%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET857-2 : 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 08:48:51 AM UTC 2026 % Result : Unsatisfiable 0.43s 0.69s % Output : Proof 0.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET857-2 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n004.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 16:15:52 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.28/0.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.43/0.69 % SZS status Unsatisfiable % 0.43/0.69 % SZS output start Proof % 0.43/0.70 ( % 0.43/0.70 (declare-sort $$unsorted 0) % 0.43/0.70 (declare-const tptp.v_n $$unsorted) % 0.43/0.70 (declare-const tptp.v_Y $$unsorted) % 0.43/0.70 (declare-const tptp.t_a $$unsorted) % 0.43/0.70 (declare-const tptp.c_Zorn_OTFin__linear__lemma1__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.70 (declare-const tptp.v_x $$unsorted) % 0.43/0.70 (declare-const tptp.c_Zorn_OTFin (-> $$unsorted $$unsorted $$unsorted)) % 0.43/0.70 (declare-const tptp.v_S $$unsorted) % 0.43/0.70 (declare-const tptp.c_Zorn_Osucc (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.70 (declare-const tptp.c_lessequals (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.70 (declare-const tptp.tc_set (-> $$unsorted $$unsorted)) % 0.43/0.70 (declare-const tptp.c_Main_OsubsetI__1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.43/0.70 (declare-const tptp.c_in (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.70 (define @t1 () (@var "T_a" $$unsorted)) % 0.43/0.70 (define @t2 () (@var "V_B" $$unsorted)) % 0.43/0.70 (define @t3 () (@var "V_c" $$unsorted)) % 0.43/0.70 (define @t4 () (tptp.tc_set @t1)) % 0.43/0.70 (define @t5 () (@var "V_A" $$unsorted)) % 0.43/0.70 (define @t6 () (tptp.c_lessequals @t5 @t2 @t4)) % 0.43/0.70 (define @t7 () (tptp.c_Main_OsubsetI__1 @t5 @t2 @t1)) % 0.43/0.70 (define @t8 () (@list @t5 @t2 @t1)) % 0.43/0.70 (define @t9 () (tptp.tc_set @t4)) % 0.43/0.70 (define @t10 () (@var "V_x" $$unsorted)) % 0.43/0.70 (define @t11 () (@var "V_S" $$unsorted)) % 0.43/0.70 (define @t12 () (@var "V_n" $$unsorted)) % 0.43/0.70 (define @t13 () (@var "V_m" $$unsorted)) % 0.43/0.70 (define @t14 () (tptp.c_lessequals (tptp.c_Zorn_Osucc @t11 @t13 @t1) @t12 @t9)) % 0.43/0.70 (define @t15 () (tptp.c_lessequals @t12 @t13 @t9)) % 0.43/0.70 (define @t16 () (tptp.c_Zorn_OTFin @t11 @t1)) % 0.43/0.70 (define @t17 () (tptp.c_Zorn_OTFin__linear__lemma1__1 @t11 @t13 @t1)) % 0.43/0.70 (define @t18 () (not (tptp.c_in @t12 @t16 @t9))) % 0.43/0.70 (define @t19 () (not (tptp.c_in @t13 @t16 @t9))) % 0.43/0.70 (define @t20 () (@list @t13 @t11 @t1 @t12)) % 0.43/0.70 (define @t21 () (not (= @t17 @t13))) % 0.43/0.70 (define @t22 () (or @t19 @t18 @t21 @t15 @t14)) % 0.43/0.70 (define @t23 () (forall @t20 @t22)) % 0.43/0.70 (define @t24 () (forall @t20 (or @t19 @t18 (not (tptp.c_lessequals (tptp.c_Zorn_Osucc @t11 @t17 @t1) @t13 @t9)) @t15 @t14))) % 0.43/0.70 (define @t25 () (tptp.tc_set tptp.t_a)) % 0.43/0.70 (define @t26 () (tptp.tc_set @t25)) % 0.43/0.70 (define @t27 () (tptp.c_Zorn_OTFin tptp.v_S tptp.t_a)) % 0.43/0.70 (define @t28 () (tptp.c_lessequals tptp.v_Y @t27 (tptp.tc_set @t26))) % 0.43/0.70 (define @t29 () (tptp.c_in tptp.v_n @t27 @t26)) % 0.43/0.70 (define @t30 () (tptp.c_in tptp.v_x tptp.v_Y @t26)) % 0.43/0.70 (define @t31 () (tptp.c_lessequals tptp.v_x tptp.v_n @t26)) % 0.43/0.70 (define @t32 () (tptp.c_lessequals (tptp.c_Zorn_Osucc tptp.v_S tptp.v_n tptp.t_a) tptp.v_x @t26)) % 0.43/0.70 (define @t33 () (@var "V_U" $$unsorted)) % 0.43/0.70 (define @t34 () (@var "V_V" $$unsorted)) % 0.43/0.70 (define @t35 () (forall (@list @t34 @t33) (or (tptp.c_lessequals (tptp.c_Zorn_Osucc tptp.v_S @t34 tptp.t_a) @t33 @t26) (= @t34 @t33) (not (tptp.c_lessequals @t34 @t33 @t26)) (not (tptp.c_in @t34 @t27 @t26)) (not (tptp.c_in @t33 tptp.v_Y @t26))))) % 0.43/0.70 (define @t36 () (not @t30)) % 0.43/0.70 (define @t37 () (tptp.c_Zorn_OTFin__linear__lemma1__1 tptp.v_S tptp.v_x tptp.t_a)) % 0.43/0.70 (define @t38 () (tptp.c_in @t37 @t27 @t26)) % 0.43/0.70 (define @t39 () (not @t38)) % 0.43/0.70 (define @t40 () (tptp.c_lessequals @t37 tptp.v_x @t26)) % 0.43/0.70 (define @t41 () (not @t40)) % 0.43/0.70 (define @t42 () (tptp.c_lessequals (tptp.c_Zorn_Osucc tptp.v_S @t37 tptp.t_a) tptp.v_x @t26)) % 0.43/0.70 (define @t43 () (or @t42 (= @t37 tptp.v_x) @t41 @t39 @t36)) % 0.43/0.70 (define @t44 () (= tptp.v_x @t37)) % 0.43/0.70 (define @t45 () (or @t42 @t44 @t41 @t39 @t36)) % 0.43/0.70 (define @t46 () (@list tptp.v_x tptp.v_S tptp.t_a tptp.v_n)) % 0.43/0.70 (define @t47 () (tptp.c_Zorn_Osucc tptp.v_S tptp.v_x tptp.t_a)) % 0.43/0.70 (define @t48 () (tptp.c_Main_OsubsetI__1 tptp.v_x tptp.v_n @t25)) % 0.43/0.70 (define @t49 () (@list tptp.v_x tptp.v_n @t25)) % 0.43/0.70 (define @t50 () (tptp.c_in @t48 tptp.v_x @t25)) % 0.43/0.70 (define @t51 () (or @t50 @t31)) % 0.43/0.70 (define @t52 () (@list true false)) % 0.43/0.70 (define @t53 () (tptp.c_in @t48 @t47 @t25)) % 0.43/0.70 (define @t54 () (tptp.c_lessequals tptp.v_x @t47 @t26)) % 0.43/0.70 (define @t55 () (not @t54)) % 0.43/0.70 (define @t56 () (not @t50)) % 0.43/0.70 (define @t57 () (or @t56 @t55 @t53)) % 0.43/0.70 (define @t58 () (@list false false false)) % 0.43/0.70 (define @t59 () (tptp.c_in @t48 tptp.v_n @t25)) % 0.43/0.70 (define @t60 () (not @t59)) % 0.43/0.70 (define @t61 () (or @t60 @t31)) % 0.43/0.70 (define @t62 () (tptp.c_lessequals @t47 tptp.v_n @t26)) % 0.43/0.70 (define @t63 () (not @t62)) % 0.43/0.70 (define @t64 () (not @t53)) % 0.43/0.70 (define @t65 () (or @t64 @t63 @t59)) % 0.43/0.70 (define @t66 () (= tptp.v_n tptp.v_x)) % 0.43/0.70 (define @t67 () (not @t66)) % 0.43/0.70 (define @t68 () (and @t50 @t66 @t60)) % 0.43/0.70 (define @t69 () (not @t29)) % 0.43/0.70 (define @t70 () (tptp.c_lessequals tptp.v_n tptp.v_x @t26)) % 0.43/0.70 (define @t71 () (not @t70)) % 0.43/0.70 (define @t72 () (or @t32 @t66 @t71 @t69 @t36)) % 0.43/0.70 (define @t73 () (tptp.c_in tptp.v_x @t27 @t26)) % 0.43/0.70 (define @t74 () (not @t28)) % 0.43/0.70 (define @t75 () (or @t36 @t74 @t73)) % 0.43/0.70 (define @t76 () (not @t73)) % 0.43/0.70 (define @t77 () (or @t76 @t69 @t38 @t70 @t62)) % 0.43/0.70 (define @t78 () (@list false false true true false)) % 0.43/0.70 (define @t79 () (or @t76 @t69 @t70 @t40 @t62)) % 0.43/0.70 (define @t80 () (not @t44)) % 0.43/0.70 (define @t81 () (or @t76 @t69 @t80 @t70 @t62)) % 0.43/0.70 (define @t82 () (not @t42)) % 0.43/0.70 (define @t83 () (or @t76 @t69 @t82 @t70 @t62)) % 0.43/0.70 (define @t84 () (not @t83)) % 0.43/0.70 (assume @p1 (forall (@list @t3 @t5 @t1 @t2) (or (not (tptp.c_in @t3 @t5 @t1)) (not @t6) (tptp.c_in @t3 @t2 @t1)))) % 0.43/0.70 (assume @p2 (forall @t8 (or (tptp.c_in @t7 @t5 @t1) @t6))) % 0.43/0.70 (assume @p3 (forall @t8 (or (not (tptp.c_in @t7 @t2 @t1)) @t6))) % 0.43/0.70 (assume @p4 (forall (@list @t10 @t11 @t1) (tptp.c_lessequals @t10 (tptp.c_Zorn_Osucc @t11 @t10 @t1) @t9))) % 0.43/0.70 (assume @p5 (forall @t20 (or @t19 @t18 (tptp.c_in @t17 @t16 @t9) @t15 @t14))) % 0.43/0.70 (assume @p6 (forall @t20 (or @t19 @t18 @t15 (tptp.c_lessequals @t17 @t13 @t9) @t14))) % 0.43/0.70 (assume @p7 @t23) % 0.43/0.70 (assume @p8 @t24) % 0.43/0.70 (assume @p9 @t28) % 0.43/0.70 (assume @p10 @t29) % 0.43/0.70 (assume @p11 @t30) % 0.43/0.70 (assume @p12 (not @t31)) % 0.43/0.70 (assume @p13 (not @t32)) % 0.43/0.70 (assume @p14 @t35) % 0.43/0.70 (step @p15 :rule refl :args (@t36)) % 0.43/0.70 (step @p16 :rule refl :args (@t39)) % 0.43/0.70 (step @p17 :rule refl :args (@t41)) % 0.43/0.70 (step @p18 :rule eq-symm :args (@t37 tptp.v_x)) % 0.43/0.70 (step @p19 :rule refl :args (@t42)) % 0.43/0.70 (step @p20 :rule nary_cong :premises (@p19 @p18 @p17 @p16 @p15) :args (@t43)) % 0.43/0.70 (step @p21 :rule refl :args (@t35)) % 0.43/0.70 (step @p22 :rule cong :premises (@p21 @p20) :args ((=> @t35 @t43))) % 0.43/0.70 (assume-push @p122 @t35) % 0.43/0.70 (step @p24 :rule instantiate :premises (@p14) :args ((@list @t37 tptp.v_x))) % 0.43/0.70 (step-pop @p123 :rule scope :premises (@p24)) % 0.43/0.70 (step @p25 :rule process_scope :premises (@p123) :args (@t43)) % 0.43/0.70 (step @p27 :rule eq_resolve :premises (@p25 @p22)) % 0.43/0.70 (step @p28 :rule implies_elim :premises (@p27)) % 0.43/0.70 (step @p29 :rule chain_m_resolution :premises (@p28 @p14) :args (@t45 (@list false) (@list @t35))) % 0.43/0.70 (step @p30 :rule instantiate :premises (@p5) :args (@t46)) % 0.43/0.70 (step @p31 :rule instantiate :premises (@p1) :args ((@list @t48 @t47 @t25 tptp.v_n))) % 0.43/0.70 (step @p32 :rule instantiate :premises (@p1) :args ((@list @t48 tptp.v_x @t25 @t47))) % 0.43/0.70 (step @p33 :rule instantiate :premises (@p4) :args ((@list tptp.v_x tptp.v_S tptp.t_a))) % 0.43/0.70 (step @p34 :rule instantiate :premises (@p2) :args (@t49)) % 0.43/0.70 (step @p35 :rule cnf_or_pos :args (@t51)) % 0.43/0.70 (step @p36 :rule reordering :premises (@p35) :args ((or @t31 @t50 (not @t51)))) % 0.43/0.70 (step @p37 :rule chain_m_resolution :premises (@p36 @p12 @p34) :args (@t50 @t52 (@list @t31 @t51))) % 0.43/0.70 (step @p38 :rule cnf_or_pos :args (@t57)) % 0.43/0.70 (step @p39 :rule reordering :premises (@p38) :args ((or @t56 @t55 @t53 (not @t57)))) % 0.43/0.70 (step @p40 :rule chain_m_resolution :premises (@p39 @p37 @p33 @p32) :args (@t53 @t58 (@list @t50 @t54 @t57))) % 0.43/0.70 (step @p41 :rule instantiate :premises (@p3) :args (@t49)) % 0.43/0.70 (step @p42 :rule cnf_or_pos :args (@t61)) % 0.43/0.70 (step @p43 :rule reordering :premises (@p42) :args ((or @t31 @t60 (not @t61)))) % 0.43/0.70 (step @p44 :rule chain_m_resolution :premises (@p43 @p12 @p41) :args (@t60 @t52 (@list @t31 @t61))) % 0.43/0.70 (step @p45 :rule cnf_or_pos :args (@t65)) % 0.43/0.70 (step @p46 :rule reordering :premises (@p45) :args ((or @t59 @t63 @t64 (not @t65)))) % 0.43/0.70 (step @p47 :rule chain_m_resolution :premises (@p46 @p44 @p40 @p31) :args (@t63 (@list true false false) (@list @t59 @t53 @t65))) % 0.43/0.70 (step @p48 :rule instantiate :premises (@p14) :args ((@list tptp.v_n tptp.v_x))) % 0.43/0.70 (step @p49 :rule refl :args (@t67)) % 0.43/0.70 (step @p50 :rule bool-double-not-elim :args (@t59)) % 0.43/0.70 (step @p51 :rule refl :args (@t56)) % 0.43/0.70 (step @p52 :rule nary_cong :premises (@p51 @p50 @p49) :args ((or @t56 (not @t60) @t67))) % 0.43/0.70 (assume-push @p124 @t50) % 0.43/0.70 (assume-push @p125 @t66) % 0.43/0.70 (assume-push @p126 @t60) % 0.43/0.70 (step @p56 :rule evaluate :args ((= false true))) % 0.43/0.70 (step @p57 :rule true_intro :premises (@p37)) % 0.43/0.70 (step @p58 :rule refl :args (@t25)) % 0.43/0.70 (step @p59 :rule refl :args (@t48)) % 0.43/0.70 (step @p60 :rule cong :premises (@p59 @p125 @p58) :args (@t59)) % 0.43/0.70 (step @p61 :rule false_intro :premises (@p44)) % 0.43/0.70 (step @p62 :rule symm :premises (@p61)) % 0.43/0.70 (step @p63 :rule trans :premises (@p62 @p60 @p57)) % 0.43/0.70 (step @p64 false :rule eq_resolve :premises (@p63 @p56)) % 0.43/0.70 (step-pop @p127 :rule scope :premises (@p64)) % 0.43/0.70 (step-pop @p128 :rule scope :premises (@p127)) % 0.43/0.70 (step-pop @p129 :rule scope :premises (@p128)) % 0.43/0.70 (step @p65 :rule process_scope :premises (@p129) :args (false)) % 0.43/0.70 (assume-push @p130 @t50) % 0.43/0.70 (assume-push @p131 @t60) % 0.43/0.70 (assume-push @p132 @t66) % 0.43/0.70 (step @p72 :rule and_intro :premises (@p37 @p132 @p44)) % 0.43/0.70 (step-pop @p133 :rule scope :premises (@p72)) % 0.43/0.70 (step-pop @p134 :rule scope :premises (@p133)) % 0.43/0.70 (step-pop @p135 :rule scope :premises (@p134)) % 0.43/0.70 (step @p73 :rule process_scope :premises (@p135) :args (@t68)) % 0.43/0.70 (step @p77 :rule implies_elim :premises (@p73)) % 0.43/0.70 (step @p78 :rule resolution :premises (@p77 @p65) :args (true @t68)) % 0.43/0.70 (step @p79 :rule not_and :premises (@p78)) % 0.43/0.70 (step @p80 :rule eq_resolve :premises (@p79 @p52)) % 0.43/0.70 (step @p81 :rule reordering :premises (@p80) :args ((or @t59 @t56 @t67))) % 0.43/0.70 (step @p82 :rule chain_m_resolution :premises (@p81 @p44 @p37) :args (@t67 @t52 (@list @t59 @t50))) % 0.43/0.70 (step @p83 :rule cnf_or_pos :args (@t72)) % 0.43/0.70 (step @p84 :rule reordering :premises (@p83) :args ((or @t32 @t69 @t36 @t66 @t71 (not @t72)))) % 0.43/0.70 (step @p85 :rule chain_m_resolution :premises (@p84 @p13 @p10 @p11 @p82 @p48) :args (@t71 (@list true false false true false) (@list @t32 @t29 @t30 @t66 @t72))) % 0.43/0.70 (step @p86 :rule instantiate :premises (@p1) :args ((@list tptp.v_x tptp.v_Y @t26 @t27))) % 0.43/0.70 (step @p87 :rule cnf_or_pos :args (@t75)) % 0.43/0.70 (step @p88 :rule reordering :premises (@p87) :args ((or @t74 @t36 @t73 (not @t75)))) % 0.43/0.70 (step @p89 :rule chain_m_resolution :premises (@p88 @p9 @p11 @p86) :args (@t73 @t58 (@list @t28 @t30 @t75))) % 0.43/0.70 (step @p90 :rule cnf_or_pos :args (@t77)) % 0.43/0.70 (step @p91 :rule reordering :premises (@p90) :args ((or @t69 @t76 @t70 @t62 @t38 (not @t77)))) % 0.43/0.70 (step @p92 :rule chain_m_resolution :premises (@p91 @p10 @p89 @p85 @p47 @p30) :args (@t38 @t78 (@list @t29 @t73 @t70 @t62 @t77))) % 0.43/0.70 (step @p93 :rule instantiate :premises (@p6) :args (@t46)) % 0.43/0.70 (step @p94 :rule cnf_or_pos :args (@t79)) % 0.43/0.70 (step @p95 :rule reordering :premises (@p94) :args ((or @t69 @t76 @t70 @t40 @t62 (not @t79)))) % 0.43/0.70 (step @p96 :rule chain_m_resolution :premises (@p95 @p10 @p89 @p85 @p47 @p93) :args (@t40 @t78 (@list @t29 @t73 @t70 @t62 @t79))) % 0.43/0.70 (step @p97 :rule refl :args (@t14)) % 0.43/0.70 (step @p98 :rule refl :args (@t15)) % 0.43/0.70 (step @p99 :rule eq-symm :args (@t17 @t13)) % 0.43/0.70 (step @p100 :rule cong :premises (@p99) :args (@t21)) % 0.43/0.70 (step @p101 :rule refl :args (@t18)) % 0.43/0.70 (step @p102 :rule refl :args (@t19)) % 0.43/0.70 (step @p103 :rule nary_cong :premises (@p102 @p101 @p100 @p98 @p97) :args (@t22)) % 0.43/0.70 (step @p104 :rule cong :premises (@p103) :args (@t23)) % 0.43/0.70 (step @p105 :rule eq_resolve :premises (@p7 @p104)) % 0.43/0.70 (step @p106 :rule instantiate :premises (@p105) :args (@t46)) % 0.43/0.70 (step @p107 :rule cnf_or_pos :args (@t81)) % 0.43/0.70 (step @p108 :rule reordering :premises (@p107) :args ((or @t69 @t76 @t70 @t62 @t80 (not @t81)))) % 0.43/0.70 (step @p109 :rule chain_m_resolution :premises (@p108 @p10 @p89 @p85 @p47 @p106) :args (@t80 @t78 (@list @t29 @t73 @t70 @t62 @t81))) % 0.43/0.70 (step @p110 :rule cnf_or_pos :args (@t45)) % 0.43/0.70 (step @p111 :rule reordering :premises (@p110) :args ((or @t36 @t44 @t42 @t41 @t39 (not @t45)))) % 0.43/0.70 (step @p112 :rule chain_m_resolution :premises (@p111 @p11 @p109 @p96 @p92 @p29) :args (@t42 (@list false true false false false) (@list @t30 @t44 @t40 @t38 @t45))) % 0.43/0.70 (step @p113 :rule cnf_or_pos :args (@t83)) % 0.43/0.70 (step @p114 :rule reordering :premises (@p113) :args ((or @t69 @t76 @t70 @t62 @t82 @t84))) % 0.43/0.70 (step @p115 :rule chain_m_resolution :premises (@p114 @p10 @p89 @p85 @p47 @p112) :args (@t84 @t78 (@list @t29 @t73 @t70 @t62 @t42))) % 0.43/0.70 (assume-push @p136 @t24) % 0.43/0.70 (step @p117 :rule instantiate :premises (@p8) :args (@t46)) % 0.43/0.70 (step-pop @p137 :rule scope :premises (@p117)) % 0.43/0.70 (step @p118 :rule process_scope :premises (@p137) :args (@t83)) % 0.43/0.70 (step @p120 :rule implies_elim :premises (@p118)) % 0.43/0.70 (step @p121 false :rule chain_m_resolution :premises (@p120 @p115 @p8) :args (false @t52 (@list @t83 @t24))) % 0.43/0.70 ) % 0.33/0.70 % SZS output end Proof % 0.33/0.70 % cvc5 exiting %------------------------------------------------------------------------------