%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU162+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 : n023.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 08:50:47 AM UTC 2026 % Result : Theorem 0.36s 0.62s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU162+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 : n023.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 16:33:58 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.62 % SZS status Theorem % 0.36/0.62 % SZS output start Proof % 0.36/0.62 ( % 0.36/0.62 (declare-sort $$unsorted 0) % 0.36/0.62 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.empty_set $$unsorted) % 0.36/0.62 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (define @t1 () (@var "A" $$unsorted)) % 0.36/0.62 (define @t2 () (@var "B" $$unsorted)) % 0.36/0.62 (define @t3 () (not (tptp.in @t2 @t1))) % 0.36/0.62 (define @t4 () (tptp.in @t1 @t2)) % 0.36/0.62 (define @t5 () (@list @t1 @t2)) % 0.36/0.62 (define @t6 () (tptp.proper_subset @t2 @t1)) % 0.36/0.62 (define @t7 () (tptp.proper_subset @t1 @t2)) % 0.36/0.62 (define @t8 () (tptp.unordered_pair @t1 @t2)) % 0.36/0.62 (define @t9 () (tptp.set_union2 @t2 @t1)) % 0.36/0.62 (define @t10 () (tptp.set_union2 @t1 @t2)) % 0.36/0.62 (define @t11 () (tptp.set_intersection2 @t1 @t2)) % 0.36/0.62 (define @t12 () (tptp.subset @t1 @t2)) % 0.36/0.62 (define @t13 () (= @t1 @t2)) % 0.36/0.62 (define @t14 () (@var "C" $$unsorted)) % 0.36/0.62 (define @t15 () (tptp.in @t14 @t2)) % 0.36/0.62 (define @t16 () (@list @t14)) % 0.36/0.62 (define @t17 () (tptp.singleton @t1)) % 0.36/0.62 (define @t18 () (= @t1 tptp.empty_set)) % 0.36/0.62 (define @t19 () (@list @t1)) % 0.36/0.62 (define @t20 () (@var "D" $$unsorted)) % 0.36/0.62 (define @t21 () (tptp.in @t20 @t14)) % 0.36/0.62 (define @t22 () (@list @t20)) % 0.36/0.62 (define @t23 () (@list @t1 @t2 @t14)) % 0.36/0.62 (define @t24 () (tptp.in @t20 @t2)) % 0.36/0.62 (define @t25 () (tptp.in @t20 @t1)) % 0.36/0.62 (define @t26 () (@var "F" $$unsorted)) % 0.36/0.62 (define @t27 () (@var "E" $$unsorted)) % 0.36/0.62 (define @t28 () (tptp.in @t14 @t1)) % 0.36/0.62 (define @t29 () (tptp.set_difference @t1 @t2)) % 0.36/0.62 (define @t30 () (tptp.ordered_pair @t1 @t2)) % 0.36/0.62 (define @t31 () (tptp.disjoint @t1 @t2)) % 0.36/0.62 (define @t32 () (not @t13)) % 0.36/0.62 (define @t33 () (tptp.empty @t1)) % 0.36/0.62 (define @t34 () (not @t33)) % 0.36/0.62 (define @t35 () (forall @t19 (not (= @t17 tptp.empty_set)))) % 0.36/0.62 (define @t36 () (tptp.disjoint @t17 @t2)) % 0.36/0.62 (define @t37 () (not @t4)) % 0.36/0.62 (define @t38 () (forall @t5 (=> @t37 @t36))) % 0.36/0.62 (define @t39 () (tptp.subset @t17 @t2)) % 0.36/0.62 (define @t40 () (forall @t5 (= @t39 @t4))) % 0.36/0.62 (define @t41 () (= @t29 tptp.empty_set)) % 0.36/0.62 (define @t42 () (forall @t5 (= @t41 @t12))) % 0.36/0.62 (define @t43 () (tptp.singleton @t2)) % 0.36/0.62 (define @t44 () (tptp.in @t1 @t14)) % 0.36/0.62 (define @t45 () (@list @t1 @t2 @t14 @t20)) % 0.36/0.62 (define @t46 () (exists @t19 @t33)) % 0.36/0.62 (define @t47 () (tptp.disjoint @t2 @t1)) % 0.36/0.62 (define @t48 () (forall @t5 (=> @t31 @t47))) % 0.36/0.62 (define @t49 () (= @t1 @t14)) % 0.36/0.62 (define @t50 () (tptp.set_intersection2 @t2 @t14)) % 0.36/0.62 (define @t51 () (tptp.subset @t1 @t14)) % 0.36/0.62 (define @t52 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 0.36/0.62 (define @t53 () (and @t28 @t15)) % 0.36/0.62 (define @t54 () (not @t31)) % 0.36/0.62 (define @t55 () (tptp.in @t14 @t11)) % 0.36/0.62 (define @t56 () (tptp.set_difference @t1 @t43)) % 0.36/0.62 (define @t57 () (= @t56 @t1)) % 0.36/0.62 (define @t58 () (forall @t5 (= @t57 @t3))) % 0.36/0.62 (define @t59 () (not @t58)) % 0.36/0.62 (define @t60 () (forall @t19 (=> @t33 @t18))) % 0.36/0.62 (define @t61 () (tptp.empty @t2)) % 0.36/0.62 (define @t62 () (= @t31 (= @t29 @t1))) % 0.36/0.62 (define @t63 () (forall @t5 @t62)) % 0.36/0.62 (define @t64 () (= @t17 (tptp.unordered_pair @t2 @t14))) % 0.36/0.62 (define @t65 () (forall @t5 (= @t3 (= @t1 @t56)))) % 0.36/0.62 (define @t66 () (@quantifiers_skolemize @t65 1)) % 0.36/0.62 (define @t67 () (tptp.singleton @t66)) % 0.36/0.62 (define @t68 () (@quantifiers_skolemize @t65 0)) % 0.36/0.62 (define @t69 () (tptp.disjoint @t68 @t67)) % 0.36/0.62 (define @t70 () (= @t68 (tptp.set_difference @t68 @t67))) % 0.36/0.62 (define @t71 () (forall @t5 (= @t31 (= @t1 @t29)))) % 0.36/0.62 (define @t72 () (= @t69 @t70)) % 0.36/0.62 (define @t73 () (@list @t68 @t67)) % 0.36/0.62 (define @t74 () (= @t70 @t69)) % 0.36/0.62 (define @t75 () (@list false)) % 0.36/0.62 (define @t76 () (not @t70)) % 0.36/0.62 (define @t77 () (tptp.in @t66 @t68)) % 0.36/0.62 (define @t78 () (not @t77)) % 0.36/0.62 (define @t79 () (= @t78 @t70)) % 0.36/0.62 (define @t80 () (@list @t66 @t68)) % 0.36/0.62 (define @t81 () (tptp.disjoint @t67 @t68)) % 0.36/0.62 (define @t82 () (or @t77 @t81)) % 0.36/0.62 (define @t83 () (not @t74)) % 0.36/0.62 (define @t84 () (not @t69)) % 0.36/0.62 (define @t85 () (@list @t67 @t68)) % 0.36/0.62 (define @t86 () (not @t81)) % 0.36/0.62 (define @t87 () (or @t86 @t69)) % 0.36/0.62 (define @t88 () (@list false false)) % 0.36/0.62 (define @t89 () (tptp.subset @t67 @t68)) % 0.36/0.62 (define @t90 () (= @t77 @t89)) % 0.36/0.62 (define @t91 () (tptp.set_difference @t67 @t68)) % 0.36/0.62 (define @t92 () (= tptp.empty_set @t91)) % 0.36/0.62 (define @t93 () (= @t89 @t92)) % 0.36/0.62 (define @t94 () (forall @t19 @t34)) % 0.36/0.62 (define @t95 () (@quantifiers_skolemize @t94 0)) % 0.36/0.62 (define @t96 () (tptp.empty @t95)) % 0.36/0.62 (define @t97 () (not @t96)) % 0.36/0.62 (define @t98 () (or @t97 (= @t95 tptp.empty_set))) % 0.36/0.62 (define @t99 () (forall @t19 (or @t34 @t18))) % 0.36/0.62 (define @t100 () (= tptp.empty_set @t95)) % 0.36/0.62 (define @t101 () (or @t97 @t100)) % 0.36/0.62 (define @t102 () (not @t94)) % 0.36/0.62 (define @t103 () (not @t97)) % 0.36/0.62 (define @t104 () (not (= @t67 tptp.empty_set))) % 0.36/0.62 (define @t105 () (= tptp.empty_set @t67)) % 0.36/0.62 (define @t106 () (not @t105)) % 0.36/0.62 (define @t107 () (= @t67 @t91)) % 0.36/0.62 (define @t108 () (not @t107)) % 0.36/0.62 (define @t109 () (not @t92)) % 0.36/0.62 (define @t110 () (not @t100)) % 0.36/0.62 (define @t111 () (and @t100 @t92 @t107 @t106)) % 0.36/0.62 (define @t112 () (= @t81 @t107)) % 0.36/0.62 (define @t113 () (@list true false)) % 0.36/0.62 (define @t114 () (or @t84 @t81)) % 0.36/0.62 (define @t115 () (not @t114)) % 0.36/0.62 (define @t116 () (forall @t5 (or @t54 @t47))) % 0.36/0.62 (assume @p1 (forall @t5 (=> @t4 @t3))) % 0.36/0.62 (assume @p2 (forall @t5 (=> @t7 (not @t6)))) % 0.36/0.62 (assume @p3 (forall @t5 (= @t8 (tptp.unordered_pair @t2 @t1)))) % 0.36/0.62 (assume @p4 (forall @t5 (= @t10 @t9))) % 0.36/0.62 (assume @p5 (forall @t5 (= @t11 (tptp.set_intersection2 @t2 @t1)))) % 0.36/0.62 (assume @p6 (forall @t5 (= @t13 (and @t12 (tptp.subset @t2 @t1))))) % 0.36/0.62 (assume @p7 (forall @t5 (= (= @t2 @t17) (forall @t16 (= @t15 (= @t14 @t1)))))) % 0.36/0.62 (assume @p8 (forall @t19 (= @t18 (forall (@list @t2) @t3)))) % 0.36/0.62 (assume @p9 (forall @t5 (= (= @t2 (tptp.powerset @t1)) (forall @t16 (= @t15 (tptp.subset @t14 @t1)))))) % 0.36/0.62 (assume @p10 (forall @t23 (= (= @t14 @t8) (forall @t22 (= @t21 (or (= @t20 @t1) (= @t20 @t2))))))) % 0.36/0.62 (assume @p11 (forall @t23 (= (= @t14 @t10) (forall @t22 (= @t21 (or @t25 @t24)))))) % 0.36/0.62 (assume @p12 (forall @t23 (= (= @t14 (tptp.cartesian_product2 @t1 @t2)) (forall @t22 (= @t21 (exists (@list @t27 @t26) (and (tptp.in @t27 @t1) (tptp.in @t26 @t2) (= @t20 (tptp.ordered_pair @t27 @t26))))))))) % 0.36/0.62 (assume @p13 (forall @t5 (= @t12 (forall @t16 (=> @t28 @t15))))) % 0.36/0.62 (assume @p14 (forall @t23 (= (= @t14 @t11) (forall @t22 (= @t21 (and @t25 @t24)))))) % 0.36/0.62 (assume @p15 (forall @t5 (= (= @t2 (tptp.union @t1)) (forall @t16 (= @t15 (exists @t22 (and (tptp.in @t14 @t20) @t25))))))) % 0.36/0.62 (assume @p16 (forall @t23 (= (= @t14 @t29) (forall @t22 (= @t21 (and @t25 (not @t24))))))) % 0.36/0.62 (assume @p17 (forall @t5 (= @t30 (tptp.unordered_pair @t8 @t17)))) % 0.36/0.62 (assume @p18 (forall @t5 (= @t31 (= @t11 tptp.empty_set)))) % 0.36/0.62 (assume @p19 (forall @t5 (= @t7 (and @t12 @t32)))) % 0.36/0.62 (assume @p20 true) % 0.36/0.62 (assume @p21 (tptp.empty tptp.empty_set)) % 0.36/0.62 (assume @p22 (forall @t5 (not (tptp.empty @t30)))) % 0.36/0.62 (assume @p23 (forall @t5 (=> @t34 (not (tptp.empty @t10))))) % 0.36/0.62 (assume @p24 (forall @t5 (=> @t34 (not (tptp.empty @t9))))) % 0.36/0.62 (assume @p25 (forall @t5 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.36/0.62 (assume @p26 (forall @t5 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.36/0.62 (assume @p27 (forall @t5 (not (tptp.proper_subset @t1 @t1)))) % 0.36/0.62 (assume @p28 @t35) % 0.36/0.62 (assume @p29 (forall @t5 (=> @t4 (= (tptp.set_union2 @t17 @t2) @t2)))) % 0.36/0.62 (assume @p30 (forall @t5 (not (and @t36 @t4)))) % 0.36/0.62 (assume @p31 @t38) % 0.36/0.62 (assume @p32 @t40) % 0.36/0.62 (assume @p33 @t42) % 0.36/0.62 (assume @p34 (forall @t23 (=> @t12 (or @t28 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t14))))))) % 0.36/0.62 (assume @p35 (forall @t5 (= (tptp.subset @t1 @t43) (or @t18 (= @t1 @t43))))) % 0.36/0.62 (assume @p36 (forall @t5 (=> @t4 (tptp.subset @t1 (tptp.union @t2))))) % 0.36/0.62 (assume @p37 (forall @t45 (= (tptp.in @t30 (tptp.cartesian_product2 @t14 @t20)) (and @t44 (tptp.in @t2 @t20))))) % 0.36/0.62 (assume @p38 @t46) % 0.36/0.62 (assume @p39 (exists @t19 @t34)) % 0.36/0.62 (assume @p40 (forall @t5 (tptp.subset @t1 @t1))) % 0.36/0.62 (assume @p41 @t48) % 0.36/0.62 (assume @p42 (forall @t45 (not (and (= @t8 (tptp.unordered_pair @t14 @t20)) (not @t49) (not (= @t1 @t20)))))) % 0.36/0.62 (assume @p43 (forall @t5 (=> @t12 (= @t10 @t2)))) % 0.36/0.62 (assume @p44 (forall @t5 (tptp.subset @t11 @t1))) % 0.36/0.62 (assume @p45 (forall @t23 (=> (and @t12 @t51) (tptp.subset @t1 @t50)))) % 0.36/0.62 (assume @p46 (forall @t19 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 0.36/0.62 (assume @p47 (forall @t23 (=> (and @t12 (tptp.subset @t2 @t14)) @t51))) % 0.36/0.62 (assume @p48 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 0.36/0.62 (assume @p49 (forall @t23 (=> @t12 (tptp.subset (tptp.set_intersection2 @t1 @t14) @t50)))) % 0.36/0.62 (assume @p50 (forall @t5 (=> @t12 (= @t11 @t1)))) % 0.36/0.62 (assume @p51 (forall @t19 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 0.36/0.62 (assume @p52 (forall @t5 (=> (forall @t16 (= @t28 @t15)) @t13))) % 0.36/0.62 (assume @p53 (forall @t19 (tptp.subset tptp.empty_set @t1))) % 0.36/0.62 (assume @p54 (forall @t23 (=> @t12 (tptp.subset (tptp.set_difference @t1 @t14) (tptp.set_difference @t2 @t14))))) % 0.36/0.62 (assume @p55 (forall @t45 (=> (= @t30 (tptp.ordered_pair @t14 @t20)) (and @t49 (= @t2 @t20))))) % 0.36/0.62 (assume @p56 (forall @t5 (tptp.subset @t29 @t1))) % 0.36/0.62 (assume @p57 (forall @t23 (= (tptp.subset @t8 @t14) (and @t44 (tptp.in @t2 @t14))))) % 0.36/0.62 (assume @p58 (forall @t5 (= @t52 @t10))) % 0.36/0.62 (assume @p59 (forall @t19 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 0.36/0.62 (assume @p60 (forall @t5 (and (not (and @t54 (forall @t16 (not @t53)))) (not (and (exists @t16 @t53) @t31))))) % 0.36/0.62 (assume @p61 (forall @t19 (=> (tptp.subset @t1 tptp.empty_set) @t18))) % 0.36/0.62 (assume @p62 (forall @t5 (= (tptp.set_difference @t10 @t2) @t29))) % 0.36/0.62 (assume @p63 (forall @t5 (=> @t12 (= @t2 @t52)))) % 0.36/0.62 (assume @p64 (forall @t5 (= (tptp.set_difference @t1 @t29) @t11))) % 0.36/0.62 (assume @p65 (forall @t19 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 0.36/0.62 (assume @p66 (forall @t5 (and (not (and @t54 (forall @t16 (not @t55)))) (not (and (exists @t16 @t55) @t31))))) % 0.36/0.62 (assume @p67 (forall @t5 (not (and @t12 @t6)))) % 0.36/0.62 (assume @p68 (forall @t23 (=> (and @t12 (tptp.disjoint @t2 @t14)) (tptp.disjoint @t1 @t14)))) % 0.36/0.62 (assume @p69 @t59) % 0.36/0.62 (assume @p70 (forall @t19 (= (tptp.unordered_pair @t1 @t1) @t17))) % 0.36/0.62 (assume @p71 @t60) % 0.36/0.62 (assume @p72 (forall @t5 (=> (tptp.subset @t17 @t43) @t13))) % 0.36/0.62 (assume @p73 (forall @t5 (not (and @t4 @t61)))) % 0.36/0.62 (assume @p74 (forall @t5 (tptp.subset @t1 @t10))) % 0.36/0.62 (assume @p75 @t63) % 0.36/0.62 (assume @p76 (forall @t5 (not (and @t33 @t32 @t61)))) % 0.36/0.62 (assume @p77 (forall @t23 (=> (and @t12 (tptp.subset @t14 @t2)) (tptp.subset (tptp.set_union2 @t1 @t14) @t2)))) % 0.36/0.62 (assume @p78 (forall @t23 (=> @t64 @t13))) % 0.36/0.62 (assume @p79 (forall @t23 (=> @t64 (= @t2 @t14)))) % 0.36/0.62 (step @p80 :rule bool-impl-elim :args (@t31 @t47)) % 0.36/0.62 (step @p81 :rule cong :premises (@p80) :args (@t48)) % 0.36/0.62 (step @p82 :rule eq_resolve :premises (@p41 @p81)) % 0.36/0.62 (step @p83 :rule eq-symm :args (@t29 @t1)) % 0.36/0.62 (step @p84 :rule refl :args (@t31)) % 0.36/0.62 (step @p85 :rule cong :premises (@p84 @p83) :args (@t62)) % 0.36/0.62 (step @p86 :rule cong :premises (@p85) :args (@t63)) % 0.36/0.62 (step @p87 :rule eq_resolve :premises (@p75 @p86)) % 0.36/0.62 (step @p88 :rule eq-symm :args (@t69 @t70)) % 0.36/0.62 (step @p89 :rule refl :args (@t71)) % 0.36/0.62 (step @p90 :rule cong :premises (@p89 @p88) :args ((=> @t71 @t72))) % 0.36/0.62 (assume-push @p251 @t71) % 0.36/0.62 (step @p92 :rule instantiate :premises (@p87) :args (@t73)) % 0.36/0.62 (step-pop @p252 :rule scope :premises (@p92)) % 0.36/0.62 (step @p93 :rule process_scope :premises (@p252) :args (@t72)) % 0.36/0.62 (step @p95 :rule eq_resolve :premises (@p93 @p90)) % 0.36/0.62 (step @p96 :rule implies_elim :premises (@p95)) % 0.36/0.62 (step @p97 :rule chain_m_resolution :premises (@p96 @p87) :args (@t74 @t75 (@list @t71))) % 0.36/0.62 (step @p98 :rule eq-symm :args (@t56 @t1)) % 0.36/0.62 (step @p99 :rule refl :args (@t3)) % 0.36/0.62 (step @p100 :rule cong :premises (@p99 @p98) :args ((= @t3 @t57))) % 0.36/0.62 (step @p101 :rule eq-symm :args (@t57 @t3)) % 0.36/0.62 (step @p102 :rule trans :premises (@p101 @p100)) % 0.36/0.62 (step @p103 :rule cong :premises (@p102) :args (@t58)) % 0.36/0.62 (step @p104 :rule cong :premises (@p103) :args (@t59)) % 0.36/0.62 (step @p105 :rule eq_resolve :premises (@p69 @p104)) % 0.36/0.62 (step @p106 :rule skolemize :premises (@p105)) % 0.36/0.62 (step @p107 :rule refl :args (@t76)) % 0.36/0.62 (step @p108 :rule bool-double-not-elim :args (@t77)) % 0.36/0.62 (step @p109 :rule refl :args (@t79)) % 0.36/0.62 (step @p110 :rule nary_cong :premises (@p109 @p108 @p107) :args ((or @t79 (not @t78) @t76))) % 0.36/0.62 (step @p111 :rule cnf_equiv_neg2 :args (@t79)) % 0.36/0.62 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.36/0.62 (step @p113 :rule reordering :premises (@p112) :args ((or @t77 @t79 @t76))) % 0.36/0.62 (step @p114 :rule refl :args (@t36)) % 0.36/0.62 (step @p115 :rule bool-double-not-elim :args (@t4)) % 0.36/0.62 (step @p116 :rule nary_cong :premises (@p115 @p114) :args ((or (not @t37) @t36))) % 0.36/0.62 (step @p117 :rule bool-impl-elim :args (@t37 @t36)) % 0.36/0.62 (step @p118 :rule trans :premises (@p117 @p116)) % 0.36/0.62 (step @p119 :rule cong :premises (@p118) :args (@t38)) % 0.36/0.62 (step @p120 :rule eq_resolve :premises (@p31 @p119)) % 0.36/0.62 (step @p121 :rule instantiate :premises (@p120) :args (@t80)) % 0.36/0.62 (step @p122 :rule cnf_or_pos :args (@t82)) % 0.36/0.62 (step @p123 :rule reordering :premises (@p122) :args ((or @t77 @t81 (not @t82)))) % 0.36/0.62 (step @p124 :rule cnf_equiv_pos2 :args (@t74)) % 0.36/0.62 (step @p125 :rule reordering :premises (@p124) :args ((or @t70 @t84 @t83))) % 0.36/0.62 (step @p126 :rule instantiate :premises (@p82) :args (@t85)) % 0.36/0.62 (step @p127 :rule cnf_or_pos :args (@t87)) % 0.36/0.62 (step @p128 :rule reordering :premises (@p127) :args ((or @t69 @t86 (not @t87)))) % 0.36/0.62 (step @p129 :rule chain_m_resolution :premises (@p128 @p126 @p125 @p97 @p123 @p121 @p113 @p106) :args (@t77 (@list false true false false false true true) (@list @t87 @t69 @t74 @t81 @t82 @t70 @t79))) % 0.36/0.62 (step @p130 :rule cnf_equiv_neg1 :args (@t79)) % 0.36/0.62 (step @p131 :rule reordering :premises (@p130) :args ((or @t78 @t70 @t79))) % 0.36/0.62 (step @p132 :rule chain_m_resolution :premises (@p131 @p129 @p106) :args (@t70 (@list false true) (@list @t77 @t79))) % 0.36/0.62 (step @p133 :rule cnf_equiv_pos1 :args (@t74)) % 0.36/0.62 (step @p134 :rule reordering :premises (@p133) :args ((or @t76 @t69 @t83))) % 0.36/0.62 (step @p135 :rule chain_m_resolution :premises (@p134 @p132 @p97) :args (@t69 @t88 (@list @t70 @t74))) % 0.36/0.62 (step @p136 :rule instantiate :premises (@p87) :args (@t85)) % 0.36/0.62 (step @p137 :rule eq-symm :args (@t29 tptp.empty_set)) % 0.36/0.62 (step @p138 :rule refl :args (@t12)) % 0.36/0.62 (step @p139 :rule cong :premises (@p138 @p137) :args ((= @t12 @t41))) % 0.36/0.62 (step @p140 :rule eq-symm :args (@t41 @t12)) % 0.36/0.62 (step @p141 :rule trans :premises (@p140 @p139)) % 0.36/0.62 (step @p142 :rule cong :premises (@p141) :args (@t42)) % 0.36/0.62 (step @p143 :rule eq_resolve :premises (@p33 @p142)) % 0.36/0.62 (step @p144 :rule instantiate :premises (@p143) :args (@t85)) % 0.36/0.62 (step @p145 :rule eq-symm :args (@t39 @t4)) % 0.36/0.62 (step @p146 :rule cong :premises (@p145) :args (@t40)) % 0.36/0.62 (step @p147 :rule eq_resolve :premises (@p32 @p146)) % 0.36/0.62 (step @p148 :rule instantiate :premises (@p147) :args (@t80)) % 0.36/0.62 (step @p149 :rule cnf_equiv_pos1 :args (@t90)) % 0.36/0.62 (step @p150 :rule reordering :premises (@p149) :args ((or @t78 @t89 (not @t90)))) % 0.36/0.62 (step @p151 :rule chain_m_resolution :premises (@p150 @p129 @p148) :args (@t89 @t88 (@list @t77 @t90))) % 0.36/0.62 (step @p152 :rule cnf_equiv_pos1 :args (@t93)) % 0.36/0.62 (step @p153 :rule reordering :premises (@p152) :args ((or (not @t89) @t92 (not @t93)))) % 0.36/0.62 (step @p154 :rule chain_m_resolution :premises (@p153 @p151 @p144) :args (@t92 @t88 (@list @t89 @t93))) % 0.36/0.62 (step @p155 :rule bool-impl-elim :args (@t33 @t18)) % 0.36/0.62 (step @p156 :rule cong :premises (@p155) :args (@t60)) % 0.36/0.62 (step @p157 :rule eq_resolve :premises (@p71 @p156)) % 0.36/0.62 (step @p158 :rule eq-symm :args (@t95 tptp.empty_set)) % 0.36/0.62 (step @p159 :rule refl :args (@t97)) % 0.36/0.62 (step @p160 :rule nary_cong :premises (@p159 @p158) :args (@t98)) % 0.36/0.62 (step @p161 :rule refl :args (@t99)) % 0.36/0.62 (step @p162 :rule cong :premises (@p161 @p160) :args ((=> @t99 @t98))) % 0.36/0.62 (assume-push @p253 @t99) % 0.36/0.62 (step @p164 :rule instantiate :premises (@p157) :args ((@list @t95))) % 0.36/0.62 (step-pop @p254 :rule scope :premises (@p164)) % 0.36/0.62 (step @p165 :rule process_scope :premises (@p254) :args (@t98)) % 0.36/0.62 (step @p167 :rule eq_resolve :premises (@p165 @p162)) % 0.36/0.62 (step @p168 :rule implies_elim :premises (@p167)) % 0.36/0.62 (step @p169 :rule chain_m_resolution :premises (@p168 @p157) :args (@t101 @t75 (@list @t99))) % 0.36/0.62 (step @p170 :rule exists-elim :args ((= @t46 @t102))) % 0.36/0.62 (step @p171 :rule eq_resolve :premises (@p38 @p170)) % 0.36/0.62 (step @p172 :rule refl :args (@t96)) % 0.36/0.62 (step @p173 :rule bool-double-not-elim :args (@t94)) % 0.36/0.62 (step @p174 :rule nary_cong :premises (@p173 @p172) :args ((or (not @t102) @t96))) % 0.36/0.62 (step @p175 :rule bool-double-not-elim :args (@t96)) % 0.36/0.62 (step @p176 :rule refl :args (@t102)) % 0.36/0.62 (step @p177 :rule cong :premises (@p176 @p175) :args ((=> @t102 @t103))) % 0.36/0.62 (assume-push @p255 @t102) % 0.36/0.62 (step @p179 :rule skolemize :premises (@p171)) % 0.36/0.62 (step-pop @p256 :rule scope :premises (@p179)) % 0.36/0.62 (step @p180 :rule process_scope :premises (@p256) :args (@t103)) % 0.36/0.62 (step @p182 :rule eq_resolve :premises (@p180 @p177)) % 0.36/0.62 (step @p183 :rule implies_elim :premises (@p182)) % 0.36/0.62 (step @p184 :rule eq_resolve :premises (@p183 @p174)) % 0.36/0.62 (step @p185 :rule chain_m_resolution :premises (@p184 @p171) :args (@t96 (@list true) (@list @t94))) % 0.36/0.62 (step @p186 :rule cnf_or_pos :args (@t101)) % 0.36/0.62 (step @p187 :rule reordering :premises (@p186) :args ((or @t97 @t100 (not @t101)))) % 0.36/0.62 (step @p188 :rule chain_m_resolution :premises (@p187 @p185 @p169) :args (@t100 @t88 (@list @t96 @t101))) % 0.36/0.62 (step @p189 :rule eq-symm :args (@t67 tptp.empty_set)) % 0.36/0.62 (step @p190 :rule cong :premises (@p189) :args (@t104)) % 0.36/0.62 (step @p191 :rule refl :args (@t35)) % 0.36/0.62 (step @p192 :rule cong :premises (@p191 @p190) :args ((=> @t35 @t104))) % 0.36/0.62 (assume-push @p257 @t35) % 0.36/0.62 (step @p194 :rule instantiate :premises (@p28) :args ((@list @t66))) % 0.36/0.62 (step-pop @p258 :rule scope :premises (@p194)) % 0.36/0.62 (step @p195 :rule process_scope :premises (@p258) :args (@t104)) % 0.36/0.62 (step @p197 :rule eq_resolve :premises (@p195 @p192)) % 0.36/0.62 (step @p198 :rule implies_elim :premises (@p197)) % 0.36/0.62 (step @p199 :rule chain_m_resolution :premises (@p198 @p28) :args (@t106 @t75 (@list @t35))) % 0.36/0.62 (step @p200 :rule refl :args (@t108)) % 0.36/0.62 (step @p201 :rule refl :args (@t109)) % 0.36/0.62 (step @p202 :rule refl :args (@t110)) % 0.36/0.62 (step @p203 :rule bool-double-not-elim :args (@t105)) % 0.36/0.62 (step @p204 :rule nary_cong :premises (@p203 @p202 @p201 @p200) :args ((or (not @t106) @t110 @t109 @t108))) % 0.36/0.62 (assume-push @p259 @t100) % 0.36/0.62 (assume-push @p260 @t92) % 0.36/0.62 (assume-push @p261 @t107) % 0.36/0.62 (assume-push @p262 @t106) % 0.36/0.62 (step @p209 :rule evaluate :args ((= false true))) % 0.36/0.62 (step @p210 :rule symm :premises (@p154)) % 0.36/0.62 (step @p211 :rule trans :premises (@p261 @p210 @p188)) % 0.36/0.62 (step @p212 :rule symm :premises (@p211)) % 0.36/0.62 (step @p213 :rule trans :premises (@p188 @p212)) % 0.36/0.62 (step @p214 :rule true_intro :premises (@p213)) % 0.36/0.62 (step @p215 :rule false_intro :premises (@p199)) % 0.36/0.62 (step @p216 :rule symm :premises (@p215)) % 0.36/0.62 (step @p217 :rule trans :premises (@p216 @p214)) % 0.36/0.62 (step @p218 false :rule eq_resolve :premises (@p217 @p209)) % 0.36/0.62 (step-pop @p263 :rule scope :premises (@p218)) % 0.36/0.62 (step-pop @p264 :rule scope :premises (@p263)) % 0.36/0.62 (step-pop @p265 :rule scope :premises (@p264)) % 0.36/0.62 (step-pop @p266 :rule scope :premises (@p265)) % 0.36/0.62 (step @p219 :rule process_scope :premises (@p266) :args (false)) % 0.36/0.62 (assume-push @p267 @t106) % 0.36/0.62 (assume-push @p268 @t100) % 0.36/0.62 (assume-push @p269 @t92) % 0.36/0.62 (assume-push @p270 @t107) % 0.36/0.62 (step @p228 :rule and_intro :premises (@p188 @p154 @p270 @p199)) % 0.36/0.62 (step-pop @p271 :rule scope :premises (@p228)) % 0.36/0.62 (step-pop @p272 :rule scope :premises (@p271)) % 0.36/0.62 (step-pop @p273 :rule scope :premises (@p272)) % 0.36/0.62 (step-pop @p274 :rule scope :premises (@p273)) % 0.36/0.62 (step @p229 :rule process_scope :premises (@p274) :args (@t111)) % 0.36/0.62 (step @p234 :rule implies_elim :premises (@p229)) % 0.36/0.62 (step @p235 :rule resolution :premises (@p234 @p219) :args (true @t111)) % 0.36/0.62 (step @p236 :rule not_and :premises (@p235)) % 0.36/0.62 (step @p237 :rule eq_resolve :premises (@p236 @p204)) % 0.36/0.62 (step @p238 :rule chain_m_resolution :premises (@p237 @p199 @p188 @p154) :args (@t108 (@list true false false) (@list @t105 @t100 @t92))) % 0.36/0.62 (step @p239 :rule cnf_equiv_pos1 :args (@t112)) % 0.36/0.62 (step @p240 :rule reordering :premises (@p239) :args ((or @t86 @t107 (not @t112)))) % 0.36/0.62 (step @p241 :rule chain_m_resolution :premises (@p240 @p238 @p136) :args (@t86 @t113 (@list @t107 @t112))) % 0.36/0.62 (step @p242 :rule cnf_or_pos :args (@t114)) % 0.36/0.62 (step @p243 :rule reordering :premises (@p242) :args ((or @t81 @t84 @t115))) % 0.36/0.62 (step @p244 :rule chain_m_resolution :premises (@p243 @p241 @p135) :args (@t115 @t113 (@list @t81 @t69))) % 0.36/0.62 (assume-push @p275 @t116) % 0.36/0.62 (step @p246 :rule instantiate :premises (@p82) :args (@t73)) % 0.36/0.62 (step-pop @p276 :rule scope :premises (@p246)) % 0.36/0.62 (step @p247 :rule process_scope :premises (@p276) :args (@t114)) % 0.36/0.62 (step @p249 :rule implies_elim :premises (@p247)) % 0.36/0.62 (step @p250 false :rule chain_m_resolution :premises (@p249 @p244 @p82) :args (false @t113 (@list @t114 @t116))) % 0.45/0.63 ) % 0.45/0.63 % SZS output end Proof % 0.45/0.63 % cvc5 exiting %------------------------------------------------------------------------------