%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM410+1 : TPTP v9.2.1. Released 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 : n014.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 08:39:19 AM UTC 2026 % Result : Theorem 0.38s 0.60s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM410+1 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n014.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 11:16:43 EDT 2026 % 0.18/0.34 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.60 % SZS status Theorem % 0.38/0.60 % SZS output start Proof % 0.38/0.60 ( % 0.38/0.60 (declare-sort $$unsorted 0) % 0.38/0.60 (declare-const tptp.relation_non_empty (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.empty_set $$unsorted) % 0.38/0.60 (declare-const tptp.with_non_empty_elements (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.function (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.38/0.60 (declare-const tptp.transfinite_sequence (-> $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (declare-const tptp.transfinite_sequence_of (-> $$unsorted $$unsorted Bool)) % 0.38/0.60 (define @t1 () (@var "A" $$unsorted)) % 0.38/0.60 (define @t2 () (@var "B" $$unsorted)) % 0.38/0.60 (define @t3 () (tptp.in @t1 @t2)) % 0.38/0.60 (define @t4 () (@list @t1 @t2)) % 0.38/0.60 (define @t5 () (tptp.function @t1)) % 0.38/0.60 (define @t6 () (tptp.empty @t1)) % 0.38/0.60 (define @t7 () (@list @t1)) % 0.38/0.60 (define @t8 () (tptp.epsilon_connected @t1)) % 0.38/0.60 (define @t9 () (tptp.epsilon_transitive @t1)) % 0.38/0.60 (define @t10 () (and @t9 @t8)) % 0.38/0.60 (define @t11 () (tptp.ordinal @t1)) % 0.38/0.60 (define @t12 () (tptp.relation @t1)) % 0.38/0.60 (define @t13 () (tptp.one_to_one @t1)) % 0.38/0.60 (define @t14 () (and @t12 @t5 @t13)) % 0.38/0.60 (define @t15 () (and @t12 @t6 @t5)) % 0.38/0.60 (define @t16 () (and @t9 @t8 @t11)) % 0.38/0.60 (define @t17 () (tptp.relation_dom @t1)) % 0.38/0.60 (define @t18 () (tptp.ordinal @t17)) % 0.38/0.60 (define @t19 () (tptp.transfinite_sequence @t1)) % 0.38/0.60 (define @t20 () (= @t19 @t18)) % 0.38/0.60 (define @t21 () (and @t12 @t5)) % 0.38/0.60 (define @t22 () (forall @t7 (=> @t21 @t20))) % 0.38/0.60 (define @t23 () (tptp.transfinite_sequence_of @t2 @t1)) % 0.38/0.60 (define @t24 () (= @t23 (tptp.subset (tptp.relation_rng @t2) @t1))) % 0.38/0.60 (define @t25 () (tptp.transfinite_sequence @t2)) % 0.38/0.60 (define @t26 () (tptp.function @t2)) % 0.38/0.60 (define @t27 () (tptp.relation @t2)) % 0.38/0.60 (define @t28 () (and @t27 @t26 @t25)) % 0.38/0.60 (define @t29 () (forall @t4 (=> @t28 @t24))) % 0.38/0.60 (define @t30 () (@list @t2)) % 0.38/0.60 (define @t31 () (tptp.relation_empty_yielding tptp.empty_set)) % 0.38/0.60 (define @t32 () (tptp.relation tptp.empty_set)) % 0.38/0.60 (define @t33 () (tptp.empty tptp.empty_set)) % 0.38/0.60 (define @t34 () (tptp.empty @t17)) % 0.38/0.60 (define @t35 () (not @t6)) % 0.38/0.60 (define @t36 () (and @t35 @t12)) % 0.38/0.60 (define @t37 () (tptp.relation_rng @t1)) % 0.38/0.60 (define @t38 () (and @t12 (tptp.relation_non_empty @t1) @t5)) % 0.38/0.60 (define @t39 () (tptp.empty @t37)) % 0.38/0.60 (define @t40 () (tptp.relation_empty_yielding @t1)) % 0.38/0.60 (define @t41 () (tptp.subset @t1 @t1)) % 0.38/0.60 (define @t42 () (forall @t4 @t41)) % 0.38/0.60 (define @t43 () (tptp.element @t1 @t2)) % 0.38/0.60 (define @t44 () (tptp.empty @t2)) % 0.38/0.60 (define @t45 () (tptp.transfinite_sequence_of @t1 @t37)) % 0.38/0.60 (define @t46 () (=> @t18 @t45)) % 0.38/0.60 (define @t47 () (forall @t7 (=> @t21 @t46))) % 0.38/0.60 (define @t48 () (not @t47)) % 0.38/0.60 (define @t49 () (@var "C" $$unsorted)) % 0.38/0.60 (define @t50 () (tptp.element @t2 (tptp.powerset @t49))) % 0.38/0.60 (define @t51 () (@list @t1 @t2 @t49)) % 0.38/0.60 (define @t52 () (forall @t7 @t41)) % 0.38/0.60 (define @t53 () (not @t25)) % 0.38/0.60 (define @t54 () (not @t26)) % 0.38/0.60 (define @t55 () (not @t27)) % 0.38/0.60 (define @t56 () (or @t55 @t54 @t53)) % 0.38/0.60 (define @t57 () (not @t18)) % 0.38/0.60 (define @t58 () (not @t5)) % 0.38/0.60 (define @t59 () (not @t12)) % 0.38/0.60 (define @t60 () (or @t59 @t58 @t57 @t45)) % 0.38/0.60 (define @t61 () (@quantifiers_skolemize (forall @t7 @t60) 0)) % 0.38/0.60 (define @t62 () (tptp.relation_rng @t61)) % 0.38/0.60 (define @t63 () (or @t59 @t58 @t20)) % 0.38/0.60 (define @t64 () (or @t59 @t58)) % 0.38/0.60 (define @t65 () (not @t21)) % 0.38/0.60 (define @t66 () (tptp.transfinite_sequence @t61)) % 0.38/0.60 (define @t67 () (tptp.ordinal (tptp.relation_dom @t61))) % 0.38/0.60 (define @t68 () (tptp.function @t61)) % 0.38/0.60 (define @t69 () (not @t68)) % 0.38/0.60 (define @t70 () (tptp.relation @t61)) % 0.38/0.60 (define @t71 () (not @t70)) % 0.38/0.60 (define @t72 () (or @t71 @t69 (= @t66 @t67))) % 0.38/0.60 (define @t73 () (forall @t7 @t63)) % 0.38/0.60 (define @t74 () (= @t67 @t66)) % 0.38/0.60 (define @t75 () (or @t71 @t69 @t74)) % 0.38/0.60 (define @t76 () (tptp.transfinite_sequence_of @t61 @t62)) % 0.38/0.60 (define @t77 () (not @t67)) % 0.38/0.60 (define @t78 () (or @t71 @t69 @t77 @t76)) % 0.38/0.60 (define @t79 () (@list true)) % 0.38/0.60 (define @t80 () (@list @t78)) % 0.38/0.60 (define @t81 () (tptp.subset @t62 @t62)) % 0.38/0.60 (define @t82 () (= @t76 @t81)) % 0.38/0.60 (define @t83 () (not @t66)) % 0.38/0.60 (define @t84 () (or @t71 @t69 @t83 @t82)) % 0.38/0.60 (define @t85 () (not @t81)) % 0.38/0.60 (define @t86 () (@list true false)) % 0.38/0.60 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 0.38/0.60 (assume @p2 (forall @t7 (=> @t6 @t5))) % 0.38/0.60 (assume @p3 (forall @t7 (=> @t11 @t10))) % 0.38/0.60 (assume @p4 (forall @t7 (=> @t6 @t12))) % 0.38/0.60 (assume @p5 (forall @t7 (=> @t15 @t14))) % 0.38/0.60 (assume @p6 (forall @t7 (=> @t10 @t11))) % 0.38/0.60 (assume @p7 (forall @t7 (=> @t6 @t16))) % 0.38/0.60 (assume @p8 @t22) % 0.38/0.60 (assume @p9 @t29) % 0.38/0.60 (assume @p10 (forall @t4 (=> @t23 @t28))) % 0.38/0.60 (assume @p11 (forall @t7 (exists @t30 @t23))) % 0.38/0.60 (assume @p12 (forall @t7 (exists @t30 (tptp.element @t2 @t1)))) % 0.38/0.60 (assume @p13 (and @t33 @t32 @t31)) % 0.38/0.60 (assume @p14 @t33) % 0.38/0.60 (assume @p15 (and @t32 @t31 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) @t33 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set))) % 0.38/0.60 (assume @p16 (and @t33 @t32)) % 0.38/0.60 (assume @p17 (forall @t7 (=> @t36 (not @t34)))) % 0.38/0.60 (assume @p18 (forall @t7 (=> @t38 (tptp.with_non_empty_elements @t37)))) % 0.38/0.60 (assume @p19 (forall @t7 (=> @t36 (not @t39)))) % 0.38/0.60 (assume @p20 (forall @t7 (=> @t6 (and @t34 (tptp.relation @t17))))) % 0.38/0.60 (assume @p21 (forall @t7 (=> @t6 (and @t39 (tptp.relation @t37))))) % 0.38/0.60 (assume @p22 (exists @t7 @t21)) % 0.38/0.60 (assume @p23 (exists @t7 @t16)) % 0.38/0.60 (assume @p24 (exists @t7 (and @t6 @t12))) % 0.38/0.60 (assume @p25 (exists @t7 @t6)) % 0.38/0.60 (assume @p26 (exists @t7 @t15)) % 0.38/0.60 (assume @p27 (exists @t7 (and @t12 @t5 @t13 @t6 @t9 @t8 @t11))) % 0.38/0.60 (assume @p28 (exists @t7 @t36)) % 0.38/0.60 (assume @p29 (exists @t7 @t35)) % 0.38/0.60 (assume @p30 (exists @t7 @t14)) % 0.38/0.60 (assume @p31 (exists @t7 (and @t35 @t9 @t8 @t11))) % 0.38/0.60 (assume @p32 (exists @t7 (and @t12 @t40))) % 0.38/0.60 (assume @p33 (exists @t7 (and @t12 @t40 @t5))) % 0.38/0.60 (assume @p34 (exists @t7 (and @t12 @t5 @t19))) % 0.38/0.60 (assume @p35 (exists @t7 @t38)) % 0.38/0.60 (assume @p36 @t42) % 0.38/0.60 (assume @p37 (forall @t4 (=> @t3 @t43))) % 0.38/0.60 (assume @p38 (forall @t4 (=> @t43 (or @t44 @t3)))) % 0.38/0.60 (assume @p39 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2)))) % 0.38/0.60 (assume @p40 @t48) % 0.38/0.60 (assume @p41 (forall @t51 (=> (and @t3 @t50) (tptp.element @t1 @t49)))) % 0.38/0.60 (assume @p42 (forall @t51 (not (and @t3 @t50 (tptp.empty @t49))))) % 0.38/0.60 (assume @p43 (forall @t7 (=> @t6 (= @t1 tptp.empty_set)))) % 0.38/0.60 (assume @p44 (forall @t4 (not (and @t3 @t44)))) % 0.38/0.60 (assume @p45 (forall @t4 (not (and @t6 (not (= @t1 @t2)) @t44)))) % 0.38/0.60 (assume @p46 true) % 0.38/0.60 (step @p47 :rule quant-unused-vars :args ((= @t42 @t52))) % 0.38/0.60 (step @p48 :rule eq_resolve :premises (@p36 @p47)) % 0.38/0.60 (step @p49 :rule aci_norm :args ((= (or @t56 @t24) (or @t55 @t54 @t53 @t24)))) % 0.38/0.60 (step @p50 :rule refl :args (@t24)) % 0.38/0.60 (step @p51 :rule aci_norm :args ((= (or @t55 (or @t54 @t53)) @t56))) % 0.38/0.60 (step @p52 :rule bool-and-de-morgan :args (@t26 @t25 true)) % 0.38/0.60 (step @p53 :rule refl :args (@t55)) % 0.38/0.60 (step @p54 :rule nary_cong :premises (@p53 @p52) :args ((or @t55 (not (and @t26 @t25))))) % 0.38/0.60 (step @p55 :rule bool-and-de-morgan :args (@t27 @t26 (and @t25))) % 0.38/0.60 (step @p56 :rule trans :premises (@p55 @p54)) % 0.38/0.60 (step @p57 :rule trans :premises (@p56 @p51)) % 0.38/0.60 (step @p58 :rule nary_cong :premises (@p57 @p50) :args ((or (not @t28) @t24))) % 0.38/0.60 (step @p59 :rule trans :premises (@p58 @p49)) % 0.38/0.60 (step @p60 :rule bool-impl-elim :args (@t28 @t24)) % 0.38/0.60 (step @p61 :rule trans :premises (@p60 @p59)) % 0.38/0.60 (step @p62 :rule cong :premises (@p61) :args (@t29)) % 0.38/0.60 (step @p63 :rule eq_resolve :premises (@p9 @p62)) % 0.38/0.60 (step @p64 :rule instantiate :premises (@p63) :args ((@list @t62 @t61))) % 0.38/0.60 (step @p65 :rule aci_norm :args ((= (or @t64 @t20) @t63))) % 0.38/0.60 (step @p66 :rule refl :args (@t20)) % 0.38/0.60 (step @p67 :rule bool-and-de-morgan :args (@t12 @t5 true)) % 0.38/0.60 (step @p68 :rule nary_cong :premises (@p67 @p66) :args ((or @t65 @t20))) % 0.38/0.60 (step @p69 :rule trans :premises (@p68 @p65)) % 0.38/0.60 (step @p70 :rule bool-impl-elim :args (@t21 @t20)) % 0.38/0.60 (step @p71 :rule trans :premises (@p70 @p69)) % 0.38/0.60 (step @p72 :rule cong :premises (@p71) :args (@t22)) % 0.38/0.60 (step @p73 :rule eq_resolve :premises (@p8 @p72)) % 0.38/0.60 (step @p74 :rule eq-symm :args (@t66 @t67)) % 0.38/0.60 (step @p75 :rule refl :args (@t69)) % 0.38/0.60 (step @p76 :rule refl :args (@t71)) % 0.38/0.60 (step @p77 :rule nary_cong :premises (@p76 @p75 @p74) :args (@t72)) % 0.38/0.60 (step @p78 :rule refl :args (@t73)) % 0.38/0.60 (step @p79 :rule cong :premises (@p78 @p77) :args ((=> @t73 @t72))) % 0.38/0.60 (assume-push @p136 @t73) % 0.38/0.60 (step @p81 :rule instantiate :premises (@p73) :args ((@list @t61))) % 0.38/0.60 (step-pop @p137 :rule scope :premises (@p81)) % 0.38/0.60 (step @p82 :rule process_scope :premises (@p137) :args (@t72)) % 0.38/0.60 (step @p84 :rule eq_resolve :premises (@p82 @p79)) % 0.38/0.60 (step @p85 :rule implies_elim :premises (@p84)) % 0.38/0.60 (step @p86 :rule chain_m_resolution :premises (@p85 @p73) :args (@t75 (@list false) (@list @t73))) % 0.38/0.60 (step @p87 :rule aci_norm :args ((= (or @t64 (or @t57 @t45)) @t60))) % 0.38/0.60 (step @p88 :rule bool-impl-elim :args (@t18 @t45)) % 0.38/0.60 (step @p89 :rule nary_cong :premises (@p67 @p88) :args ((or @t65 @t46))) % 0.38/0.60 (step @p90 :rule trans :premises (@p89 @p87)) % 0.38/0.60 (step @p91 :rule bool-impl-elim :args (@t21 @t46)) % 0.38/0.60 (step @p92 :rule trans :premises (@p91 @p90)) % 0.38/0.60 (step @p93 :rule cong :premises (@p92) :args (@t47)) % 0.38/0.60 (step @p94 :rule cong :premises (@p93) :args (@t48)) % 0.38/0.60 (step @p95 :rule eq_resolve :premises (@p40 @p94)) % 0.38/0.60 (step @p96 :rule skolemize :premises (@p95)) % 0.38/0.60 (step @p97 :rule bool-double-not-elim :args (@t68)) % 0.38/0.60 (step @p98 :rule refl :args (@t78)) % 0.38/0.60 (step @p99 :rule nary_cong :premises (@p98 @p97) :args ((or @t78 (not @t69)))) % 0.38/0.60 (step @p100 :rule cnf_or_neg :args (@t78 1)) % 0.38/0.60 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.38/0.60 (step @p102 :rule reordering :premises (@p101) :args ((or @t68 @t78))) % 0.38/0.60 (step @p103 :rule chain_m_resolution :premises (@p102 @p96) :args (@t68 @t79 @t80)) % 0.38/0.60 (step @p104 :rule bool-double-not-elim :args (@t70)) % 0.38/0.60 (step @p105 :rule nary_cong :premises (@p98 @p104) :args ((or @t78 (not @t71)))) % 0.38/0.60 (step @p106 :rule cnf_or_neg :args (@t78 0)) % 0.38/0.60 (step @p107 :rule eq_resolve :premises (@p106 @p105)) % 0.38/0.60 (step @p108 :rule reordering :premises (@p107) :args ((or @t70 @t78))) % 0.38/0.60 (step @p109 :rule chain_m_resolution :premises (@p108 @p96) :args (@t70 @t79 @t80)) % 0.38/0.60 (step @p110 :rule cnf_or_pos :args (@t75)) % 0.38/0.60 (step @p111 :rule reordering :premises (@p110) :args ((or @t71 @t69 @t74 (not @t75)))) % 0.38/0.60 (step @p112 :rule chain_m_resolution :premises (@p111 @p109 @p103 @p86) :args (@t74 (@list false false false) (@list @t70 @t68 @t75))) % 0.38/0.60 (step @p113 :rule bool-double-not-elim :args (@t67)) % 0.38/0.60 (step @p114 :rule nary_cong :premises (@p98 @p113) :args ((or @t78 (not @t77)))) % 0.38/0.60 (step @p115 :rule cnf_or_neg :args (@t78 2)) % 0.38/0.60 (step @p116 :rule eq_resolve :premises (@p115 @p114)) % 0.38/0.60 (step @p117 :rule reordering :premises (@p116) :args ((or @t67 @t78))) % 0.38/0.60 (step @p118 :rule chain_m_resolution :premises (@p117 @p96) :args (@t67 @t79 @t80)) % 0.38/0.60 (step @p119 :rule cnf_equiv_pos1 :args (@t74)) % 0.38/0.60 (step @p120 :rule reordering :premises (@p119) :args ((or @t77 @t66 (not @t74)))) % 0.38/0.60 (step @p121 :rule chain_m_resolution :premises (@p120 @p118 @p112) :args (@t66 (@list false false) (@list @t67 @t74))) % 0.38/0.60 (step @p122 :rule cnf_or_pos :args (@t84)) % 0.38/0.60 (step @p123 :rule reordering :premises (@p122) :args ((or @t71 @t69 @t83 @t82 (not @t84)))) % 0.38/0.60 (step @p124 :rule chain_m_resolution :premises (@p123 @p109 @p103 @p121 @p64) :args (@t82 (@list false false false false) (@list @t70 @t68 @t66 @t84))) % 0.38/0.60 (step @p125 :rule cnf_or_neg :args (@t78 3)) % 0.38/0.60 (step @p126 :rule chain_m_resolution :premises (@p125 @p96) :args ((not @t76) @t79 @t80)) % 0.38/0.60 (step @p127 :rule cnf_equiv_pos2 :args (@t82)) % 0.38/0.60 (step @p128 :rule reordering :premises (@p127) :args ((or @t76 @t85 (not @t82)))) % 0.38/0.60 (step @p129 :rule chain_m_resolution :premises (@p128 @p126 @p124) :args (@t85 @t86 (@list @t76 @t82))) % 0.38/0.60 (assume-push @p138 @t52) % 0.38/0.60 (step @p131 :rule instantiate :premises (@p48) :args ((@list @t62))) % 0.38/0.60 (step-pop @p139 :rule scope :premises (@p131)) % 0.38/0.60 (step @p132 :rule process_scope :premises (@p139) :args (@t81)) % 0.38/0.60 (step @p134 :rule implies_elim :premises (@p132)) % 0.38/0.60 (step @p135 false :rule chain_m_resolution :premises (@p134 @p129 @p48) :args (false @t86 (@list @t81 @t52))) % 0.38/0.60 ) % 0.38/0.60 % SZS output end Proof % 0.38/0.60 % cvc5 exiting %------------------------------------------------------------------------------