%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET984+1 : TPTP v9.2.1. Released v3.2.0. % 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 08:49:05 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 : SET984+1 : TPTP v9.2.1. Released v3.2.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n017.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 16:19:31 EDT 2026 % 0.18/0.34 % CPUTime : % 0.28/0.49 %----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 $$unsorted 0) % 0.37/0.56 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.37/0.56 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.56 (declare-const tptp.empty_set $$unsorted) % 0.37/0.56 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.56 (define @t1 () (@var "A" $$unsorted)) % 0.37/0.56 (define @t2 () (@var "B" $$unsorted)) % 0.37/0.56 (define @t3 () (tptp.set_intersection2 @t1 @t2)) % 0.37/0.56 (define @t4 () (@list @t1 @t2)) % 0.37/0.56 (define @t5 () (tptp.empty @t1)) % 0.37/0.56 (define @t6 () (@list @t1)) % 0.37/0.56 (define @t7 () (= @t2 tptp.empty_set)) % 0.37/0.56 (define @t8 () (= @t1 tptp.empty_set)) % 0.37/0.56 (define @t9 () (or @t8 @t7)) % 0.37/0.56 (define @t10 () (tptp.cartesian_product2 @t1 @t2)) % 0.37/0.56 (define @t11 () (= @t10 tptp.empty_set)) % 0.37/0.56 (define @t12 () (= @t11 @t9)) % 0.37/0.56 (define @t13 () (forall @t4 @t12)) % 0.37/0.56 (define @t14 () (@var "D" $$unsorted)) % 0.37/0.56 (define @t15 () (@var "C" $$unsorted)) % 0.37/0.56 (define @t16 () (@list @t1 @t2 @t15 @t14)) % 0.37/0.56 (define @t17 () (forall @t16 (= (tptp.cartesian_product2 @t3 (tptp.set_intersection2 @t15 @t14)) (tptp.set_intersection2 (tptp.cartesian_product2 @t1 @t15) (tptp.cartesian_product2 @t2 @t14))))) % 0.37/0.56 (define @t18 () (and (= @t1 @t15) (= @t2 @t14))) % 0.37/0.56 (define @t19 () (or @t8 @t7 @t18)) % 0.37/0.56 (define @t20 () (tptp.cartesian_product2 @t15 @t14)) % 0.37/0.56 (define @t21 () (= @t10 @t20)) % 0.37/0.56 (define @t22 () (forall @t16 (=> @t21 @t19))) % 0.37/0.56 (define @t23 () (and (tptp.subset @t1 @t15) (tptp.subset @t2 @t14))) % 0.37/0.56 (define @t24 () (or @t11 @t23)) % 0.37/0.56 (define @t25 () (tptp.subset @t10 @t20)) % 0.37/0.56 (define @t26 () (=> @t25 @t24)) % 0.37/0.56 (define @t27 () (forall @t16 @t26)) % 0.37/0.56 (define @t28 () (not @t27)) % 0.37/0.56 (define @t29 () (tptp.subset @t1 @t2)) % 0.37/0.56 (define @t30 () (=> @t29 (= @t3 @t1))) % 0.37/0.56 (define @t31 () (forall @t4 @t30)) % 0.37/0.56 (define @t32 () (= tptp.empty_set @t10)) % 0.37/0.56 (define @t33 () (not @t25)) % 0.37/0.56 (define @t34 () (or @t33 @t32 @t23)) % 0.37/0.56 (define @t35 () (or @t32 @t23)) % 0.37/0.56 (define @t36 () (forall @t16 @t34)) % 0.37/0.56 (define @t37 () (@quantifiers_skolemize @t36 3)) % 0.37/0.56 (define @t38 () (@quantifiers_skolemize @t36 1)) % 0.37/0.56 (define @t39 () (tptp.subset @t38 @t37)) % 0.37/0.56 (define @t40 () (@quantifiers_skolemize @t36 2)) % 0.37/0.56 (define @t41 () (@quantifiers_skolemize @t36 0)) % 0.37/0.56 (define @t42 () (tptp.subset @t41 @t40)) % 0.37/0.56 (define @t43 () (and @t42 @t39)) % 0.37/0.56 (define @t44 () (tptp.cartesian_product2 @t41 @t38)) % 0.37/0.56 (define @t45 () (= tptp.empty_set @t44)) % 0.37/0.56 (define @t46 () (tptp.cartesian_product2 @t40 @t37)) % 0.37/0.56 (define @t47 () (tptp.subset @t44 @t46)) % 0.37/0.56 (define @t48 () (not @t47)) % 0.37/0.56 (define @t49 () (or @t48 @t45 @t43)) % 0.37/0.56 (define @t50 () (@list true)) % 0.37/0.56 (define @t51 () (@list @t49)) % 0.37/0.56 (define @t52 () (not @t21)) % 0.37/0.56 (define @t53 () (or @t52 @t8 @t7 @t18)) % 0.37/0.56 (define @t54 () (tptp.set_intersection2 @t38 @t37)) % 0.37/0.56 (define @t55 () (= @t38 @t54)) % 0.37/0.56 (define @t56 () (tptp.set_intersection2 @t41 @t40)) % 0.37/0.56 (define @t57 () (= @t41 @t56)) % 0.37/0.56 (define @t58 () (and @t57 @t55)) % 0.37/0.56 (define @t59 () (tptp.cartesian_product2 @t56 @t54)) % 0.37/0.56 (define @t60 () (= @t44 @t59)) % 0.37/0.56 (define @t61 () (not @t60)) % 0.37/0.56 (define @t62 () (= @t38 tptp.empty_set)) % 0.37/0.56 (define @t63 () (= @t41 tptp.empty_set)) % 0.37/0.56 (define @t64 () (or @t61 @t63 @t62 @t58)) % 0.37/0.56 (define @t65 () (forall @t16 @t53)) % 0.37/0.56 (define @t66 () (= tptp.empty_set @t38)) % 0.37/0.56 (define @t67 () (= tptp.empty_set @t41)) % 0.37/0.56 (define @t68 () (or @t61 @t67 @t66 @t58)) % 0.37/0.56 (define @t69 () (@list false)) % 0.37/0.56 (define @t70 () (tptp.set_intersection2 @t44 @t46)) % 0.37/0.56 (define @t71 () (= @t59 @t70)) % 0.37/0.56 (define @t72 () (= @t1 @t3)) % 0.37/0.56 (define @t73 () (= @t44 @t70)) % 0.37/0.56 (define @t74 () (or @t48 @t73)) % 0.37/0.56 (define @t75 () (or @t63 @t62)) % 0.37/0.56 (define @t76 () (forall @t4 (= @t9 @t32))) % 0.37/0.56 (define @t77 () (= @t75 @t45)) % 0.37/0.56 (define @t78 () (or @t67 @t66)) % 0.37/0.56 (define @t79 () (= @t45 @t78)) % 0.37/0.56 (define @t80 () (not @t78)) % 0.37/0.56 (define @t81 () (@list @t78)) % 0.37/0.56 (define @t82 () (not @t58)) % 0.37/0.56 (define @t83 () (@list @t58)) % 0.37/0.56 (assume @p1 (forall @t4 (= @t3 (tptp.set_intersection2 @t2 @t1)))) % 0.37/0.56 (assume @p2 (tptp.empty tptp.empty_set)) % 0.37/0.56 (assume @p3 (forall @t4 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 0.37/0.56 (assume @p4 (exists @t6 @t5)) % 0.37/0.56 (assume @p5 (exists @t6 (not @t5))) % 0.37/0.56 (assume @p6 (forall @t4 (tptp.subset @t1 @t1))) % 0.37/0.56 (assume @p7 @t13) % 0.37/0.56 (assume @p8 @t17) % 0.37/0.56 (assume @p9 @t22) % 0.37/0.56 (assume @p10 @t28) % 0.37/0.56 (assume @p11 (forall @t4 (tptp.subset @t3 @t1))) % 0.37/0.56 (assume @p12 @t31) % 0.37/0.56 (assume @p13 true) % 0.37/0.56 (step @p14 :rule aci_norm :args ((= (or @t33 @t35) @t34))) % 0.37/0.56 (step @p15 :rule bool-impl-elim :args (@t25 @t35)) % 0.37/0.56 (step @p16 :rule trans :premises (@p15 @p14)) % 0.37/0.56 (step @p17 :rule cong :premises (@p16) :args ((forall @t16 (=> @t25 @t35)))) % 0.37/0.56 (step @p18 :rule refl :args (@t23)) % 0.37/0.56 (step @p19 :rule eq-symm :args (@t10 tptp.empty_set)) % 0.37/0.56 (step @p20 :rule nary_cong :premises (@p19 @p18) :args (@t24)) % 0.37/0.56 (step @p21 :rule refl :args (@t25)) % 0.37/0.56 (step @p22 :rule cong :premises (@p21 @p20) :args (@t26)) % 0.37/0.56 (step @p23 :rule cong :premises (@p22) :args (@t27)) % 0.37/0.56 (step @p24 :rule trans :premises (@p23 @p17)) % 0.37/0.56 (step @p25 :rule cong :premises (@p24) :args (@t28)) % 0.37/0.56 (step @p26 :rule eq_resolve :premises (@p10 @p25)) % 0.37/0.56 (step @p27 :rule skolemize :premises (@p26)) % 0.37/0.56 (step @p28 :rule cnf_or_neg :args (@t49 2)) % 0.37/0.56 (step @p29 :rule chain_m_resolution :premises (@p28 @p27) :args ((not @t43) @t50 @t51)) % 0.37/0.56 (step @p30 :rule instantiate :premises (@p11) :args ((@list @t40 @t41))) % 0.37/0.56 (step @p31 :rule true_intro :premises (@p30)) % 0.37/0.56 (step @p32 :rule refl :args (@t40)) % 0.37/0.56 (step @p33 :rule instantiate :premises (@p1) :args ((@list @t41 @t40))) % 0.37/0.56 (step @p34 :rule aci_norm :args ((= (or @t52 @t19) @t53))) % 0.37/0.56 (step @p35 :rule bool-impl-elim :args (@t21 @t19)) % 0.37/0.56 (step @p36 :rule trans :premises (@p35 @p34)) % 0.37/0.56 (step @p37 :rule cong :premises (@p36) :args (@t22)) % 0.37/0.56 (step @p38 :rule eq_resolve :premises (@p9 @p37)) % 0.37/0.56 (step @p39 :rule refl :args (@t58)) % 0.37/0.56 (step @p40 :rule eq-symm :args (@t38 tptp.empty_set)) % 0.37/0.56 (step @p41 :rule eq-symm :args (@t41 tptp.empty_set)) % 0.37/0.56 (step @p42 :rule refl :args (@t61)) % 0.37/0.56 (step @p43 :rule nary_cong :premises (@p42 @p41 @p40 @p39) :args (@t64)) % 0.37/0.56 (step @p44 :rule refl :args (@t65)) % 0.37/0.56 (step @p45 :rule cong :premises (@p44 @p43) :args ((=> @t65 @t64))) % 0.37/0.56 (assume-push @p135 @t65) % 0.37/0.56 (step @p47 :rule instantiate :premises (@p38) :args ((@list @t41 @t38 @t56 @t54))) % 0.37/0.56 (step-pop @p136 :rule scope :premises (@p47)) % 0.37/0.56 (step @p48 :rule process_scope :premises (@p136) :args (@t64)) % 0.37/0.56 (step @p50 :rule eq_resolve :premises (@p48 @p45)) % 0.37/0.56 (step @p51 :rule implies_elim :premises (@p50)) % 0.37/0.56 (step @p52 :rule chain_m_resolution :premises (@p51 @p38) :args (@t68 @t69 (@list @t65))) % 0.37/0.56 (step @p53 :rule eq-symm :args (@t59 @t70)) % 0.37/0.56 (step @p54 :rule refl :args (@t17)) % 0.37/0.56 (step @p55 :rule cong :premises (@p54 @p53) :args ((=> @t17 @t71))) % 0.37/0.56 (assume-push @p137 @t17) % 0.37/0.56 (step @p57 :rule instantiate :premises (@p8) :args ((@list @t41 @t40 @t38 @t37))) % 0.37/0.56 (step-pop @p138 :rule scope :premises (@p57)) % 0.37/0.56 (step @p58 :rule process_scope :premises (@p138) :args (@t71)) % 0.37/0.56 (step @p60 :rule eq_resolve :premises (@p58 @p55)) % 0.37/0.56 (step @p61 :rule implies_elim :premises (@p60)) % 0.37/0.56 (step @p62 :rule chain_m_resolution :premises (@p61 @p8) :args ((= @t70 @t59) @t69 (@list @t17))) % 0.37/0.56 (step @p63 :rule bool-impl-elim :args (@t29 @t72)) % 0.37/0.56 (step @p64 :rule cong :premises (@p63) :args ((forall @t4 (=> @t29 @t72)))) % 0.37/0.56 (step @p65 :rule eq-symm :args (@t3 @t1)) % 0.37/0.56 (step @p66 :rule refl :args (@t29)) % 0.37/0.56 (step @p67 :rule cong :premises (@p66 @p65) :args (@t30)) % 0.37/0.56 (step @p68 :rule cong :premises (@p67) :args (@t31)) % 0.37/0.56 (step @p69 :rule trans :premises (@p68 @p64)) % 0.37/0.56 (step @p70 :rule eq_resolve :premises (@p12 @p69)) % 0.37/0.56 (step @p71 :rule instantiate :premises (@p70) :args ((@list @t44 @t46))) % 0.37/0.56 (step @p72 :rule bool-double-not-elim :args (@t47)) % 0.37/0.56 (step @p73 :rule refl :args (@t49)) % 0.37/0.56 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t49 (not @t48)))) % 0.37/0.56 (step @p75 :rule cnf_or_neg :args (@t49 0)) % 0.37/0.56 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.37/0.56 (step @p77 :rule reordering :premises (@p76) :args ((or @t47 @t49))) % 0.37/0.56 (step @p78 :rule chain_m_resolution :premises (@p77 @p27) :args (@t47 @t50 @t51)) % 0.37/0.56 (step @p79 :rule cnf_or_pos :args (@t74)) % 0.37/0.56 (step @p80 :rule reordering :premises (@p79) :args ((or @t48 @t73 (not @t74)))) % 0.37/0.56 (step @p81 :rule chain_m_resolution :premises (@p80 @p78 @p71) :args (@t73 (@list false false) (@list @t47 @t74))) % 0.37/0.56 (step @p82 :rule trans :premises (@p81 @p62)) % 0.37/0.56 (step @p83 :rule eq-symm :args (@t32 @t9)) % 0.37/0.56 (step @p84 :rule refl :args (@t9)) % 0.37/0.56 (step @p85 :rule cong :premises (@p19 @p84) :args (@t12)) % 0.37/0.57 (step @p86 :rule trans :premises (@p85 @p83)) % 0.37/0.57 (step @p87 :rule cong :premises (@p86) :args (@t13)) % 0.37/0.57 (step @p88 :rule eq_resolve :premises (@p7 @p87)) % 0.37/0.57 (step @p89 :rule nary_cong :premises (@p41 @p40) :args (@t75)) % 0.37/0.57 (step @p90 :rule refl :args (@t45)) % 0.37/0.57 (step @p91 :rule cong :premises (@p90 @p89) :args ((= @t45 @t75))) % 0.37/0.57 (step @p92 :rule eq-symm :args (@t75 @t45)) % 0.37/0.57 (step @p93 :rule trans :premises (@p92 @p91)) % 0.37/0.57 (step @p94 :rule refl :args (@t76)) % 0.37/0.57 (step @p95 :rule cong :premises (@p94 @p93) :args ((=> @t76 @t77))) % 0.37/0.57 (assume-push @p139 @t76) % 0.37/0.57 (step @p97 :rule instantiate :premises (@p88) :args ((@list @t41 @t38))) % 0.37/0.57 (step-pop @p140 :rule scope :premises (@p97)) % 0.37/0.57 (step @p98 :rule process_scope :premises (@p140) :args (@t77)) % 0.37/0.57 (step @p100 :rule eq_resolve :premises (@p98 @p95)) % 0.37/0.57 (step @p101 :rule implies_elim :premises (@p100)) % 0.37/0.57 (step @p102 :rule chain_m_resolution :premises (@p101 @p88) :args (@t79 @t69 (@list @t76))) % 0.37/0.57 (step @p103 :rule cnf_or_neg :args (@t49 1)) % 0.37/0.57 (step @p104 :rule chain_m_resolution :premises (@p103 @p27) :args ((not @t45) @t50 @t51)) % 0.37/0.57 (step @p105 :rule cnf_equiv_pos2 :args (@t79)) % 0.37/0.57 (step @p106 :rule reordering :premises (@p105) :args ((or @t45 @t80 (not @t79)))) % 0.37/0.57 (step @p107 :rule chain_m_resolution :premises (@p106 @p104 @p102) :args (@t80 (@list true false) (@list @t45 @t79))) % 0.37/0.57 (step @p108 :rule cnf_or_neg :args (@t78 1)) % 0.37/0.57 (step @p109 :rule chain_m_resolution :premises (@p108 @p107) :args ((not @t66) @t50 @t81)) % 0.37/0.57 (step @p110 :rule cnf_or_neg :args (@t78 0)) % 0.37/0.57 (step @p111 :rule chain_m_resolution :premises (@p110 @p107) :args ((not @t67) @t50 @t81)) % 0.37/0.57 (step @p112 :rule cnf_or_pos :args (@t68)) % 0.37/0.57 (step @p113 :rule reordering :premises (@p112) :args ((or @t67 @t66 @t61 @t58 (not @t68)))) % 0.37/0.57 (step @p114 :rule chain_m_resolution :premises (@p113 @p111 @p109 @p82 @p52) :args (@t58 (@list true true false false) (@list @t67 @t66 @t60 @t68))) % 0.37/0.57 (step @p115 :rule cnf_and_pos :args (@t58 0)) % 0.37/0.57 (step @p116 :rule reordering :premises (@p115) :args ((or @t57 @t82))) % 0.37/0.57 (step @p117 :rule chain_m_resolution :premises (@p116 @p114) :args (@t57 @t69 @t83)) % 0.37/0.57 (step @p118 :rule trans :premises (@p117 @p33)) % 0.37/0.57 (step @p119 :rule cong :premises (@p118 @p32) :args (@t42)) % 0.37/0.57 (step @p120 :rule trans :premises (@p119 @p31)) % 0.37/0.57 (step @p121 :rule true_elim :premises (@p120)) % 0.37/0.57 (step @p122 :rule instantiate :premises (@p11) :args ((@list @t37 @t38))) % 0.37/0.57 (step @p123 :rule true_intro :premises (@p122)) % 0.37/0.57 (step @p124 :rule refl :args (@t37)) % 0.37/0.57 (step @p125 :rule instantiate :premises (@p1) :args ((@list @t38 @t37))) % 0.37/0.57 (step @p126 :rule cnf_and_pos :args (@t58 1)) % 0.37/0.57 (step @p127 :rule reordering :premises (@p126) :args ((or @t55 @t82))) % 0.37/0.57 (step @p128 :rule chain_m_resolution :premises (@p127 @p114) :args (@t55 @t69 @t83)) % 0.37/0.57 (step @p129 :rule trans :premises (@p128 @p125)) % 0.37/0.57 (step @p130 :rule cong :premises (@p129 @p124) :args (@t39)) % 0.37/0.57 (step @p131 :rule trans :premises (@p130 @p123)) % 0.37/0.57 (step @p132 :rule true_elim :premises (@p131)) % 0.37/0.57 (step @p133 :rule cnf_and_neg :args (@t43)) % 0.37/0.57 (step @p134 false :rule chain_m_resolution :premises (@p133 @p132 @p121 @p29) :args (false (@list false false true) (@list @t39 @t42 @t43))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------