%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET694+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 : n024.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 08:48:27 AM UTC 2026 % Result : Theorem 0.16s 0.37s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SET694+4 : TPTP v9.2.1. Released v2.2.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 11:07:15 EDT 2026 % 0.07/0.25 % CPUTime : % 0.07/0.32 %----Proving TF0_NAR, FOF, or CNF % 0.16/0.37 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.16/0.37 % SZS status Theorem % 0.16/0.37 % SZS output start Proof % 0.16/0.37 ( % 0.16/0.37 (declare-sort $$unsorted 0) % 0.16/0.37 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.empty_set $$unsorted) % 0.16/0.37 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.16/0.37 (define @t1 () (@var "B" $$unsorted)) % 0.16/0.37 (define @t2 () (@var "X" $$unsorted)) % 0.16/0.37 (define @t3 () (tptp.member @t2 @t1)) % 0.16/0.37 (define @t4 () (@var "A" $$unsorted)) % 0.16/0.37 (define @t5 () (tptp.member @t2 @t4)) % 0.16/0.37 (define @t6 () (@list @t2)) % 0.16/0.37 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.16/0.37 (define @t8 () (tptp.subset @t4 @t1)) % 0.16/0.37 (define @t9 () (= @t8 @t7)) % 0.16/0.37 (define @t10 () (@list @t4 @t1)) % 0.16/0.37 (define @t11 () (forall @t10 @t9)) % 0.16/0.37 (define @t12 () (tptp.power_set @t4)) % 0.16/0.37 (define @t13 () (@list @t2 @t4)) % 0.16/0.37 (define @t14 () (@list @t2 @t4 @t1)) % 0.16/0.37 (define @t15 () (tptp.union @t4 @t1)) % 0.16/0.37 (define @t16 () (@var "E" $$unsorted)) % 0.16/0.37 (define @t17 () (= @t2 @t4)) % 0.16/0.37 (define @t18 () (@var "Y" $$unsorted)) % 0.16/0.37 (define @t19 () (tptp.member @t2 @t18)) % 0.16/0.37 (define @t20 () (tptp.member @t18 @t4)) % 0.16/0.37 (define @t21 () (@list @t18)) % 0.16/0.37 (define @t22 () (forall @t10 (tptp.subset (tptp.union @t12 (tptp.power_set @t1)) (tptp.power_set @t15)))) % 0.16/0.37 (define @t23 () (@quantifiers_skolemize @t22 1)) % 0.16/0.37 (define @t24 () (@quantifiers_skolemize @t22 0)) % 0.16/0.37 (define @t25 () (tptp.union @t24 @t23)) % 0.16/0.37 (define @t26 () (tptp.power_set @t25)) % 0.16/0.37 (define @t27 () (tptp.power_set @t23)) % 0.16/0.37 (define @t28 () (tptp.power_set @t24)) % 0.16/0.37 (define @t29 () (tptp.union @t28 @t27)) % 0.16/0.37 (define @t30 () (forall @t6 (or (not (tptp.member @t2 @t29)) (tptp.member @t2 @t26)))) % 0.16/0.37 (define @t31 () (@quantifiers_skolemize @t30 0)) % 0.16/0.37 (define @t32 () (@list @t31 @t23)) % 0.16/0.37 (define @t33 () (tptp.subset @t29 @t26)) % 0.16/0.37 (define @t34 () (= @t33 @t30)) % 0.16/0.37 (define @t35 () (not @t30)) % 0.16/0.37 (define @t36 () (@list true false)) % 0.16/0.37 (define @t37 () (tptp.member @t31 @t29)) % 0.16/0.37 (define @t38 () (tptp.member @t31 @t26)) % 0.16/0.37 (define @t39 () (not @t37)) % 0.16/0.37 (define @t40 () (or @t39 @t38)) % 0.16/0.37 (define @t41 () (@list true)) % 0.16/0.37 (define @t42 () (@list @t40)) % 0.16/0.37 (define @t43 () (tptp.member @t31 @t27)) % 0.16/0.37 (define @t44 () (tptp.member @t31 @t28)) % 0.16/0.37 (define @t45 () (or @t44 @t43)) % 0.16/0.37 (define @t46 () (= @t37 @t45)) % 0.16/0.37 (define @t47 () (@list false false)) % 0.16/0.37 (define @t48 () (@list @t31 @t24)) % 0.16/0.37 (define @t49 () (not (tptp.member @t2 @t31))) % 0.16/0.37 (define @t50 () (forall @t6 (or @t49 (tptp.member @t2 @t25)))) % 0.16/0.37 (define @t51 () (@quantifiers_skolemize @t50 0)) % 0.16/0.37 (define @t52 () (@list @t31 @t25)) % 0.16/0.37 (define @t53 () (tptp.subset @t31 @t25)) % 0.16/0.37 (define @t54 () (= @t38 @t53)) % 0.16/0.37 (define @t55 () (not @t53)) % 0.16/0.37 (define @t56 () (= @t53 @t50)) % 0.16/0.37 (define @t57 () (not @t50)) % 0.16/0.37 (define @t58 () (tptp.member @t51 @t25)) % 0.16/0.37 (define @t59 () (tptp.member @t51 @t31)) % 0.16/0.37 (define @t60 () (not @t59)) % 0.16/0.37 (define @t61 () (or @t60 @t58)) % 0.16/0.37 (define @t62 () (@list @t61)) % 0.16/0.37 (define @t63 () (tptp.member @t51 @t23)) % 0.16/0.37 (define @t64 () (tptp.member @t51 @t24)) % 0.16/0.37 (define @t65 () (or @t64 @t63)) % 0.16/0.37 (define @t66 () (= @t58 @t65)) % 0.16/0.37 (define @t67 () (not @t65)) % 0.16/0.37 (define @t68 () (@list @t65)) % 0.16/0.37 (define @t69 () (or @t60 @t64)) % 0.16/0.37 (define @t70 () (not @t69)) % 0.16/0.37 (define @t71 () (@list false true)) % 0.16/0.37 (define @t72 () (forall @t6 (or @t49 (tptp.member @t2 @t24)))) % 0.16/0.37 (define @t73 () (@list @t51)) % 0.16/0.37 (define @t74 () (tptp.subset @t31 @t24)) % 0.16/0.37 (define @t75 () (= @t74 @t72)) % 0.16/0.37 (define @t76 () (not @t74)) % 0.16/0.37 (define @t77 () (= @t44 @t74)) % 0.16/0.37 (define @t78 () (not @t44)) % 0.16/0.37 (define @t79 () (tptp.subset @t31 @t23)) % 0.16/0.37 (define @t80 () (= @t43 @t79)) % 0.16/0.37 (define @t81 () (forall @t6 (or @t49 (tptp.member @t2 @t23)))) % 0.16/0.37 (define @t82 () (= @t79 @t81)) % 0.16/0.37 (define @t83 () (or @t60 @t63)) % 0.16/0.37 (define @t84 () (not @t83)) % 0.16/0.37 (assume @p1 @t11) % 0.16/0.37 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.16/0.37 (assume @p3 (forall @t13 (= (tptp.member @t2 @t12) (tptp.subset @t2 @t4)))) % 0.16/0.37 (assume @p4 (forall @t14 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.16/0.37 (assume @p5 (forall @t14 (= (tptp.member @t2 @t15) (or @t5 @t3)))) % 0.16/0.37 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.16/0.37 (assume @p7 (forall (@list @t1 @t4 @t16) (= (tptp.member @t1 (tptp.difference @t16 @t4)) (and (tptp.member @t1 @t16) (not (tptp.member @t1 @t4)))))) % 0.16/0.37 (assume @p8 (forall @t13 (= (tptp.member @t2 (tptp.singleton @t4)) @t17))) % 0.16/0.37 (assume @p9 (forall @t14 (= (tptp.member @t2 (tptp.unordered_pair @t4 @t1)) (or @t17 (= @t2 @t1))))) % 0.16/0.37 (assume @p10 (forall @t13 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t21 (and @t20 @t19))))) % 0.16/0.37 (assume @p11 (forall @t13 (= (tptp.member @t2 (tptp.product @t4)) (forall @t21 (=> @t20 @t19))))) % 0.16/0.37 (assume @p12 (not @t22)) % 0.16/0.37 (assume @p13 true) % 0.16/0.37 (step @p14 :rule bool-impl-elim :args (@t5 @t3)) % 0.16/0.37 (step @p15 :rule cong :premises (@p14) :args (@t7)) % 0.16/0.37 (step @p16 :rule refl :args (@t8)) % 0.16/0.37 (step @p17 :rule cong :premises (@p16 @p15) :args (@t9)) % 0.16/0.37 (step @p18 :rule cong :premises (@p17) :args (@t11)) % 0.16/0.37 (step @p19 :rule eq_resolve :premises (@p1 @p18)) % 0.16/0.37 (step @p20 :rule instantiate :premises (@p19) :args (@t32)) % 0.16/0.37 (step @p21 :rule instantiate :premises (@p3) :args (@t32)) % 0.16/0.37 (step @p22 :rule instantiate :premises (@p5) :args ((@list @t31 @t28 @t27))) % 0.16/0.37 (step @p23 :rule instantiate :premises (@p19) :args ((@list @t29 @t26))) % 0.16/0.37 (step @p24 :rule skolemize :premises (@p12)) % 0.16/0.37 (step @p25 :rule cnf_equiv_pos2 :args (@t34)) % 0.16/0.37 (step @p26 :rule reordering :premises (@p25) :args ((or @t33 @t35 (not @t34)))) % 0.16/0.37 (step @p27 :rule chain_m_resolution :premises (@p26 @p24 @p23) :args (@t35 @t36 (@list @t33 @t34))) % 0.16/0.37 (step @p28 :rule skolemize :premises (@p27)) % 0.16/0.37 (step @p29 :rule bool-double-not-elim :args (@t37)) % 0.16/0.37 (step @p30 :rule refl :args (@t40)) % 0.16/0.37 (step @p31 :rule nary_cong :premises (@p30 @p29) :args ((or @t40 (not @t39)))) % 0.16/0.37 (step @p32 :rule cnf_or_neg :args (@t40 0)) % 0.16/0.37 (step @p33 :rule eq_resolve :premises (@p32 @p31)) % 0.16/0.37 (step @p34 :rule reordering :premises (@p33) :args ((or @t37 @t40))) % 0.16/0.37 (step @p35 :rule chain_m_resolution :premises (@p34 @p28) :args (@t37 @t41 @t42)) % 0.16/0.37 (step @p36 :rule cnf_equiv_pos1 :args (@t46)) % 0.16/0.37 (step @p37 :rule reordering :premises (@p36) :args ((or @t39 @t45 (not @t46)))) % 0.16/0.37 (step @p38 :rule chain_m_resolution :premises (@p37 @p35 @p22) :args (@t45 @t47 (@list @t37 @t46))) % 0.16/0.37 (step @p39 :rule instantiate :premises (@p3) :args (@t48)) % 0.16/0.37 (step @p40 :rule instantiate :premises (@p19) :args (@t48)) % 0.16/0.37 (step @p41 :rule instantiate :premises (@p5) :args ((@list @t51 @t24 @t23))) % 0.16/0.37 (step @p42 :rule instantiate :premises (@p19) :args (@t52)) % 0.16/0.37 (step @p43 :rule instantiate :premises (@p3) :args (@t52)) % 0.16/0.37 (step @p44 :rule cnf_or_neg :args (@t40 1)) % 0.16/0.37 (step @p45 :rule chain_m_resolution :premises (@p44 @p28) :args ((not @t38) @t41 @t42)) % 0.16/0.37 (step @p46 :rule cnf_equiv_pos2 :args (@t54)) % 0.16/0.37 (step @p47 :rule reordering :premises (@p46) :args ((or @t38 @t55 (not @t54)))) % 0.16/0.37 (step @p48 :rule chain_m_resolution :premises (@p47 @p45 @p43) :args (@t55 @t36 (@list @t38 @t54))) % 0.16/0.37 (step @p49 :rule cnf_equiv_pos2 :args (@t56)) % 0.16/0.37 (step @p50 :rule reordering :premises (@p49) :args ((or @t53 @t57 (not @t56)))) % 0.16/0.37 (step @p51 :rule chain_m_resolution :premises (@p50 @p48 @p42) :args (@t57 @t36 (@list @t53 @t56))) % 0.16/0.37 (step @p52 :rule skolemize :premises (@p51)) % 0.16/0.37 (step @p53 :rule cnf_or_neg :args (@t61 1)) % 0.16/0.37 (step @p54 :rule chain_m_resolution :premises (@p53 @p52) :args ((not @t58) @t41 @t62)) % 0.16/0.37 (step @p55 :rule cnf_equiv_pos2 :args (@t66)) % 0.16/0.37 (step @p56 :rule reordering :premises (@p55) :args ((or @t58 @t67 (not @t66)))) % 0.16/0.37 (step @p57 :rule chain_m_resolution :premises (@p56 @p54 @p41) :args (@t67 @t36 (@list @t58 @t66))) % 0.16/0.37 (step @p58 :rule cnf_or_neg :args (@t65 0)) % 0.16/0.37 (step @p59 :rule chain_m_resolution :premises (@p58 @p57) :args ((not @t64) @t41 @t68)) % 0.16/0.37 (step @p60 :rule bool-double-not-elim :args (@t59)) % 0.16/0.37 (step @p61 :rule refl :args (@t61)) % 0.16/0.37 (step @p62 :rule nary_cong :premises (@p61 @p60) :args ((or @t61 (not @t60)))) % 0.16/0.37 (step @p63 :rule cnf_or_neg :args (@t61 0)) % 0.16/0.37 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 0.16/0.37 (step @p65 :rule reordering :premises (@p64) :args ((or @t59 @t61))) % 0.16/0.37 (step @p66 :rule chain_m_resolution :premises (@p65 @p52) :args (@t59 @t41 @t62)) % 0.16/0.37 (step @p67 :rule cnf_or_pos :args (@t69)) % 0.16/0.37 (step @p68 :rule reordering :premises (@p67) :args ((or @t60 @t64 @t70))) % 0.16/0.37 (step @p69 :rule chain_m_resolution :premises (@p68 @p66 @p59) :args (@t70 @t71 (@list @t59 @t64))) % 0.16/0.37 (assume-push @p102 @t72) % 0.16/0.37 (step @p71 :rule instantiate :premises (@p102) :args (@t73)) % 0.16/0.37 (step-pop @p103 :rule scope :premises (@p71)) % 0.16/0.37 (step @p72 :rule process_scope :premises (@p103) :args (@t69)) % 0.16/0.37 (step @p74 :rule implies_elim :premises (@p72)) % 0.16/0.37 (step @p75 :rule chain_m_resolution :premises (@p74 @p69) :args ((not @t72) @t41 (@list @t69))) % 0.16/0.37 (step @p76 :rule cnf_equiv_pos1 :args (@t75)) % 0.16/0.37 (step @p77 :rule reordering :premises (@p76) :args ((or @t76 @t72 (not @t75)))) % 0.16/0.37 (step @p78 :rule chain_m_resolution :premises (@p77 @p75 @p40) :args (@t76 @t36 (@list @t72 @t75))) % 0.16/0.37 (step @p79 :rule cnf_equiv_pos1 :args (@t77)) % 0.16/0.37 (step @p80 :rule reordering :premises (@p79) :args ((or @t78 @t74 (not @t77)))) % 0.16/0.37 (step @p81 :rule chain_m_resolution :premises (@p80 @p78 @p39) :args (@t78 @t36 (@list @t74 @t77))) % 0.16/0.37 (step @p82 :rule cnf_or_pos :args (@t45)) % 0.16/0.37 (step @p83 :rule reordering :premises (@p82) :args ((or @t44 @t43 (not @t45)))) % 0.16/0.37 (step @p84 :rule chain_m_resolution :premises (@p83 @p81 @p38) :args (@t43 @t36 (@list @t44 @t45))) % 0.16/0.37 (step @p85 :rule cnf_equiv_pos1 :args (@t80)) % 0.16/0.37 (step @p86 :rule reordering :premises (@p85) :args ((or (not @t43) @t79 (not @t80)))) % 0.16/0.37 (step @p87 :rule chain_m_resolution :premises (@p86 @p84 @p21) :args (@t79 @t47 (@list @t43 @t80))) % 0.16/0.37 (step @p88 :rule cnf_equiv_pos1 :args (@t82)) % 0.16/0.37 (step @p89 :rule reordering :premises (@p88) :args ((or (not @t79) @t81 (not @t82)))) % 0.16/0.37 (step @p90 :rule chain_m_resolution :premises (@p89 @p87 @p20) :args (@t81 @t47 (@list @t79 @t82))) % 0.16/0.37 (step @p91 :rule cnf_or_neg :args (@t65 1)) % 0.16/0.37 (step @p92 :rule chain_m_resolution :premises (@p91 @p57) :args ((not @t63) @t41 @t68)) % 0.16/0.37 (step @p93 :rule cnf_or_pos :args (@t83)) % 0.16/0.37 (step @p94 :rule reordering :premises (@p93) :args ((or @t60 @t63 @t84))) % 0.16/0.37 (step @p95 :rule chain_m_resolution :premises (@p94 @p66 @p92) :args (@t84 @t71 (@list @t59 @t63))) % 0.16/0.37 (assume-push @p104 @t81) % 0.16/0.37 (step @p97 :rule instantiate :premises (@p104) :args (@t73)) % 0.16/0.37 (step-pop @p105 :rule scope :premises (@p97)) % 0.16/0.37 (step @p98 :rule process_scope :premises (@p105) :args (@t83)) % 0.16/0.37 (step @p100 :rule implies_elim :premises (@p98)) % 0.16/0.37 (step @p101 false :rule chain_m_resolution :premises (@p100 @p95 @p90) :args (false @t36 (@list @t83 @t81))) % 0.16/0.37 ) % 0.16/0.37 % SZS output end Proof % 0.16/0.37 % cvc5 exiting %------------------------------------------------------------------------------