%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET810+4 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n024.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:48:42 AM UTC 2026 % Result : Theorem 0.14s 0.38s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SET810+4 : TPTP v9.2.1. Released v3.2.0. % 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.24 % Computer : n024.cluster.edu % 0.07/0.24 % Model : x86_64 x86_64 % 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.24 % Memory : 8042.1875MB % 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.24 % CPULimit : 300 % 0.07/0.24 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 11:12:45 EDT 2026 % 0.07/0.25 % CPUTime : % 0.07/0.32 %----Proving TF0_NAR, FOF, or CNF % 0.14/0.38 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.14/0.38 % SZS status Theorem % 0.14/0.38 % SZS output start Proof % 0.14/0.38 ( % 0.14/0.38 (declare-sort $$unsorted 0) % 0.14/0.38 (declare-const tptp.strict_order (-> $$unsorted $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.on $$unsorted) % 0.14/0.38 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.set (-> $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.suc (-> $$unsorted $$unsorted)) % 0.14/0.38 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.14/0.38 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.14/0.38 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.initial_segment (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.14/0.38 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.14/0.38 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.14/0.38 (declare-const tptp.empty_set $$unsorted) % 0.14/0.38 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.14/0.38 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.14/0.38 (declare-const tptp.least (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.14/0.38 (declare-const tptp.strict_well_order (-> $$unsorted $$unsorted Bool)) % 0.14/0.38 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.14/0.38 (declare-const tptp.member_predicate $$unsorted) % 0.14/0.38 (define @t1 () (@var "B" $$unsorted)) % 0.14/0.38 (define @t2 () (@var "X" $$unsorted)) % 0.14/0.38 (define @t3 () (tptp.member @t2 @t1)) % 0.14/0.38 (define @t4 () (@var "A" $$unsorted)) % 0.14/0.38 (define @t5 () (tptp.member @t2 @t4)) % 0.14/0.38 (define @t6 () (@list @t2)) % 0.14/0.38 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.14/0.38 (define @t8 () (tptp.subset @t4 @t1)) % 0.14/0.38 (define @t9 () (= @t8 @t7)) % 0.14/0.38 (define @t10 () (@list @t4 @t1)) % 0.14/0.38 (define @t11 () (forall @t10 @t9)) % 0.14/0.38 (define @t12 () (tptp.subset @t2 @t4)) % 0.14/0.38 (define @t13 () (@list @t2 @t4)) % 0.14/0.38 (define @t14 () (@list @t2 @t4 @t1)) % 0.14/0.38 (define @t15 () (tptp.member @t1 @t4)) % 0.14/0.38 (define @t16 () (not @t15)) % 0.14/0.38 (define @t17 () (@var "E" $$unsorted)) % 0.14/0.38 (define @t18 () (= @t2 @t4)) % 0.14/0.38 (define @t19 () (tptp.singleton @t4)) % 0.14/0.38 (define @t20 () (@var "Y" $$unsorted)) % 0.14/0.38 (define @t21 () (tptp.member @t2 @t20)) % 0.14/0.38 (define @t22 () (tptp.member @t20 @t4)) % 0.14/0.38 (define @t23 () (@list @t20)) % 0.14/0.38 (define @t24 () (forall @t6 (=> @t5 @t12))) % 0.14/0.38 (define @t25 () (tptp.strict_well_order tptp.member_predicate @t4)) % 0.14/0.38 (define @t26 () (tptp.set @t4)) % 0.14/0.38 (define @t27 () (and @t26 @t25 @t24)) % 0.14/0.38 (define @t28 () (tptp.member @t4 tptp.on)) % 0.14/0.38 (define @t29 () (= @t28 @t27)) % 0.14/0.38 (define @t30 () (@list @t4)) % 0.14/0.38 (define @t31 () (forall @t30 @t29)) % 0.14/0.38 (define @t32 () (@var "R" $$unsorted)) % 0.14/0.38 (define @t33 () (tptp.least @t20 @t32 @t4)) % 0.14/0.38 (define @t34 () (exists @t23 @t33)) % 0.14/0.38 (define @t35 () (exists @t6 @t5)) % 0.14/0.38 (define @t36 () (tptp.subset @t4 @t17)) % 0.14/0.38 (define @t37 () (and @t36 @t35)) % 0.14/0.38 (define @t38 () (=> @t37 @t34)) % 0.14/0.38 (define @t39 () (forall @t30 @t38)) % 0.14/0.38 (define @t40 () (tptp.strict_order @t32 @t17)) % 0.14/0.38 (define @t41 () (and @t40 @t39)) % 0.14/0.38 (define @t42 () (tptp.strict_well_order @t32 @t17)) % 0.14/0.38 (define @t43 () (= @t42 @t41)) % 0.14/0.38 (define @t44 () (@list @t32 @t17)) % 0.14/0.38 (define @t45 () (forall @t44 @t43)) % 0.14/0.38 (define @t46 () (@var "M" $$unsorted)) % 0.14/0.38 (define @t47 () (tptp.member @t2 @t17)) % 0.14/0.38 (define @t48 () (tptp.apply tptp.member_predicate @t2 @t20)) % 0.14/0.38 (define @t49 () (@list @t2 @t20)) % 0.14/0.38 (define @t50 () (forall @t49 (= @t48 @t21))) % 0.14/0.38 (define @t51 () (@var "Z" $$unsorted)) % 0.14/0.38 (define @t52 () (tptp.apply @t32 @t2 @t51)) % 0.14/0.38 (define @t53 () (tptp.apply @t32 @t20 @t51)) % 0.14/0.38 (define @t54 () (tptp.apply @t32 @t2 @t20)) % 0.14/0.38 (define @t55 () (and @t54 @t53)) % 0.14/0.38 (define @t56 () (=> @t55 @t52)) % 0.14/0.38 (define @t57 () (tptp.member @t51 @t17)) % 0.14/0.38 (define @t58 () (tptp.member @t20 @t17)) % 0.14/0.38 (define @t59 () (and @t47 @t58 @t57)) % 0.14/0.38 (define @t60 () (@list @t2 @t20 @t51)) % 0.14/0.38 (define @t61 () (forall @t60 (=> @t59 @t56))) % 0.14/0.38 (define @t62 () (tptp.apply @t32 @t20 @t2)) % 0.14/0.38 (define @t63 () (not (and @t54 @t62))) % 0.14/0.38 (define @t64 () (and @t47 @t58)) % 0.14/0.38 (define @t65 () (forall @t49 (=> @t64 @t63))) % 0.14/0.38 (define @t66 () (and @t65 @t61)) % 0.14/0.38 (define @t67 () (= @t40 @t66)) % 0.14/0.38 (define @t68 () (forall @t44 @t67)) % 0.14/0.38 (define @t69 () (tptp.member @t4 @t1)) % 0.14/0.38 (define @t70 () (not (and @t69 @t15))) % 0.14/0.38 (define @t71 () (tptp.member @t1 tptp.on)) % 0.14/0.38 (define @t72 () (and @t28 @t71)) % 0.14/0.38 (define @t73 () (forall @t10 (=> @t72 @t70))) % 0.14/0.38 (define @t74 () (not @t73)) % 0.14/0.38 (define @t75 () (not @t69)) % 0.14/0.38 (define @t76 () (not @t71)) % 0.14/0.38 (define @t77 () (not @t28)) % 0.14/0.38 (define @t78 () (or @t77 @t76 @t75 @t16)) % 0.14/0.38 (define @t79 () (forall @t10 @t78)) % 0.14/0.38 (define @t80 () (@quantifiers_skolemize @t79 0)) % 0.14/0.38 (define @t81 () (@quantifiers_skolemize @t79 1)) % 0.14/0.38 (define @t82 () (tptp.member @t81 @t80)) % 0.14/0.38 (define @t83 () (not @t82)) % 0.14/0.38 (define @t84 () (tptp.member @t80 @t81)) % 0.14/0.38 (define @t85 () (not @t84)) % 0.14/0.38 (define @t86 () (tptp.member @t80 tptp.on)) % 0.14/0.38 (define @t87 () (not @t86)) % 0.14/0.38 (define @t88 () (or @t87 (not (tptp.member @t81 tptp.on)) @t85 @t83)) % 0.14/0.38 (define @t89 () (@list true)) % 0.14/0.38 (define @t90 () (@list @t88)) % 0.14/0.38 (define @t91 () (@list @t80 @t81)) % 0.14/0.38 (define @t92 () (tptp.apply tptp.member_predicate @t80 @t81)) % 0.14/0.38 (define @t93 () (= @t84 @t92)) % 0.14/0.38 (define @t94 () (@list false false)) % 0.14/0.38 (define @t95 () (@list @t81 @t80)) % 0.14/0.38 (define @t96 () (tptp.apply tptp.member_predicate @t81 @t80)) % 0.14/0.38 (define @t97 () (= @t82 @t96)) % 0.14/0.38 (define @t98 () (not @t53)) % 0.14/0.38 (define @t99 () (not @t54)) % 0.14/0.38 (define @t100 () (not @t57)) % 0.14/0.38 (define @t101 () (not @t58)) % 0.14/0.38 (define @t102 () (not @t47)) % 0.14/0.38 (define @t103 () (or @t99 @t98 @t52)) % 0.14/0.38 (define @t104 () (or @t102 @t101 @t100)) % 0.14/0.38 (define @t105 () (not @t62)) % 0.14/0.38 (define @t106 () (@list tptp.member_predicate @t80)) % 0.14/0.38 (define @t107 () (not (forall @t23 (not @t33)))) % 0.14/0.38 (define @t108 () (@var "BOUND_VARIABLE_7647" $$unsorted)) % 0.14/0.38 (define @t109 () (not (tptp.member @t108 @t4))) % 0.14/0.38 (define @t110 () (not @t36)) % 0.14/0.38 (define @t111 () (or @t110 @t109 @t107)) % 0.14/0.38 (define @t112 () (@list @t4 @t108)) % 0.14/0.38 (define @t113 () (@list @t108)) % 0.14/0.38 (define @t114 () (forall @t113 @t111)) % 0.14/0.38 (define @t115 () (forall @t113 @t109)) % 0.14/0.38 (define @t116 () (or @t110 @t115 @t107)) % 0.14/0.38 (define @t117 () (forall @t6 (not @t5))) % 0.14/0.38 (define @t118 () (or @t110 @t117 @t107)) % 0.14/0.38 (define @t119 () (not @t117)) % 0.14/0.38 (define @t120 () (and @t36 @t119)) % 0.14/0.38 (define @t121 () (@list @t80)) % 0.14/0.38 (define @t122 () (tptp.member @t2 @t80)) % 0.14/0.38 (define @t123 () (not @t122)) % 0.14/0.38 (define @t124 () (forall @t6 (or @t123 (tptp.subset @t2 @t80)))) % 0.14/0.38 (define @t125 () (tptp.strict_well_order tptp.member_predicate @t80)) % 0.14/0.38 (define @t126 () (and (tptp.set @t80) @t125 @t124)) % 0.14/0.38 (define @t127 () (= @t86 @t126)) % 0.14/0.38 (define @t128 () (not @t126)) % 0.14/0.38 (define @t129 () (@list false)) % 0.14/0.38 (define @t130 () (@list @t126)) % 0.14/0.38 (define @t131 () (tptp.strict_order tptp.member_predicate @t80)) % 0.14/0.38 (define @t132 () (and @t131 (forall @t112 (or (not (tptp.subset @t4 @t80)) @t109 (not (forall @t23 (not (tptp.least @t20 tptp.member_predicate @t4)))))))) % 0.14/0.38 (define @t133 () (= @t125 @t132)) % 0.14/0.38 (define @t134 () (not @t48)) % 0.14/0.38 (define @t135 () (not (tptp.member @t20 @t80))) % 0.14/0.38 (define @t136 () (forall @t49 (or @t123 @t135 @t134 (not (tptp.apply tptp.member_predicate @t20 @t2))))) % 0.14/0.38 (define @t137 () (and @t136 (forall @t60 (or @t123 @t135 (not (tptp.member @t51 @t80)) @t134 (not (tptp.apply tptp.member_predicate @t20 @t51)) (tptp.apply tptp.member_predicate @t2 @t51))))) % 0.14/0.38 (define @t138 () (= @t131 @t137)) % 0.14/0.38 (define @t139 () (tptp.subset @t81 @t80)) % 0.14/0.38 (define @t140 () (or @t83 @t139)) % 0.14/0.38 (define @t141 () (forall @t6 (or (not (tptp.member @t2 @t81)) @t122))) % 0.14/0.38 (define @t142 () (= @t139 @t141)) % 0.14/0.38 (define @t143 () (tptp.member @t80 @t80)) % 0.14/0.38 (define @t144 () (or @t85 @t143)) % 0.14/0.38 (define @t145 () (not @t96)) % 0.14/0.38 (define @t146 () (not @t92)) % 0.14/0.38 (define @t147 () (not @t143)) % 0.14/0.38 (define @t148 () (or @t147 @t83 @t146 @t145)) % 0.14/0.38 (assume @p1 @t11) % 0.14/0.38 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.14/0.38 (assume @p3 (forall @t13 (= (tptp.member @t2 (tptp.power_set @t4)) @t12))) % 0.14/0.38 (assume @p4 (forall @t14 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.14/0.38 (assume @p5 (forall @t14 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.14/0.38 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.14/0.38 (assume @p7 (forall (@list @t1 @t4 @t17) (= (tptp.member @t1 (tptp.difference @t17 @t4)) (and (tptp.member @t1 @t17) @t16)))) % 0.14/0.38 (assume @p8 (forall @t13 (= (tptp.member @t2 @t19) @t18))) % 0.14/0.38 (assume @p9 (forall @t14 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t18 (= @t2 @t1))))) % 0.14/0.38 (assume @p10 (forall @t13 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t23 (and @t22 @t21))))) % 0.14/0.38 (assume @p11 (forall @t13 (= (tptp.member @t2 (tptp.product @t4)) (forall @t23 (=> @t22 @t21))))) % 0.14/0.38 (assume @p12 @t31) % 0.14/0.38 (assume @p13 @t45) % 0.14/0.38 (assume @p14 (forall (@list @t32 @t17 @t46) (= (tptp.least @t46 @t32 @t17) (and (tptp.member @t46 @t17) (forall @t6 (=> @t47 (or (= @t46 @t2) (tptp.apply @t32 @t46 @t2)))))))) % 0.14/0.38 (assume @p15 @t50) % 0.14/0.38 (assume @p16 @t68) % 0.14/0.38 (assume @p17 (forall @t6 (=> (tptp.set @t2) (forall @t23 (=> (tptp.member @t20 @t2) (tptp.set @t20)))))) % 0.14/0.38 (assume @p18 (forall (@list @t2 @t32 @t4 @t20) (= (tptp.member @t20 (tptp.initial_segment @t2 @t32 @t4)) (and @t22 @t62)))) % 0.14/0.38 (assume @p19 (forall (@list @t4 @t2) (= (tptp.member @t2 (tptp.suc @t4)) (tptp.member @t2 (tptp.union @t4 @t19))))) % 0.14/0.38 (assume @p20 @t74) % 0.14/0.38 (assume @p21 true) % 0.14/0.38 (step @p22 :rule aci_norm :args ((= (or (or @t77 @t76) (or @t75 @t16)) @t78))) % 0.14/0.38 (step @p23 :rule bool-and-de-morgan :args (@t69 @t15 true)) % 0.14/0.38 (step @p24 :rule bool-and-de-morgan :args (@t28 @t71 true)) % 0.14/0.38 (step @p25 :rule nary_cong :premises (@p24 @p23) :args ((or (not @t72) @t70))) % 0.14/0.38 (step @p26 :rule trans :premises (@p25 @p22)) % 0.14/0.38 (step @p27 :rule bool-impl-elim :args (@t72 @t70)) % 0.14/0.38 (step @p28 :rule trans :premises (@p27 @p26)) % 0.14/0.38 (step @p29 :rule cong :premises (@p28) :args (@t73)) % 0.14/0.38 (step @p30 :rule cong :premises (@p29) :args (@t74)) % 0.14/0.38 (step @p31 :rule eq_resolve :premises (@p20 @p30)) % 0.14/0.38 (step @p32 :rule skolemize :premises (@p31)) % 0.14/0.38 (step @p33 :rule bool-double-not-elim :args (@t82)) % 0.14/0.38 (step @p34 :rule refl :args (@t88)) % 0.14/0.38 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or @t88 (not @t83)))) % 0.14/0.38 (step @p36 :rule cnf_or_neg :args (@t88 3)) % 0.14/0.38 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.14/0.38 (step @p38 :rule reordering :premises (@p37) :args ((or @t82 @t88))) % 0.14/0.38 (step @p39 :rule chain_m_resolution :premises (@p38 @p32) :args (@t82 @t89 @t90)) % 0.14/0.38 (step @p40 :rule eq-symm :args (@t48 @t21)) % 0.14/0.38 (step @p41 :rule cong :premises (@p40) :args (@t50)) % 0.14/0.38 (step @p42 :rule eq_resolve :premises (@p15 @p41)) % 0.14/0.38 (step @p43 :rule instantiate :premises (@p42) :args (@t91)) % 0.14/0.38 (step @p44 :rule bool-double-not-elim :args (@t84)) % 0.14/0.38 (step @p45 :rule nary_cong :premises (@p34 @p44) :args ((or @t88 (not @t85)))) % 0.14/0.38 (step @p46 :rule cnf_or_neg :args (@t88 2)) % 0.14/0.38 (step @p47 :rule eq_resolve :premises (@p46 @p45)) % 0.14/0.38 (step @p48 :rule reordering :premises (@p47) :args ((or @t84 @t88))) % 0.14/0.38 (step @p49 :rule chain_m_resolution :premises (@p48 @p32) :args (@t84 @t89 @t90)) % 0.14/0.38 (step @p50 :rule cnf_equiv_pos1 :args (@t93)) % 0.14/0.38 (step @p51 :rule reordering :premises (@p50) :args ((or @t85 @t92 (not @t93)))) % 0.14/0.38 (step @p52 :rule chain_m_resolution :premises (@p51 @p49 @p43) :args (@t92 @t94 (@list @t84 @t93))) % 0.14/0.38 (step @p53 :rule instantiate :premises (@p42) :args (@t95)) % 0.14/0.38 (step @p54 :rule cnf_equiv_pos1 :args (@t97)) % 0.14/0.38 (step @p55 :rule reordering :premises (@p54) :args ((or @t83 @t96 (not @t97)))) % 0.14/0.38 (step @p56 :rule chain_m_resolution :premises (@p55 @p39 @p53) :args (@t96 @t94 (@list @t82 @t97))) % 0.14/0.38 (step @p57 :rule aci_norm :args ((= (or @t104 @t103) (or @t102 @t101 @t100 @t99 @t98 @t52)))) % 0.14/0.38 (step @p58 :rule aci_norm :args ((= (or (or @t99 @t98) @t52) @t103))) % 0.14/0.38 (step @p59 :rule refl :args (@t52)) % 0.14/0.38 (step @p60 :rule bool-and-de-morgan :args (@t54 @t53 true)) % 0.14/0.38 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or (not @t55) @t52))) % 0.14/0.38 (step @p62 :rule trans :premises (@p61 @p58)) % 0.14/0.38 (step @p63 :rule bool-impl-elim :args (@t55 @t52)) % 0.14/0.38 (step @p64 :rule trans :premises (@p63 @p62)) % 0.14/0.38 (step @p65 :rule aci_norm :args ((= (or @t102 (or @t101 @t100)) @t104))) % 0.14/0.38 (step @p66 :rule bool-and-de-morgan :args (@t58 @t57 true)) % 0.14/0.38 (step @p67 :rule refl :args (@t102)) % 0.14/0.38 (step @p68 :rule nary_cong :premises (@p67 @p66) :args ((or @t102 (not (and @t58 @t57))))) % 0.14/0.38 (step @p69 :rule bool-and-de-morgan :args (@t47 @t58 (and @t57))) % 0.14/0.38 (step @p70 :rule trans :premises (@p69 @p68)) % 0.14/0.38 (step @p71 :rule trans :premises (@p70 @p65)) % 0.14/0.38 (step @p72 :rule nary_cong :premises (@p71 @p64) :args ((or (not @t59) @t56))) % 0.14/0.38 (step @p73 :rule trans :premises (@p72 @p57)) % 0.14/0.38 (step @p74 :rule bool-impl-elim :args (@t59 @t56)) % 0.14/0.38 (step @p75 :rule trans :premises (@p74 @p73)) % 0.14/0.38 (step @p76 :rule cong :premises (@p75) :args (@t61)) % 0.14/0.38 (step @p77 :rule aci_norm :args ((= (or (or @t102 @t101) (or @t99 @t105)) (or @t102 @t101 @t99 @t105)))) % 0.14/0.38 (step @p78 :rule bool-and-de-morgan :args (@t54 @t62 true)) % 0.14/0.38 (step @p79 :rule bool-and-de-morgan :args (@t47 @t58 true)) % 0.14/0.38 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or (not @t64) @t63))) % 0.14/0.38 (step @p81 :rule trans :premises (@p80 @p77)) % 0.14/0.38 (step @p82 :rule bool-impl-elim :args (@t64 @t63)) % 0.14/0.38 (step @p83 :rule trans :premises (@p82 @p81)) % 0.14/0.38 (step @p84 :rule cong :premises (@p83) :args (@t65)) % 0.14/0.38 (step @p85 :rule nary_cong :premises (@p84 @p76) :args (@t66)) % 0.14/0.38 (step @p86 :rule refl :args (@t40)) % 0.14/0.38 (step @p87 :rule cong :premises (@p86 @p85) :args (@t67)) % 0.14/0.38 (step @p88 :rule cong :premises (@p87) :args (@t68)) % 0.14/0.38 (step @p89 :rule eq_resolve :premises (@p16 @p88)) % 0.14/0.38 (step @p90 :rule instantiate :premises (@p89) :args (@t106)) % 0.14/0.38 (step @p91 :rule quant-merge-prenex :args ((= (forall @t30 @t114) (forall @t112 @t111)))) % 0.14/0.38 (step @p92 :rule refl :args (@t107)) % 0.14/0.38 (step @p93 :rule alpha_equiv :args (@t115 (@list @t108) (@list @t2))) % 0.14/0.38 (step @p94 :rule refl :args (@t110)) % 0.14/0.38 (step @p95 :rule nary_cong :premises (@p94 @p93 @p92) :args (@t116)) % 0.14/0.38 (step @p96 :rule quant-miniscope-or :args ((= @t114 @t116))) % 0.14/0.38 (step @p97 :rule trans :premises (@p96 @p95)) % 0.14/0.38 (step @p98 :rule symm :premises (@p97)) % 0.14/0.38 (step @p99 :rule cong :premises (@p98) :args ((forall @t30 @t118))) % 0.14/0.38 (step @p100 :rule trans :premises (@p99 @p91)) % 0.14/0.38 (step @p101 :rule aci_norm :args ((= (or (or @t110 @t117) @t107) @t118))) % 0.14/0.38 (step @p102 :rule bool-double-not-elim :args (@t117)) % 0.14/0.38 (step @p103 :rule nary_cong :premises (@p94 @p102) :args ((or @t110 (not @t119)))) % 0.14/0.38 (step @p104 :rule bool-and-de-morgan :args (@t36 @t119 true)) % 0.14/0.38 (step @p105 :rule trans :premises (@p104 @p103)) % 0.14/0.38 (step @p106 :rule nary_cong :premises (@p105 @p92) :args ((or (not @t120) @t107))) % 0.14/0.38 (step @p107 :rule trans :premises (@p106 @p101)) % 0.14/0.38 (step @p108 :rule bool-impl-elim :args (@t120 @t107)) % 0.14/0.38 (step @p109 :rule trans :premises (@p108 @p107)) % 0.14/0.38 (step @p110 :rule cong :premises (@p109) :args ((forall @t30 (=> @t120 @t107)))) % 0.14/0.38 (step @p111 :rule trans :premises (@p110 @p100)) % 0.14/0.38 (step @p112 :rule exists-elim :args ((= @t34 @t107))) % 0.14/0.38 (step @p113 :rule exists-elim :args ((= @t35 @t119))) % 0.14/0.38 (step @p114 :rule refl :args (@t36)) % 0.14/0.38 (step @p115 :rule nary_cong :premises (@p114 @p113) :args (@t37)) % 0.14/0.38 (step @p116 :rule cong :premises (@p115 @p112) :args (@t38)) % 0.14/0.38 (step @p117 :rule cong :premises (@p116) :args (@t39)) % 0.14/0.38 (step @p118 :rule trans :premises (@p117 @p111)) % 0.14/0.38 (step @p119 :rule nary_cong :premises (@p86 @p118) :args (@t41)) % 0.14/0.38 (step @p120 :rule refl :args (@t42)) % 0.14/0.38 (step @p121 :rule cong :premises (@p120 @p119) :args (@t43)) % 0.14/0.38 (step @p122 :rule cong :premises (@p121) :args (@t45)) % 0.14/0.38 (step @p123 :rule eq_resolve :premises (@p13 @p122)) % 0.14/0.38 (step @p124 :rule instantiate :premises (@p123) :args (@t106)) % 0.14/0.38 (step @p125 :rule bool-impl-elim :args (@t5 @t12)) % 0.14/0.38 (step @p126 :rule cong :premises (@p125) :args (@t24)) % 0.14/0.38 (step @p127 :rule refl :args (@t25)) % 0.14/0.38 (step @p128 :rule refl :args (@t26)) % 0.14/0.38 (step @p129 :rule nary_cong :premises (@p128 @p127 @p126) :args (@t27)) % 0.14/0.38 (step @p130 :rule refl :args (@t28)) % 0.14/0.38 (step @p131 :rule cong :premises (@p130 @p129) :args (@t29)) % 0.14/0.38 (step @p132 :rule cong :premises (@p131) :args (@t31)) % 0.14/0.38 (step @p133 :rule eq_resolve :premises (@p12 @p132)) % 0.14/0.38 (step @p134 :rule instantiate :premises (@p133) :args (@t121)) % 0.14/0.38 (step @p135 :rule bool-double-not-elim :args (@t86)) % 0.14/0.38 (step @p136 :rule nary_cong :premises (@p34 @p135) :args ((or @t88 (not @t87)))) % 0.14/0.38 (step @p137 :rule cnf_or_neg :args (@t88 0)) % 0.14/0.38 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.14/0.38 (step @p139 :rule reordering :premises (@p138) :args ((or @t86 @t88))) % 0.14/0.38 (step @p140 :rule chain_m_resolution :premises (@p139 @p32) :args (@t86 @t89 @t90)) % 0.14/0.38 (step @p141 :rule cnf_equiv_pos1 :args (@t127)) % 0.14/0.38 (step @p142 :rule reordering :premises (@p141) :args ((or @t87 @t126 (not @t127)))) % 0.14/0.38 (step @p143 :rule chain_m_resolution :premises (@p142 @p140 @p134) :args (@t126 @t94 (@list @t86 @t127))) % 0.14/0.38 (step @p144 :rule cnf_and_pos :args (@t126 1)) % 0.14/0.38 (step @p145 :rule reordering :premises (@p144) :args ((or @t125 @t128))) % 0.14/0.38 (step @p146 :rule chain_m_resolution :premises (@p145 @p143) :args (@t125 @t129 @t130)) % 0.14/0.38 (step @p147 :rule cnf_equiv_pos1 :args (@t133)) % 0.14/0.38 (step @p148 :rule reordering :premises (@p147) :args ((or (not @t125) @t132 (not @t133)))) % 0.14/0.38 (step @p149 :rule chain_m_resolution :premises (@p148 @p146 @p124) :args (@t132 @t94 (@list @t125 @t133))) % 0.14/0.38 (step @p150 :rule cnf_and_pos :args (@t132 0)) % 0.14/0.38 (step @p151 :rule reordering :premises (@p150) :args ((or @t131 (not @t132)))) % 0.14/0.38 (step @p152 :rule chain_m_resolution :premises (@p151 @p149) :args (@t131 @t129 (@list @t132))) % 0.14/0.38 (step @p153 :rule cnf_equiv_pos1 :args (@t138)) % 0.14/0.38 (step @p154 :rule reordering :premises (@p153) :args ((or (not @t131) @t137 (not @t138)))) % 0.14/0.38 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p90) :args (@t137 @t94 (@list @t131 @t138))) % 0.14/0.38 (step @p156 :rule cnf_and_pos :args (@t137 0)) % 0.14/0.38 (step @p157 :rule reordering :premises (@p156) :args ((or @t136 (not @t137)))) % 0.14/0.38 (step @p158 :rule chain_m_resolution :premises (@p157 @p155) :args (@t136 @t129 (@list @t137))) % 0.14/0.38 (step @p159 :rule instantiate :premises (@p158) :args (@t91)) % 0.14/0.38 (step @p160 :rule bool-impl-elim :args (@t5 @t3)) % 0.14/0.38 (step @p161 :rule cong :premises (@p160) :args (@t7)) % 0.14/0.38 (step @p162 :rule refl :args (@t8)) % 0.14/0.38 (step @p163 :rule cong :premises (@p162 @p161) :args (@t9)) % 0.14/0.38 (step @p164 :rule cong :premises (@p163) :args (@t11)) % 0.14/0.38 (step @p165 :rule eq_resolve :premises (@p1 @p164)) % 0.14/0.38 (step @p166 :rule instantiate :premises (@p165) :args (@t95)) % 0.14/0.38 (step @p167 :rule cnf_and_pos :args (@t126 2)) % 0.14/0.38 (step @p168 :rule reordering :premises (@p167) :args ((or @t124 @t128))) % 0.14/0.38 (step @p169 :rule chain_m_resolution :premises (@p168 @p143) :args (@t124 @t129 @t130)) % 0.14/0.38 (step @p170 :rule instantiate :premises (@p169) :args ((@list @t81))) % 0.14/0.38 (step @p171 :rule cnf_or_pos :args (@t140)) % 0.14/0.38 (step @p172 :rule reordering :premises (@p171) :args ((or @t83 @t139 (not @t140)))) % 0.14/0.38 (step @p173 :rule chain_m_resolution :premises (@p172 @p39 @p170) :args (@t139 @t94 (@list @t82 @t140))) % 0.14/0.38 (step @p174 :rule cnf_equiv_pos1 :args (@t142)) % 0.14/0.38 (step @p175 :rule reordering :premises (@p174) :args ((or (not @t139) @t141 (not @t142)))) % 0.14/0.38 (step @p176 :rule chain_m_resolution :premises (@p175 @p173 @p166) :args (@t141 @t94 (@list @t139 @t142))) % 0.14/0.38 (step @p177 :rule instantiate :premises (@p176) :args (@t121)) % 0.14/0.38 (step @p178 :rule cnf_or_pos :args (@t144)) % 0.14/0.38 (step @p179 :rule reordering :premises (@p178) :args ((or @t85 @t143 (not @t144)))) % 0.14/0.38 (step @p180 :rule chain_m_resolution :premises (@p179 @p49 @p177) :args (@t143 @t94 (@list @t84 @t144))) % 0.14/0.38 (step @p181 :rule cnf_or_pos :args (@t148)) % 0.14/0.38 (step @p182 :rule reordering :premises (@p181) :args ((or @t83 @t146 @t145 @t147 (not @t148)))) % 0.14/0.38 (step @p183 false :rule chain_m_resolution :premises (@p182 @p180 @p159 @p56 @p52 @p39) :args (false (@list false false false false false) (@list @t143 @t148 @t96 @t92 @t82))) % 0.14/0.38 ) % 0.14/0.38 % SZS output end Proof % 0.14/0.38 % cvc5 exiting %------------------------------------------------------------------------------