%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET703+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 : n016.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 08:48:28 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 % 0.00/0.12 % Problem : SET703+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 % 0.17/0.34 % Computer : n016.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 16:10:24 EDT 2026 % 0.17/0.34 % CPUTime : % 0.26/0.49 %----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" $$unsorted)) % 0.36/0.56 (define @t5 () (tptp.member @t2 @t4)) % 0.36/0.56 (define @t6 () (@list @t2)) % 0.36/0.56 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.36/0.56 (define @t8 () (tptp.subset @t4 @t1)) % 0.36/0.56 (define @t9 () (= @t8 @t7)) % 0.36/0.56 (define @t10 () (@list @t4 @t1)) % 0.36/0.56 (define @t11 () (forall @t10 @t9)) % 0.36/0.56 (define @t12 () (@list @t2 @t4)) % 0.36/0.56 (define @t13 () (@list @t2 @t4 @t1)) % 0.36/0.56 (define @t14 () (@var "E" $$unsorted)) % 0.36/0.56 (define @t15 () (= @t2 @t4)) % 0.36/0.56 (define @t16 () (tptp.singleton @t4)) % 0.36/0.56 (define @t17 () (tptp.member @t2 @t16)) % 0.36/0.56 (define @t18 () (= @t17 @t15)) % 0.36/0.56 (define @t19 () (forall @t12 @t18)) % 0.36/0.56 (define @t20 () (or @t15 (= @t2 @t1))) % 0.36/0.56 (define @t21 () (tptp.unordered_pair @t4 @t1)) % 0.36/0.56 (define @t22 () (tptp.member @t2 @t21)) % 0.36/0.56 (define @t23 () (= @t22 @t20)) % 0.36/0.56 (define @t24 () (forall @t13 @t23)) % 0.36/0.56 (define @t25 () (@var "Y" $$unsorted)) % 0.36/0.56 (define @t26 () (tptp.member @t2 @t25)) % 0.36/0.56 (define @t27 () (tptp.member @t25 @t4)) % 0.36/0.56 (define @t28 () (@list @t25)) % 0.36/0.56 (define @t29 () (forall @t10 (tptp.equal_set (tptp.union @t16 (tptp.singleton @t1)) @t21))) % 0.36/0.56 (define @t30 () (@quantifiers_skolemize @t29 1)) % 0.36/0.56 (define @t31 () (@quantifiers_skolemize @t29 0)) % 0.36/0.56 (define @t32 () (tptp.singleton @t30)) % 0.36/0.56 (define @t33 () (tptp.singleton @t31)) % 0.36/0.56 (define @t34 () (tptp.union @t33 @t32)) % 0.36/0.56 (define @t35 () (tptp.member @t2 @t34)) % 0.36/0.56 (define @t36 () (tptp.unordered_pair @t31 @t30)) % 0.36/0.56 (define @t37 () (tptp.member @t2 @t36)) % 0.36/0.56 (define @t38 () (forall @t6 (or (not @t37) @t35))) % 0.36/0.56 (define @t39 () (@quantifiers_skolemize @t38 0)) % 0.36/0.56 (define @t40 () (@list @t34 @t36)) % 0.36/0.56 (define @t41 () (forall @t6 (or (not @t35) @t37))) % 0.36/0.56 (define @t42 () (@quantifiers_skolemize @t41 0)) % 0.36/0.56 (define @t43 () (tptp.member @t42 @t34)) % 0.36/0.56 (define @t44 () (tptp.member @t42 @t36)) % 0.36/0.56 (define @t45 () (not @t43)) % 0.36/0.56 (define @t46 () (or @t45 @t44)) % 0.36/0.56 (define @t47 () (tptp.member @t42 @t32)) % 0.36/0.56 (define @t48 () (tptp.member @t42 @t33)) % 0.36/0.56 (define @t49 () (or @t48 @t47)) % 0.36/0.56 (define @t50 () (= @t43 @t49)) % 0.36/0.56 (define @t51 () (= @t30 @t42)) % 0.36/0.56 (define @t52 () (= @t31 @t42)) % 0.36/0.56 (define @t53 () (or @t52 @t51)) % 0.36/0.56 (define @t54 () (= @t44 @t53)) % 0.36/0.56 (define @t55 () (= @t48 @t52)) % 0.36/0.56 (define @t56 () (= @t47 @t51)) % 0.36/0.56 (define @t57 () (not @t46)) % 0.36/0.56 (define @t58 () (not @t41)) % 0.36/0.56 (define @t59 () (tptp.subset @t34 @t36)) % 0.36/0.56 (define @t60 () (= @t59 @t41)) % 0.36/0.56 (define @t61 () (@list false false)) % 0.36/0.56 (define @t62 () (tptp.subset @t36 @t34)) % 0.36/0.56 (define @t63 () (and @t59 @t62)) % 0.36/0.56 (define @t64 () (tptp.equal_set @t34 @t36)) % 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 @t38)) % 0.36/0.56 (define @t69 () (not @t38)) % 0.36/0.56 (define @t70 () (tptp.member @t39 @t34)) % 0.36/0.56 (define @t71 () (tptp.member @t39 @t36)) % 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 () (= @t30 @t39)) % 0.36/0.56 (define @t78 () (= @t31 @t39)) % 0.36/0.56 (define @t79 () (or @t78 @t77)) % 0.36/0.56 (define @t80 () (= @t71 @t79)) % 0.36/0.56 (define @t81 () (tptp.member @t39 @t32)) % 0.36/0.56 (define @t82 () (tptp.member @t39 @t33)) % 0.36/0.56 (define @t83 () (or @t82 @t81)) % 0.36/0.56 (define @t84 () (= @t70 @t83)) % 0.36/0.56 (define @t85 () (not @t83)) % 0.36/0.56 (define @t86 () (@list @t83)) % 0.36/0.56 (define @t87 () (= @t81 @t77)) % 0.36/0.56 (define @t88 () (not @t77)) % 0.36/0.56 (define @t89 () (= @t82 @t78)) % 0.36/0.56 (define @t90 () (not @t89)) % 0.36/0.56 (define @t91 () (forall @t12 (= @t17 (= @t4 @t2)))) % 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 @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.36/0.56 (assume @p5 (forall @t13 (= (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 @t14) (= (tptp.member @t1 (tptp.difference @t14 @t4)) (and (tptp.member @t1 @t14) (not (tptp.member @t1 @t4)))))) % 0.36/0.56 (assume @p8 @t19) % 0.36/0.56 (assume @p9 @t24) % 0.36/0.56 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t28 (and @t27 @t26))))) % 0.36/0.56 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t28 (=> @t27 @t26))))) % 0.36/0.56 (assume @p12 (not @t29)) % 0.36/0.56 (assume @p13 true) % 0.36/0.56 (step @p14 :rule eq-symm :args (@t2 @t4)) % 0.36/0.57 (step @p15 :rule refl :args (@t17)) % 0.36/0.57 (step @p16 :rule cong :premises (@p15 @p14) :args (@t18)) % 0.36/0.57 (step @p17 :rule cong :premises (@p16) :args (@t19)) % 0.36/0.57 (step @p18 :rule eq_resolve :premises (@p8 @p17)) % 0.36/0.57 (step @p19 :rule eq-symm :args (@t2 @t1)) % 0.36/0.57 (step @p20 :rule nary_cong :premises (@p14 @p19) :args (@t20)) % 0.36/0.57 (step @p21 :rule refl :args (@t22)) % 0.36/0.57 (step @p22 :rule cong :premises (@p21 @p20) :args (@t23)) % 0.36/0.57 (step @p23 :rule cong :premises (@p22) :args (@t24)) % 0.36/0.57 (step @p24 :rule eq_resolve :premises (@p9 @p23)) % 0.36/0.57 (step @p25 :rule instantiate :premises (@p24) :args ((@list @t39 @t31 @t30))) % 0.36/0.57 (step @p26 :rule bool-impl-elim :args (@t5 @t3)) % 0.36/0.57 (step @p27 :rule cong :premises (@p26) :args (@t7)) % 0.36/0.57 (step @p28 :rule refl :args (@t8)) % 0.36/0.57 (step @p29 :rule cong :premises (@p28 @p27) :args (@t9)) % 0.36/0.57 (step @p30 :rule cong :premises (@p29) :args (@t11)) % 0.36/0.57 (step @p31 :rule eq_resolve :premises (@p1 @p30)) % 0.36/0.57 (step @p32 :rule instantiate :premises (@p31) :args ((@list @t36 @t34))) % 0.36/0.57 (step @p33 :rule instantiate :premises (@p31) :args (@t40)) % 0.36/0.57 (step @p34 :rule bool-double-not-elim :args (@t43)) % 0.36/0.57 (step @p35 :rule refl :args (@t46)) % 0.36/0.57 (step @p36 :rule nary_cong :premises (@p35 @p34) :args ((or @t46 (not @t45)))) % 0.36/0.57 (step @p37 :rule cnf_or_neg :args (@t46 0)) % 0.36/0.57 (step @p38 :rule eq_resolve :premises (@p37 @p36)) % 0.36/0.57 (step @p39 :rule reordering :premises (@p38) :args ((or @t43 @t46))) % 0.36/0.57 (step @p40 :rule cnf_or_neg :args (@t46 1)) % 0.36/0.57 (step @p41 :rule instantiate :premises (@p5) :args ((@list @t42 @t33 @t32))) % 0.36/0.57 (step @p42 :rule cnf_equiv_pos1 :args (@t50)) % 0.36/0.57 (step @p43 :rule reordering :premises (@p42) :args ((or @t45 @t49 (not @t50)))) % 0.36/0.57 (step @p44 :rule instantiate :premises (@p24) :args ((@list @t42 @t31 @t30))) % 0.36/0.57 (step @p45 :rule cnf_equiv_pos2 :args (@t54)) % 0.36/0.57 (step @p46 :rule reordering :premises (@p45) :args ((or @t44 (not @t53) (not @t54)))) % 0.36/0.57 (step @p47 :rule cnf_or_neg :args (@t53 0)) % 0.36/0.57 (step @p48 :rule cnf_or_neg :args (@t53 1)) % 0.36/0.57 (step @p49 :rule instantiate :premises (@p18) :args ((@list @t42 @t31))) % 0.36/0.57 (step @p50 :rule cnf_equiv_pos1 :args (@t55)) % 0.36/0.57 (step @p51 :rule reordering :premises (@p50) :args ((or @t52 (not @t48) (not @t55)))) % 0.36/0.57 (step @p52 :rule instantiate :premises (@p18) :args ((@list @t42 @t30))) % 0.36/0.57 (step @p53 :rule cnf_equiv_pos1 :args (@t56)) % 0.36/0.57 (step @p54 :rule reordering :premises (@p53) :args ((or @t51 (not @t47) (not @t56)))) % 0.36/0.57 (step @p55 :rule cnf_or_pos :args (@t49)) % 0.36/0.57 (step @p56 :rule reordering :premises (@p55) :args ((or @t48 @t47 (not @t49)))) % 0.36/0.57 (step @p57 :rule chain_m_resolution :premises (@p56 @p54 @p52 @p51 @p49 @p48 @p47 @p46 @p44 @p43 @p41 @p40 @p39) :args (@t46 (@list true false true false true true true false false false true false) (@list @t47 @t56 @t48 @t55 @t51 @t52 @t53 @t54 @t49 @t50 @t44 @t43))) % 0.36/0.57 (step @p58 :rule refl :args (@t57)) % 0.36/0.57 (step @p59 :rule bool-double-not-elim :args (@t41)) % 0.36/0.57 (step @p60 :rule nary_cong :premises (@p59 @p58) :args ((or (not @t58) @t57))) % 0.36/0.57 (assume-push @p127 @t58) % 0.36/0.57 (step @p62 :rule skolemize :premises (@p127)) % 0.36/0.57 (step-pop @p128 :rule scope :premises (@p62)) % 0.36/0.57 (step @p63 :rule process_scope :premises (@p128) :args (@t57)) % 0.36/0.57 (step @p65 :rule implies_elim :premises (@p63)) % 0.36/0.57 (step @p66 :rule eq_resolve :premises (@p65 @p60)) % 0.36/0.57 (step @p67 :rule chain_m_resolution :premises (@p66 @p57) :args (@t41 (@list false) (@list @t46))) % 0.36/0.57 (step @p68 :rule cnf_equiv_pos2 :args (@t60)) % 0.36/0.57 (step @p69 :rule reordering :premises (@p68) :args ((or @t59 @t58 (not @t60)))) % 0.36/0.57 (step @p70 :rule chain_m_resolution :premises (@p69 @p67 @p33) :args (@t59 @t61 (@list @t41 @t60))) % 0.36/0.57 (step @p71 :rule instantiate :premises (@p2) :args (@t40)) % 0.36/0.57 (step @p72 :rule skolemize :premises (@p12)) % 0.36/0.57 (step @p73 :rule cnf_equiv_pos2 :args (@t65)) % 0.36/0.57 (step @p74 :rule reordering :premises (@p73) :args ((or @t64 @t66 (not @t65)))) % 0.36/0.57 (step @p75 :rule chain_m_resolution :premises (@p74 @p72 @p71) :args (@t66 @t67 (@list @t64 @t65))) % 0.36/0.57 (step @p76 :rule cnf_and_neg :args (@t63)) % 0.36/0.57 (step @p77 :rule chain_m_resolution :premises (@p76 @p75 @p70) :args ((not @t62) @t67 (@list @t63 @t59))) % 0.36/0.57 (step @p78 :rule cnf_equiv_pos2 :args (@t68)) % 0.36/0.57 (step @p79 :rule reordering :premises (@p78) :args ((or @t62 @t69 (not @t68)))) % 0.36/0.57 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p32) :args (@t69 @t67 (@list @t62 @t68))) % 0.36/0.57 (step @p81 :rule refl :args (@t74)) % 0.36/0.57 (step @p82 :rule bool-double-not-elim :args (@t38)) % 0.36/0.57 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or (not @t69) @t74))) % 0.36/0.57 (assume-push @p129 @t69) % 0.36/0.57 (step @p85 :rule skolemize :premises (@p129)) % 0.36/0.57 (step-pop @p130 :rule scope :premises (@p85)) % 0.36/0.57 (step @p86 :rule process_scope :premises (@p130) :args (@t74)) % 0.36/0.57 (step @p88 :rule implies_elim :premises (@p86)) % 0.36/0.57 (step @p89 :rule eq_resolve :premises (@p88 @p83)) % 0.36/0.57 (step @p90 :rule chain_m_resolution :premises (@p89 @p80) :args (@t74 @t75 (@list @t38))) % 0.36/0.57 (step @p91 :rule bool-double-not-elim :args (@t71)) % 0.36/0.57 (step @p92 :rule refl :args (@t73)) % 0.36/0.57 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or @t73 (not @t72)))) % 0.36/0.57 (step @p94 :rule cnf_or_neg :args (@t73 0)) % 0.36/0.57 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 0.36/0.57 (step @p96 :rule reordering :premises (@p95) :args ((or @t71 @t73))) % 0.36/0.57 (step @p97 :rule chain_m_resolution :premises (@p96 @p90) :args (@t71 @t75 @t76)) % 0.36/0.57 (step @p98 :rule cnf_equiv_pos1 :args (@t80)) % 0.36/0.57 (step @p99 :rule reordering :premises (@p98) :args ((or @t72 @t79 (not @t80)))) % 0.36/0.57 (step @p100 :rule chain_m_resolution :premises (@p99 @p97 @p25) :args (@t79 @t61 (@list @t71 @t80))) % 0.36/0.57 (step @p101 :rule instantiate :premises (@p18) :args ((@list @t39 @t30))) % 0.36/0.57 (step @p102 :rule instantiate :premises (@p5) :args ((@list @t39 @t33 @t32))) % 0.36/0.57 (step @p103 :rule cnf_or_neg :args (@t73 1)) % 0.36/0.57 (step @p104 :rule chain_m_resolution :premises (@p103 @p90) :args ((not @t70) @t75 @t76)) % 0.36/0.57 (step @p105 :rule cnf_equiv_pos2 :args (@t84)) % 0.36/0.57 (step @p106 :rule reordering :premises (@p105) :args ((or @t70 @t85 (not @t84)))) % 0.36/0.57 (step @p107 :rule chain_m_resolution :premises (@p106 @p104 @p102) :args (@t85 @t67 (@list @t70 @t84))) % 0.36/0.57 (step @p108 :rule cnf_or_neg :args (@t83 1)) % 0.36/0.57 (step @p109 :rule chain_m_resolution :premises (@p108 @p107) :args ((not @t81) @t75 @t86)) % 0.36/0.57 (step @p110 :rule cnf_equiv_pos2 :args (@t87)) % 0.36/0.57 (step @p111 :rule reordering :premises (@p110) :args ((or @t81 @t88 (not @t87)))) % 0.36/0.57 (step @p112 :rule chain_m_resolution :premises (@p111 @p109 @p101) :args (@t88 @t67 (@list @t81 @t87))) % 0.36/0.57 (step @p113 :rule cnf_or_pos :args (@t79)) % 0.36/0.57 (step @p114 :rule reordering :premises (@p113) :args ((or @t78 @t77 (not @t79)))) % 0.36/0.57 (step @p115 :rule chain_m_resolution :premises (@p114 @p112 @p100) :args (@t78 @t67 (@list @t77 @t79))) % 0.36/0.57 (step @p116 :rule cnf_or_neg :args (@t83 0)) % 0.36/0.57 (step @p117 :rule chain_m_resolution :premises (@p116 @p107) :args ((not @t82) @t75 @t86)) % 0.36/0.57 (step @p118 :rule cnf_equiv_pos2 :args (@t89)) % 0.36/0.57 (step @p119 :rule reordering :premises (@p118) :args ((or @t82 (not @t78) @t90))) % 0.36/0.57 (step @p120 :rule chain_m_resolution :premises (@p119 @p117 @p115) :args (@t90 @t67 (@list @t82 @t78))) % 0.36/0.57 (assume-push @p131 @t91) % 0.36/0.57 (step @p122 :rule instantiate :premises (@p18) :args ((@list @t39 @t31))) % 0.36/0.57 (step-pop @p132 :rule scope :premises (@p122)) % 0.36/0.57 (step @p123 :rule process_scope :premises (@p132) :args (@t89)) % 0.36/0.57 (step @p125 :rule implies_elim :premises (@p123)) % 0.36/0.57 (step @p126 false :rule chain_m_resolution :premises (@p125 @p120 @p18) :args (false @t67 (@list @t89 @t91))) % 0.36/0.57 ) % 0.36/0.57 % SZS output end Proof % 0.36/0.57 % cvc5 exiting %------------------------------------------------------------------------------