%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GRA005+1 : TPTP v9.2.1. Bugfixed v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:18:30 AM UTC 2026 % Result : Theorem 0.36s 0.59s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRA005+1 : TPTP v9.2.1. Bugfixed v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n002.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 00:14:03 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.59 % SZS status Theorem % 0.36/0.59 % SZS output start Proof % 0.36/0.59 ( % 0.36/0.59 (declare-sort $$unsorted 0) % 0.36/0.59 (declare-const tptp.graph $$unsorted) % 0.36/0.59 (declare-const tptp.number_of_in (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.edges $$unsorted) % 0.36/0.59 (declare-const tptp.triangle (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.shortest_path (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.less_or_equal (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.tail_of (-> $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.triangles $$unsorted) % 0.36/0.59 (declare-const tptp.in_path (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.head_of (-> $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.sequential_pairs $$unsorted) % 0.36/0.59 (declare-const tptp.edge (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.path_cons (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.59 (declare-const tptp.precedes (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.complete Bool) % 0.36/0.59 (declare-const tptp.path (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.vertex (-> $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.on_path (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.empty $$unsorted) % 0.36/0.59 (declare-const tptp.n1 $$unsorted) % 0.36/0.59 (declare-const tptp.sequential (-> $$unsorted $$unsorted Bool)) % 0.36/0.59 (declare-const tptp.length_of (-> $$unsorted $$unsorted)) % 0.36/0.59 (define @t1 () (@var "E" $$unsorted)) % 0.36/0.59 (define @t2 () (tptp.tail_of @t1)) % 0.36/0.59 (define @t3 () (tptp.head_of @t1)) % 0.36/0.59 (define @t4 () (tptp.edge @t1)) % 0.36/0.59 (define @t5 () (@list @t1)) % 0.36/0.59 (define @t6 () (@var "V1" $$unsorted)) % 0.36/0.59 (define @t7 () (= @t6 @t2)) % 0.36/0.59 (define @t8 () (@var "V2" $$unsorted)) % 0.36/0.59 (define @t9 () (= @t8 @t3)) % 0.36/0.59 (define @t10 () (not (= @t6 @t8))) % 0.36/0.59 (define @t11 () (tptp.vertex @t8)) % 0.36/0.59 (define @t12 () (tptp.vertex @t6)) % 0.36/0.59 (define @t13 () (@var "P" $$unsorted)) % 0.36/0.59 (define @t14 () (tptp.path @t6 @t8 @t13)) % 0.36/0.59 (define @t15 () (@var "TP" $$unsorted)) % 0.36/0.59 (define @t16 () (exists (@list @t15) (and (tptp.path @t3 @t8 @t15) (= @t13 (tptp.path_cons @t1 @t15))))) % 0.36/0.59 (define @t17 () (and @t9 (= @t13 (tptp.path_cons @t1 tptp.empty)))) % 0.36/0.59 (define @t18 () (@list @t6 @t8 @t13)) % 0.36/0.59 (define @t19 () (tptp.on_path @t1 @t13)) % 0.36/0.59 (define @t20 () (@var "V" $$unsorted)) % 0.36/0.59 (define @t21 () (@var "E2" $$unsorted)) % 0.36/0.59 (define @t22 () (@var "E1" $$unsorted)) % 0.36/0.59 (define @t23 () (tptp.edge @t21)) % 0.36/0.59 (define @t24 () (tptp.edge @t22)) % 0.36/0.59 (define @t25 () (tptp.sequential @t22 @t21)) % 0.36/0.59 (define @t26 () (@list @t22 @t21)) % 0.36/0.59 (define @t27 () (tptp.precedes @t22 @t21 @t13)) % 0.36/0.59 (define @t28 () (@var "E3" $$unsorted)) % 0.36/0.59 (define @t29 () (@list @t28)) % 0.36/0.59 (define @t30 () (exists @t29 (and (tptp.sequential @t22 @t28) (tptp.precedes @t28 @t21 @t13)))) % 0.36/0.59 (define @t31 () (tptp.on_path @t21 @t13)) % 0.36/0.59 (define @t32 () (tptp.on_path @t22 @t13)) % 0.36/0.59 (define @t33 () (@list @t13 @t6 @t8)) % 0.36/0.59 (define @t34 () (tptp.length_of @t13)) % 0.36/0.59 (define @t35 () (@var "SP" $$unsorted)) % 0.36/0.59 (define @t36 () (not (tptp.precedes @t21 @t22 @t13))) % 0.36/0.59 (define @t37 () (tptp.head_of @t21)) % 0.36/0.59 (define @t38 () (= (tptp.head_of @t28) @t37)) % 0.36/0.59 (define @t39 () (tptp.tail_of @t22)) % 0.36/0.59 (define @t40 () (= (tptp.tail_of @t28) @t39)) % 0.36/0.59 (define @t41 () (and @t40 @t38)) % 0.36/0.59 (define @t42 () (exists @t29 @t41)) % 0.36/0.59 (define @t43 () (not @t42)) % 0.36/0.59 (define @t44 () (and @t43 @t36)) % 0.36/0.59 (define @t45 () (tptp.shortest_path @t6 @t8 @t13)) % 0.36/0.59 (define @t46 () (and @t45 @t27)) % 0.36/0.59 (define @t47 () (=> @t46 @t44)) % 0.36/0.59 (define @t48 () (@list @t6 @t8 @t22 @t21 @t13)) % 0.36/0.59 (define @t49 () (forall @t48 @t47)) % 0.36/0.59 (define @t50 () (tptp.edge @t28)) % 0.36/0.59 (define @t51 () (tptp.triangle @t22 @t21 @t28)) % 0.36/0.59 (define @t52 () (tptp.number_of_in tptp.sequential_pairs @t13)) % 0.36/0.59 (define @t53 () (@var "Things" $$unsorted)) % 0.36/0.59 (define @t54 () (@var "InThese" $$unsorted)) % 0.36/0.59 (define @t55 () (and @t50 @t40 @t38)) % 0.36/0.59 (define @t56 () (exists @t29 @t55)) % 0.36/0.59 (define @t57 () (not @t56)) % 0.36/0.59 (define @t58 () (=> @t46 @t57)) % 0.36/0.59 (define @t59 () (forall @t48 @t58)) % 0.36/0.59 (define @t60 () (not @t59)) % 0.36/0.59 (define @t61 () (@var "BOUND_VARIABLE_7980" $$unsorted)) % 0.36/0.59 (define @t62 () (tptp.head_of @t61)) % 0.36/0.59 (define @t63 () (not (= @t62 @t37))) % 0.36/0.59 (define @t64 () (tptp.tail_of @t61)) % 0.36/0.59 (define @t65 () (not (= @t64 @t39))) % 0.36/0.59 (define @t66 () (not (tptp.edge @t61))) % 0.36/0.59 (define @t67 () (not @t27)) % 0.36/0.59 (define @t68 () (not @t45)) % 0.36/0.59 (define @t69 () (or @t68 @t67 @t66 @t65 @t63)) % 0.36/0.59 (define @t70 () (or @t66 @t65 @t63)) % 0.36/0.59 (define @t71 () (or @t68 @t67 @t70)) % 0.36/0.59 (define @t72 () (@list @t6 @t8 @t22 @t21 @t13 @t61)) % 0.36/0.59 (define @t73 () (forall @t72 @t71)) % 0.36/0.59 (define @t74 () (@list @t61)) % 0.36/0.59 (define @t75 () (forall @t74 @t71)) % 0.36/0.59 (define @t76 () (forall @t74 @t70)) % 0.36/0.59 (define @t77 () (@list @t28)) % 0.36/0.59 (define @t78 () (or @t68 @t67 @t76)) % 0.36/0.59 (define @t79 () (not @t38)) % 0.36/0.59 (define @t80 () (not @t40)) % 0.36/0.59 (define @t81 () (not @t50)) % 0.36/0.59 (define @t82 () (or @t81 @t80 @t79)) % 0.36/0.59 (define @t83 () (forall @t29 @t82)) % 0.36/0.59 (define @t84 () (or @t68 @t67 @t83)) % 0.36/0.59 (define @t85 () (or @t68 @t67)) % 0.36/0.59 (define @t86 () (not @t46)) % 0.36/0.59 (define @t87 () (or @t80 @t79)) % 0.36/0.59 (define @t88 () (not @t41)) % 0.36/0.59 (define @t89 () (forall @t29 (not @t55))) % 0.36/0.59 (define @t90 () (not @t89)) % 0.36/0.59 (define @t91 () (forall @t72 (or @t68 @t67 @t66 (not (= @t39 @t64)) (not (= @t37 @t62))))) % 0.36/0.59 (define @t92 () (@quantifiers_skolemize @t91 4)) % 0.36/0.59 (define @t93 () (@quantifiers_skolemize @t91 1)) % 0.36/0.59 (define @t94 () (@quantifiers_skolemize @t91 0)) % 0.36/0.59 (define @t95 () (tptp.shortest_path @t94 @t93 @t92)) % 0.36/0.59 (define @t96 () (@quantifiers_skolemize @t91 5)) % 0.36/0.59 (define @t97 () (@quantifiers_skolemize @t91 3)) % 0.36/0.59 (define @t98 () (= (tptp.head_of @t97) (tptp.head_of @t96))) % 0.36/0.59 (define @t99 () (not @t98)) % 0.36/0.59 (define @t100 () (@quantifiers_skolemize @t91 2)) % 0.36/0.59 (define @t101 () (= (tptp.tail_of @t100) (tptp.tail_of @t96))) % 0.36/0.59 (define @t102 () (not @t101)) % 0.36/0.59 (define @t103 () (tptp.precedes @t100 @t97 @t92)) % 0.36/0.59 (define @t104 () (not @t103)) % 0.36/0.59 (define @t105 () (not @t95)) % 0.36/0.59 (define @t106 () (or @t105 @t104 (not (tptp.edge @t96)) @t102 @t99)) % 0.36/0.59 (define @t107 () (@list true)) % 0.36/0.59 (define @t108 () (@list @t106)) % 0.36/0.59 (define @t109 () (@var "BOUND_VARIABLE_7922" $$unsorted)) % 0.36/0.59 (define @t110 () (tptp.head_of @t109)) % 0.36/0.59 (define @t111 () (not (= @t110 @t37))) % 0.36/0.59 (define @t112 () (tptp.tail_of @t109)) % 0.36/0.59 (define @t113 () (not (= @t112 @t39))) % 0.36/0.59 (define @t114 () (or @t113 @t111)) % 0.36/0.59 (define @t115 () (and @t114 @t36)) % 0.36/0.59 (define @t116 () (or @t68 @t67 @t115)) % 0.36/0.59 (define @t117 () (forall (@list @t6 @t8 @t22 @t21 @t13 @t109) @t116)) % 0.36/0.59 (define @t118 () (@list @t109)) % 0.36/0.59 (define @t119 () (forall @t118 @t116)) % 0.36/0.59 (define @t120 () (forall @t118 @t36)) % 0.36/0.59 (define @t121 () (forall @t118 @t114)) % 0.36/0.59 (define @t122 () (and @t121 @t120)) % 0.36/0.59 (define @t123 () (forall @t118 @t115)) % 0.36/0.59 (define @t124 () (or @t68 @t67 @t123)) % 0.36/0.59 (define @t125 () (forall @t29 @t87)) % 0.36/0.59 (define @t126 () (and @t125 @t36)) % 0.36/0.59 (define @t127 () (or @t68 @t67 @t126)) % 0.36/0.59 (define @t128 () (forall @t29 @t88)) % 0.36/0.59 (define @t129 () (not @t128)) % 0.36/0.59 (define @t130 () (or @t102 @t99)) % 0.36/0.59 (define @t131 () (not @t130)) % 0.36/0.59 (define @t132 () (and @t130 (not (tptp.precedes @t97 @t100 @t92)))) % 0.36/0.59 (define @t133 () (not @t132)) % 0.36/0.59 (define @t134 () (or @t105 @t104 @t132)) % 0.36/0.59 (assume @p1 (forall @t5 (=> @t4 (not (= @t3 @t2))))) % 0.36/0.59 (assume @p2 (forall @t5 (=> @t4 (and (tptp.vertex @t3) (tptp.vertex @t2))))) % 0.36/0.59 (assume @p3 (=> tptp.complete (forall (@list @t6 @t8) (=> (and @t12 @t11 @t10) (exists @t5 (and @t4 (xor (and (= @t6 @t3) (= @t8 @t2)) (and @t9 @t7)))))))) % 0.36/0.59 (assume @p4 (forall @t18 (=> (and @t12 @t11 (exists @t5 (and @t4 @t7 (or @t17 @t16)))) @t14))) % 0.36/0.59 (assume @p5 (forall @t18 (=> @t14 (and @t12 @t11 (exists @t5 (and @t4 @t7 (xor @t17 @t16))))))) % 0.36/0.59 (assume @p6 (forall (@list @t6 @t8 @t13 @t1) (=> (and @t14 @t19) (and @t4 (tptp.in_path @t3 @t13) (tptp.in_path @t2 @t13))))) % 0.36/0.59 (assume @p7 (forall (@list @t6 @t8 @t13 @t20) (=> (and @t14 (tptp.in_path @t20 @t13)) (and (tptp.vertex @t20) (exists @t5 (and @t19 (or (= @t20 @t3) (= @t20 @t2)))))))) % 0.36/0.59 (assume @p8 (forall @t26 (= @t25 (and @t24 @t23 (not (= @t22 @t21)) (= (tptp.head_of @t22) (tptp.tail_of @t21)))))) % 0.36/0.59 (assume @p9 (forall @t33 (=> @t14 (forall @t26 (=> (and @t32 @t31 (or @t25 @t30)) @t27))))) % 0.36/0.59 (assume @p10 (forall @t33 (=> @t14 (forall @t26 (=> @t27 (and @t32 @t31 (xor @t25 @t30))))))) % 0.36/0.59 (assume @p11 (forall (@list @t6 @t8 @t35) (= (tptp.shortest_path @t6 @t8 @t35) (and (tptp.path @t6 @t8 @t35) @t10 (forall (@list @t13) (=> @t14 (tptp.less_or_equal (tptp.length_of @t35) @t34))))))) % 0.36/0.59 (assume @p12 @t49) % 0.36/0.59 (assume @p13 (forall (@list @t22 @t21 @t28) (= @t51 (and @t24 @t23 @t50 @t25 (tptp.sequential @t21 @t28) (tptp.sequential @t28 @t22))))) % 0.36/0.59 (assume @p14 (forall @t18 (=> @t14 (= @t34 (tptp.number_of_in tptp.edges @t13))))) % 0.36/0.59 (assume @p15 (forall @t18 (=> @t14 (= @t52 (tptp.minus @t34 tptp.n1))))) % 0.36/0.59 (assume @p16 (forall @t33 (=> (and @t14 (forall @t26 (=> (and @t32 @t31 @t25) (exists @t29 @t51)))) (= @t52 (tptp.number_of_in tptp.triangles @t13))))) % 0.36/0.59 (assume @p17 (forall (@list @t53 @t54) (tptp.less_or_equal (tptp.number_of_in @t53 @t54) (tptp.number_of_in @t53 tptp.graph)))) % 0.36/0.59 (assume @p18 @t60) % 0.36/0.59 (assume @p19 true) % 0.36/0.59 (step @p20 :rule eq-symm :args (@t62 @t37)) % 0.36/0.59 (step @p21 :rule cong :premises (@p20) :args (@t63)) % 0.36/0.59 (step @p22 :rule eq-symm :args (@t64 @t39)) % 0.36/0.59 (step @p23 :rule cong :premises (@p22) :args (@t65)) % 0.36/0.59 (step @p24 :rule refl :args (@t66)) % 0.36/0.59 (step @p25 :rule refl :args (@t67)) % 0.36/0.59 (step @p26 :rule refl :args (@t68)) % 0.36/0.59 (step @p27 :rule nary_cong :premises (@p26 @p25 @p24 @p23 @p21) :args (@t69)) % 0.36/0.59 (step @p28 :rule aci_norm :args ((= @t71 @t69))) % 0.36/0.59 (step @p29 :rule trans :premises (@p28 @p27)) % 0.36/0.59 (step @p30 :rule cong :premises (@p29) :args (@t73)) % 0.36/0.59 (step @p31 :rule quant-merge-prenex :args ((= (forall @t48 @t75) @t73))) % 0.36/0.59 (step @p32 :rule alpha_equiv :args (@t76 (@list @t61) @t77)) % 0.36/0.59 (step @p33 :rule refl :args (@t67)) % 0.36/0.59 (step @p34 :rule refl :args (@t68)) % 0.36/0.59 (step @p35 :rule nary_cong :premises (@p34 @p33 @p32) :args (@t78)) % 0.36/0.59 (step @p36 :rule quant-miniscope-or :args ((= @t75 @t78))) % 0.36/0.59 (step @p37 :rule trans :premises (@p36 @p35)) % 0.36/0.59 (step @p38 :rule symm :premises (@p37)) % 0.36/0.59 (step @p39 :rule cong :premises (@p38) :args ((forall @t48 @t84))) % 0.36/0.59 (step @p40 :rule trans :premises (@p39 @p31)) % 0.36/0.59 (step @p41 :rule trans :premises (@p40 @p30)) % 0.36/0.59 (step @p42 :rule aci_norm :args ((= (or @t85 @t83) @t84))) % 0.36/0.59 (step @p43 :rule refl :args (@t83)) % 0.36/0.59 (step @p44 :rule bool-and-de-morgan :args (@t45 @t27 true)) % 0.36/0.59 (step @p45 :rule nary_cong :premises (@p44 @p43) :args ((or @t86 @t83))) % 0.36/0.59 (step @p46 :rule trans :premises (@p45 @p42)) % 0.36/0.59 (step @p47 :rule bool-impl-elim :args (@t46 @t83)) % 0.36/0.59 (step @p48 :rule trans :premises (@p47 @p46)) % 0.36/0.59 (step @p49 :rule cong :premises (@p48) :args ((forall @t48 (=> @t46 @t83)))) % 0.36/0.59 (step @p50 :rule trans :premises (@p49 @p41)) % 0.36/0.59 (step @p51 :rule bool-double-not-elim :args (@t83)) % 0.36/0.59 (step @p52 :rule aci_norm :args ((= (or @t81 @t87) @t82))) % 0.36/0.59 (step @p53 :rule bool-and-de-morgan :args (@t40 @t38 true)) % 0.36/0.59 (step @p54 :rule refl :args (@t81)) % 0.36/0.59 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t81 @t88))) % 0.36/0.59 (step @p56 :rule bool-and-de-morgan :args (@t50 @t40 (and @t38))) % 0.36/0.59 (step @p57 :rule trans :premises (@p56 @p55)) % 0.36/0.59 (step @p58 :rule trans :premises (@p57 @p52)) % 0.36/0.59 (step @p59 :rule cong :premises (@p58) :args (@t89)) % 0.36/0.59 (step @p60 :rule cong :premises (@p59) :args (@t90)) % 0.36/0.59 (step @p61 :rule exists-elim :args ((= @t56 @t90))) % 0.36/0.59 (step @p62 :rule trans :premises (@p61 @p60)) % 0.36/0.59 (step @p63 :rule cong :premises (@p62) :args (@t57)) % 0.36/0.59 (step @p64 :rule trans :premises (@p63 @p51)) % 0.36/0.59 (step @p65 :rule refl :args (@t46)) % 0.36/0.59 (step @p66 :rule cong :premises (@p65 @p64) :args (@t58)) % 0.36/0.59 (step @p67 :rule cong :premises (@p66) :args (@t59)) % 0.36/0.59 (step @p68 :rule trans :premises (@p67 @p50)) % 0.36/0.59 (step @p69 :rule cong :premises (@p68) :args (@t60)) % 0.36/0.59 (step @p70 :rule eq_resolve :premises (@p18 @p69)) % 0.36/0.59 (step @p71 :rule skolemize :premises (@p70)) % 0.36/0.59 (step @p72 :rule bool-double-not-elim :args (@t95)) % 0.36/0.59 (step @p73 :rule refl :args (@t106)) % 0.36/0.59 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t106 (not @t105)))) % 0.36/0.59 (step @p75 :rule cnf_or_neg :args (@t106 0)) % 0.36/0.59 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.36/0.59 (step @p77 :rule reordering :premises (@p76) :args ((or @t95 @t106))) % 0.36/0.59 (step @p78 :rule chain_m_resolution :premises (@p77 @p71) :args (@t95 @t107 @t108)) % 0.36/0.59 (step @p79 :rule bool-double-not-elim :args (@t103)) % 0.36/0.59 (step @p80 :rule nary_cong :premises (@p73 @p79) :args ((or @t106 (not @t104)))) % 0.36/0.59 (step @p81 :rule cnf_or_neg :args (@t106 1)) % 0.36/0.59 (step @p82 :rule eq_resolve :premises (@p81 @p80)) % 0.36/0.59 (step @p83 :rule reordering :premises (@p82) :args ((or @t103 @t106))) % 0.36/0.59 (step @p84 :rule chain_m_resolution :premises (@p83 @p71) :args (@t103 @t107 @t108)) % 0.36/0.59 (step @p85 :rule refl :args (@t36)) % 0.36/0.59 (step @p86 :rule eq-symm :args (@t110 @t37)) % 0.36/0.59 (step @p87 :rule cong :premises (@p86) :args (@t111)) % 0.36/0.59 (step @p88 :rule eq-symm :args (@t112 @t39)) % 0.36/0.59 (step @p89 :rule cong :premises (@p88) :args (@t113)) % 0.36/0.59 (step @p90 :rule nary_cong :premises (@p89 @p87) :args (@t114)) % 0.36/0.59 (step @p91 :rule nary_cong :premises (@p90 @p85) :args (@t115)) % 0.36/0.59 (step @p92 :rule nary_cong :premises (@p26 @p25 @p91) :args (@t116)) % 0.36/0.59 (step @p93 :rule cong :premises (@p92) :args (@t117)) % 0.36/0.59 (step @p94 :rule quant-merge-prenex :args ((= (forall @t48 @t119) @t117))) % 0.36/0.59 (step @p95 :rule quant-unused-vars :args ((= @t120 @t36))) % 0.36/0.59 (step @p96 :rule alpha_equiv :args (@t121 (@list @t109) @t77)) % 0.36/0.59 (step @p97 :rule nary_cong :premises (@p96 @p95) :args (@t122)) % 0.36/0.59 (step @p98 :rule quant-miniscope-and :args ((= @t123 @t122))) % 0.36/0.59 (step @p99 :rule trans :premises (@p98 @p97)) % 0.36/0.59 (step @p100 :rule nary_cong :premises (@p34 @p33 @p99) :args (@t124)) % 0.36/0.59 (step @p101 :rule quant-miniscope-or :args ((= @t119 @t124))) % 0.36/0.59 (step @p102 :rule trans :premises (@p101 @p100)) % 0.36/0.59 (step @p103 :rule symm :premises (@p102)) % 0.36/0.59 (step @p104 :rule cong :premises (@p103) :args ((forall @t48 @t127))) % 0.36/0.59 (step @p105 :rule trans :premises (@p104 @p94)) % 0.36/0.59 (step @p106 :rule trans :premises (@p105 @p93)) % 0.36/0.59 (step @p107 :rule aci_norm :args ((= (or @t85 @t126) @t127))) % 0.36/0.59 (step @p108 :rule refl :args (@t126)) % 0.36/0.59 (step @p109 :rule nary_cong :premises (@p44 @p108) :args ((or @t86 @t126))) % 0.36/0.59 (step @p110 :rule trans :premises (@p109 @p107)) % 0.36/0.59 (step @p111 :rule bool-impl-elim :args (@t46 @t126)) % 0.36/0.59 (step @p112 :rule trans :premises (@p111 @p110)) % 0.36/0.59 (step @p113 :rule cong :premises (@p112) :args ((forall @t48 (=> @t46 @t126)))) % 0.36/0.59 (step @p114 :rule trans :premises (@p113 @p106)) % 0.36/0.59 (step @p115 :rule bool-double-not-elim :args (@t125)) % 0.36/0.59 (step @p116 :rule cong :premises (@p53) :args (@t128)) % 0.36/0.59 (step @p117 :rule cong :premises (@p116) :args (@t129)) % 0.36/0.59 (step @p118 :rule exists-elim :args ((= @t42 @t129))) % 0.36/0.59 (step @p119 :rule trans :premises (@p118 @p117)) % 0.36/0.59 (step @p120 :rule cong :premises (@p119) :args (@t43)) % 0.36/0.59 (step @p121 :rule trans :premises (@p120 @p115)) % 0.36/0.59 (step @p122 :rule nary_cong :premises (@p121 @p85) :args (@t44)) % 0.36/0.59 (step @p123 :rule cong :premises (@p65 @p122) :args (@t47)) % 0.36/0.59 (step @p124 :rule cong :premises (@p123) :args (@t49)) % 0.36/0.59 (step @p125 :rule trans :premises (@p124 @p114)) % 0.36/0.59 (step @p126 :rule eq_resolve :premises (@p12 @p125)) % 0.36/0.59 (step @p127 :rule instantiate :premises (@p126) :args ((@list @t94 @t93 @t100 @t97 @t92 @t96))) % 0.36/0.59 (step @p128 :rule bool-double-not-elim :args (@t98)) % 0.36/0.59 (step @p129 :rule nary_cong :premises (@p73 @p128) :args ((or @t106 (not @t99)))) % 0.36/0.59 (step @p130 :rule cnf_or_neg :args (@t106 4)) % 0.36/0.59 (step @p131 :rule eq_resolve :premises (@p130 @p129)) % 0.36/0.59 (step @p132 :rule reordering :premises (@p131) :args ((or @t98 @t106))) % 0.36/0.59 (step @p133 :rule chain_m_resolution :premises (@p132 @p71) :args (@t98 @t107 @t108)) % 0.36/0.59 (step @p134 :rule bool-double-not-elim :args (@t101)) % 0.36/0.59 (step @p135 :rule nary_cong :premises (@p73 @p134) :args ((or @t106 (not @t102)))) % 0.36/0.59 (step @p136 :rule cnf_or_neg :args (@t106 3)) % 0.36/0.59 (step @p137 :rule eq_resolve :premises (@p136 @p135)) % 0.36/0.59 (step @p138 :rule reordering :premises (@p137) :args ((or @t101 @t106))) % 0.36/0.59 (step @p139 :rule chain_m_resolution :premises (@p138 @p71) :args (@t101 @t107 @t108)) % 0.36/0.59 (step @p140 :rule cnf_or_pos :args (@t130)) % 0.36/0.59 (step @p141 :rule reordering :premises (@p140) :args ((or @t102 @t99 @t131))) % 0.36/0.59 (step @p142 :rule chain_m_resolution :premises (@p141 @p139 @p133) :args (@t131 (@list false false) (@list @t101 @t98))) % 0.36/0.59 (step @p143 :rule cnf_and_pos :args (@t132 0)) % 0.36/0.59 (step @p144 :rule reordering :premises (@p143) :args ((or @t130 @t133))) % 0.36/0.59 (step @p145 :rule chain_m_resolution :premises (@p144 @p142) :args (@t133 @t107 (@list @t130))) % 0.36/0.59 (step @p146 :rule cnf_or_pos :args (@t134)) % 0.36/0.59 (step @p147 :rule reordering :premises (@p146) :args ((or @t105 @t104 @t132 (not @t134)))) % 0.36/0.59 (step @p148 false :rule chain_m_resolution :premises (@p147 @p145 @p127 @p84 @p78) :args (false (@list true false false false) (@list @t132 @t134 @t103 @t95))) % 0.36/0.59 ) % 0.36/0.59 % SZS output end Proof % 0.36/0.59 % cvc5 exiting %------------------------------------------------------------------------------