%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET606+3 : 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 : n025.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 08:48:11 AM UTC 2026 % Result : Theorem 0.46s 0.69s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET606+3 : TPTP v9.2.1. Released v2.2.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n025.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:04:46 EDT 2026 % 0.18/0.35 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.46/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.46/0.69 % SZS status Theorem % 0.46/0.69 % SZS output start Proof % 0.46/0.69 ( % 0.46/0.69 (declare-sort $$unsorted 0) % 0.46/0.69 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.46/0.69 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.69 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.69 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.46/0.69 (define @t1 () (@var "C" $$unsorted)) % 0.46/0.69 (define @t2 () (@var "B" $$unsorted)) % 0.46/0.69 (define @t3 () (= @t2 @t1)) % 0.46/0.69 (define @t4 () (@var "D" $$unsorted)) % 0.46/0.69 (define @t5 () (tptp.member @t4 @t1)) % 0.46/0.69 (define @t6 () (tptp.member @t4 @t2)) % 0.46/0.69 (define @t7 () (@list @t4)) % 0.46/0.69 (define @t8 () (forall @t7 (= @t6 @t5))) % 0.46/0.69 (define @t9 () (@list @t2 @t1)) % 0.46/0.69 (define @t10 () (forall @t9 (=> @t8 @t3))) % 0.46/0.69 (define @t11 () (tptp.intersection @t2 @t1)) % 0.46/0.69 (define @t12 () (@list @t2 @t1 @t4)) % 0.46/0.69 (define @t13 () (tptp.difference @t2 @t1)) % 0.46/0.69 (define @t14 () (tptp.subset @t2 @t1)) % 0.46/0.69 (define @t15 () (tptp.difference @t2 @t11)) % 0.46/0.69 (define @t16 () (forall @t9 (= @t15 @t13))) % 0.46/0.69 (define @t17 () (not @t16)) % 0.46/0.69 (define @t18 () (forall @t9 (= @t13 @t15))) % 0.46/0.69 (define @t19 () (@quantifiers_skolemize @t18 1)) % 0.46/0.69 (define @t20 () (@quantifiers_skolemize @t18 0)) % 0.46/0.69 (define @t21 () (tptp.intersection @t20 @t19)) % 0.46/0.69 (define @t22 () (tptp.difference @t20 @t21)) % 0.46/0.69 (define @t23 () (tptp.member @t4 @t22)) % 0.46/0.69 (define @t24 () (tptp.difference @t20 @t19)) % 0.46/0.69 (define @t25 () (tptp.member @t4 @t24)) % 0.46/0.69 (define @t26 () (forall @t7 (= @t25 @t23))) % 0.46/0.69 (define @t27 () (@quantifiers_skolemize @t26 0)) % 0.46/0.69 (define @t28 () (@list @t20 @t19 @t27)) % 0.46/0.69 (define @t29 () (forall @t7 (= @t23 @t25))) % 0.46/0.69 (define @t30 () (not @t29)) % 0.46/0.69 (define @t31 () (or @t30 (= @t22 @t24))) % 0.46/0.69 (define @t32 () (forall @t9 (or (not @t8) @t3))) % 0.46/0.69 (define @t33 () (= @t24 @t22)) % 0.46/0.69 (define @t34 () (not @t26)) % 0.46/0.69 (define @t35 () (or @t34 @t33)) % 0.46/0.69 (define @t36 () (@list false)) % 0.46/0.69 (define @t37 () (@list true false)) % 0.46/0.69 (define @t38 () (tptp.member @t27 @t22)) % 0.46/0.69 (define @t39 () (tptp.member @t27 @t24)) % 0.46/0.69 (define @t40 () (= @t39 @t38)) % 0.46/0.69 (define @t41 () (tptp.member @t27 @t19)) % 0.46/0.69 (define @t42 () (not @t41)) % 0.46/0.69 (define @t43 () (tptp.member @t27 @t20)) % 0.46/0.69 (define @t44 () (and @t43 @t42)) % 0.46/0.69 (define @t45 () (= @t39 @t44)) % 0.46/0.69 (define @t46 () (not @t45)) % 0.46/0.69 (define @t47 () (not @t39)) % 0.46/0.69 (define @t48 () (tptp.member @t27 @t21)) % 0.46/0.69 (define @t49 () (not @t48)) % 0.46/0.69 (define @t50 () (and @t43 @t49)) % 0.46/0.69 (define @t51 () (= @t38 @t50)) % 0.46/0.69 (define @t52 () (not @t51)) % 0.46/0.69 (define @t53 () (not @t50)) % 0.46/0.69 (define @t54 () (not @t44)) % 0.46/0.69 (define @t55 () (forall @t7 (or (not @t25) (tptp.member @t4 @t20)))) % 0.46/0.69 (define @t56 () (@quantifiers_skolemize @t55 0)) % 0.46/0.69 (define @t57 () (tptp.member @t56 @t24)) % 0.46/0.69 (define @t58 () (tptp.member @t56 @t20)) % 0.46/0.69 (define @t59 () (not @t57)) % 0.46/0.69 (define @t60 () (or @t59 @t58)) % 0.46/0.69 (define @t61 () (and @t58 (not (tptp.member @t56 @t19)))) % 0.46/0.69 (define @t62 () (= @t57 @t61)) % 0.46/0.69 (define @t63 () (@list false false true false)) % 0.46/0.69 (define @t64 () (not @t60)) % 0.46/0.69 (define @t65 () (not @t55)) % 0.46/0.69 (define @t66 () (@list @t27)) % 0.46/0.69 (define @t67 () (or @t47 @t43)) % 0.46/0.69 (define @t68 () (not @t43)) % 0.46/0.69 (define @t69 () (forall @t7 (or (not (tptp.member @t4 @t21)) (tptp.member @t4 @t19)))) % 0.46/0.69 (define @t70 () (@quantifiers_skolemize @t69 0)) % 0.46/0.69 (define @t71 () (tptp.member @t70 @t21)) % 0.46/0.69 (define @t72 () (tptp.member @t70 @t19)) % 0.46/0.69 (define @t73 () (not @t71)) % 0.46/0.69 (define @t74 () (or @t73 @t72)) % 0.46/0.69 (define @t75 () (and (tptp.member @t70 @t20) @t72)) % 0.46/0.69 (define @t76 () (= @t71 @t75)) % 0.46/0.69 (define @t77 () (not @t74)) % 0.46/0.69 (define @t78 () (not @t69)) % 0.46/0.69 (define @t79 () (or @t49 @t41)) % 0.46/0.69 (define @t80 () (@list false false)) % 0.46/0.69 (define @t81 () (and @t43 @t41)) % 0.46/0.69 (define @t82 () (= @t48 @t81)) % 0.46/0.69 (assume @p1 @t10) % 0.46/0.69 (assume @p2 (forall @t12 (= (tptp.member @t4 @t11) (and @t6 @t5)))) % 0.46/0.69 (assume @p3 (forall @t12 (= (tptp.member @t4 @t13) (and @t6 (not @t5))))) % 0.46/0.69 (assume @p4 (forall @t9 (= @t3 (and @t14 (tptp.subset @t1 @t2))))) % 0.46/0.69 (assume @p5 (forall @t9 (= @t11 (tptp.intersection @t1 @t2)))) % 0.46/0.69 (assume @p6 (forall @t9 (= @t3 @t8))) % 0.46/0.69 (assume @p7 (forall @t9 (= @t14 (forall @t7 (=> @t6 @t5))))) % 0.46/0.69 (assume @p8 (forall (@list @t2) (tptp.subset @t2 @t2))) % 0.46/0.69 (assume @p9 @t17) % 0.46/0.69 (assume @p10 true) % 0.46/0.69 (step @p11 :rule instantiate :premises (@p2) :args (@t28)) % 0.46/0.69 (step @p12 :rule instantiate :premises (@p3) :args ((@list @t20 @t21 @t27))) % 0.46/0.69 (step @p13 :rule bool-impl-elim :args (@t8 @t3)) % 0.46/0.69 (step @p14 :rule cong :premises (@p13) :args (@t10)) % 0.46/0.69 (step @p15 :rule eq_resolve :premises (@p1 @p14)) % 0.46/0.69 (step @p16 :rule eq-symm :args (@t22 @t24)) % 0.46/0.69 (step @p17 :rule eq-symm :args (@t23 @t25)) % 0.46/0.69 (step @p18 :rule cong :premises (@p17) :args (@t29)) % 0.46/0.69 (step @p19 :rule cong :premises (@p18) :args (@t30)) % 0.46/0.69 (step @p20 :rule nary_cong :premises (@p19 @p16) :args (@t31)) % 0.46/0.69 (step @p21 :rule refl :args (@t32)) % 0.46/0.69 (step @p22 :rule cong :premises (@p21 @p20) :args ((=> @t32 @t31))) % 0.46/0.69 (assume-push @p145 @t32) % 0.46/0.69 (step @p24 :rule instantiate :premises (@p15) :args ((@list @t22 @t24))) % 0.46/0.69 (step-pop @p146 :rule scope :premises (@p24)) % 0.46/0.69 (step @p25 :rule process_scope :premises (@p146) :args (@t31)) % 0.46/0.69 (step @p27 :rule eq_resolve :premises (@p25 @p22)) % 0.46/0.69 (step @p28 :rule implies_elim :premises (@p27)) % 0.46/0.69 (step @p29 :rule chain_m_resolution :premises (@p28 @p15) :args (@t35 @t36 (@list @t32))) % 0.46/0.69 (step @p30 :rule eq-symm :args (@t15 @t13)) % 0.46/0.69 (step @p31 :rule cong :premises (@p30) :args (@t16)) % 0.46/0.69 (step @p32 :rule cong :premises (@p31) :args (@t17)) % 0.46/0.69 (step @p33 :rule eq_resolve :premises (@p9 @p32)) % 0.46/0.69 (step @p34 :rule skolemize :premises (@p33)) % 0.46/0.69 (step @p35 :rule cnf_or_pos :args (@t35)) % 0.46/0.69 (step @p36 :rule reordering :premises (@p35) :args ((or @t33 @t34 (not @t35)))) % 0.46/0.69 (step @p37 :rule chain_m_resolution :premises (@p36 @p34 @p29) :args (@t34 @t37 (@list @t33 @t35))) % 0.46/0.69 (step @p38 :rule skolemize :premises (@p37)) % 0.46/0.69 (step @p39 :rule cnf_equiv_neg2 :args (@t40)) % 0.46/0.69 (step @p40 :rule instantiate :premises (@p3) :args (@t28)) % 0.46/0.69 (step @p41 :rule cnf_equiv_pos1 :args (@t45)) % 0.46/0.69 (step @p42 :rule reordering :premises (@p41) :args ((or @t47 @t44 @t46))) % 0.46/0.69 (step @p43 :rule cnf_equiv_pos2 :args (@t51)) % 0.46/0.69 (step @p44 :rule reordering :premises (@p43) :args ((or @t38 @t53 @t52))) % 0.46/0.69 (step @p45 :rule cnf_and_pos :args (@t44 1)) % 0.46/0.69 (step @p46 :rule reordering :premises (@p45) :args ((or @t42 @t54))) % 0.46/0.69 (step @p47 :rule cnf_and_pos :args (@t50 0)) % 0.46/0.69 (step @p48 :rule reordering :premises (@p47) :args ((or @t43 @t53))) % 0.46/0.69 (step @p49 :rule bool-double-not-elim :args (@t57)) % 0.46/0.69 (step @p50 :rule refl :args (@t60)) % 0.46/0.69 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or @t60 (not @t59)))) % 0.46/0.69 (step @p52 :rule cnf_or_neg :args (@t60 0)) % 0.46/0.69 (step @p53 :rule eq_resolve :premises (@p52 @p51)) % 0.46/0.69 (step @p54 :rule reordering :premises (@p53) :args ((or @t57 @t60))) % 0.46/0.69 (step @p55 :rule cnf_or_neg :args (@t60 1)) % 0.46/0.69 (step @p56 :rule instantiate :premises (@p3) :args ((@list @t20 @t19 @t56))) % 0.46/0.69 (step @p57 :rule cnf_equiv_pos1 :args (@t62)) % 0.46/0.69 (step @p58 :rule reordering :premises (@p57) :args ((or @t59 @t61 (not @t62)))) % 0.46/0.69 (step @p59 :rule cnf_and_pos :args (@t61 0)) % 0.46/0.69 (step @p60 :rule reordering :premises (@p59) :args ((or @t58 (not @t61)))) % 0.46/0.69 (step @p61 :rule chain_m_resolution :premises (@p60 @p58 @p56 @p55 @p54) :args (@t60 @t63 (@list @t61 @t62 @t58 @t57))) % 0.46/0.69 (step @p62 :rule refl :args (@t64)) % 0.46/0.69 (step @p63 :rule bool-double-not-elim :args (@t55)) % 0.46/0.69 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((or (not @t65) @t64))) % 0.46/0.69 (assume-push @p147 @t65) % 0.46/0.69 (step @p66 :rule skolemize :premises (@p147)) % 0.46/0.69 (step-pop @p148 :rule scope :premises (@p66)) % 0.46/0.69 (step @p67 :rule process_scope :premises (@p148) :args (@t64)) % 0.46/0.69 (step @p69 :rule implies_elim :premises (@p67)) % 0.46/0.69 (step @p70 :rule eq_resolve :premises (@p69 @p64)) % 0.46/0.69 (step @p71 :rule chain_m_resolution :premises (@p70 @p61) :args (@t55 @t36 (@list @t60))) % 0.46/0.69 (assume-push @p149 @t55) % 0.46/0.69 (step @p73 :rule instantiate :premises (@p149) :args (@t66)) % 0.46/0.69 (step-pop @p150 :rule scope :premises (@p73)) % 0.46/0.69 (step @p74 :rule process_scope :premises (@p150) :args (@t67)) % 0.46/0.69 (step @p76 :rule implies_elim :premises (@p74)) % 0.46/0.69 (step @p77 :rule chain_m_resolution :premises (@p76 @p71) :args (@t67 @t36 (@list @t55))) % 0.46/0.69 (step @p78 :rule cnf_or_pos :args (@t67)) % 0.46/0.69 (step @p79 :rule reordering :premises (@p78) :args ((or @t47 @t43 (not @t67)))) % 0.46/0.69 (step @p80 :rule cnf_equiv_pos1 :args (@t51)) % 0.46/0.69 (step @p81 :rule reordering :premises (@p80) :args ((or (not @t38) @t50 @t52))) % 0.46/0.69 (step @p82 :rule cnf_equiv_neg1 :args (@t40)) % 0.46/0.69 (step @p83 :rule reordering :premises (@p82) :args ((or @t39 @t38 @t40))) % 0.46/0.69 (step @p84 :rule chain_m_resolution :premises (@p83 @p38 @p81 @p12 @p79 @p77 @p48) :args (@t43 (@list true true false true false true) (@list @t40 @t38 @t51 @t39 @t67 @t50))) % 0.46/0.69 (step @p85 :rule bool-double-not-elim :args (@t48)) % 0.46/0.69 (step @p86 :rule refl :args (@t68)) % 0.46/0.69 (step @p87 :rule refl :args (@t50)) % 0.46/0.69 (step @p88 :rule nary_cong :premises (@p87 @p86 @p85) :args ((or @t50 @t68 (not @t49)))) % 0.46/0.69 (step @p89 :rule cnf_and_neg :args (@t50)) % 0.46/0.69 (step @p90 :rule eq_resolve :premises (@p89 @p88)) % 0.46/0.69 (step @p91 :rule reordering :premises (@p90) :args ((or @t48 @t50 @t68))) % 0.46/0.69 (step @p92 :rule bool-double-not-elim :args (@t71)) % 0.46/0.69 (step @p93 :rule refl :args (@t74)) % 0.46/0.69 (step @p94 :rule nary_cong :premises (@p93 @p92) :args ((or @t74 (not @t73)))) % 0.46/0.69 (step @p95 :rule cnf_or_neg :args (@t74 0)) % 0.46/0.69 (step @p96 :rule eq_resolve :premises (@p95 @p94)) % 0.46/0.69 (step @p97 :rule reordering :premises (@p96) :args ((or @t71 @t74))) % 0.46/0.69 (step @p98 :rule cnf_or_neg :args (@t74 1)) % 0.46/0.69 (step @p99 :rule instantiate :premises (@p2) :args ((@list @t20 @t19 @t70))) % 0.46/0.69 (step @p100 :rule cnf_equiv_pos1 :args (@t76)) % 0.46/0.69 (step @p101 :rule reordering :premises (@p100) :args ((or @t73 @t75 (not @t76)))) % 0.46/0.69 (step @p102 :rule cnf_and_pos :args (@t75 1)) % 0.46/0.69 (step @p103 :rule reordering :premises (@p102) :args ((or @t72 (not @t75)))) % 0.46/0.69 (step @p104 :rule chain_m_resolution :premises (@p103 @p101 @p99 @p98 @p97) :args (@t74 @t63 (@list @t75 @t76 @t72 @t71))) % 0.46/0.69 (step @p105 :rule refl :args (@t77)) % 0.46/0.69 (step @p106 :rule bool-double-not-elim :args (@t69)) % 0.46/0.69 (step @p107 :rule nary_cong :premises (@p106 @p105) :args ((or (not @t78) @t77))) % 0.46/0.69 (assume-push @p151 @t78) % 0.46/0.69 (step @p109 :rule skolemize :premises (@p151)) % 0.46/0.69 (step-pop @p152 :rule scope :premises (@p109)) % 0.46/0.69 (step @p110 :rule process_scope :premises (@p152) :args (@t77)) % 0.46/0.69 (step @p112 :rule implies_elim :premises (@p110)) % 0.46/0.69 (step @p113 :rule eq_resolve :premises (@p112 @p107)) % 0.46/0.69 (step @p114 :rule chain_m_resolution :premises (@p113 @p104) :args (@t69 @t36 (@list @t74))) % 0.46/0.69 (assume-push @p153 @t69) % 0.46/0.69 (step @p116 :rule instantiate :premises (@p153) :args (@t66)) % 0.46/0.69 (step-pop @p154 :rule scope :premises (@p116)) % 0.46/0.69 (step @p117 :rule process_scope :premises (@p154) :args (@t79)) % 0.46/0.69 (step @p119 :rule implies_elim :premises (@p117)) % 0.46/0.69 (step @p120 :rule chain_m_resolution :premises (@p119 @p114) :args (@t79 @t36 (@list @t69))) % 0.46/0.69 (step @p121 :rule cnf_or_pos :args (@t79)) % 0.46/0.69 (step @p122 :rule reordering :premises (@p121) :args ((or @t41 @t49 (not @t79)))) % 0.46/0.69 (step @p123 :rule chain_m_resolution :premises (@p122 @p120 @p91 @p84 @p46 @p44 @p12 @p42 @p40 @p39 @p38) :args (@t47 (@list false false false true true false false false true true) (@list @t79 @t48 @t43 @t41 @t50 @t51 @t44 @t45 @t38 @t40))) % 0.46/0.69 (step @p124 :rule chain_m_resolution :premises (@p83 @p123 @p38) :args (@t38 (@list true true) (@list @t39 @t40))) % 0.46/0.69 (step @p125 :rule chain_m_resolution :premises (@p81 @p124 @p12) :args (@t50 @t80 (@list @t38 @t51))) % 0.46/0.69 (step @p126 :rule cnf_and_pos :args (@t50 1)) % 0.46/0.69 (step @p127 :rule reordering :premises (@p126) :args ((or @t49 @t53))) % 0.46/0.69 (step @p128 :rule chain_m_resolution :premises (@p127 @p125) :args (@t49 @t36 (@list @t50))) % 0.46/0.69 (step @p129 :rule cnf_equiv_pos2 :args (@t45)) % 0.46/0.69 (step @p130 :rule reordering :premises (@p129) :args ((or @t39 @t54 @t46))) % 0.46/0.69 (step @p131 :rule chain_m_resolution :premises (@p130 @p123 @p40) :args (@t54 @t37 (@list @t39 @t45))) % 0.46/0.69 (step @p132 :rule bool-double-not-elim :args (@t41)) % 0.46/0.69 (step @p133 :rule refl :args (@t44)) % 0.46/0.69 (step @p134 :rule nary_cong :premises (@p133 @p86 @p132) :args ((or @t44 @t68 (not @t42)))) % 0.46/0.69 (step @p135 :rule cnf_and_neg :args (@t44)) % 0.46/0.69 (step @p136 :rule eq_resolve :premises (@p135 @p134)) % 0.46/0.69 (step @p137 :rule reordering :premises (@p136) :args ((or @t41 @t44 @t68))) % 0.46/0.69 (step @p138 :rule chain_m_resolution :premises (@p137 @p131 @p84) :args (@t41 @t37 (@list @t44 @t43))) % 0.46/0.69 (step @p139 :rule cnf_and_neg :args (@t81)) % 0.46/0.69 (step @p140 :rule reordering :premises (@p139) :args ((or @t42 @t68 @t81))) % 0.46/0.69 (step @p141 :rule chain_m_resolution :premises (@p140 @p138 @p84) :args (@t81 @t80 (@list @t41 @t43))) % 0.46/0.69 (step @p142 :rule cnf_equiv_pos2 :args (@t82)) % 0.46/0.69 (step @p143 :rule reordering :premises (@p142) :args ((or @t48 (not @t81) (not @t82)))) % 0.46/0.69 (step @p144 false :rule chain_m_resolution :premises (@p143 @p141 @p128 @p11) :args (false (@list false true false) (@list @t81 @t48 @t82))) % 0.46/0.69 ) % 0.46/0.69 % SZS output end Proof % 0.46/0.70 % cvc5 exiting %------------------------------------------------------------------------------