%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET979+1 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n006.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 08:49:05 AM UTC 2026 % Result : Theorem 0.33s 0.58s % Output : Proof 0.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET979+1 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n006.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:21:04 EDT 2026 % 0.17/0.35 % CPUTime : % 0.26/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.33/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.33/0.58 % SZS status Theorem % 0.33/0.58 % SZS output start Proof % 0.33/0.58 ( % 0.33/0.58 (declare-sort $$unsorted 0) % 0.33/0.58 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.33/0.58 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.33/0.58 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.33/0.58 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.33/0.58 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.33/0.58 (define @t1 () (@var "A" $$unsorted)) % 0.33/0.58 (define @t2 () (@var "B" $$unsorted)) % 0.33/0.58 (define @t3 () (tptp.unordered_pair @t1 @t2)) % 0.33/0.58 (define @t4 () (@list @t1 @t2)) % 0.33/0.58 (define @t5 () (tptp.set_union2 @t2 @t1)) % 0.33/0.58 (define @t6 () (tptp.set_union2 @t1 @t2)) % 0.33/0.58 (define @t7 () (tptp.empty @t1)) % 0.33/0.58 (define @t8 () (not @t7)) % 0.33/0.58 (define @t9 () (@list @t1)) % 0.33/0.58 (define @t10 () (@var "C" $$unsorted)) % 0.33/0.58 (define @t11 () (= (tptp.cartesian_product2 @t10 @t6) (tptp.set_union2 (tptp.cartesian_product2 @t10 @t1) (tptp.cartesian_product2 @t10 @t2)))) % 0.33/0.58 (define @t12 () (= (tptp.cartesian_product2 @t6 @t10) (tptp.set_union2 (tptp.cartesian_product2 @t1 @t10) (tptp.cartesian_product2 @t2 @t10)))) % 0.33/0.58 (define @t13 () (@list @t1 @t2 @t10)) % 0.33/0.58 (define @t14 () (forall @t13 (and @t12 @t11))) % 0.33/0.58 (define @t15 () (tptp.singleton @t2)) % 0.33/0.58 (define @t16 () (tptp.singleton @t1)) % 0.33/0.58 (define @t17 () (= (tptp.cartesian_product2 @t10 @t3) (tptp.set_union2 (tptp.cartesian_product2 @t10 @t16) (tptp.cartesian_product2 @t10 @t15)))) % 0.33/0.58 (define @t18 () (= (tptp.cartesian_product2 @t3 @t10) (tptp.set_union2 (tptp.cartesian_product2 @t16 @t10) (tptp.cartesian_product2 @t15 @t10)))) % 0.33/0.58 (define @t19 () (forall @t13 (and @t18 @t17))) % 0.33/0.58 (define @t20 () (not @t19)) % 0.33/0.58 (define @t21 () (forall @t13 @t11)) % 0.33/0.58 (define @t22 () (@list @t1 @t2 @t10)) % 0.33/0.58 (define @t23 () (forall @t13 @t12)) % 0.33/0.58 (define @t24 () (and @t23 @t21)) % 0.33/0.58 (define @t25 () (@var "BOUND_VARIABLE_7527" $$unsorted)) % 0.33/0.58 (define @t26 () (@var "BOUND_VARIABLE_7525" $$unsorted)) % 0.33/0.58 (define @t27 () (@var "BOUND_VARIABLE_7523" $$unsorted)) % 0.33/0.58 (define @t28 () (forall (@list @t27 @t26 @t25) (= (tptp.cartesian_product2 (tptp.unordered_pair @t27 @t26) @t25) (tptp.set_union2 (tptp.cartesian_product2 (tptp.singleton @t27) @t25) (tptp.cartesian_product2 (tptp.singleton @t26) @t25))))) % 0.33/0.58 (define @t29 () (@quantifiers_skolemize @t28 2)) % 0.33/0.58 (define @t30 () (@quantifiers_skolemize @t28 1)) % 0.33/0.58 (define @t31 () (tptp.singleton @t30)) % 0.33/0.58 (define @t32 () (@quantifiers_skolemize @t28 0)) % 0.33/0.58 (define @t33 () (tptp.singleton @t32)) % 0.33/0.58 (define @t34 () (tptp.cartesian_product2 (tptp.unordered_pair @t32 @t30) @t29)) % 0.33/0.58 (define @t35 () (= @t34 (tptp.set_union2 (tptp.cartesian_product2 @t33 @t29) (tptp.cartesian_product2 @t31 @t29)))) % 0.33/0.58 (define @t36 () (not @t35)) % 0.33/0.58 (define @t37 () (not @t28)) % 0.33/0.58 (define @t38 () (@list false)) % 0.33/0.58 (define @t39 () (@var "BOUND_VARIABLE_7541" $$unsorted)) % 0.33/0.58 (define @t40 () (@var "BOUND_VARIABLE_7543" $$unsorted)) % 0.33/0.58 (define @t41 () (@var "BOUND_VARIABLE_7539" $$unsorted)) % 0.33/0.58 (define @t42 () (forall (@list @t41 @t39 @t40) (= (tptp.cartesian_product2 @t40 (tptp.unordered_pair @t41 @t39)) (tptp.set_union2 (tptp.cartesian_product2 @t40 (tptp.singleton @t41)) (tptp.cartesian_product2 @t40 (tptp.singleton @t39)))))) % 0.33/0.58 (define @t43 () (@quantifiers_skolemize @t42 2)) % 0.33/0.58 (define @t44 () (@quantifiers_skolemize @t42 1)) % 0.33/0.58 (define @t45 () (tptp.singleton @t44)) % 0.33/0.58 (define @t46 () (@quantifiers_skolemize @t42 0)) % 0.33/0.58 (define @t47 () (tptp.singleton @t46)) % 0.33/0.58 (define @t48 () (tptp.cartesian_product2 @t43 (tptp.unordered_pair @t46 @t44))) % 0.33/0.58 (define @t49 () (= @t48 (tptp.set_union2 (tptp.cartesian_product2 @t43 @t47) (tptp.cartesian_product2 @t43 @t45)))) % 0.33/0.58 (define @t50 () (not @t49)) % 0.33/0.58 (define @t51 () (not @t42)) % 0.33/0.58 (define @t52 () (forall @t13 @t17)) % 0.33/0.58 (define @t53 () (forall @t13 @t18)) % 0.33/0.58 (define @t54 () (and @t53 @t52)) % 0.33/0.58 (assume @p1 (forall @t4 (= @t3 (tptp.unordered_pair @t2 @t1)))) % 0.33/0.58 (assume @p2 (forall @t4 (= @t6 @t5))) % 0.33/0.58 (assume @p3 (forall @t4 (=> @t8 (not (tptp.empty @t6))))) % 0.33/0.58 (assume @p4 (forall @t4 (=> @t8 (not (tptp.empty @t5))))) % 0.33/0.58 (assume @p5 (forall @t4 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.33/0.58 (assume @p6 (exists @t9 @t7)) % 0.33/0.58 (assume @p7 (exists @t9 @t8)) % 0.33/0.58 (assume @p8 @t14) % 0.33/0.58 (assume @p9 @t20) % 0.33/0.58 (assume @p10 (forall @t4 (= @t3 (tptp.set_union2 @t16 @t15)))) % 0.33/0.58 (assume @p11 true) % 0.33/0.58 (step @p12 :rule alpha_equiv :args (@t21 @t22 (@list (@var "BOUND_VARIABLE_7507" $$unsorted) (@var "BOUND_VARIABLE_7509" $$unsorted) (@var "BOUND_VARIABLE_7511" $$unsorted)))) % 0.33/0.58 (step @p13 :rule alpha_equiv :args (@t23 @t22 (@list (@var "BOUND_VARIABLE_7493" $$unsorted) (@var "BOUND_VARIABLE_7495" $$unsorted) (@var "BOUND_VARIABLE_7497" $$unsorted)))) % 0.33/0.58 (step @p14 :rule nary_cong :premises (@p13 @p12) :args (@t24)) % 0.33/0.58 (step @p15 :rule quant-miniscope-and :args ((= @t14 @t24))) % 0.33/0.58 (step @p16 :rule trans :premises (@p15 @p14)) % 0.33/0.58 (step @p17 :rule eq_resolve :premises (@p8 @p16)) % 0.33/0.58 (step @p18 :rule and_elim :premises (@p17) :args (0)) % 0.33/0.58 (step @p19 :rule instantiate :premises (@p18) :args ((@list @t33 @t31 @t29))) % 0.33/0.58 (step @p20 :rule refl :args (@t29)) % 0.33/0.58 (step @p21 :rule instantiate :premises (@p10) :args ((@list @t32 @t30))) % 0.33/0.58 (step @p22 :rule cong :premises (@p21 @p20) :args (@t34)) % 0.33/0.58 (step @p23 :rule trans :premises (@p22 @p19)) % 0.33/0.58 (step @p24 :rule refl :args (@t36)) % 0.33/0.58 (step @p25 :rule bool-double-not-elim :args (@t28)) % 0.33/0.58 (step @p26 :rule nary_cong :premises (@p25 @p24) :args ((or (not @t37) @t36))) % 0.33/0.58 (assume-push @p59 @t37) % 0.33/0.58 (step @p28 :rule skolemize :premises (@p59)) % 0.33/0.58 (step-pop @p60 :rule scope :premises (@p28)) % 0.33/0.58 (step @p29 :rule process_scope :premises (@p60) :args (@t36)) % 0.33/0.58 (step @p31 :rule implies_elim :premises (@p29)) % 0.33/0.58 (step @p32 :rule eq_resolve :premises (@p31 @p26)) % 0.33/0.58 (step @p33 :rule chain_m_resolution :premises (@p32 @p23) :args (@t28 @t38 (@list @t35))) % 0.33/0.58 (step @p34 :rule and_elim :premises (@p17) :args (1)) % 0.33/0.58 (step @p35 :rule instantiate :premises (@p34) :args ((@list @t47 @t45 @t43))) % 0.33/0.58 (step @p36 :rule instantiate :premises (@p10) :args ((@list @t46 @t44))) % 0.33/0.58 (step @p37 :rule refl :args (@t43)) % 0.33/0.58 (step @p38 :rule cong :premises (@p37 @p36) :args (@t48)) % 0.33/0.58 (step @p39 :rule trans :premises (@p38 @p35)) % 0.33/0.58 (step @p40 :rule refl :args (@t50)) % 0.33/0.58 (step @p41 :rule bool-double-not-elim :args (@t42)) % 0.33/0.58 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or (not @t51) @t50))) % 0.33/0.58 (assume-push @p61 @t51) % 0.33/0.58 (step @p44 :rule skolemize :premises (@p61)) % 0.33/0.58 (step-pop @p62 :rule scope :premises (@p44)) % 0.33/0.58 (step @p45 :rule process_scope :premises (@p62) :args (@t50)) % 0.33/0.58 (step @p47 :rule implies_elim :premises (@p45)) % 0.33/0.58 (step @p48 :rule eq_resolve :premises (@p47 @p42)) % 0.33/0.58 (step @p49 :rule chain_m_resolution :premises (@p48 @p39) :args (@t42 @t38 (@list @t49))) % 0.33/0.58 (step @p50 :rule alpha_equiv :args (@t52 @t22 (@list @t41 @t39 @t40))) % 0.33/0.58 (step @p51 :rule alpha_equiv :args (@t53 @t22 (@list @t27 @t26 @t25))) % 0.33/0.58 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t54)) % 0.33/0.58 (step @p53 :rule quant-miniscope-and :args ((= @t19 @t54))) % 0.33/0.58 (step @p54 :rule trans :premises (@p53 @p52)) % 0.33/0.58 (step @p55 :rule cong :premises (@p54) :args (@t20)) % 0.33/0.58 (step @p56 :rule eq_resolve :premises (@p9 @p55)) % 0.33/0.58 (step @p57 :rule not_and :premises (@p56)) % 0.33/0.58 (step @p58 false :rule chain_m_resolution :premises (@p57 @p49 @p33) :args (false (@list false false) (@list @t42 @t28))) % 0.33/0.58 ) % 0.33/0.58 % SZS output end Proof % 0.33/0.59 % cvc5 exiting %------------------------------------------------------------------------------