%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET862-2 : 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 : n004.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 08:48:52 AM UTC 2026 % Result : Unsatisfiable 0.38s 0.62s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET862-2 : TPTP v9.2.1. Released v3.2.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n004.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 16:16:07 EDT 2026 % 0.18/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.31/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.62 % SZS status Unsatisfiable % 0.38/0.62 % SZS output start Proof % 0.38/0.62 ( % 0.38/0.62 (declare-sort $$unsorted 0) % 0.38/0.62 (declare-const tptp.v_x (-> $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.v_y $$unsorted) % 0.38/0.62 (declare-const tptp.v_c $$unsorted) % 0.38/0.62 (declare-const tptp.t_a $$unsorted) % 0.38/0.62 (declare-const tptp.c_in (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.c_Main_OsubsetI__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.c_lessequals (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.62 (declare-const tptp.c_emptyset $$unsorted) % 0.38/0.62 (declare-const tptp.tc_set (-> $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.c_Zorn_Ochain (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.c_Zorn_Omaxchain__super__lemma__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.c_insert (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.c_union (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.c_Zorn_Ochain__extend__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.c_Zorn_Omaxchain (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.62 (declare-const tptp.v_S $$unsorted) % 0.38/0.62 (define @t1 () (@var "V_B" $$unsorted)) % 0.38/0.62 (define @t2 () (@var "V_A" $$unsorted)) % 0.38/0.62 (define @t3 () (@var "T_a" $$unsorted)) % 0.38/0.62 (define @t4 () (tptp.tc_set @t3)) % 0.38/0.62 (define @t5 () (tptp.c_lessequals @t2 @t1 @t4)) % 0.38/0.62 (define @t6 () (not @t5)) % 0.38/0.62 (define @t7 () (not (tptp.c_lessequals @t1 @t2 @t4))) % 0.38/0.62 (define @t8 () (or @t7 @t6 (= @t2 @t1))) % 0.38/0.62 (define @t9 () (forall (@list @t1 @t2 @t3) @t8)) % 0.38/0.62 (define @t10 () (@var "V_c" $$unsorted)) % 0.38/0.62 (define @t11 () (tptp.c_Main_OsubsetI__1 @t2 @t1 @t3)) % 0.38/0.62 (define @t12 () (@list @t2 @t1 @t3)) % 0.38/0.62 (define @t13 () (tptp.tc_set @t4)) % 0.38/0.62 (define @t14 () (@var "V_S" $$unsorted)) % 0.38/0.62 (define @t15 () (tptp.c_Zorn_Ochain @t14 @t3)) % 0.38/0.62 (define @t16 () (@var "V_z" $$unsorted)) % 0.38/0.62 (define @t17 () (tptp.c_in (tptp.c_union (tptp.c_insert @t16 tptp.c_emptyset @t4) @t10 @t4) @t15 @t13)) % 0.38/0.62 (define @t18 () (tptp.c_Zorn_Ochain__extend__1 @t10 @t16 @t3)) % 0.38/0.62 (define @t19 () (not (tptp.c_in @t10 @t15 @t13))) % 0.38/0.62 (define @t20 () (not (tptp.c_in @t16 @t14 @t4))) % 0.38/0.62 (define @t21 () (@list @t16 @t14 @t3 @t10)) % 0.38/0.62 (define @t22 () (@var "V_y" $$unsorted)) % 0.38/0.62 (define @t23 () (tptp.c_Zorn_Omaxchain__super__lemma__1 @t10 @t22 @t3)) % 0.38/0.62 (define @t24 () (tptp.c_in @t16 @t22 @t3)) % 0.38/0.62 (define @t25 () (@var "V_x" $$unsorted)) % 0.38/0.62 (define @t26 () (not (tptp.c_in (tptp.c_union (tptp.c_insert @t25 tptp.c_emptyset @t4) @t10 @t4) @t15 @t13))) % 0.38/0.62 (define @t27 () (not (tptp.c_in @t10 (tptp.c_Zorn_Omaxchain @t14 @t3) @t13))) % 0.38/0.62 (define @t28 () (not (tptp.c_in @t16 @t25 @t3))) % 0.38/0.62 (define @t29 () (@list @t16 @t25 @t3 @t10 @t14 @t22)) % 0.38/0.62 (define @t30 () (tptp.tc_set tptp.t_a)) % 0.38/0.62 (define @t31 () (tptp.tc_set @t30)) % 0.38/0.62 (define @t32 () (tptp.c_in tptp.v_c (tptp.c_Zorn_Omaxchain tptp.v_S tptp.t_a) @t31)) % 0.38/0.62 (define @t33 () (tptp.c_Zorn_Ochain tptp.v_S tptp.t_a)) % 0.38/0.62 (define @t34 () (tptp.c_in tptp.v_c @t33 @t31)) % 0.38/0.62 (define @t35 () (tptp.c_in tptp.v_y tptp.v_S @t30)) % 0.38/0.62 (define @t36 () (@var "V_U" $$unsorted)) % 0.38/0.62 (define @t37 () (@list @t36)) % 0.38/0.62 (define @t38 () (not (tptp.c_in @t36 tptp.v_S @t30))) % 0.38/0.62 (define @t39 () (tptp.v_x @t36)) % 0.38/0.62 (define @t40 () (tptp.v_x tptp.v_y)) % 0.38/0.62 (define @t41 () (@list @t40 tptp.v_S tptp.t_a tptp.v_c)) % 0.38/0.62 (define @t42 () (@list @t40 tptp.v_y tptp.t_a)) % 0.38/0.62 (define @t43 () (@list tptp.v_y)) % 0.38/0.62 (define @t44 () (not @t35)) % 0.38/0.62 (define @t45 () (tptp.c_lessequals tptp.v_y @t40 @t30)) % 0.38/0.62 (define @t46 () (or @t45 @t44)) % 0.38/0.62 (define @t47 () (@list false false)) % 0.38/0.62 (define @t48 () (= tptp.v_y @t40)) % 0.38/0.62 (define @t49 () (not @t48)) % 0.38/0.62 (define @t50 () (or @t49 @t44)) % 0.38/0.62 (define @t51 () (tptp.c_lessequals @t40 tptp.v_y @t30)) % 0.38/0.62 (define @t52 () (not @t51)) % 0.38/0.62 (define @t53 () (not @t45)) % 0.38/0.62 (define @t54 () (or @t53 @t52 @t48)) % 0.38/0.62 (define @t55 () (tptp.c_Main_OsubsetI__1 @t40 tptp.v_y tptp.t_a)) % 0.38/0.62 (define @t56 () (tptp.c_in @t55 @t40 tptp.t_a)) % 0.38/0.62 (define @t57 () (or @t56 @t51)) % 0.38/0.62 (define @t58 () (@list true false)) % 0.38/0.62 (define @t59 () (tptp.c_in @t55 tptp.v_y tptp.t_a)) % 0.38/0.62 (define @t60 () (not @t59)) % 0.38/0.62 (define @t61 () (or @t60 @t51)) % 0.38/0.62 (define @t62 () (@list @t55 @t40 tptp.t_a tptp.v_c tptp.v_S tptp.v_y)) % 0.38/0.62 (define @t63 () (tptp.c_Zorn_Omaxchain__super__lemma__1 tptp.v_c tptp.v_y tptp.t_a)) % 0.38/0.62 (define @t64 () (tptp.c_lessequals @t63 tptp.v_y @t30)) % 0.38/0.62 (define @t65 () (not @t64)) % 0.38/0.62 (define @t66 () (tptp.c_in (tptp.c_union (tptp.c_insert @t40 tptp.c_emptyset @t30) tptp.v_c @t30) @t33 @t31)) % 0.38/0.62 (define @t67 () (not @t66)) % 0.38/0.62 (define @t68 () (not @t32)) % 0.38/0.62 (define @t69 () (not @t56)) % 0.38/0.62 (define @t70 () (or @t69 @t68 @t67 @t65 @t59)) % 0.38/0.62 (define @t71 () (tptp.c_in @t63 tptp.v_c @t30)) % 0.38/0.62 (define @t72 () (or @t69 @t68 @t67 @t59 @t71)) % 0.38/0.62 (define @t73 () (not @t71)) % 0.38/0.62 (define @t74 () (or @t64 @t73)) % 0.38/0.62 (define @t75 () (tptp.c_in @t40 tptp.v_S @t30)) % 0.38/0.62 (define @t76 () (or @t75 @t44)) % 0.38/0.62 (define @t77 () (tptp.c_Zorn_Ochain__extend__1 tptp.v_c @t40 tptp.t_a)) % 0.38/0.62 (define @t78 () (tptp.c_lessequals @t77 @t40 @t30)) % 0.38/0.62 (define @t79 () (not @t78)) % 0.38/0.62 (define @t80 () (not @t34)) % 0.38/0.62 (define @t81 () (not @t75)) % 0.38/0.62 (define @t82 () (or @t81 @t80 @t79 @t66)) % 0.38/0.62 (define @t83 () (@list false false true false)) % 0.38/0.62 (define @t84 () (tptp.c_in @t77 tptp.v_c @t30)) % 0.38/0.62 (define @t85 () (or @t81 @t80 @t84 @t66)) % 0.38/0.62 (define @t86 () (not @t84)) % 0.38/0.62 (define @t87 () (tptp.c_lessequals @t77 tptp.v_y @t30)) % 0.38/0.62 (define @t88 () (or @t87 @t86)) % 0.38/0.62 (define @t89 () (@list @t77 @t40 tptp.t_a)) % 0.38/0.62 (define @t90 () (tptp.c_Main_OsubsetI__1 @t77 @t40 tptp.t_a)) % 0.38/0.62 (define @t91 () (tptp.c_in @t90 @t77 tptp.t_a)) % 0.38/0.62 (define @t92 () (or @t91 @t78)) % 0.38/0.62 (define @t93 () (tptp.c_in @t90 @t40 tptp.t_a)) % 0.38/0.62 (define @t94 () (not @t93)) % 0.38/0.62 (define @t95 () (or @t94 @t78)) % 0.38/0.62 (define @t96 () (tptp.c_in @t90 tptp.v_y tptp.t_a)) % 0.38/0.62 (define @t97 () (not @t87)) % 0.38/0.62 (define @t98 () (not @t91)) % 0.38/0.62 (define @t99 () (or @t98 @t97 @t96)) % 0.38/0.62 (define @t100 () (not @t96)) % 0.38/0.62 (define @t101 () (or @t100 @t53 @t93)) % 0.38/0.62 (assume @p1 @t9) % 0.38/0.62 (assume @p2 (forall (@list @t10 @t2 @t3 @t1) (or (not (tptp.c_in @t10 @t2 @t3)) @t6 (tptp.c_in @t10 @t1 @t3)))) % 0.38/0.62 (assume @p3 (forall @t12 (or (tptp.c_in @t11 @t2 @t3) @t5))) % 0.38/0.62 (assume @p4 (forall @t12 (or (not (tptp.c_in @t11 @t1 @t3)) @t5))) % 0.38/0.62 (assume @p5 (forall @t21 (or @t20 @t19 (tptp.c_in @t18 @t10 @t4) @t17))) % 0.38/0.62 (assume @p6 (forall @t21 (or @t20 @t19 (not (tptp.c_lessequals @t18 @t16 @t4)) @t17))) % 0.38/0.62 (assume @p7 (forall @t29 (or @t28 @t27 @t26 @t24 (tptp.c_in @t23 @t10 @t4)))) % 0.38/0.62 (assume @p8 (forall @t29 (or @t28 @t27 @t26 (not (tptp.c_lessequals @t23 @t22 @t4)) @t24))) % 0.38/0.62 (assume @p9 @t32) % 0.38/0.62 (assume @p10 @t34) % 0.38/0.62 (assume @p11 @t35) % 0.38/0.62 (assume @p12 (forall @t37 (or (tptp.c_lessequals @t36 tptp.v_y @t30) (not (tptp.c_in @t36 tptp.v_c @t30))))) % 0.38/0.62 (assume @p13 (forall @t37 (or (tptp.c_in @t39 tptp.v_S @t30) @t38))) % 0.38/0.62 (assume @p14 (forall @t37 (or (tptp.c_lessequals @t36 @t39 @t30) @t38))) % 0.38/0.62 (assume @p15 (forall @t37 (or (not (= @t36 @t39)) @t38))) % 0.38/0.62 (step @p16 :rule instantiate :premises (@p6) :args (@t41)) % 0.38/0.62 (step @p17 :rule instantiate :premises (@p3) :args (@t42)) % 0.38/0.62 (step @p18 :rule eq-symm :args (@t2 @t1)) % 0.38/0.62 (step @p19 :rule refl :args (@t6)) % 0.38/0.62 (step @p20 :rule refl :args (@t7)) % 0.38/0.62 (step @p21 :rule nary_cong :premises (@p20 @p19 @p18) :args (@t8)) % 0.38/0.62 (step @p22 :rule cong :premises (@p21) :args (@t9)) % 0.38/0.62 (step @p23 :rule eq_resolve :premises (@p1 @p22)) % 0.38/0.62 (step @p24 :rule instantiate :premises (@p23) :args ((@list tptp.v_y @t40 tptp.t_a))) % 0.38/0.62 (step @p25 :rule instantiate :premises (@p14) :args (@t43)) % 0.38/0.62 (step @p26 :rule cnf_or_pos :args (@t46)) % 0.38/0.62 (step @p27 :rule reordering :premises (@p26) :args ((or @t44 @t45 (not @t46)))) % 0.38/0.62 (step @p28 :rule chain_m_resolution :premises (@p27 @p11 @p25) :args (@t45 @t47 (@list @t35 @t46))) % 0.38/0.62 (step @p29 :rule instantiate :premises (@p15) :args (@t43)) % 0.38/0.62 (step @p30 :rule cnf_or_pos :args (@t50)) % 0.38/0.62 (step @p31 :rule reordering :premises (@p30) :args ((or @t44 @t49 (not @t50)))) % 0.38/0.62 (step @p32 :rule chain_m_resolution :premises (@p31 @p11 @p29) :args (@t49 @t47 (@list @t35 @t50))) % 0.38/0.62 (step @p33 :rule cnf_or_pos :args (@t54)) % 0.38/0.62 (step @p34 :rule reordering :premises (@p33) :args ((or @t48 @t53 @t52 (not @t54)))) % 0.38/0.62 (step @p35 :rule chain_m_resolution :premises (@p34 @p32 @p28 @p24) :args (@t52 (@list true false false) (@list @t48 @t45 @t54))) % 0.38/0.62 (step @p36 :rule cnf_or_pos :args (@t57)) % 0.38/0.62 (step @p37 :rule reordering :premises (@p36) :args ((or @t51 @t56 (not @t57)))) % 0.38/0.62 (step @p38 :rule chain_m_resolution :premises (@p37 @p35 @p17) :args (@t56 @t58 (@list @t51 @t57))) % 0.38/0.62 (step @p39 :rule instantiate :premises (@p4) :args (@t42)) % 0.38/0.62 (step @p40 :rule cnf_or_pos :args (@t61)) % 0.38/0.62 (step @p41 :rule reordering :premises (@p40) :args ((or @t51 @t60 (not @t61)))) % 0.38/0.62 (step @p42 :rule chain_m_resolution :premises (@p41 @p35 @p39) :args (@t60 @t58 (@list @t51 @t61))) % 0.38/0.62 (step @p43 :rule instantiate :premises (@p8) :args (@t62)) % 0.38/0.62 (step @p44 :rule cnf_or_pos :args (@t70)) % 0.38/0.62 (step @p45 :rule reordering :premises (@p44) :args ((or @t68 @t59 @t69 @t67 @t65 (not @t70)))) % 0.38/0.62 (step @p46 :rule instantiate :premises (@p7) :args (@t62)) % 0.38/0.62 (step @p47 :rule cnf_or_pos :args (@t72)) % 0.38/0.62 (step @p48 :rule reordering :premises (@p47) :args ((or @t68 @t59 @t69 @t67 @t71 (not @t72)))) % 0.38/0.62 (step @p49 :rule instantiate :premises (@p12) :args ((@list @t63))) % 0.38/0.62 (step @p50 :rule cnf_or_pos :args (@t74)) % 0.38/0.62 (step @p51 :rule reordering :premises (@p50) :args ((or @t64 @t73 (not @t74)))) % 0.38/0.62 (step @p52 :rule chain_m_resolution :premises (@p51 @p49 @p48 @p46 @p42 @p38 @p9 @p45 @p43 @p42 @p38 @p9) :args (@t67 (@list false false false true false false true false true false false) (@list @t74 @t71 @t72 @t59 @t56 @t32 @t64 @t70 @t59 @t56 @t32))) % 0.38/0.62 (step @p53 :rule instantiate :premises (@p13) :args (@t43)) % 0.38/0.62 (step @p54 :rule cnf_or_pos :args (@t76)) % 0.38/0.62 (step @p55 :rule reordering :premises (@p54) :args ((or @t44 @t75 (not @t76)))) % 0.38/0.62 (step @p56 :rule chain_m_resolution :premises (@p55 @p11 @p53) :args (@t75 @t47 (@list @t35 @t76))) % 0.38/0.62 (step @p57 :rule cnf_or_pos :args (@t82)) % 0.38/0.62 (step @p58 :rule reordering :premises (@p57) :args ((or @t80 @t81 @t66 @t79 (not @t82)))) % 0.38/0.62 (step @p59 :rule chain_m_resolution :premises (@p58 @p10 @p56 @p52 @p16) :args (@t79 @t83 (@list @t34 @t75 @t66 @t82))) % 0.38/0.62 (step @p60 :rule instantiate :premises (@p12) :args ((@list @t77))) % 0.38/0.62 (step @p61 :rule instantiate :premises (@p5) :args (@t41)) % 0.38/0.62 (step @p62 :rule cnf_or_pos :args (@t85)) % 0.38/0.62 (step @p63 :rule reordering :premises (@p62) :args ((or @t80 @t81 @t66 @t84 (not @t85)))) % 0.38/0.62 (step @p64 :rule chain_m_resolution :premises (@p63 @p10 @p56 @p52 @p61) :args (@t84 @t83 (@list @t34 @t75 @t66 @t85))) % 0.38/0.62 (step @p65 :rule cnf_or_pos :args (@t88)) % 0.38/0.62 (step @p66 :rule reordering :premises (@p65) :args ((or @t86 @t87 (not @t88)))) % 0.38/0.62 (step @p67 :rule chain_m_resolution :premises (@p66 @p64 @p60) :args (@t87 @t47 (@list @t84 @t88))) % 0.38/0.62 (step @p68 :rule instantiate :premises (@p3) :args (@t89)) % 0.38/0.62 (step @p69 :rule cnf_or_pos :args (@t92)) % 0.38/0.62 (step @p70 :rule reordering :premises (@p69) :args ((or @t78 @t91 (not @t92)))) % 0.38/0.62 (step @p71 :rule instantiate :premises (@p4) :args (@t89)) % 0.38/0.62 (step @p72 :rule cnf_or_pos :args (@t95)) % 0.38/0.62 (step @p73 :rule reordering :premises (@p72) :args ((or @t78 @t94 (not @t95)))) % 0.38/0.62 (step @p74 :rule instantiate :premises (@p2) :args ((@list @t90 @t77 tptp.t_a tptp.v_y))) % 0.38/0.62 (step @p75 :rule cnf_or_pos :args (@t99)) % 0.38/0.62 (step @p76 :rule reordering :premises (@p75) :args ((or @t98 @t97 @t96 (not @t99)))) % 0.38/0.62 (step @p77 :rule instantiate :premises (@p2) :args ((@list @t90 tptp.v_y tptp.t_a @t40))) % 0.38/0.62 (step @p78 :rule cnf_or_pos :args (@t101)) % 0.38/0.62 (step @p79 :rule reordering :premises (@p78) :args ((or @t53 @t93 @t100 (not @t101)))) % 0.38/0.62 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p28 @p76 @p74 @p73 @p71 @p70 @p68) :args ((or @t78 @t97) (@list false false false false true false false false) (@list @t101 @t45 @t96 @t99 @t93 @t95 @t91 @t92))) % 0.38/0.62 (step @p81 false :rule chain_m_resolution :premises (@p80 @p67 @p59) :args (false (@list false true) (@list @t87 @t78))) % 0.38/0.62 ) % 0.38/0.62 % SZS output end Proof % 0.38/0.62 % cvc5 exiting %------------------------------------------------------------------------------