%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GRA002+4 : TPTP v9.2.1. Bugfixed 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 : 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 08:18:30 AM UTC 2026 % Result : Theorem 0.39s 0.59s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRA002+4 : TPTP v9.2.1. Bugfixed v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n017.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 00:12:31 EDT 2026 % 0.19/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.59 % SZS status Theorem % 0.39/0.59 % SZS output start Proof % 0.39/0.59 ( % 0.39/0.59 (declare-sort $$unsorted 0) % 0.39/0.59 (declare-const tptp.graph $$unsorted) % 0.39/0.59 (declare-const tptp.number_of_in (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.edges $$unsorted) % 0.39/0.59 (declare-const tptp.triangle (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.shortest_path (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.less_or_equal (-> $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.minus (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.tail_of (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.triangles $$unsorted) % 0.39/0.59 (declare-const tptp.in_path (-> $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.head_of (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.sequential_pairs $$unsorted) % 0.39/0.59 (declare-const tptp.edge (-> $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.path_cons (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.precedes (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.complete Bool) % 0.39/0.59 (declare-const tptp.path (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.vertex (-> $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.on_path (-> $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.empty $$unsorted) % 0.39/0.59 (declare-const tptp.n1 $$unsorted) % 0.39/0.59 (declare-const tptp.sequential (-> $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.length_of (-> $$unsorted $$unsorted)) % 0.39/0.59 (define @t1 () (@var "E" $$unsorted)) % 0.39/0.59 (define @t2 () (tptp.tail_of @t1)) % 0.39/0.59 (define @t3 () (tptp.head_of @t1)) % 0.39/0.59 (define @t4 () (tptp.edge @t1)) % 0.39/0.59 (define @t5 () (@list @t1)) % 0.39/0.59 (define @t6 () (@var "V1" $$unsorted)) % 0.39/0.59 (define @t7 () (= @t6 @t2)) % 0.39/0.59 (define @t8 () (@var "V2" $$unsorted)) % 0.39/0.59 (define @t9 () (= @t8 @t3)) % 0.39/0.59 (define @t10 () (not (= @t6 @t8))) % 0.39/0.59 (define @t11 () (tptp.vertex @t8)) % 0.39/0.59 (define @t12 () (tptp.vertex @t6)) % 0.39/0.59 (define @t13 () (@var "P" $$unsorted)) % 0.39/0.59 (define @t14 () (tptp.path @t6 @t8 @t13)) % 0.39/0.59 (define @t15 () (@var "TP" $$unsorted)) % 0.39/0.59 (define @t16 () (exists (@list @t15) (and (tptp.path @t3 @t8 @t15) (= @t13 (tptp.path_cons @t1 @t15))))) % 0.39/0.59 (define @t17 () (and @t9 (= @t13 (tptp.path_cons @t1 tptp.empty)))) % 0.39/0.59 (define @t18 () (@list @t6 @t8 @t13)) % 0.39/0.59 (define @t19 () (tptp.on_path @t1 @t13)) % 0.39/0.59 (define @t20 () (@var "V" $$unsorted)) % 0.39/0.59 (define @t21 () (@var "E2" $$unsorted)) % 0.39/0.59 (define @t22 () (@var "E1" $$unsorted)) % 0.39/0.59 (define @t23 () (tptp.edge @t21)) % 0.39/0.59 (define @t24 () (tptp.edge @t22)) % 0.39/0.59 (define @t25 () (tptp.sequential @t22 @t21)) % 0.39/0.59 (define @t26 () (@list @t22 @t21)) % 0.39/0.59 (define @t27 () (tptp.precedes @t22 @t21 @t13)) % 0.39/0.59 (define @t28 () (@var "E3" $$unsorted)) % 0.39/0.59 (define @t29 () (@list @t28)) % 0.39/0.59 (define @t30 () (exists @t29 (and (tptp.sequential @t22 @t28) (tptp.precedes @t28 @t21 @t13)))) % 0.39/0.59 (define @t31 () (tptp.on_path @t21 @t13)) % 0.39/0.59 (define @t32 () (tptp.on_path @t22 @t13)) % 0.39/0.59 (define @t33 () (@list @t13 @t6 @t8)) % 0.39/0.59 (define @t34 () (tptp.length_of @t13)) % 0.39/0.59 (define @t35 () (@var "SP" $$unsorted)) % 0.39/0.59 (define @t36 () (tptp.less_or_equal (tptp.length_of @t35) @t34)) % 0.39/0.59 (define @t37 () (@list @t13)) % 0.39/0.59 (define @t38 () (forall @t37 (=> @t14 @t36))) % 0.39/0.59 (define @t39 () (tptp.path @t6 @t8 @t35)) % 0.39/0.59 (define @t40 () (and @t39 @t10 @t38)) % 0.39/0.59 (define @t41 () (tptp.shortest_path @t6 @t8 @t35)) % 0.39/0.59 (define @t42 () (= @t41 @t40)) % 0.39/0.59 (define @t43 () (forall (@list @t6 @t8 @t35) @t42)) % 0.39/0.59 (define @t44 () (tptp.shortest_path @t6 @t8 @t13)) % 0.39/0.59 (define @t45 () (tptp.triangle @t22 @t21 @t28)) % 0.39/0.59 (define @t46 () (tptp.minus @t34 tptp.n1)) % 0.39/0.59 (define @t47 () (tptp.number_of_in tptp.sequential_pairs @t13)) % 0.39/0.59 (define @t48 () (= @t47 @t46)) % 0.39/0.59 (define @t49 () (forall @t18 (=> @t14 @t48))) % 0.39/0.59 (define @t50 () (= @t47 (tptp.number_of_in tptp.triangles @t13))) % 0.39/0.59 (define @t51 () (@var "Things" $$unsorted)) % 0.39/0.59 (define @t52 () (@var "InThese" $$unsorted)) % 0.39/0.59 (define @t53 () (forall @t33 (=> @t44 @t50))) % 0.39/0.59 (define @t54 () (=> tptp.complete @t53)) % 0.39/0.59 (define @t55 () (tptp.number_of_in tptp.triangles tptp.graph)) % 0.39/0.59 (define @t56 () (tptp.less_or_equal @t46 @t55)) % 0.39/0.59 (define @t57 () (forall @t33 (=> @t44 @t56))) % 0.39/0.59 (define @t58 () (=> tptp.complete @t57)) % 0.39/0.59 (define @t59 () (not @t58)) % 0.39/0.59 (define @t60 () (not @t44)) % 0.39/0.59 (define @t61 () (forall @t33 (or @t60 @t56))) % 0.39/0.59 (define @t62 () (@quantifiers_skolemize @t61 0)) % 0.39/0.59 (define @t63 () (forall @t33 (or @t60 @t50))) % 0.39/0.59 (define @t64 () (@list false)) % 0.39/0.59 (define @t65 () (@quantifiers_skolemize @t61 2)) % 0.39/0.59 (define @t66 () (@quantifiers_skolemize @t61 1)) % 0.39/0.59 (define @t67 () (tptp.shortest_path @t66 @t65 @t62)) % 0.39/0.59 (define @t68 () (tptp.length_of @t62)) % 0.39/0.59 (define @t69 () (tptp.minus @t68 tptp.n1)) % 0.39/0.59 (define @t70 () (tptp.less_or_equal @t69 @t55)) % 0.39/0.59 (define @t71 () (not @t67)) % 0.39/0.59 (define @t72 () (or @t71 @t70)) % 0.39/0.59 (define @t73 () (@list true)) % 0.39/0.59 (define @t74 () (@list @t72)) % 0.39/0.59 (define @t75 () (tptp.number_of_in tptp.sequential_pairs @t62)) % 0.39/0.59 (define @t76 () (= @t75 (tptp.number_of_in tptp.triangles @t62))) % 0.39/0.59 (define @t77 () (or @t71 @t76)) % 0.39/0.59 (define @t78 () (@list false false)) % 0.39/0.59 (define @t79 () (tptp.path @t66 @t65 @t62)) % 0.39/0.59 (define @t80 () (not @t79)) % 0.39/0.59 (define @t81 () (or @t80 (= @t75 @t69))) % 0.39/0.59 (define @t82 () (forall @t18 (or (not @t14) @t48))) % 0.39/0.59 (define @t83 () (@list @t66 @t65 @t62)) % 0.39/0.59 (define @t84 () (= @t69 @t75)) % 0.39/0.59 (define @t85 () (or @t80 @t84)) % 0.39/0.59 (define @t86 () (and @t79 (not (= @t66 @t65)) (forall @t37 (or (not (tptp.path @t66 @t65 @t13)) (tptp.less_or_equal @t68 @t34))))) % 0.39/0.59 (define @t87 () (= @t67 @t86)) % 0.39/0.59 (assume @p1 (forall @t5 (=> @t4 (not (= @t3 @t2))))) % 0.39/0.59 (assume @p2 (forall @t5 (=> @t4 (and (tptp.vertex @t3) (tptp.vertex @t2))))) % 0.39/0.59 (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)))))))) % 0.39/0.59 (assume @p4 (forall @t18 (=> (and @t12 @t11 (exists @t5 (and @t4 @t7 (or @t17 @t16)))) @t14))) % 0.39/0.59 (assume @p5 (forall @t18 (=> @t14 (and @t12 @t11 (exists @t5 (and @t4 @t7 (xor @t17 @t16))))))) % 0.39/0.59 (assume @p6 (forall (@list @t6 @t8 @t13 @t1) (=> (and @t14 @t19) (and @t4 (tptp.in_path @t3 @t13) (tptp.in_path @t2 @t13))))) % 0.39/0.59 (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)))))))) % 0.39/0.59 (assume @p8 (forall @t26 (= @t25 (and @t24 @t23 (not (= @t22 @t21)) (= (tptp.head_of @t22) (tptp.tail_of @t21)))))) % 0.39/0.59 (assume @p9 (forall @t33 (=> @t14 (forall @t26 (=> (and @t32 @t31 (or @t25 @t30)) @t27))))) % 0.39/0.59 (assume @p10 (forall @t33 (=> @t14 (forall @t26 (=> @t27 (and @t32 @t31 (xor @t25 @t30))))))) % 0.39/0.59 (assume @p11 @t43) % 0.39/0.59 (assume @p12 (forall (@list @t6 @t8 @t22 @t21 @t13) (=> (and @t44 @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)))))) % 0.39/0.59 (assume @p13 (forall (@list @t22 @t21 @t28) (= @t45 (and @t24 @t23 (tptp.edge @t28) @t25 (tptp.sequential @t21 @t28) (tptp.sequential @t28 @t22))))) % 0.39/0.59 (assume @p14 (forall @t18 (=> @t14 (= @t34 (tptp.number_of_in tptp.edges @t13))))) % 0.39/0.59 (assume @p15 @t49) % 0.39/0.59 (assume @p16 (forall @t33 (=> (and @t14 (forall @t26 (=> (and @t32 @t31 @t25) (exists @t29 @t45)))) @t50))) % 0.39/0.59 (assume @p17 (forall (@list @t51 @t52) (tptp.less_or_equal (tptp.number_of_in @t51 @t52) (tptp.number_of_in @t51 tptp.graph)))) % 0.39/0.59 (assume @p18 @t54) % 0.39/0.59 (assume @p19 @t59) % 0.39/0.59 (assume @p20 true) % 0.39/0.59 (step @p21 :rule evaluate :args ((= false true))) % 0.39/0.59 (step @p22 :rule instantiate :premises (@p17) :args ((@list tptp.triangles @t62))) % 0.39/0.59 (step @p23 :rule true_intro :premises (@p22)) % 0.39/0.59 (step @p24 :rule refl :args (@t55)) % 0.39/0.59 (step @p25 :rule bool-impl-elim :args (@t44 @t56)) % 0.39/0.59 (step @p26 :rule cong :premises (@p25) :args (@t57)) % 0.39/0.59 (step @p27 :rule refl :args (tptp.complete)) % 0.39/0.59 (step @p28 :rule cong :premises (@p27 @p26) :args (@t58)) % 0.39/0.59 (step @p29 :rule cong :premises (@p28) :args (@t59)) % 0.39/0.59 (step @p30 :rule eq_resolve :premises (@p19 @p29)) % 0.39/0.59 (step @p31 :rule not_implies_elim1 :premises (@p30)) % 0.39/0.59 (step @p32 :rule bool-impl-elim :args (@t44 @t50)) % 0.39/0.59 (step @p33 :rule cong :premises (@p32) :args (@t53)) % 0.39/0.59 (step @p34 :rule cong :premises (@p27 @p33) :args (@t54)) % 0.39/0.59 (step @p35 :rule eq_resolve :premises (@p18 @p34)) % 0.39/0.59 (step @p36 :rule implies_elim :premises (@p35)) % 0.39/0.59 (step @p37 :rule reordering :premises (@p36) :args ((or @t63 (not tptp.complete)))) % 0.39/0.59 (step @p38 :rule chain_m_resolution :premises (@p37 @p31) :args (@t63 @t64 (@list tptp.complete))) % 0.39/0.59 (step @p39 :rule instantiate :premises (@p38) :args ((@list @t62 @t66 @t65))) % 0.39/0.59 (step @p40 :rule not_implies_elim2 :premises (@p30)) % 0.39/0.59 (step @p41 :rule skolemize :premises (@p40)) % 0.39/0.59 (step @p42 :rule bool-double-not-elim :args (@t67)) % 0.39/0.59 (step @p43 :rule refl :args (@t72)) % 0.39/0.59 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or @t72 (not @t71)))) % 0.39/0.59 (step @p45 :rule cnf_or_neg :args (@t72 0)) % 0.39/0.59 (step @p46 :rule eq_resolve :premises (@p45 @p44)) % 0.39/0.59 (step @p47 :rule reordering :premises (@p46) :args ((or @t67 @t72))) % 0.39/0.59 (step @p48 :rule chain_m_resolution :premises (@p47 @p41) :args (@t67 @t73 @t74)) % 0.39/0.59 (step @p49 :rule cnf_or_pos :args (@t77)) % 0.39/0.59 (step @p50 :rule reordering :premises (@p49) :args ((or @t71 @t76 (not @t77)))) % 0.39/0.59 (step @p51 :rule chain_m_resolution :premises (@p50 @p48 @p39) :args (@t76 @t78 (@list @t67 @t77))) % 0.39/0.59 (step @p52 :rule bool-impl-elim :args (@t14 @t48)) % 0.39/0.59 (step @p53 :rule cong :premises (@p52) :args (@t49)) % 0.39/0.59 (step @p54 :rule eq_resolve :premises (@p15 @p53)) % 0.39/0.59 (step @p55 :rule eq-symm :args (@t75 @t69)) % 0.39/0.59 (step @p56 :rule refl :args (@t80)) % 0.39/0.59 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t81)) % 0.39/0.59 (step @p58 :rule refl :args (@t82)) % 0.39/0.59 (step @p59 :rule cong :premises (@p58 @p57) :args ((=> @t82 @t81))) % 0.39/0.59 (assume-push @p94 @t82) % 0.39/0.59 (step @p61 :rule instantiate :premises (@p54) :args (@t83)) % 0.39/0.59 (step-pop @p95 :rule scope :premises (@p61)) % 0.39/0.59 (step @p62 :rule process_scope :premises (@p95) :args (@t81)) % 0.39/0.59 (step @p64 :rule eq_resolve :premises (@p62 @p59)) % 0.39/0.59 (step @p65 :rule implies_elim :premises (@p64)) % 0.39/0.59 (step @p66 :rule chain_m_resolution :premises (@p65 @p54) :args (@t85 @t64 (@list @t82))) % 0.39/0.59 (step @p67 :rule bool-impl-elim :args (@t14 @t36)) % 0.39/0.59 (step @p68 :rule cong :premises (@p67) :args (@t38)) % 0.39/0.59 (step @p69 :rule refl :args (@t10)) % 0.39/0.59 (step @p70 :rule refl :args (@t39)) % 0.39/0.59 (step @p71 :rule nary_cong :premises (@p70 @p69 @p68) :args (@t40)) % 0.39/0.59 (step @p72 :rule refl :args (@t41)) % 0.39/0.59 (step @p73 :rule cong :premises (@p72 @p71) :args (@t42)) % 0.39/0.59 (step @p74 :rule cong :premises (@p73) :args (@t43)) % 0.39/0.59 (step @p75 :rule eq_resolve :premises (@p11 @p74)) % 0.39/0.59 (step @p76 :rule instantiate :premises (@p75) :args (@t83)) % 0.39/0.59 (step @p77 :rule cnf_equiv_pos1 :args (@t87)) % 0.39/0.59 (step @p78 :rule reordering :premises (@p77) :args ((or @t71 @t86 (not @t87)))) % 0.39/0.59 (step @p79 :rule chain_m_resolution :premises (@p78 @p48 @p76) :args (@t86 @t78 (@list @t67 @t87))) % 0.39/0.59 (step @p80 :rule cnf_and_pos :args (@t86 0)) % 0.39/0.59 (step @p81 :rule reordering :premises (@p80) :args ((or @t79 (not @t86)))) % 0.39/0.59 (step @p82 :rule chain_m_resolution :premises (@p81 @p79) :args (@t79 @t64 (@list @t86))) % 0.39/0.59 (step @p83 :rule cnf_or_pos :args (@t85)) % 0.39/0.59 (step @p84 :rule reordering :premises (@p83) :args ((or @t80 @t84 (not @t85)))) % 0.39/0.59 (step @p85 :rule chain_m_resolution :premises (@p84 @p82 @p66) :args (@t84 @t78 (@list @t79 @t85))) % 0.39/0.59 (step @p86 :rule trans :premises (@p85 @p51)) % 0.39/0.59 (step @p87 :rule cong :premises (@p86 @p24) :args (@t70)) % 0.39/0.59 (step @p88 :rule cnf_or_neg :args (@t72 1)) % 0.39/0.59 (step @p89 :rule chain_m_resolution :premises (@p88 @p41) :args ((not @t70) @t73 @t74)) % 0.39/0.59 (step @p90 :rule false_intro :premises (@p89)) % 0.39/0.59 (step @p91 :rule symm :premises (@p90)) % 0.39/0.59 (step @p92 :rule trans :premises (@p91 @p87 @p23)) % 0.39/0.59 (step @p93 false :rule eq_resolve :premises (@p92 @p21)) % 0.39/0.59 ) % 0.39/0.59 % SZS output end Proof % 0.39/0.59 % cvc5 exiting %------------------------------------------------------------------------------