%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU159+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:50:46 AM UTC 2026 % Result : Theorem 15.93s 16.18s % Output : Proof 15.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU159+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 16:31:31 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 15.93/16.18 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.93/16.18 --- Run --no-e-matching --full-saturate-quant at 6... % 15.93/16.18 % SZS status Theorem % 15.93/16.18 % SZS output start Proof % 15.93/16.18 ( % 15.93/16.18 (declare-sort $$unsorted 0) % 15.93/16.18 (declare-const tptp.empty (-> $$unsorted Bool)) % 15.93/16.18 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 15.93/16.18 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 15.93/16.18 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 15.93/16.18 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 15.93/16.18 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 15.93/16.18 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 15.93/16.18 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 15.93/16.18 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 15.93/16.18 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 15.93/16.18 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 15.93/16.18 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 15.93/16.18 (declare-const tptp.empty_set $$unsorted) % 15.93/16.18 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 15.93/16.18 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 15.93/16.18 (define @t1 () (@var "A" $$unsorted)) % 15.93/16.18 (define @t2 () (@var "B" $$unsorted)) % 15.93/16.18 (define @t3 () (not (tptp.in @t2 @t1))) % 15.93/16.18 (define @t4 () (tptp.in @t1 @t2)) % 15.93/16.18 (define @t5 () (@list @t1 @t2)) % 15.93/16.18 (define @t6 () (tptp.proper_subset @t2 @t1)) % 15.93/16.18 (define @t7 () (tptp.proper_subset @t1 @t2)) % 15.93/16.18 (define @t8 () (tptp.unordered_pair @t1 @t2)) % 15.93/16.18 (define @t9 () (tptp.set_union2 @t2 @t1)) % 15.93/16.18 (define @t10 () (tptp.set_union2 @t1 @t2)) % 15.93/16.18 (define @t11 () (tptp.set_intersection2 @t1 @t2)) % 15.93/16.18 (define @t12 () (tptp.subset @t1 @t2)) % 15.93/16.18 (define @t13 () (= @t1 @t2)) % 15.93/16.18 (define @t14 () (@var "C" $$unsorted)) % 15.93/16.18 (define @t15 () (tptp.in @t14 @t2)) % 15.93/16.18 (define @t16 () (@list @t14)) % 15.93/16.18 (define @t17 () (tptp.singleton @t1)) % 15.93/16.18 (define @t18 () (= @t1 tptp.empty_set)) % 15.93/16.18 (define @t19 () (@list @t1)) % 15.93/16.18 (define @t20 () (@var "D" $$unsorted)) % 15.93/16.18 (define @t21 () (or (= @t20 @t1) (= @t20 @t2))) % 15.93/16.18 (define @t22 () (tptp.in @t20 @t14)) % 15.93/16.18 (define @t23 () (= @t22 @t21)) % 15.93/16.18 (define @t24 () (@list @t20)) % 15.93/16.18 (define @t25 () (forall @t24 @t23)) % 15.93/16.18 (define @t26 () (= (= @t14 @t8) @t25)) % 15.93/16.18 (define @t27 () (@list @t1 @t2 @t14)) % 15.93/16.18 (define @t28 () (forall @t27 @t26)) % 15.93/16.18 (define @t29 () (tptp.in @t20 @t2)) % 15.93/16.18 (define @t30 () (tptp.in @t20 @t1)) % 15.93/16.18 (define @t31 () (@var "F" $$unsorted)) % 15.93/16.18 (define @t32 () (@var "E" $$unsorted)) % 15.93/16.18 (define @t33 () (tptp.in @t14 @t1)) % 15.93/16.18 (define @t34 () (forall @t16 (=> @t33 @t15))) % 15.93/16.18 (define @t35 () (= @t12 @t34)) % 15.93/16.18 (define @t36 () (forall @t5 @t35)) % 15.93/16.18 (define @t37 () (tptp.set_difference @t1 @t2)) % 15.93/16.18 (define @t38 () (tptp.ordered_pair @t1 @t2)) % 15.93/16.18 (define @t39 () (tptp.disjoint @t1 @t2)) % 15.93/16.18 (define @t40 () (not @t13)) % 15.93/16.18 (define @t41 () (tptp.empty @t1)) % 15.93/16.18 (define @t42 () (not @t41)) % 15.93/16.18 (define @t43 () (tptp.disjoint @t17 @t2)) % 15.93/16.18 (define @t44 () (tptp.singleton @t2)) % 15.93/16.18 (define @t45 () (tptp.in @t1 @t14)) % 15.93/16.18 (define @t46 () (@list @t1 @t2 @t14 @t20)) % 15.93/16.18 (define @t47 () (= @t1 @t20)) % 15.93/16.18 (define @t48 () (= @t1 @t14)) % 15.93/16.18 (define @t49 () (tptp.set_intersection2 @t2 @t14)) % 15.93/16.18 (define @t50 () (tptp.subset @t1 @t14)) % 15.93/16.18 (define @t51 () (= @t2 @t20)) % 15.93/16.18 (define @t52 () (forall @t27 (= (tptp.subset @t8 @t14) (and @t45 (tptp.in @t2 @t14))))) % 15.93/16.18 (define @t53 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 15.93/16.18 (define @t54 () (and @t33 @t15)) % 15.93/16.18 (define @t55 () (not @t39)) % 15.93/16.18 (define @t56 () (tptp.in @t14 @t11)) % 15.93/16.18 (define @t57 () (tptp.empty @t2)) % 15.93/16.18 (define @t58 () (= @t17 (tptp.unordered_pair @t2 @t14))) % 15.93/16.18 (define @t59 () (@quantifiers_skolemize @t52 2)) % 15.93/16.18 (define @t60 () (@quantifiers_skolemize @t52 1)) % 15.93/16.18 (define @t61 () (tptp.in @t60 @t59)) % 15.93/16.18 (define @t62 () (@quantifiers_skolemize @t52 0)) % 15.93/16.18 (define @t63 () (tptp.in @t62 @t59)) % 15.93/16.18 (define @t64 () (and @t63 @t61)) % 15.93/16.18 (define @t65 () (tptp.unordered_pair @t62 @t60)) % 15.93/16.18 (define @t66 () (tptp.subset @t65 @t59)) % 15.93/16.18 (define @t67 () (= @t66 @t64)) % 15.93/16.18 (define @t68 () (forall @t16 (or (not (tptp.in @t14 @t65)) (tptp.in @t14 @t59)))) % 15.93/16.18 (define @t69 () (= @t66 @t68)) % 15.93/16.18 (define @t70 () (not @t69)) % 15.93/16.18 (define @t71 () (not @t66)) % 15.93/16.18 (define @t72 () (@list @t62)) % 15.93/16.18 (define @t73 () (tptp.in @t62 @t65)) % 15.93/16.18 (define @t74 () (not @t73)) % 15.93/16.18 (define @t75 () (or @t74 @t63)) % 15.93/16.18 (define @t76 () (@list @t60)) % 15.93/16.18 (define @t77 () (tptp.in @t60 @t65)) % 15.93/16.18 (define @t78 () (not @t77)) % 15.93/16.18 (define @t79 () (or @t78 @t61)) % 15.93/16.18 (define @t80 () (tptp.in @t20 @t65)) % 15.93/16.18 (define @t81 () (forall @t24 (= @t80 (or (= @t20 @t62) (= @t20 @t60))))) % 15.93/16.18 (define @t82 () (or (= @t62 @t20) (= @t60 @t20))) % 15.93/16.18 (define @t83 () (= @t80 @t82)) % 15.93/16.18 (define @t84 () (forall @t24 @t83)) % 15.93/16.18 (define @t85 () (= (= @t65 @t65) @t84)) % 15.93/16.18 (define @t86 () (forall @t27 (= (= @t8 @t14) (forall @t24 (= @t22 (or @t47 @t51)))))) % 15.93/16.18 (define @t87 () (@list false)) % 15.93/16.18 (define @t88 () (= @t62 @t60)) % 15.93/16.18 (define @t89 () (or (= @t62 @t62) @t88)) % 15.93/16.18 (define @t90 () (= @t73 @t89)) % 15.93/16.18 (define @t91 () (@list @t81)) % 15.93/16.18 (define @t92 () (or (= @t60 @t62) (= @t60 @t60))) % 15.93/16.18 (define @t93 () (= @t77 @t92)) % 15.93/16.18 (define @t94 () (not @t64)) % 15.93/16.18 (define @t95 () (@list @t64)) % 15.93/16.18 (define @t96 () (not @t68)) % 15.93/16.18 (define @t97 () (@list true false)) % 15.93/16.18 (define @t98 () (@quantifiers_skolemize @t68 0)) % 15.93/16.18 (define @t99 () (tptp.in @t98 @t59)) % 15.93/16.18 (define @t100 () (tptp.in @t98 @t65)) % 15.93/16.18 (define @t101 () (not @t100)) % 15.93/16.18 (define @t102 () (or @t101 @t99)) % 15.93/16.18 (define @t103 () (not @t102)) % 15.93/16.18 (define @t104 () (@list true)) % 15.93/16.18 (define @t105 () (not @t99)) % 15.93/16.18 (define @t106 () (@list @t102)) % 15.93/16.18 (define @t107 () (or (= @t98 @t62) (= @t98 @t60))) % 15.93/16.18 (define @t108 () (= @t100 @t107)) % 15.93/16.18 (define @t109 () (= @t60 @t98)) % 15.93/16.18 (define @t110 () (= @t62 @t98)) % 15.93/16.18 (define @t111 () (or @t110 @t109)) % 15.93/16.18 (define @t112 () (= @t100 @t111)) % 15.93/16.18 (define @t113 () (not @t109)) % 15.93/16.18 (define @t114 () (not @t61)) % 15.93/16.18 (define @t115 () (not @t105)) % 15.93/16.18 (define @t116 () (= false true)) % 15.93/16.18 (define @t117 () (and @t61 @t109 @t105)) % 15.93/16.18 (define @t118 () (not @t110)) % 15.93/16.18 (define @t119 () (not @t63)) % 15.93/16.18 (define @t120 () (and @t63 @t110 @t105)) % 15.93/16.18 (assume @p1 (forall @t5 (=> @t4 @t3))) % 15.93/16.18 (assume @p2 (forall @t5 (=> @t7 (not @t6)))) % 15.93/16.18 (assume @p3 (forall @t5 (= @t8 (tptp.unordered_pair @t2 @t1)))) % 15.93/16.18 (assume @p4 (forall @t5 (= @t10 @t9))) % 15.93/16.18 (assume @p5 (forall @t5 (= @t11 (tptp.set_intersection2 @t2 @t1)))) % 15.93/16.18 (assume @p6 (forall @t5 (= @t13 (and @t12 (tptp.subset @t2 @t1))))) % 15.93/16.18 (assume @p7 (forall @t5 (= (= @t2 @t17) (forall @t16 (= @t15 (= @t14 @t1)))))) % 15.93/16.18 (assume @p8 (forall @t19 (= @t18 (forall (@list @t2) @t3)))) % 15.93/16.18 (assume @p9 (forall @t5 (= (= @t2 (tptp.powerset @t1)) (forall @t16 (= @t15 (tptp.subset @t14 @t1)))))) % 15.93/16.18 (assume @p10 @t28) % 15.93/16.18 (assume @p11 (forall @t27 (= (= @t14 @t10) (forall @t24 (= @t22 (or @t30 @t29)))))) % 15.93/16.18 (assume @p12 (forall @t27 (= (= @t14 (tptp.cartesian_product2 @t1 @t2)) (forall @t24 (= @t22 (exists (@list @t32 @t31) (and (tptp.in @t32 @t1) (tptp.in @t31 @t2) (= @t20 (tptp.ordered_pair @t32 @t31))))))))) % 15.93/16.18 (assume @p13 @t36) % 15.93/16.18 (assume @p14 (forall @t27 (= (= @t14 @t11) (forall @t24 (= @t22 (and @t30 @t29)))))) % 15.93/16.18 (assume @p15 (forall @t5 (= (= @t2 (tptp.union @t1)) (forall @t16 (= @t15 (exists @t24 (and (tptp.in @t14 @t20) @t30))))))) % 15.93/16.18 (assume @p16 (forall @t27 (= (= @t14 @t37) (forall @t24 (= @t22 (and @t30 (not @t29))))))) % 15.93/16.18 (assume @p17 (forall @t5 (= @t38 (tptp.unordered_pair @t8 @t17)))) % 15.93/16.18 (assume @p18 (forall @t5 (= @t39 (= @t11 tptp.empty_set)))) % 15.93/16.18 (assume @p19 (forall @t5 (= @t7 (and @t12 @t40)))) % 15.93/16.18 (assume @p20 true) % 15.93/16.18 (assume @p21 (tptp.empty tptp.empty_set)) % 15.93/16.18 (assume @p22 (forall @t5 (not (tptp.empty @t38)))) % 15.93/16.18 (assume @p23 (forall @t5 (=> @t42 (not (tptp.empty @t10))))) % 15.93/16.18 (assume @p24 (forall @t5 (=> @t42 (not (tptp.empty @t9))))) % 15.93/16.18 (assume @p25 (forall @t5 (= (tptp.set_union2 @t1 @t1) @t1))) % 15.93/16.18 (assume @p26 (forall @t5 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 15.93/16.18 (assume @p27 (forall @t5 (not (tptp.proper_subset @t1 @t1)))) % 15.93/16.18 (assume @p28 (forall @t19 (not (= @t17 tptp.empty_set)))) % 15.93/16.18 (assume @p29 (forall @t5 (=> @t4 (= (tptp.set_union2 @t17 @t2) @t2)))) % 15.93/16.18 (assume @p30 (forall @t5 (not (and @t43 @t4)))) % 15.93/16.18 (assume @p31 (forall @t5 (=> (not @t4) @t43))) % 15.93/16.18 (assume @p32 (forall @t5 (= (tptp.subset @t17 @t2) @t4))) % 15.93/16.18 (assume @p33 (forall @t5 (= (= @t37 tptp.empty_set) @t12))) % 15.93/16.18 (assume @p34 (forall @t27 (=> @t12 (or @t33 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t14))))))) % 15.93/16.18 (assume @p35 (forall @t5 (= (tptp.subset @t1 @t44) (or @t18 (= @t1 @t44))))) % 15.93/16.18 (assume @p36 (forall @t5 (=> @t4 (tptp.subset @t1 (tptp.union @t2))))) % 15.93/16.18 (assume @p37 (forall @t46 (= (tptp.in @t38 (tptp.cartesian_product2 @t14 @t20)) (and @t45 (tptp.in @t2 @t20))))) % 15.93/16.18 (assume @p38 (exists @t19 @t41)) % 15.93/16.18 (assume @p39 (exists @t19 @t42)) % 15.93/16.18 (assume @p40 (forall @t5 (tptp.subset @t1 @t1))) % 15.93/16.18 (assume @p41 (forall @t5 (=> @t39 (tptp.disjoint @t2 @t1)))) % 15.93/16.18 (assume @p42 (forall @t46 (not (and (= @t8 (tptp.unordered_pair @t14 @t20)) (not @t48) (not @t47))))) % 15.93/16.18 (assume @p43 (forall @t5 (=> @t12 (= @t10 @t2)))) % 15.93/16.18 (assume @p44 (forall @t5 (tptp.subset @t11 @t1))) % 15.93/16.18 (assume @p45 (forall @t27 (=> (and @t12 @t50) (tptp.subset @t1 @t49)))) % 15.93/16.18 (assume @p46 (forall @t19 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 15.93/16.18 (assume @p47 (forall @t27 (=> (and @t12 (tptp.subset @t2 @t14)) @t50))) % 15.93/16.18 (assume @p48 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 15.93/16.18 (assume @p49 (forall @t27 (=> @t12 (tptp.subset (tptp.set_intersection2 @t1 @t14) @t49)))) % 15.93/16.18 (assume @p50 (forall @t5 (=> @t12 (= @t11 @t1)))) % 15.93/16.18 (assume @p51 (forall @t19 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 15.93/16.18 (assume @p52 (forall @t5 (=> (forall @t16 (= @t33 @t15)) @t13))) % 15.93/16.18 (assume @p53 (forall @t19 (tptp.subset tptp.empty_set @t1))) % 15.93/16.18 (assume @p54 (forall @t27 (=> @t12 (tptp.subset (tptp.set_difference @t1 @t14) (tptp.set_difference @t2 @t14))))) % 15.93/16.18 (assume @p55 (forall @t46 (=> (= @t38 (tptp.ordered_pair @t14 @t20)) (and @t48 @t51)))) % 15.93/16.18 (assume @p56 (forall @t5 (tptp.subset @t37 @t1))) % 15.93/16.18 (assume @p57 (not @t52)) % 15.93/16.18 (assume @p58 (forall @t5 (= @t53 @t10))) % 15.93/16.18 (assume @p59 (forall @t19 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 15.93/16.18 (assume @p60 (forall @t5 (and (not (and @t55 (forall @t16 (not @t54)))) (not (and (exists @t16 @t54) @t39))))) % 15.93/16.18 (assume @p61 (forall @t19 (=> (tptp.subset @t1 tptp.empty_set) @t18))) % 15.93/16.18 (assume @p62 (forall @t5 (= (tptp.set_difference @t10 @t2) @t37))) % 15.93/16.18 (assume @p63 (forall @t5 (=> @t12 (= @t2 @t53)))) % 15.93/16.18 (assume @p64 (forall @t5 (= (tptp.set_difference @t1 @t37) @t11))) % 15.93/16.18 (assume @p65 (forall @t19 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 15.93/16.18 (assume @p66 (forall @t5 (and (not (and @t55 (forall @t16 (not @t56)))) (not (and (exists @t16 @t56) @t39))))) % 15.93/16.18 (assume @p67 (forall @t5 (not (and @t12 @t6)))) % 15.93/16.18 (assume @p68 (forall @t27 (=> (and @t12 (tptp.disjoint @t2 @t14)) (tptp.disjoint @t1 @t14)))) % 15.93/16.18 (assume @p69 (forall @t19 (= (tptp.unordered_pair @t1 @t1) @t17))) % 15.93/16.18 (assume @p70 (forall @t19 (=> @t41 @t18))) % 15.93/16.18 (assume @p71 (forall @t5 (=> (tptp.subset @t17 @t44) @t13))) % 15.93/16.18 (assume @p72 (forall @t5 (not (and @t4 @t57)))) % 15.93/16.18 (assume @p73 (forall @t5 (tptp.subset @t1 @t10))) % 15.93/16.18 (assume @p74 (forall @t5 (= @t39 (= @t37 @t1)))) % 15.93/16.18 (assume @p75 (forall @t5 (not (and @t41 @t40 @t57)))) % 15.93/16.18 (assume @p76 (forall @t27 (=> (and @t12 (tptp.subset @t14 @t2)) (tptp.subset (tptp.set_union2 @t1 @t14) @t2)))) % 15.93/16.18 (assume @p77 (forall @t27 (=> @t58 @t13))) % 15.93/16.18 (assume @p78 (forall @t27 (=> @t58 (= @t2 @t14)))) % 15.93/16.18 (step @p79 :rule skolemize :premises (@p57)) % 15.93/16.18 (step @p80 :rule cnf_equiv_neg2 :args (@t67)) % 15.93/16.18 (step @p81 :rule bool-impl-elim :args (@t33 @t15)) % 15.93/16.18 (step @p82 :rule cong :premises (@p81) :args (@t34)) % 15.93/16.18 (step @p83 :rule refl :args (@t12)) % 15.93/16.18 (step @p84 :rule cong :premises (@p83 @p82) :args (@t35)) % 15.93/16.18 (step @p85 :rule cong :premises (@p84) :args (@t36)) % 15.93/16.18 (step @p86 :rule eq_resolve :premises (@p13 @p85)) % 15.93/16.18 (step @p87 :rule instantiate :premises (@p86) :args ((@list @t65 @t59))) % 15.93/16.18 (step @p88 :rule cnf_equiv_pos1 :args (@t69)) % 15.93/16.18 (step @p89 :rule reordering :premises (@p88) :args ((or @t71 @t68 @t70))) % 15.93/16.18 (assume-push @p285 @t68) % 15.93/16.18 (step @p91 :rule instantiate :premises (@p285) :args (@t72)) % 15.93/16.18 (step-pop @p286 :rule scope :premises (@p91)) % 15.93/16.18 (step @p92 :rule process_scope :premises (@p286) :args (@t75)) % 15.93/16.18 (step @p94 :rule implies_elim :premises (@p92)) % 15.93/16.18 (assume-push @p287 @t68) % 15.93/16.18 (step @p96 :rule instantiate :premises (@p287) :args (@t76)) % 15.93/16.18 (step-pop @p288 :rule scope :premises (@p96)) % 15.93/16.18 (step @p97 :rule process_scope :premises (@p288) :args (@t79)) % 15.93/16.18 (step @p99 :rule implies_elim :premises (@p97)) % 15.93/16.18 (step @p100 :rule eq-symm :args (@t20 @t2)) % 15.93/16.18 (step @p101 :rule eq-symm :args (@t20 @t1)) % 15.93/16.18 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t21)) % 15.93/16.18 (step @p103 :rule refl :args (@t22)) % 15.93/16.18 (step @p104 :rule cong :premises (@p103 @p102) :args (@t23)) % 15.93/16.18 (step @p105 :rule cong :premises (@p104) :args (@t25)) % 15.93/16.18 (step @p106 :rule eq-symm :args (@t14 @t8)) % 15.93/16.18 (step @p107 :rule cong :premises (@p106 @p105) :args (@t26)) % 15.93/16.18 (step @p108 :rule cong :premises (@p107) :args (@t28)) % 15.93/16.18 (step @p109 :rule eq_resolve :premises (@p10 @p108)) % 15.93/16.18 (step @p110 :rule bool-eq-true :args (@t81)) % 15.93/16.18 (step @p111 :rule eq-symm :args (true @t81)) % 15.93/16.18 (step @p112 :rule trans :premises (@p111 @p110)) % 15.93/16.18 (step @p113 :rule eq-symm :args (@t60 @t20)) % 15.93/16.18 (step @p114 :rule eq-symm :args (@t62 @t20)) % 15.93/16.18 (step @p115 :rule nary_cong :premises (@p114 @p113) :args (@t82)) % 15.93/16.18 (step @p116 :rule refl :args (@t80)) % 15.93/16.18 (step @p117 :rule cong :premises (@p116 @p115) :args (@t83)) % 15.93/16.18 (step @p118 :rule cong :premises (@p117) :args (@t84)) % 15.93/16.18 (step @p119 :rule eq-refl :args (@t65)) % 15.93/16.18 (step @p120 :rule cong :premises (@p119 @p118) :args (@t85)) % 15.93/16.18 (step @p121 :rule trans :premises (@p120 @p112)) % 15.93/16.18 (step @p122 :rule refl :args (@t86)) % 15.93/16.18 (step @p123 :rule cong :premises (@p122 @p121) :args ((=> @t86 @t85))) % 15.93/16.18 (assume-push @p289 @t86) % 15.93/16.18 (step @p125 :rule instantiate :premises (@p109) :args ((@list @t62 @t60 @t65))) % 15.93/16.18 (step-pop @p290 :rule scope :premises (@p125)) % 15.93/16.18 (step @p126 :rule process_scope :premises (@p290) :args (@t85)) % 15.93/16.18 (step @p128 :rule eq_resolve :premises (@p126 @p123)) % 15.93/16.18 (step @p129 :rule implies_elim :premises (@p128)) % 15.93/16.18 (step @p130 :rule chain_m_resolution :premises (@p129 @p109) :args (@t81 @t87 (@list @t86))) % 15.93/16.18 (step @p131 :rule bool-eq-true :args (@t73)) % 15.93/16.18 (step @p132 :rule absorb :args ((= (or true @t88) true))) % 15.93/16.18 (step @p133 :rule refl :args (@t88)) % 15.93/16.18 (step @p134 :rule eq-refl :args (@t62)) % 15.93/16.18 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t89)) % 15.93/16.18 (step @p136 :rule trans :premises (@p135 @p132)) % 15.93/16.18 (step @p137 :rule refl :args (@t73)) % 15.93/16.18 (step @p138 :rule cong :premises (@p137 @p136) :args (@t90)) % 15.93/16.18 (step @p139 :rule trans :premises (@p138 @p131)) % 15.93/16.18 (step @p140 :rule refl :args (@t81)) % 15.93/16.18 (step @p141 :rule cong :premises (@p140 @p139) :args ((=> @t81 @t90))) % 15.93/16.18 (assume-push @p291 @t81) % 15.93/16.18 (step @p143 :rule instantiate :premises (@p130) :args (@t72)) % 15.93/16.18 (step-pop @p292 :rule scope :premises (@p143)) % 15.93/16.18 (step @p144 :rule process_scope :premises (@p292) :args (@t90)) % 15.93/16.18 (step @p146 :rule eq_resolve :premises (@p144 @p141)) % 15.93/16.18 (step @p147 :rule implies_elim :premises (@p146)) % 15.93/16.18 (step @p148 :rule chain_m_resolution :premises (@p147 @p130) :args (@t73 @t87 @t91)) % 15.93/16.18 (step @p149 :rule cnf_or_pos :args (@t75)) % 15.93/16.18 (step @p150 :rule reordering :premises (@p149) :args ((or @t63 @t74 (not @t75)))) % 15.93/16.18 (step @p151 :rule bool-eq-true :args (@t77)) % 15.93/16.18 (step @p152 :rule absorb :args ((= (or @t88 true) true))) % 15.93/16.18 (step @p153 :rule eq-refl :args (@t60)) % 15.93/16.18 (step @p154 :rule eq-symm :args (@t60 @t62)) % 15.93/16.18 (step @p155 :rule nary_cong :premises (@p154 @p153) :args (@t92)) % 15.93/16.18 (step @p156 :rule trans :premises (@p155 @p152)) % 15.93/16.18 (step @p157 :rule refl :args (@t77)) % 15.93/16.18 (step @p158 :rule cong :premises (@p157 @p156) :args (@t93)) % 15.93/16.18 (step @p159 :rule trans :premises (@p158 @p151)) % 15.93/16.18 (step @p160 :rule cong :premises (@p140 @p159) :args ((=> @t81 @t93))) % 15.93/16.18 (assume-push @p293 @t81) % 15.93/16.18 (step @p162 :rule instantiate :premises (@p130) :args (@t76)) % 15.93/16.18 (step-pop @p294 :rule scope :premises (@p162)) % 15.93/16.18 (step @p163 :rule process_scope :premises (@p294) :args (@t93)) % 15.93/16.18 (step @p165 :rule eq_resolve :premises (@p163 @p160)) % 15.93/16.18 (step @p166 :rule implies_elim :premises (@p165)) % 15.93/16.18 (step @p167 :rule chain_m_resolution :premises (@p166 @p130) :args (@t77 @t87 @t91)) % 15.93/16.18 (step @p168 :rule cnf_or_pos :args (@t79)) % 15.93/16.18 (step @p169 :rule reordering :premises (@p168) :args ((or @t61 @t78 (not @t79)))) % 15.93/16.18 (step @p170 :rule cnf_and_neg :args (@t64)) % 15.93/16.18 (step @p171 :rule chain_m_resolution :premises (@p170 @p169 @p167 @p150 @p148 @p99 @p94 @p89 @p87 @p80 @p79) :args (@t71 (@list false false false false false false false false true true) (@list @t61 @t77 @t63 @t73 @t79 @t75 @t68 @t69 @t64 @t67))) % 15.93/16.18 (step @p172 :rule cnf_equiv_neg1 :args (@t67)) % 15.93/16.18 (step @p173 :rule reordering :premises (@p172) :args ((or @t66 @t64 @t67))) % 15.93/16.18 (step @p174 :rule chain_m_resolution :premises (@p173 @p171 @p79) :args (@t64 (@list true true) (@list @t66 @t67))) % 15.93/16.18 (step @p175 :rule cnf_and_pos :args (@t64 0)) % 15.93/16.18 (step @p176 :rule reordering :premises (@p175) :args ((or @t63 @t94))) % 15.93/16.18 (step @p177 :rule chain_m_resolution :premises (@p176 @p174) :args (@t63 @t87 @t95)) % 15.93/16.18 (step @p178 :rule cnf_equiv_pos2 :args (@t69)) % 15.93/16.18 (step @p179 :rule reordering :premises (@p178) :args ((or @t66 @t96 @t70))) % 15.93/16.18 (step @p180 :rule chain_m_resolution :premises (@p179 @p171 @p87) :args (@t96 @t97 (@list @t66 @t69))) % 15.93/16.18 (step @p181 :rule refl :args (@t103)) % 15.93/16.18 (step @p182 :rule bool-double-not-elim :args (@t68)) % 15.93/16.18 (step @p183 :rule nary_cong :premises (@p182 @p181) :args ((or (not @t96) @t103))) % 15.93/16.18 (assume-push @p295 @t96) % 15.93/16.18 (step @p185 :rule skolemize :premises (@p295)) % 15.93/16.18 (step-pop @p296 :rule scope :premises (@p185)) % 15.93/16.18 (step @p186 :rule process_scope :premises (@p296) :args (@t103)) % 15.93/16.18 (step @p188 :rule implies_elim :premises (@p186)) % 15.93/16.18 (step @p189 :rule eq_resolve :premises (@p188 @p183)) % 15.93/16.18 (step @p190 :rule chain_m_resolution :premises (@p189 @p180) :args (@t103 @t104 (@list @t68))) % 15.93/16.18 (step @p191 :rule cnf_or_neg :args (@t102 1)) % 15.93/16.18 (step @p192 :rule chain_m_resolution :premises (@p191 @p190) :args (@t105 @t104 @t106)) % 15.93/16.18 (step @p193 :rule eq-symm :args (@t98 @t60)) % 15.93/16.18 (step @p194 :rule eq-symm :args (@t98 @t62)) % 15.93/16.18 (step @p195 :rule nary_cong :premises (@p194 @p193) :args (@t107)) % 15.93/16.18 (step @p196 :rule refl :args (@t100)) % 15.93/16.18 (step @p197 :rule cong :premises (@p196 @p195) :args (@t108)) % 15.93/16.18 (step @p198 :rule cong :premises (@p140 @p197) :args ((=> @t81 @t108))) % 15.93/16.18 (assume-push @p297 @t81) % 15.93/16.18 (step @p200 :rule instantiate :premises (@p130) :args ((@list @t98))) % 15.93/16.18 (step-pop @p298 :rule scope :premises (@p200)) % 15.93/16.18 (step @p201 :rule process_scope :premises (@p298) :args (@t108)) % 15.93/16.18 (step @p203 :rule eq_resolve :premises (@p201 @p198)) % 15.93/16.18 (step @p204 :rule implies_elim :premises (@p203)) % 15.93/16.18 (step @p205 :rule chain_m_resolution :premises (@p204 @p130) :args (@t112 @t87 @t91)) % 15.93/16.18 (step @p206 :rule bool-double-not-elim :args (@t100)) % 15.93/16.18 (step @p207 :rule refl :args (@t102)) % 15.93/16.18 (step @p208 :rule nary_cong :premises (@p207 @p206) :args ((or @t102 (not @t101)))) % 15.93/16.18 (step @p209 :rule cnf_or_neg :args (@t102 0)) % 15.93/16.18 (step @p210 :rule eq_resolve :premises (@p209 @p208)) % 15.93/16.18 (step @p211 :rule reordering :premises (@p210) :args ((or @t100 @t102))) % 15.93/16.18 (step @p212 :rule chain_m_resolution :premises (@p211 @p190) :args (@t100 @t104 @t106)) % 15.93/16.18 (step @p213 :rule cnf_equiv_pos1 :args (@t112)) % 15.93/16.18 (step @p214 :rule reordering :premises (@p213) :args ((or @t101 @t111 (not @t112)))) % 15.93/16.18 (step @p215 :rule chain_m_resolution :premises (@p214 @p212 @p205) :args (@t111 (@list false false) (@list @t100 @t112))) % 15.93/16.18 (step @p216 :rule cnf_and_pos :args (@t64 1)) % 15.93/16.18 (step @p217 :rule reordering :premises (@p216) :args ((or @t61 @t94))) % 15.93/16.18 (step @p218 :rule chain_m_resolution :premises (@p217 @p174) :args (@t61 @t87 @t95)) % 15.93/16.18 (step @p219 :rule refl :args (@t113)) % 15.93/16.18 (step @p220 :rule bool-double-not-elim :args (@t99)) % 15.93/16.18 (step @p221 :rule refl :args (@t114)) % 15.93/16.18 (step @p222 :rule nary_cong :premises (@p221 @p220 @p219) :args ((or @t114 @t115 @t113))) % 15.93/16.18 (assume-push @p299 @t61) % 15.93/16.18 (assume-push @p300 @t109) % 15.93/16.18 (assume-push @p301 @t105) % 15.93/16.18 (step @p226 :rule evaluate :args (@t116)) % 15.93/16.18 (step @p227 :rule true_intro :premises (@p299)) % 15.93/16.18 (step @p228 :rule refl :args (@t59)) % 15.93/16.18 (step @p229 :rule symm :premises (@p300)) % 15.93/16.18 (step @p230 :rule cong :premises (@p229 @p228) :args (@t99)) % 15.93/16.18 (step @p231 :rule false_intro :premises (@p301)) % 15.93/16.18 (step @p232 :rule symm :premises (@p231)) % 15.93/16.18 (step @p233 :rule trans :premises (@p232 @p230 @p227)) % 15.93/16.18 (step @p234 false :rule eq_resolve :premises (@p233 @p226)) % 15.93/16.18 (step-pop @p302 :rule scope :premises (@p234)) % 15.93/16.18 (step-pop @p303 :rule scope :premises (@p302)) % 15.93/16.18 (step-pop @p304 :rule scope :premises (@p303)) % 15.93/16.18 (step @p235 :rule process_scope :premises (@p304) :args (false)) % 15.93/16.18 (assume-push @p305 @t61) % 15.93/16.18 (assume-push @p306 @t105) % 15.93/16.18 (assume-push @p307 @t109) % 15.93/16.18 (step @p242 :rule and_intro :premises (@p305 @p307 @p306)) % 15.93/16.18 (step-pop @p308 :rule scope :premises (@p242)) % 15.93/16.18 (step-pop @p309 :rule scope :premises (@p308)) % 15.93/16.18 (step-pop @p310 :rule scope :premises (@p309)) % 15.93/16.18 (step @p243 :rule process_scope :premises (@p310) :args (@t117)) % 15.93/16.18 (step @p247 :rule implies_elim :premises (@p243)) % 15.93/16.18 (step @p248 :rule resolution :premises (@p247 @p235) :args (true @t117)) % 15.93/16.18 (step @p249 :rule not_and :premises (@p248)) % 15.93/16.18 (step @p250 :rule eq_resolve :premises (@p249 @p222)) % 15.93/16.18 (step @p251 :rule chain_m_resolution :premises (@p250 @p218 @p192) :args (@t113 (@list false true) (@list @t61 @t99))) % 15.93/16.18 (step @p252 :rule cnf_or_pos :args (@t111)) % 15.93/16.18 (step @p253 :rule reordering :premises (@p252) :args ((or @t110 @t109 (not @t111)))) % 15.93/16.18 (step @p254 :rule chain_m_resolution :premises (@p253 @p251 @p215) :args (@t110 @t97 (@list @t109 @t111))) % 15.93/16.18 (step @p255 :rule refl :args (@t118)) % 15.93/16.18 (step @p256 :rule refl :args (@t119)) % 15.93/16.18 (step @p257 :rule nary_cong :premises (@p256 @p220 @p255) :args ((or @t119 @t115 @t118))) % 15.93/16.18 (assume-push @p311 @t63) % 15.93/16.18 (assume-push @p312 @t110) % 15.93/16.18 (assume-push @p313 @t105) % 15.93/16.18 (step @p226 :rule evaluate :args (@t116)) % 15.93/16.18 (step @p261 :rule true_intro :premises (@p311)) % 15.93/16.18 (step @p228 :rule refl :args (@t59)) % 15.93/16.18 (step @p262 :rule symm :premises (@p312)) % 15.93/16.18 (step @p263 :rule cong :premises (@p262 @p228) :args (@t99)) % 15.93/16.18 (step @p264 :rule false_intro :premises (@p313)) % 15.93/16.18 (step @p265 :rule symm :premises (@p264)) % 15.93/16.18 (step @p266 :rule trans :premises (@p265 @p263 @p261)) % 15.93/16.18 (step @p267 false :rule eq_resolve :premises (@p266 @p226)) % 15.93/16.18 (step-pop @p314 :rule scope :premises (@p267)) % 15.93/16.18 (step-pop @p315 :rule scope :premises (@p314)) % 15.93/16.18 (step-pop @p316 :rule scope :premises (@p315)) % 15.93/16.18 (step @p268 :rule process_scope :premises (@p316) :args (false)) % 15.93/16.18 (assume-push @p317 @t63) % 15.93/16.18 (assume-push @p318 @t105) % 15.93/16.18 (assume-push @p319 @t110) % 15.93/16.18 (step @p275 :rule and_intro :premises (@p317 @p319 @p318)) % 15.93/16.18 (step-pop @p320 :rule scope :premises (@p275)) % 15.93/16.18 (step-pop @p321 :rule scope :premises (@p320)) % 15.93/16.18 (step-pop @p322 :rule scope :premises (@p321)) % 15.93/16.18 (step @p276 :rule process_scope :premises (@p322) :args (@t120)) % 15.93/16.18 (step @p280 :rule implies_elim :premises (@p276)) % 15.93/16.18 (step @p281 :rule resolution :premises (@p280 @p268) :args (true @t120)) % 15.93/16.18 (step @p282 :rule not_and :premises (@p281)) % 15.93/16.18 (step @p283 :rule eq_resolve :premises (@p282 @p257)) % 15.93/16.18 (step @p284 false :rule chain_m_resolution :premises (@p283 @p254 @p192 @p177) :args (false (@list false true false) (@list @t110 @t99 @t63))) % 15.93/16.18 ) % 15.93/16.18 % SZS output end Proof % 15.93/16.18 % cvc5 exiting %------------------------------------------------------------------------------