%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET143+4 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:47:30 AM UTC 2026 % Result : Theorem 0.36s 0.56s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SET143+4 : TPTP v9.2.1. Released v2.2.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.33 % Computer : n021.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Jun 2 15:04:05 EDT 2026 % 0.16/0.33 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.56 % SZS status Theorem % 0.36/0.56 % SZS output start Proof % 0.36/0.56 ( % 0.36/0.56 (declare-sort $$unsorted 0) % 0.36/0.56 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.56 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.56 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.56 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.36/0.56 (declare-const tptp.empty_set $$unsorted) % 0.36/0.56 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.56 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.36/0.56 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.36/0.56 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.36/0.56 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.36/0.56 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.36/0.56 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.36/0.56 (define @t1 () (@var "B" $$unsorted)) % 0.36/0.56 (define @t2 () (@var "X" $$unsorted)) % 0.36/0.56 (define @t3 () (tptp.member @t2 @t1)) % 0.36/0.56 (define @t4 () (@var "A" $$unsorted)) % 0.36/0.56 (define @t5 () (tptp.member @t2 @t4)) % 0.36/0.56 (define @t6 () (@list @t2)) % 0.36/0.56 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.36/0.56 (define @t8 () (tptp.subset @t4 @t1)) % 0.36/0.56 (define @t9 () (= @t8 @t7)) % 0.36/0.56 (define @t10 () (@list @t4 @t1)) % 0.36/0.56 (define @t11 () (forall @t10 @t9)) % 0.36/0.56 (define @t12 () (@list @t2 @t4)) % 0.36/0.56 (define @t13 () (tptp.intersection @t4 @t1)) % 0.36/0.56 (define @t14 () (@list @t2 @t4 @t1)) % 0.36/0.56 (define @t15 () (@var "E" $$unsorted)) % 0.36/0.56 (define @t16 () (= @t2 @t4)) % 0.36/0.56 (define @t17 () (@var "Y" $$unsorted)) % 0.36/0.56 (define @t18 () (tptp.member @t2 @t17)) % 0.36/0.56 (define @t19 () (tptp.member @t17 @t4)) % 0.36/0.56 (define @t20 () (@list @t17)) % 0.36/0.56 (define @t21 () (@var "C" $$unsorted)) % 0.36/0.56 (define @t22 () (forall (@list @t4 @t1 @t21) (tptp.equal_set (tptp.intersection @t13 @t21) (tptp.intersection @t4 (tptp.intersection @t1 @t21))))) % 0.36/0.56 (define @t23 () (@quantifiers_skolemize @t22 1)) % 0.36/0.56 (define @t24 () (@quantifiers_skolemize @t22 0)) % 0.36/0.56 (define @t25 () (@quantifiers_skolemize @t22 2)) % 0.36/0.56 (define @t26 () (tptp.intersection @t24 @t23)) % 0.36/0.56 (define @t27 () (tptp.intersection @t26 @t25)) % 0.36/0.56 (define @t28 () (tptp.member @t2 @t27)) % 0.36/0.56 (define @t29 () (tptp.intersection @t23 @t25)) % 0.36/0.56 (define @t30 () (tptp.intersection @t24 @t29)) % 0.36/0.56 (define @t31 () (tptp.member @t2 @t30)) % 0.36/0.56 (define @t32 () (forall @t6 (or (not @t31) @t28))) % 0.36/0.56 (define @t33 () (@quantifiers_skolemize @t32 0)) % 0.36/0.56 (define @t34 () (@list @t27 @t30)) % 0.36/0.56 (define @t35 () (forall @t6 (or (not @t28) @t31))) % 0.36/0.56 (define @t36 () (@quantifiers_skolemize @t35 0)) % 0.36/0.56 (define @t37 () (tptp.member @t36 @t27)) % 0.36/0.56 (define @t38 () (tptp.member @t36 @t30)) % 0.36/0.56 (define @t39 () (not @t37)) % 0.36/0.56 (define @t40 () (or @t39 @t38)) % 0.36/0.56 (define @t41 () (tptp.member @t36 @t25)) % 0.36/0.56 (define @t42 () (tptp.member @t36 @t26)) % 0.36/0.56 (define @t43 () (and @t42 @t41)) % 0.36/0.56 (define @t44 () (= @t37 @t43)) % 0.36/0.56 (define @t45 () (tptp.member @t36 @t29)) % 0.36/0.56 (define @t46 () (tptp.member @t36 @t24)) % 0.36/0.56 (define @t47 () (and @t46 @t45)) % 0.36/0.56 (define @t48 () (= @t38 @t47)) % 0.36/0.56 (define @t49 () (not @t43)) % 0.36/0.56 (define @t50 () (tptp.member @t36 @t23)) % 0.36/0.56 (define @t51 () (and @t46 @t50)) % 0.36/0.56 (define @t52 () (= @t42 @t51)) % 0.36/0.56 (define @t53 () (not @t51)) % 0.36/0.56 (define @t54 () (and @t50 @t41)) % 0.36/0.56 (define @t55 () (= @t45 @t54)) % 0.36/0.56 (define @t56 () (not @t40)) % 0.36/0.56 (define @t57 () (not @t35)) % 0.36/0.56 (define @t58 () (@list false)) % 0.36/0.56 (define @t59 () (tptp.subset @t27 @t30)) % 0.36/0.56 (define @t60 () (= @t59 @t35)) % 0.36/0.56 (define @t61 () (@list false false)) % 0.36/0.56 (define @t62 () (tptp.subset @t30 @t27)) % 0.36/0.56 (define @t63 () (and @t59 @t62)) % 0.36/0.56 (define @t64 () (tptp.equal_set @t27 @t30)) % 0.36/0.56 (define @t65 () (= @t64 @t63)) % 0.36/0.56 (define @t66 () (not @t63)) % 0.36/0.56 (define @t67 () (@list true false)) % 0.36/0.56 (define @t68 () (= @t62 @t32)) % 0.36/0.56 (define @t69 () (not @t32)) % 0.36/0.56 (define @t70 () (tptp.member @t33 @t27)) % 0.36/0.56 (define @t71 () (tptp.member @t33 @t30)) % 0.36/0.56 (define @t72 () (not @t71)) % 0.36/0.56 (define @t73 () (or @t72 @t70)) % 0.36/0.56 (define @t74 () (not @t73)) % 0.36/0.56 (define @t75 () (@list true)) % 0.36/0.56 (define @t76 () (@list @t73)) % 0.36/0.56 (define @t77 () (tptp.member @t33 @t29)) % 0.36/0.56 (define @t78 () (tptp.member @t33 @t24)) % 0.36/0.56 (define @t79 () (and @t78 @t77)) % 0.36/0.56 (define @t80 () (= @t71 @t79)) % 0.36/0.56 (define @t81 () (not @t79)) % 0.36/0.56 (define @t82 () (@list @t79)) % 0.36/0.56 (define @t83 () (tptp.member @t33 @t25)) % 0.36/0.56 (define @t84 () (tptp.member @t33 @t23)) % 0.36/0.56 (define @t85 () (and @t84 @t83)) % 0.36/0.56 (define @t86 () (= @t77 @t85)) % 0.36/0.56 (define @t87 () (not @t85)) % 0.36/0.56 (define @t88 () (@list @t85)) % 0.36/0.56 (define @t89 () (and @t78 @t84)) % 0.36/0.56 (define @t90 () (tptp.member @t33 @t26)) % 0.36/0.56 (define @t91 () (and @t90 @t83)) % 0.36/0.56 (define @t92 () (= @t70 @t91)) % 0.36/0.56 (define @t93 () (not @t91)) % 0.36/0.56 (define @t94 () (= @t90 @t89)) % 0.36/0.56 (assume @p1 @t11) % 0.36/0.56 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.36/0.56 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.36/0.56 (assume @p4 (forall @t14 (= (tptp.member @t2 @t13) (and @t5 @t3)))) % 0.36/0.56 (assume @p5 (forall @t14 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.36/0.56 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.36/0.56 (assume @p7 (forall (@list @t1 @t4 @t15) (= (tptp.member @t1 (tptp.difference @t15 @t4)) (and (tptp.member @t1 @t15) (not (tptp.member @t1 @t4)))))) % 0.36/0.56 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t16))) % 0.36/0.56 (assume @p9 (forall @t14 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t16 (= @t2 @t1))))) % 0.36/0.56 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t20 (and @t19 @t18))))) % 0.36/0.56 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t20 (=> @t19 @t18))))) % 0.36/0.56 (assume @p12 (not @t22)) % 0.36/0.56 (assume @p13 true) % 0.36/0.56 (step @p14 :rule instantiate :premises (@p4) :args ((@list @t33 @t24 @t23))) % 0.36/0.56 (step @p15 :rule instantiate :premises (@p4) :args ((@list @t33 @t23 @t25))) % 0.36/0.56 (step @p16 :rule instantiate :premises (@p4) :args ((@list @t33 @t24 @t29))) % 0.36/0.56 (step @p17 :rule bool-impl-elim :args (@t5 @t3)) % 0.36/0.56 (step @p18 :rule cong :premises (@p17) :args (@t7)) % 0.36/0.56 (step @p19 :rule refl :args (@t8)) % 0.36/0.56 (step @p20 :rule cong :premises (@p19 @p18) :args (@t9)) % 0.36/0.56 (step @p21 :rule cong :premises (@p20) :args (@t11)) % 0.36/0.56 (step @p22 :rule eq_resolve :premises (@p1 @p21)) % 0.36/0.56 (step @p23 :rule instantiate :premises (@p22) :args ((@list @t30 @t27))) % 0.36/0.56 (step @p24 :rule instantiate :premises (@p22) :args (@t34)) % 0.36/0.56 (step @p25 :rule bool-double-not-elim :args (@t37)) % 0.36/0.56 (step @p26 :rule refl :args (@t40)) % 0.36/0.56 (step @p27 :rule nary_cong :premises (@p26 @p25) :args ((or @t40 (not @t39)))) % 0.36/0.56 (step @p28 :rule cnf_or_neg :args (@t40 0)) % 0.36/0.56 (step @p29 :rule eq_resolve :premises (@p28 @p27)) % 0.36/0.56 (step @p30 :rule reordering :premises (@p29) :args ((or @t37 @t40))) % 0.36/0.56 (step @p31 :rule cnf_or_neg :args (@t40 1)) % 0.36/0.56 (step @p32 :rule instantiate :premises (@p4) :args ((@list @t36 @t26 @t25))) % 0.36/0.56 (step @p33 :rule cnf_equiv_pos1 :args (@t44)) % 0.36/0.56 (step @p34 :rule reordering :premises (@p33) :args ((or @t39 @t43 (not @t44)))) % 0.36/0.56 (step @p35 :rule instantiate :premises (@p4) :args ((@list @t36 @t24 @t29))) % 0.36/0.56 (step @p36 :rule cnf_equiv_pos2 :args (@t48)) % 0.36/0.56 (step @p37 :rule reordering :premises (@p36) :args ((or @t38 (not @t47) (not @t48)))) % 0.36/0.56 (step @p38 :rule cnf_and_pos :args (@t43 0)) % 0.36/0.56 (step @p39 :rule reordering :premises (@p38) :args ((or @t42 @t49))) % 0.36/0.56 (step @p40 :rule cnf_and_pos :args (@t43 1)) % 0.36/0.56 (step @p41 :rule reordering :premises (@p40) :args ((or @t41 @t49))) % 0.36/0.56 (step @p42 :rule instantiate :premises (@p4) :args ((@list @t36 @t24 @t23))) % 0.36/0.56 (step @p43 :rule cnf_equiv_pos1 :args (@t52)) % 0.36/0.56 (step @p44 :rule reordering :premises (@p43) :args ((or (not @t42) @t51 (not @t52)))) % 0.36/0.56 (step @p45 :rule cnf_and_pos :args (@t51 0)) % 0.36/0.56 (step @p46 :rule reordering :premises (@p45) :args ((or @t46 @t53))) % 0.36/0.56 (step @p47 :rule cnf_and_pos :args (@t51 1)) % 0.36/0.56 (step @p48 :rule reordering :premises (@p47) :args ((or @t50 @t53))) % 0.36/0.56 (step @p49 :rule cnf_and_neg :args (@t47)) % 0.36/0.56 (step @p50 :rule cnf_and_neg :args (@t54)) % 0.36/0.56 (step @p51 :rule reordering :premises (@p50) :args ((or (not @t41) @t54 (not @t50)))) % 0.36/0.56 (step @p52 :rule instantiate :premises (@p4) :args ((@list @t36 @t23 @t25))) % 0.36/0.56 (step @p53 :rule cnf_equiv_pos2 :args (@t55)) % 0.36/0.56 (step @p54 :rule reordering :premises (@p53) :args ((or @t45 (not @t54) (not @t55)))) % 0.36/0.56 (step @p55 :rule chain_m_resolution :premises (@p54 @p52 @p51 @p49 @p48 @p46 @p44 @p42 @p41 @p39 @p37 @p35 @p34 @p32 @p31 @p30) :args (@t40 (@list false false true false false false false false false true false false false true false) (@list @t55 @t54 @t45 @t50 @t46 @t51 @t52 @t41 @t42 @t47 @t48 @t43 @t44 @t38 @t37))) % 0.36/0.56 (step @p56 :rule refl :args (@t56)) % 0.36/0.56 (step @p57 :rule bool-double-not-elim :args (@t35)) % 0.36/0.56 (step @p58 :rule nary_cong :premises (@p57 @p56) :args ((or (not @t57) @t56))) % 0.36/0.56 (assume-push @p128 @t57) % 0.36/0.56 (step @p60 :rule skolemize :premises (@p128)) % 0.36/0.56 (step-pop @p129 :rule scope :premises (@p60)) % 0.36/0.56 (step @p61 :rule process_scope :premises (@p129) :args (@t56)) % 0.36/0.56 (step @p63 :rule implies_elim :premises (@p61)) % 0.36/0.56 (step @p64 :rule eq_resolve :premises (@p63 @p58)) % 0.36/0.56 (step @p65 :rule chain_m_resolution :premises (@p64 @p55) :args (@t35 @t58 (@list @t40))) % 0.36/0.56 (step @p66 :rule cnf_equiv_pos2 :args (@t60)) % 0.36/0.56 (step @p67 :rule reordering :premises (@p66) :args ((or @t59 @t57 (not @t60)))) % 0.36/0.56 (step @p68 :rule chain_m_resolution :premises (@p67 @p65 @p24) :args (@t59 @t61 (@list @t35 @t60))) % 0.36/0.56 (step @p69 :rule instantiate :premises (@p2) :args (@t34)) % 0.36/0.56 (step @p70 :rule skolemize :premises (@p12)) % 0.36/0.56 (step @p71 :rule cnf_equiv_pos2 :args (@t65)) % 0.36/0.56 (step @p72 :rule reordering :premises (@p71) :args ((or @t64 @t66 (not @t65)))) % 0.36/0.56 (step @p73 :rule chain_m_resolution :premises (@p72 @p70 @p69) :args (@t66 @t67 (@list @t64 @t65))) % 0.36/0.56 (step @p74 :rule cnf_and_neg :args (@t63)) % 0.36/0.56 (step @p75 :rule chain_m_resolution :premises (@p74 @p73 @p68) :args ((not @t62) @t67 (@list @t63 @t59))) % 0.36/0.56 (step @p76 :rule cnf_equiv_pos2 :args (@t68)) % 0.36/0.56 (step @p77 :rule reordering :premises (@p76) :args ((or @t62 @t69 (not @t68)))) % 0.36/0.56 (step @p78 :rule chain_m_resolution :premises (@p77 @p75 @p23) :args (@t69 @t67 (@list @t62 @t68))) % 0.36/0.56 (step @p79 :rule refl :args (@t74)) % 0.36/0.56 (step @p80 :rule bool-double-not-elim :args (@t32)) % 0.36/0.56 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or (not @t69) @t74))) % 0.36/0.56 (assume-push @p130 @t69) % 0.36/0.56 (step @p83 :rule skolemize :premises (@p130)) % 0.36/0.56 (step-pop @p131 :rule scope :premises (@p83)) % 0.36/0.56 (step @p84 :rule process_scope :premises (@p131) :args (@t74)) % 0.36/0.56 (step @p86 :rule implies_elim :premises (@p84)) % 0.36/0.56 (step @p87 :rule eq_resolve :premises (@p86 @p81)) % 0.36/0.56 (step @p88 :rule chain_m_resolution :premises (@p87 @p78) :args (@t74 @t75 (@list @t32))) % 0.36/0.56 (step @p89 :rule bool-double-not-elim :args (@t71)) % 0.36/0.56 (step @p90 :rule refl :args (@t73)) % 0.36/0.56 (step @p91 :rule nary_cong :premises (@p90 @p89) :args ((or @t73 (not @t72)))) % 0.36/0.56 (step @p92 :rule cnf_or_neg :args (@t73 0)) % 0.36/0.56 (step @p93 :rule eq_resolve :premises (@p92 @p91)) % 0.36/0.56 (step @p94 :rule reordering :premises (@p93) :args ((or @t71 @t73))) % 0.36/0.56 (step @p95 :rule chain_m_resolution :premises (@p94 @p88) :args (@t71 @t75 @t76)) % 0.36/0.56 (step @p96 :rule cnf_equiv_pos1 :args (@t80)) % 0.36/0.56 (step @p97 :rule reordering :premises (@p96) :args ((or @t72 @t79 (not @t80)))) % 0.36/0.56 (step @p98 :rule chain_m_resolution :premises (@p97 @p95 @p16) :args (@t79 @t61 (@list @t71 @t80))) % 0.36/0.56 (step @p99 :rule cnf_and_pos :args (@t79 1)) % 0.36/0.56 (step @p100 :rule reordering :premises (@p99) :args ((or @t77 @t81))) % 0.36/0.56 (step @p101 :rule chain_m_resolution :premises (@p100 @p98) :args (@t77 @t58 @t82)) % 0.36/0.56 (step @p102 :rule cnf_equiv_pos1 :args (@t86)) % 0.36/0.56 (step @p103 :rule reordering :premises (@p102) :args ((or (not @t77) @t85 (not @t86)))) % 0.36/0.56 (step @p104 :rule chain_m_resolution :premises (@p103 @p101 @p15) :args (@t85 @t61 (@list @t77 @t86))) % 0.36/0.56 (step @p105 :rule cnf_and_pos :args (@t85 0)) % 0.36/0.56 (step @p106 :rule reordering :premises (@p105) :args ((or @t84 @t87))) % 0.36/0.56 (step @p107 :rule chain_m_resolution :premises (@p106 @p104) :args (@t84 @t58 @t88)) % 0.36/0.56 (step @p108 :rule cnf_and_pos :args (@t79 0)) % 0.36/0.56 (step @p109 :rule reordering :premises (@p108) :args ((or @t78 @t81))) % 0.36/0.56 (step @p110 :rule chain_m_resolution :premises (@p109 @p98) :args (@t78 @t58 @t82)) % 0.36/0.56 (step @p111 :rule cnf_and_neg :args (@t89)) % 0.36/0.56 (step @p112 :rule reordering :premises (@p111) :args ((or (not @t78) @t89 (not @t84)))) % 0.36/0.56 (step @p113 :rule chain_m_resolution :premises (@p112 @p110 @p107) :args (@t89 @t61 (@list @t78 @t84))) % 0.36/0.56 (step @p114 :rule cnf_and_pos :args (@t85 1)) % 0.36/0.56 (step @p115 :rule reordering :premises (@p114) :args ((or @t83 @t87))) % 0.36/0.56 (step @p116 :rule chain_m_resolution :premises (@p115 @p104) :args (@t83 @t58 @t88)) % 0.36/0.56 (step @p117 :rule instantiate :premises (@p4) :args ((@list @t33 @t26 @t25))) % 0.36/0.56 (step @p118 :rule cnf_or_neg :args (@t73 1)) % 0.36/0.56 (step @p119 :rule chain_m_resolution :premises (@p118 @p88) :args ((not @t70) @t75 @t76)) % 0.36/0.56 (step @p120 :rule cnf_equiv_pos2 :args (@t92)) % 0.36/0.56 (step @p121 :rule reordering :premises (@p120) :args ((or @t70 @t93 (not @t92)))) % 0.36/0.56 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p117) :args (@t93 @t67 (@list @t70 @t92))) % 0.36/0.56 (step @p123 :rule cnf_and_neg :args (@t91)) % 0.36/0.56 (step @p124 :rule chain_m_resolution :premises (@p123 @p122 @p116) :args ((not @t90) @t67 (@list @t91 @t83))) % 0.36/0.56 (step @p125 :rule cnf_equiv_pos2 :args (@t94)) % 0.36/0.56 (step @p126 :rule reordering :premises (@p125) :args ((or @t90 (not @t89) (not @t94)))) % 0.36/0.56 (step @p127 false :rule chain_m_resolution :premises (@p126 @p124 @p113 @p14) :args (false (@list true false false) (@list @t90 @t89 @t94))) % 0.36/0.56 ) % 0.36/0.56 % SZS output end Proof % 0.36/0.56 % cvc5 exiting %------------------------------------------------------------------------------