%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET012+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 : n017.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 08:46:54 AM UTC 2026 % Result : Theorem 0.37s 0.56s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET012+4 : TPTP v9.2.1. Released v2.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n017.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 14:38:46 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.56 % SZS status Theorem % 0.37/0.56 % SZS output start Proof % 0.37/0.56 ( % 0.37/0.56 (declare-sort $$unsorted 0) % 0.37/0.56 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.empty_set $$unsorted) % 0.37/0.56 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.37/0.56 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.56 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.37/0.56 (define @t1 () (@var "B" $$unsorted)) % 0.37/0.56 (define @t2 () (@var "X" $$unsorted)) % 0.37/0.56 (define @t3 () (tptp.member @t2 @t1)) % 0.37/0.56 (define @t4 () (@var "A" $$unsorted)) % 0.37/0.56 (define @t5 () (tptp.member @t2 @t4)) % 0.37/0.56 (define @t6 () (@list @t2)) % 0.37/0.56 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.37/0.56 (define @t8 () (tptp.subset @t4 @t1)) % 0.37/0.56 (define @t9 () (= @t8 @t7)) % 0.37/0.56 (define @t10 () (@list @t4 @t1)) % 0.37/0.56 (define @t11 () (forall @t10 @t9)) % 0.37/0.56 (define @t12 () (@list @t2 @t4)) % 0.37/0.56 (define @t13 () (@list @t2 @t4 @t1)) % 0.37/0.56 (define @t14 () (@var "E" $$unsorted)) % 0.37/0.56 (define @t15 () (tptp.difference @t14 @t4)) % 0.37/0.56 (define @t16 () (= @t2 @t4)) % 0.37/0.56 (define @t17 () (@var "Y" $$unsorted)) % 0.37/0.56 (define @t18 () (tptp.member @t2 @t17)) % 0.37/0.56 (define @t19 () (tptp.member @t17 @t4)) % 0.37/0.56 (define @t20 () (@list @t17)) % 0.37/0.56 (define @t21 () (tptp.equal_set (tptp.difference @t14 @t15) @t4)) % 0.37/0.56 (define @t22 () (tptp.subset @t4 @t14)) % 0.37/0.56 (define @t23 () (@list @t4 @t14)) % 0.37/0.56 (define @t24 () (forall @t23 (=> @t22 @t21))) % 0.37/0.56 (define @t25 () (not @t24)) % 0.37/0.56 (define @t26 () (forall @t23 (or (not @t22) @t21))) % 0.37/0.56 (define @t27 () (@quantifiers_skolemize @t26 1)) % 0.37/0.56 (define @t28 () (@quantifiers_skolemize @t26 0)) % 0.37/0.56 (define @t29 () (tptp.difference @t27 @t28)) % 0.37/0.56 (define @t30 () (tptp.difference @t27 @t29)) % 0.37/0.56 (define @t31 () (tptp.member @t2 @t30)) % 0.37/0.56 (define @t32 () (tptp.member @t2 @t28)) % 0.37/0.56 (define @t33 () (not @t32)) % 0.37/0.56 (define @t34 () (forall @t6 (or @t33 @t31))) % 0.37/0.56 (define @t35 () (@quantifiers_skolemize @t34 0)) % 0.37/0.56 (define @t36 () (@list @t30 @t28)) % 0.37/0.56 (define @t37 () (forall @t6 (or (not @t31) @t32))) % 0.37/0.56 (define @t38 () (@quantifiers_skolemize @t37 0)) % 0.37/0.56 (define @t39 () (tptp.member @t38 @t30)) % 0.37/0.56 (define @t40 () (tptp.member @t38 @t28)) % 0.37/0.56 (define @t41 () (not @t39)) % 0.37/0.56 (define @t42 () (or @t41 @t40)) % 0.37/0.56 (define @t43 () (tptp.member @t38 @t29)) % 0.37/0.56 (define @t44 () (not @t43)) % 0.37/0.56 (define @t45 () (tptp.member @t38 @t27)) % 0.37/0.56 (define @t46 () (and @t45 @t44)) % 0.37/0.56 (define @t47 () (= @t39 @t46)) % 0.37/0.56 (define @t48 () (not @t46)) % 0.37/0.56 (define @t49 () (not @t45)) % 0.37/0.56 (define @t50 () (not @t40)) % 0.37/0.56 (define @t51 () (and @t45 @t50)) % 0.37/0.56 (define @t52 () (= @t43 @t51)) % 0.37/0.56 (define @t53 () (not @t42)) % 0.37/0.56 (define @t54 () (not @t37)) % 0.37/0.56 (define @t55 () (@list false)) % 0.37/0.56 (define @t56 () (tptp.subset @t30 @t28)) % 0.37/0.56 (define @t57 () (= @t56 @t37)) % 0.37/0.56 (define @t58 () (@list false false)) % 0.37/0.56 (define @t59 () (tptp.equal_set @t30 @t28)) % 0.37/0.56 (define @t60 () (tptp.subset @t28 @t27)) % 0.37/0.56 (define @t61 () (not @t60)) % 0.37/0.56 (define @t62 () (or @t61 @t59)) % 0.37/0.56 (define @t63 () (@list true)) % 0.37/0.56 (define @t64 () (@list @t62)) % 0.37/0.56 (define @t65 () (tptp.subset @t28 @t30)) % 0.37/0.56 (define @t66 () (and @t56 @t65)) % 0.37/0.56 (define @t67 () (= @t59 @t66)) % 0.37/0.56 (define @t68 () (not @t66)) % 0.37/0.56 (define @t69 () (@list true false)) % 0.37/0.56 (define @t70 () (= @t65 @t34)) % 0.37/0.56 (define @t71 () (not @t34)) % 0.37/0.56 (define @t72 () (tptp.member @t35 @t30)) % 0.37/0.56 (define @t73 () (tptp.member @t35 @t28)) % 0.37/0.56 (define @t74 () (not @t73)) % 0.37/0.56 (define @t75 () (or @t74 @t72)) % 0.37/0.56 (define @t76 () (not @t75)) % 0.37/0.56 (define @t77 () (forall @t6 (or @t33 (tptp.member @t2 @t27)))) % 0.37/0.56 (define @t78 () (= @t60 @t77)) % 0.37/0.56 (define @t79 () (tptp.member @t35 @t27)) % 0.37/0.56 (define @t80 () (or @t74 @t79)) % 0.37/0.56 (define @t81 () (tptp.member @t35 @t29)) % 0.37/0.56 (define @t82 () (not @t81)) % 0.37/0.56 (define @t83 () (and @t79 @t82)) % 0.37/0.56 (define @t84 () (= @t72 @t83)) % 0.37/0.56 (define @t85 () (not @t79)) % 0.37/0.56 (define @t86 () (@list @t75)) % 0.37/0.56 (define @t87 () (and @t79 @t74)) % 0.37/0.56 (define @t88 () (not @t87)) % 0.37/0.56 (define @t89 () (= @t81 @t87)) % 0.37/0.56 (assume @p1 @t11) % 0.37/0.56 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.37/0.56 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.37/0.56 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.37/0.56 (assume @p5 (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.37/0.56 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.37/0.56 (assume @p7 (forall (@list @t1 @t4 @t14) (= (tptp.member @t1 @t15) (and (tptp.member @t1 @t14) (not (tptp.member @t1 @t4)))))) % 0.37/0.56 (assume @p8 (forall @t12 (= (tptp.member @t2 (tptp.singleton @t4)) @t16))) % 0.37/0.56 (assume @p9 (forall @t13 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t16 (= @t2 @t1))))) % 0.37/0.56 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t20 (and @t19 @t18))))) % 0.37/0.56 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t20 (=> @t19 @t18))))) % 0.37/0.56 (assume @p12 @t25) % 0.37/0.56 (assume @p13 true) % 0.37/0.56 (step @p14 :rule instantiate :premises (@p7) :args ((@list @t35 @t28 @t27))) % 0.37/0.56 (step @p15 :rule bool-impl-elim :args (@t5 @t3)) % 0.37/0.56 (step @p16 :rule cong :premises (@p15) :args (@t7)) % 0.37/0.56 (step @p17 :rule refl :args (@t8)) % 0.37/0.56 (step @p18 :rule cong :premises (@p17 @p16) :args (@t9)) % 0.37/0.56 (step @p19 :rule cong :premises (@p18) :args (@t11)) % 0.37/0.56 (step @p20 :rule eq_resolve :premises (@p1 @p19)) % 0.37/0.56 (step @p21 :rule instantiate :premises (@p20) :args ((@list @t28 @t30))) % 0.37/0.56 (step @p22 :rule instantiate :premises (@p20) :args (@t36)) % 0.37/0.56 (step @p23 :rule bool-double-not-elim :args (@t39)) % 0.37/0.56 (step @p24 :rule refl :args (@t42)) % 0.37/0.56 (step @p25 :rule nary_cong :premises (@p24 @p23) :args ((or @t42 (not @t41)))) % 0.37/0.56 (step @p26 :rule cnf_or_neg :args (@t42 0)) % 0.37/0.56 (step @p27 :rule eq_resolve :premises (@p26 @p25)) % 0.37/0.56 (step @p28 :rule reordering :premises (@p27) :args ((or @t39 @t42))) % 0.37/0.56 (step @p29 :rule cnf_or_neg :args (@t42 1)) % 0.37/0.56 (step @p30 :rule instantiate :premises (@p7) :args ((@list @t38 @t29 @t27))) % 0.37/0.56 (step @p31 :rule cnf_equiv_pos1 :args (@t47)) % 0.37/0.56 (step @p32 :rule reordering :premises (@p31) :args ((or @t41 @t46 (not @t47)))) % 0.37/0.56 (step @p33 :rule cnf_and_pos :args (@t46 0)) % 0.37/0.56 (step @p34 :rule reordering :premises (@p33) :args ((or @t45 @t48))) % 0.37/0.56 (step @p35 :rule cnf_and_pos :args (@t46 1)) % 0.37/0.56 (step @p36 :rule reordering :premises (@p35) :args ((or @t44 @t48))) % 0.37/0.56 (step @p37 :rule bool-double-not-elim :args (@t40)) % 0.37/0.56 (step @p38 :rule refl :args (@t49)) % 0.37/0.56 (step @p39 :rule refl :args (@t51)) % 0.37/0.56 (step @p40 :rule nary_cong :premises (@p39 @p38 @p37) :args ((or @t51 @t49 (not @t50)))) % 0.37/0.56 (step @p41 :rule cnf_and_neg :args (@t51)) % 0.37/0.56 (step @p42 :rule eq_resolve :premises (@p41 @p40)) % 0.37/0.56 (step @p43 :rule reordering :premises (@p42) :args ((or @t40 @t49 @t51))) % 0.37/0.56 (step @p44 :rule instantiate :premises (@p7) :args ((@list @t38 @t28 @t27))) % 0.37/0.56 (step @p45 :rule cnf_equiv_pos2 :args (@t52)) % 0.37/0.56 (step @p46 :rule reordering :premises (@p45) :args ((or @t43 (not @t51) (not @t52)))) % 0.37/0.56 (step @p47 :rule chain_m_resolution :premises (@p46 @p44 @p43 @p36 @p34 @p32 @p30 @p29 @p28) :args (@t42 (@list false false true false false false true false) (@list @t52 @t51 @t43 @t45 @t46 @t47 @t40 @t39))) % 0.37/0.56 (step @p48 :rule refl :args (@t53)) % 0.37/0.56 (step @p49 :rule bool-double-not-elim :args (@t37)) % 0.37/0.56 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((or (not @t54) @t53))) % 0.37/0.56 (assume-push @p127 @t54) % 0.37/0.56 (step @p52 :rule skolemize :premises (@p127)) % 0.37/0.56 (step-pop @p128 :rule scope :premises (@p52)) % 0.37/0.56 (step @p53 :rule process_scope :premises (@p128) :args (@t53)) % 0.37/0.56 (step @p55 :rule implies_elim :premises (@p53)) % 0.37/0.56 (step @p56 :rule eq_resolve :premises (@p55 @p50)) % 0.37/0.56 (step @p57 :rule chain_m_resolution :premises (@p56 @p47) :args (@t37 @t55 (@list @t42))) % 0.37/0.56 (step @p58 :rule cnf_equiv_pos2 :args (@t57)) % 0.37/0.56 (step @p59 :rule reordering :premises (@p58) :args ((or @t56 @t54 (not @t57)))) % 0.37/0.56 (step @p60 :rule chain_m_resolution :premises (@p59 @p57 @p22) :args (@t56 @t58 (@list @t37 @t57))) % 0.37/0.56 (step @p61 :rule instantiate :premises (@p2) :args (@t36)) % 0.37/0.56 (step @p62 :rule bool-impl-elim :args (@t22 @t21)) % 0.37/0.56 (step @p63 :rule cong :premises (@p62) :args (@t24)) % 0.37/0.56 (step @p64 :rule cong :premises (@p63) :args (@t25)) % 0.37/0.56 (step @p65 :rule eq_resolve :premises (@p12 @p64)) % 0.37/0.56 (step @p66 :rule skolemize :premises (@p65)) % 0.37/0.56 (step @p67 :rule cnf_or_neg :args (@t62 1)) % 0.37/0.56 (step @p68 :rule chain_m_resolution :premises (@p67 @p66) :args ((not @t59) @t63 @t64)) % 0.37/0.56 (step @p69 :rule cnf_equiv_pos2 :args (@t67)) % 0.37/0.56 (step @p70 :rule reordering :premises (@p69) :args ((or @t59 @t68 (not @t67)))) % 0.37/0.56 (step @p71 :rule chain_m_resolution :premises (@p70 @p68 @p61) :args (@t68 @t69 (@list @t59 @t67))) % 0.37/0.56 (step @p72 :rule cnf_and_neg :args (@t66)) % 0.37/0.56 (step @p73 :rule chain_m_resolution :premises (@p72 @p71 @p60) :args ((not @t65) @t69 (@list @t66 @t56))) % 0.37/0.56 (step @p74 :rule cnf_equiv_pos2 :args (@t70)) % 0.37/0.56 (step @p75 :rule reordering :premises (@p74) :args ((or @t65 @t71 (not @t70)))) % 0.37/0.56 (step @p76 :rule chain_m_resolution :premises (@p75 @p73 @p21) :args (@t71 @t69 (@list @t65 @t70))) % 0.37/0.56 (step @p77 :rule refl :args (@t76)) % 0.37/0.56 (step @p78 :rule bool-double-not-elim :args (@t34)) % 0.37/0.56 (step @p79 :rule nary_cong :premises (@p78 @p77) :args ((or (not @t71) @t76))) % 0.37/0.56 (assume-push @p129 @t71) % 0.37/0.56 (step @p81 :rule skolemize :premises (@p129)) % 0.37/0.56 (step-pop @p130 :rule scope :premises (@p81)) % 0.37/0.56 (step @p82 :rule process_scope :premises (@p130) :args (@t76)) % 0.37/0.56 (step @p84 :rule implies_elim :premises (@p82)) % 0.37/0.56 (step @p85 :rule eq_resolve :premises (@p84 @p79)) % 0.37/0.56 (step @p86 :rule chain_m_resolution :premises (@p85 @p76) :args (@t76 @t63 (@list @t34))) % 0.37/0.56 (step @p87 :rule bool-double-not-elim :args (@t73)) % 0.37/0.56 (step @p88 :rule refl :args (@t75)) % 0.37/0.56 (step @p89 :rule nary_cong :premises (@p88 @p87) :args ((or @t75 (not @t74)))) % 0.37/0.56 (step @p90 :rule cnf_or_neg :args (@t75 0)) % 0.37/0.56 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 0.37/0.56 (step @p92 :rule reordering :premises (@p91) :args ((or @t73 @t75))) % 0.37/0.56 (step @p93 :rule cnf_or_neg :args (@t75 1)) % 0.37/0.56 (step @p94 :rule instantiate :premises (@p20) :args ((@list @t28 @t27))) % 0.37/0.56 (step @p95 :rule bool-double-not-elim :args (@t60)) % 0.37/0.56 (step @p96 :rule refl :args (@t62)) % 0.37/0.56 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or @t62 (not @t61)))) % 0.37/0.56 (step @p98 :rule cnf_or_neg :args (@t62 0)) % 0.37/0.56 (step @p99 :rule eq_resolve :premises (@p98 @p97)) % 0.37/0.56 (step @p100 :rule reordering :premises (@p99) :args ((or @t60 @t62))) % 0.37/0.56 (step @p101 :rule chain_m_resolution :premises (@p100 @p66) :args (@t60 @t63 @t64)) % 0.37/0.56 (step @p102 :rule cnf_equiv_pos1 :args (@t78)) % 0.37/0.56 (step @p103 :rule reordering :premises (@p102) :args ((or @t61 @t77 (not @t78)))) % 0.37/0.56 (step @p104 :rule chain_m_resolution :premises (@p103 @p101 @p94) :args (@t77 @t58 (@list @t60 @t78))) % 0.37/0.56 (step @p105 :rule instantiate :premises (@p104) :args ((@list @t35))) % 0.37/0.56 (step @p106 :rule cnf_or_pos :args (@t80)) % 0.37/0.56 (step @p107 :rule reordering :premises (@p106) :args ((or @t74 @t79 (not @t80)))) % 0.37/0.56 (step @p108 :rule instantiate :premises (@p7) :args ((@list @t35 @t29 @t27))) % 0.37/0.56 (step @p109 :rule cnf_equiv_pos2 :args (@t84)) % 0.37/0.56 (step @p110 :rule reordering :premises (@p109) :args ((or @t72 (not @t83) (not @t84)))) % 0.37/0.56 (step @p111 :rule bool-double-not-elim :args (@t81)) % 0.37/0.56 (step @p112 :rule refl :args (@t85)) % 0.37/0.56 (step @p113 :rule refl :args (@t83)) % 0.37/0.56 (step @p114 :rule nary_cong :premises (@p113 @p112 @p111) :args ((or @t83 @t85 (not @t82)))) % 0.37/0.56 (step @p115 :rule cnf_and_neg :args (@t83)) % 0.37/0.56 (step @p116 :rule eq_resolve :premises (@p115 @p114)) % 0.37/0.56 (step @p117 :rule reordering :premises (@p116) :args ((or @t81 @t83 @t85))) % 0.37/0.56 (step @p118 :rule chain_m_resolution :premises (@p117 @p110 @p108 @p107 @p105 @p93 @p92) :args ((or @t75 @t81) (@list true false false false true false) (@list @t83 @t84 @t79 @t80 @t72 @t73))) % 0.37/0.56 (step @p119 :rule chain_m_resolution :premises (@p118 @p86) :args (@t81 @t63 @t86)) % 0.37/0.56 (step @p120 :rule chain_m_resolution :premises (@p92 @p86) :args (@t73 @t63 @t86)) % 0.37/0.56 (step @p121 :rule cnf_and_pos :args (@t87 1)) % 0.37/0.56 (step @p122 :rule reordering :premises (@p121) :args ((or @t74 @t88))) % 0.37/0.56 (step @p123 :rule chain_m_resolution :premises (@p122 @p120) :args (@t88 @t55 (@list @t73))) % 0.37/0.56 (step @p124 :rule cnf_equiv_pos1 :args (@t89)) % 0.37/0.56 (step @p125 :rule reordering :premises (@p124) :args ((or @t82 @t87 (not @t89)))) % 0.37/0.56 (step @p126 false :rule chain_m_resolution :premises (@p125 @p123 @p119 @p14) :args (false (@list true false false) (@list @t87 @t81 @t89))) % 0.37/0.56 ) % 0.37/0.56 % SZS output end Proof % 0.37/0.56 % cvc5 exiting %------------------------------------------------------------------------------