%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GRA010+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 08:18:31 AM UTC 2026 % Result : Theorem 0.36s 0.57s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRA010+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 00:14:33 EDT 2026 % 0.15/0.34 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.57 % SZS status Theorem % 0.36/0.57 % SZS output start Proof % 0.36/0.57 ( % 0.36/0.57 (declare-sort $$unsorted 0) % 0.36/0.57 (declare-const tptp.graph $$unsorted) % 0.36/0.57 (declare-const tptp.number_of_in (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.edges $$unsorted) % 0.36/0.57 (declare-const tptp.triangle (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.shortest_path (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.less_or_equal (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.tail_of (-> $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.triangles $$unsorted) % 0.36/0.57 (declare-const tptp.in_path (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.head_of (-> $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.sequential_pairs $$unsorted) % 0.36/0.57 (declare-const tptp.edge (-> $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.path_cons (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.precedes (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.complete Bool) % 0.36/0.57 (declare-const tptp.path (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.vertex (-> $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.on_path (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.empty $$unsorted) % 0.36/0.57 (declare-const tptp.n1 $$unsorted) % 0.36/0.57 (declare-const tptp.sequential (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.length_of (-> $$unsorted $$unsorted)) % 0.36/0.57 (define @t1 () (@var "E" $$unsorted)) % 0.36/0.57 (define @t2 () (tptp.tail_of @t1)) % 0.36/0.57 (define @t3 () (tptp.head_of @t1)) % 0.36/0.57 (define @t4 () (tptp.edge @t1)) % 0.36/0.57 (define @t5 () (@list @t1)) % 0.36/0.57 (define @t6 () (@var "V1" $$unsorted)) % 0.36/0.57 (define @t7 () (= @t6 @t2)) % 0.36/0.57 (define @t8 () (@var "V2" $$unsorted)) % 0.36/0.57 (define @t9 () (= @t8 @t3)) % 0.36/0.57 (define @t10 () (not (= @t6 @t8))) % 0.36/0.57 (define @t11 () (tptp.vertex @t8)) % 0.36/0.57 (define @t12 () (tptp.vertex @t6)) % 0.36/0.57 (define @t13 () (@var "P" $$unsorted)) % 0.36/0.57 (define @t14 () (tptp.path @t6 @t8 @t13)) % 0.36/0.57 (define @t15 () (@var "TP" $$unsorted)) % 0.36/0.57 (define @t16 () (exists (@list @t15) (and (tptp.path @t3 @t8 @t15) (= @t13 (tptp.path_cons @t1 @t15))))) % 0.36/0.57 (define @t17 () (and @t9 (= @t13 (tptp.path_cons @t1 tptp.empty)))) % 0.36/0.57 (define @t18 () (@list @t6 @t8 @t13)) % 0.36/0.57 (define @t19 () (tptp.on_path @t1 @t13)) % 0.36/0.57 (define @t20 () (@var "V" $$unsorted)) % 0.36/0.57 (define @t21 () (@var "E2" $$unsorted)) % 0.36/0.57 (define @t22 () (@var "E1" $$unsorted)) % 0.36/0.57 (define @t23 () (tptp.edge @t21)) % 0.36/0.57 (define @t24 () (tptp.edge @t22)) % 0.36/0.57 (define @t25 () (tptp.sequential @t22 @t21)) % 0.36/0.57 (define @t26 () (@list @t22 @t21)) % 0.36/0.57 (define @t27 () (tptp.precedes @t22 @t21 @t13)) % 0.36/0.57 (define @t28 () (@var "E3" $$unsorted)) % 0.36/0.57 (define @t29 () (@list @t28)) % 0.36/0.57 (define @t30 () (exists @t29 (and (tptp.sequential @t22 @t28) (tptp.precedes @t28 @t21 @t13)))) % 0.36/0.57 (define @t31 () (tptp.on_path @t21 @t13)) % 0.36/0.57 (define @t32 () (tptp.on_path @t22 @t13)) % 0.36/0.57 (define @t33 () (@list @t13 @t6 @t8)) % 0.36/0.57 (define @t34 () (tptp.length_of @t13)) % 0.36/0.57 (define @t35 () (@var "SP" $$unsorted)) % 0.36/0.57 (define @t36 () (tptp.triangle @t22 @t21 @t28)) % 0.36/0.57 (define @t37 () (tptp.number_of_in tptp.sequential_pairs @t13)) % 0.36/0.57 (define @t38 () (= @t37 (tptp.number_of_in tptp.triangles @t13))) % 0.36/0.57 (define @t39 () (exists @t29 @t36)) % 0.36/0.57 (define @t40 () (and @t32 @t31 @t25)) % 0.36/0.57 (define @t41 () (=> @t40 @t39)) % 0.36/0.57 (define @t42 () (forall @t26 @t41)) % 0.36/0.57 (define @t43 () (and @t14 @t42)) % 0.36/0.57 (define @t44 () (=> @t43 @t38)) % 0.36/0.57 (define @t45 () (forall @t33 @t44)) % 0.36/0.57 (define @t46 () (@var "Things" $$unsorted)) % 0.36/0.57 (define @t47 () (@var "InThese" $$unsorted)) % 0.36/0.57 (define @t48 () (=> tptp.complete @t45)) % 0.36/0.57 (define @t49 () (not @t48)) % 0.36/0.57 (define @t50 () (not (forall @t29 (not @t36)))) % 0.36/0.57 (define @t51 () (not @t25)) % 0.36/0.57 (define @t52 () (not @t31)) % 0.36/0.57 (define @t53 () (not @t32)) % 0.36/0.57 (define @t54 () (or @t53 @t52 @t51 @t50)) % 0.36/0.57 (define @t55 () (forall @t26 @t54)) % 0.36/0.57 (define @t56 () (not @t55)) % 0.36/0.57 (define @t57 () (not @t14)) % 0.36/0.57 (define @t58 () (or @t57 @t56 @t38)) % 0.36/0.57 (define @t59 () (and @t14 @t55)) % 0.36/0.57 (define @t60 () (or @t53 @t52 @t51)) % 0.36/0.57 (assume @p1 (forall @t5 (=> @t4 (not (= @t3 @t2))))) % 0.36/0.57 (assume @p2 (forall @t5 (=> @t4 (and (tptp.vertex @t3) (tptp.vertex @t2))))) % 0.36/0.57 (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)))))))) % 0.36/0.57 (assume @p4 (forall @t18 (=> (and @t12 @t11 (exists @t5 (and @t4 @t7 (or @t17 @t16)))) @t14))) % 0.36/0.57 (assume @p5 (forall @t18 (=> @t14 (and @t12 @t11 (exists @t5 (and @t4 @t7 (xor @t17 @t16))))))) % 0.36/0.57 (assume @p6 (forall (@list @t6 @t8 @t13 @t1) (=> (and @t14 @t19) (and @t4 (tptp.in_path @t3 @t13) (tptp.in_path @t2 @t13))))) % 0.36/0.57 (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)))))))) % 0.36/0.57 (assume @p8 (forall @t26 (= @t25 (and @t24 @t23 (not (= @t22 @t21)) (= (tptp.head_of @t22) (tptp.tail_of @t21)))))) % 0.36/0.57 (assume @p9 (forall @t33 (=> @t14 (forall @t26 (=> (and @t32 @t31 (or @t25 @t30)) @t27))))) % 0.36/0.57 (assume @p10 (forall @t33 (=> @t14 (forall @t26 (=> @t27 (and @t32 @t31 (xor @t25 @t30))))))) % 0.36/0.57 (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))))))) % 0.36/0.57 (assume @p12 (forall (@list @t6 @t8 @t22 @t21 @t13) (=> (and (tptp.shortest_path @t6 @t8 @t13) @t27) (and (not (exists @t29 (and (= (tptp.tail_of @t28) (tptp.tail_of @t22)) (= (tptp.head_of @t28) (tptp.head_of @t21))))) (not (tptp.precedes @t21 @t22 @t13)))))) % 0.36/0.57 (assume @p13 (forall (@list @t22 @t21 @t28) (= @t36 (and @t24 @t23 (tptp.edge @t28) @t25 (tptp.sequential @t21 @t28) (tptp.sequential @t28 @t22))))) % 0.36/0.57 (assume @p14 (forall @t18 (=> @t14 (= @t34 (tptp.number_of_in tptp.edges @t13))))) % 0.36/0.57 (assume @p15 (forall @t18 (=> @t14 (= @t37 (tptp.minus @t34 tptp.n1))))) % 0.36/0.57 (assume @p16 @t45) % 0.36/0.57 (assume @p17 (forall (@list @t46 @t47) (tptp.less_or_equal (tptp.number_of_in @t46 @t47) (tptp.number_of_in @t46 tptp.graph)))) % 0.36/0.57 (assume @p18 @t49) % 0.36/0.57 (assume @p19 true) % 0.36/0.57 (step @p20 :rule aci_norm :args ((= (or (or @t57 @t56) @t38) @t58))) % 0.36/0.57 (step @p21 :rule refl :args (@t38)) % 0.36/0.57 (step @p22 :rule bool-and-de-morgan :args (@t14 @t55 true)) % 0.36/0.57 (step @p23 :rule nary_cong :premises (@p22 @p21) :args ((or (not @t59) @t38))) % 0.36/0.57 (step @p24 :rule trans :premises (@p23 @p20)) % 0.36/0.57 (step @p25 :rule bool-impl-elim :args (@t59 @t38)) % 0.36/0.57 (step @p26 :rule trans :premises (@p25 @p24)) % 0.36/0.57 (step @p27 :rule cong :premises (@p26) :args ((forall @t33 (=> @t59 @t38)))) % 0.36/0.57 (step @p28 :rule refl :args (@t38)) % 0.36/0.57 (step @p29 :rule aci_norm :args ((= (or @t60 @t50) @t54))) % 0.36/0.57 (step @p30 :rule refl :args (@t50)) % 0.36/0.57 (step @p31 :rule aci_norm :args ((= (or @t53 (or @t52 @t51)) @t60))) % 0.36/0.57 (step @p32 :rule bool-and-de-morgan :args (@t31 @t25 true)) % 0.36/0.57 (step @p33 :rule refl :args (@t53)) % 0.36/0.57 (step @p34 :rule nary_cong :premises (@p33 @p32) :args ((or @t53 (not (and @t31 @t25))))) % 0.36/0.57 (step @p35 :rule bool-and-de-morgan :args (@t32 @t31 (and @t25))) % 0.36/0.57 (step @p36 :rule trans :premises (@p35 @p34)) % 0.36/0.57 (step @p37 :rule trans :premises (@p36 @p31)) % 0.36/0.57 (step @p38 :rule nary_cong :premises (@p37 @p30) :args ((or (not @t40) @t50))) % 0.36/0.57 (step @p39 :rule trans :premises (@p38 @p29)) % 0.36/0.57 (step @p40 :rule bool-impl-elim :args (@t40 @t50)) % 0.36/0.57 (step @p41 :rule trans :premises (@p40 @p39)) % 0.36/0.57 (step @p42 :rule cong :premises (@p41) :args ((forall @t26 (=> @t40 @t50)))) % 0.36/0.57 (step @p43 :rule exists-elim :args ((= @t39 @t50))) % 0.36/0.57 (step @p44 :rule refl :args (@t40)) % 0.36/0.57 (step @p45 :rule cong :premises (@p44 @p43) :args (@t41)) % 0.36/0.57 (step @p46 :rule cong :premises (@p45) :args (@t42)) % 0.36/0.57 (step @p47 :rule trans :premises (@p46 @p42)) % 0.36/0.57 (step @p48 :rule refl :args (@t14)) % 0.36/0.57 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t43)) % 0.36/0.57 (step @p50 :rule cong :premises (@p49 @p28) :args (@t44)) % 0.36/0.57 (step @p51 :rule cong :premises (@p50) :args (@t45)) % 0.36/0.57 (step @p52 :rule trans :premises (@p51 @p27)) % 0.36/0.57 (step @p53 :rule eq_resolve :premises (@p16 @p52)) % 0.36/0.57 (step @p54 :rule refl :args (tptp.complete)) % 0.36/0.57 (step @p55 :rule cong :premises (@p54 @p52) :args (@t48)) % 0.36/0.57 (step @p56 :rule cong :premises (@p55) :args (@t49)) % 0.36/0.57 (step @p57 :rule eq_resolve :premises (@p18 @p56)) % 0.36/0.57 (step @p58 :rule not_implies_elim2 :premises (@p57)) % 0.36/0.57 (step @p59 false :rule chain_m_resolution :premises (@p58 @p53) :args (false (@list false) (@list (forall @t33 @t58)))) % 0.36/0.57 ) % 0.36/0.57 % SZS output end Proof % 0.36/0.57 % cvc5 exiting %------------------------------------------------------------------------------