.19 (assume-push @p267 @t87) % 127.65/158.19 (step @p152 :rule instantiate :premises (@p267) :args ((@list @t79 @t78))) % 127.65/158.19 (step-pop @p268 :rule scope :premises (@p152)) % 127.65/158.19 (step @p153 :rule process_scope :premises (@p268) :args (@t100)) % 127.65/158.19 (step @p155 :rule eq_resolve :premises (@p153 @p150)) % 127.65/158.19 (step @p156 :rule implies_elim :premises (@p155)) % 127.65/158.19 (step @p157 :rule chain_m_resolution :premises (@p156 @p139 @p137 @p135 @p133 @p131 @p130 @p128) :args (@t88 (@list true false false false true true false) (@list @t98 @t91 @t92 @t93 @t94 @t85 @t89))) % 127.65/158.19 (step @p158 :rule bool-double-not-elim :args (@t87)) % 127.65/158.19 (step @p159 :rule refl :args (@t90)) % 127.65/158.19 (step @p160 :rule nary_cong :premises (@p159 @p119 @p158) :args ((or @t90 @t85 @t101))) % 127.65/158.19 (step @p161 :rule cnf_equiv_pos2 :args (@t89)) % 127.65/158.19 (step @p162 :rule eq_resolve :premises (@p161 @p160)) % 127.65/158.19 (step @p163 :rule reordering :premises (@p162) :args ((or @t85 @t87 @t90))) % 127.65/158.19 (step @p164 :rule chain_m_resolution :premises (@p163 @p157 @p128) :args (@t85 @t102 (@list @t87 @t89))) % 127.65/158.19 (step @p165 :rule cnf_equiv_neg2 :args (@t94)) % 127.65/158.19 (step @p166 :rule chain_m_resolution :premises (@p165 @p131 @p164) :args (@t95 @t102 (@list @t94 @t85))) % 127.65/158.19 (step @p167 :rule bool-impl-elim :args (@t55 @t54)) % 127.65/158.19 (step @p168 :rule cong :premises (@p167) :args (@t56)) % 127.65/158.19 (step @p169 :rule eq_resolve :premises (@p55 @p168)) % 127.65/158.19 (step @p170 :rule instantiate :premises (@p169) :args ((@list @t79 @t78 @t104 @t103))) % 127.65/158.19 (step @p171 :rule refl :args (@t113)) % 127.65/158.19 (step @p172 :rule nary_cong :premises (@p158 @p171) :args ((or @t101 @t113))) % 127.65/158.19 (step @p173 :rule eq-symm :args (@t105 @t80)) % 127.65/158.19 (step @p174 :rule cong :premises (@p173) :args (@t114)) % 127.65/158.19 (step @p175 :rule refl :args (@t109)) % 127.65/158.19 (step @p176 :rule refl :args (@t111)) % 127.65/158.19 (step @p177 :rule nary_cong :premises (@p176 @p175 @p174) :args (@t115)) % 127.65/158.19 (step @p178 :rule cong :premises (@p177) :args (@t116)) % 127.65/158.19 (step @p179 :rule refl :args (@t88)) % 127.65/158.19 (step @p180 :rule cong :premises (@p179 @p178) :args ((=> @t88 @t116))) % 127.65/158.19 (assume-push @p269 @t88) % 127.65/158.19 (step @p182 :rule skolemize :premises (@p269)) % 127.65/158.19 (step-pop @p270 :rule scope :premises (@p182)) % 127.65/158.19 (step @p183 :rule process_scope :premises (@p270) :args (@t116)) % 127.65/158.19 (step @p185 :rule eq_resolve :premises (@p183 @p180)) % 127.65/158.19 (step @p186 :rule implies_elim :premises (@p185)) % 127.65/158.19 (step @p187 :rule eq_resolve :premises (@p186 @p172)) % 127.65/158.19 (step @p188 :rule chain_m_resolution :premises (@p187 @p157) :args (@t113 @t117 (@list @t87))) % 127.65/158.19 (step @p189 :rule bool-double-not-elim :args (@t106)) % 127.65/158.19 (step @p190 :rule refl :args (@t112)) % 127.65/158.19 (step @p191 :rule nary_cong :premises (@p190 @p189) :args ((or @t112 (not @t107)))) % 127.65/158.19 (step @p192 :rule cnf_or_neg :args (@t112 2)) % 127.65/158.19 (step @p193 :rule eq_resolve :premises (@p192 @p191)) % 127.65/158.19 (step @p194 :rule reordering :premises (@p193) :args ((or @t106 @t112))) % 127.65/158.19 (step @p195 :rule chain_m_resolution :premises (@p194 @p188) :args (@t106 @t117 @t118)) % 127.65/158.19 (step @p196 :rule cnf_or_pos :args (@t122)) % 127.65/158.19 (step @p197 :rule reordering :premises (@p196) :args ((or @t107 @t121 (not @t122)))) % 127.65/158.19 (step @p198 :rule chain_m_resolution :premises (@p197 @p195 @p170) :args (@t121 @t123 (@list @t106 @t122))) % 127.65/158.19 (step @p199 :rule cnf_and_pos :args (@t121 0)) % 127.65/158.19 (step @p200 :rule reordering :premises (@p199) :args ((or @t120 @t124))) % 127.65/158.19 (step @p201 :rule chain_m_resolution :premises (@p200 @p198) :args (@t120 @t77 @t125)) % 127.65/158.19 (step @p202 :rule bool-double-not-elim :args (@t110)) % 127.65/158.19 (step @p203 :rule nary_cong :premises (@p190 @p202) :args ((or @t112 (not @t111)))) % 127.65/158.19 (step @p204 :rule cnf_or_neg :args (@t112 0)) % 127.65/158.19 (step @p205 :rule eq_resolve :premises (@p204 @p203)) % 127.65/158.19 (step @p206 :rule reordering :premises (@p205) :args ((or @t110 @t112))) % 127.65/158.19 (step @p207 :rule chain_m_resolution :premises (@p206 @p188) :args (@t110 @t117 @t118)) % 127.65/158.19 (assume-push @p271 @t110) % 127.65/158.19 (assume-push @p272 @t120) % 127.65/158.19 (assume-push @p273 @t110) % 127.65/158.19 (assume-push @p274 @t120) % 127.65/158.19 (step @p212 :rule true_intro :premises (@p271)) % 127.65/158.19 (step @p213 :rule refl :args (@t71)) % 127.65/158.19 (step @p214 :rule cong :premises (@p272 @p213) :args (@t92)) % 127.65/158.19 (step @p215 :rule trans :premises (@p214 @p212)) % 127.65/158.19 (step @p216 :rule true_elim :premises (@p215)) % 127.65/158.19 (step-pop @p275 :rule scope :premises (@p216)) % 127.65/158.19 (step-pop @p276 :rule scope :premises (@p275)) % 127.65/158.19 (step @p217 :rule process_scope :premises (@p276) :args (@t92)) % 127.65/158.19 (step @p220 :rule and_intro :premises (@p271 @p272)) % 127.65/158.19 (step @p221 :rule modus_ponens :premises (@p220 @p217)) % 127.65/158.19 (step-pop @p277 :rule scope :premises (@p221)) % 127.65/158.19 (step-pop @p278 :rule scope :premises (@p277)) % 127.65/158.19 (step @p222 :rule process_scope :premises (@p278) :args (@t92)) % 127.65/158.19 (step @p225 :rule implies_elim :premises (@p222)) % 127.65/158.19 (step @p226 :rule cnf_and_neg :args (@t126)) % 127.65/158.19 (step @p227 :rule resolution :premises (@p226 @p225) :args (true @t126)) % 127.65/158.19 (step @p228 :rule reordering :premises (@p227) :args ((or @t92 @t111 (not @t120)))) % 127.65/158.19 (step @p229 :rule chain_m_resolution :premises (@p228 @p207 @p201) :args (@t92 @t123 (@list @t110 @t120))) % 127.65/158.19 (step @p230 :rule cnf_and_pos :args (@t121 1)) % 127.65/158.19 (step @p231 :rule reordering :premises (@p230) :args ((or @t119 @t124))) % 127.65/158.19 (step @p232 :rule chain_m_resolution :premises (@p231 @p198) :args (@t119 @t77 @t125)) % 127.65/158.19 (step @p233 :rule bool-double-not-elim :args (@t108)) % 127.65/158.19 (step @p234 :rule nary_cong :premises (@p190 @p233) :args ((or @t112 (not @t109)))) % 127.65/158.19 (step @p235 :rule cnf_or_neg :args (@t112 1)) % 127.65/158.19 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 127.65/158.19 (step @p237 :rule reordering :premises (@p236) :args ((or @t108 @t112))) % 127.65/158.19 (step @p238 :rule chain_m_resolution :premises (@p237 @p188) :args (@t108 @t117 @t118)) % 127.65/158.19 (assume-push @p279 @t108) % 127.65/158.19 (assume-push @p280 @t119) % 127.65/158.19 (assume-push @p281 @t108) % 127.65/158.19 (assume-push @p282 @t119) % 127.65/158.19 (step @p243 :rule true_intro :premises (@p279)) % 127.65/158.19 (step @p244 :rule refl :args (@t69)) % 127.65/158.19 (step @p245 :rule cong :premises (@p280 @p244) :args (@t91)) % 127.65/158.19 (step @p246 :rule trans :premises (@p245 @p243)) % 127.65/158.19 (step @p247 :rule true_elim :premises (@p246)) % 127.65/158.19 (step-pop @p283 :rule scope :premises (@p247)) % 127.65/158.19 (step-pop @p284 :rule scope :premises (@p283)) % 127.65/158.19 (step @p248 :rule process_scope :premises (@p284) :args (@t91)) % 127.65/158.19 (step @p251 :rule and_intro :premises (@p279 @p280)) % 127.65/158.19 (step @p252 :rule modus_ponens :premises (@p251 @p248)) % 127.65/158.19 (step-pop @p285 :rule scope :premises (@p252)) % 127.65/158.19 (step-pop @p286 :rule scope :premises (@p285)) % 127.65/158.19 (step @p253 :rule process_scope :premises (@p286) :args (@t91)) % 127.65/158.19 (step @p256 :rule implies_elim :premises (@p253)) % 127.65/158.19 (step @p257 :rule cnf_and_neg :args (@t127)) % 127.65/158.19 (step @p258 :rule resolution :premises (@p257 @p256) :args (true @t127)) % 127.65/158.19 (step @p259 :rule reordering :premises (@p258) :args ((or @t91 @t109 (not @t119)))) % 127.65/158.19 (step @p260 :rule chain_m_resolution :premises (@p259 @p238 @p232) :args (@t91 @t123 (@list @t108 @t119))) % 127.65/158.19 (step @p261 :rule cnf_and_neg :args (@t93)) % 127.65/158.19 (step @p262 false :rule chain_m_resolution :premises (@p261 @p260 @p229 @p166) :args (false (@list false false true) (@list @t91 @t92 @t93))) % 127.65/158.19 ) % 127.65/158.19 % SZS output end Proof % 127.65/158.19 % cvc5 exiting %------------------------------------------------------------------------------