%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET950+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 : n010.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 08:49:03 AM UTC 2026 % Result : Theorem 16.10s 16.31s % Output : Proof 16.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET950+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 % 0.15/0.34 % Computer : n010.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 16:18:25 EDT 2026 % 0.15/0.34 % CPUTime : % 0.26/0.50 %----Proving TF0_NAR, FOF, or CNF % 16.10/16.31 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 16.10/16.31 --- Run --no-e-matching --full-saturate-quant at 6... % 16.10/16.31 % SZS status Theorem % 16.10/16.31 % SZS output start Proof % 16.10/16.31 ( % 16.10/16.31 (declare-sort $$unsorted 0) % 16.10/16.31 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 16.10/16.31 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 16.10/16.31 (declare-const tptp.empty (-> $$unsorted Bool)) % 16.10/16.31 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 16.10/16.31 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 16.10/16.31 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 16.10/16.31 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 16.10/16.31 (define @t1 () (@var "A" $$unsorted)) % 16.10/16.31 (define @t2 () (@var "B" $$unsorted)) % 16.10/16.31 (define @t3 () (@list @t1 @t2)) % 16.10/16.31 (define @t4 () (tptp.unordered_pair @t1 @t2)) % 16.10/16.31 (define @t5 () (@var "F" $$unsorted)) % 16.10/16.31 (define @t6 () (@var "E" $$unsorted)) % 16.10/16.31 (define @t7 () (tptp.ordered_pair @t6 @t5)) % 16.10/16.31 (define @t8 () (@var "D" $$unsorted)) % 16.10/16.31 (define @t9 () (= @t8 @t7)) % 16.10/16.31 (define @t10 () (tptp.in @t5 @t2)) % 16.10/16.31 (define @t11 () (tptp.in @t6 @t1)) % 16.10/16.31 (define @t12 () (and @t11 @t10 @t9)) % 16.10/16.31 (define @t13 () (@list @t6 @t5)) % 16.10/16.31 (define @t14 () (exists @t13 @t12)) % 16.10/16.31 (define @t15 () (@var "C" $$unsorted)) % 16.10/16.31 (define @t16 () (tptp.in @t8 @t15)) % 16.10/16.31 (define @t17 () (= @t16 @t14)) % 16.10/16.31 (define @t18 () (@list @t8)) % 16.10/16.31 (define @t19 () (forall @t18 @t17)) % 16.10/16.31 (define @t20 () (= @t15 (tptp.cartesian_product2 @t1 @t2))) % 16.10/16.31 (define @t21 () (= @t20 @t19)) % 16.10/16.31 (define @t22 () (@list @t1 @t2 @t15)) % 16.10/16.31 (define @t23 () (forall @t22 @t21)) % 16.10/16.31 (define @t24 () (tptp.in @t15 @t2)) % 16.10/16.31 (define @t25 () (tptp.in @t15 @t1)) % 16.10/16.31 (define @t26 () (@list @t15)) % 16.10/16.31 (define @t27 () (forall @t26 (=> @t25 @t24))) % 16.10/16.31 (define @t28 () (tptp.subset @t1 @t2)) % 16.10/16.31 (define @t29 () (= @t28 @t27)) % 16.10/16.31 (define @t30 () (forall @t3 @t29)) % 16.10/16.31 (define @t31 () (tptp.ordered_pair @t1 @t2)) % 16.10/16.31 (define @t32 () (tptp.empty @t1)) % 16.10/16.31 (define @t33 () (@list @t1)) % 16.10/16.31 (define @t34 () (tptp.in @t5 @t15)) % 16.10/16.31 (define @t35 () (tptp.in @t6 @t2)) % 16.10/16.31 (define @t36 () (forall @t13 (not (and @t35 @t34 @t9)))) % 16.10/16.31 (define @t37 () (tptp.in @t8 @t1)) % 16.10/16.31 (define @t38 () (tptp.subset @t1 (tptp.cartesian_product2 @t2 @t15))) % 16.10/16.31 (define @t39 () (and @t38 @t37 @t36)) % 16.10/16.31 (define @t40 () (not @t39)) % 16.10/16.31 (define @t41 () (@list @t1 @t2 @t15 @t8)) % 16.10/16.31 (define @t42 () (forall @t41 @t40)) % 16.10/16.31 (define @t43 () (not @t42)) % 16.10/16.31 (define @t44 () (not @t9)) % 16.10/16.31 (define @t45 () (not @t10)) % 16.10/16.31 (define @t46 () (not @t11)) % 16.10/16.31 (define @t47 () (or @t46 @t45 @t44)) % 16.10/16.31 (define @t48 () (forall @t13 (not @t12))) % 16.10/16.31 (define @t49 () (not @t48)) % 16.10/16.31 (define @t50 () (not @t34)) % 16.10/16.31 (define @t51 () (not @t35)) % 16.10/16.31 (define @t52 () (or @t51 @t50 @t44)) % 16.10/16.31 (define @t53 () (forall @t13 @t52)) % 16.10/16.31 (define @t54 () (not @t53)) % 16.10/16.31 (define @t55 () (not @t37)) % 16.10/16.31 (define @t56 () (not @t38)) % 16.10/16.31 (define @t57 () (or @t56 @t55 @t54)) % 16.10/16.31 (define @t58 () (forall @t41 @t57)) % 16.10/16.31 (define @t59 () (@quantifiers_skolemize @t58 2)) % 16.10/16.31 (define @t60 () (@quantifiers_skolemize @t58 1)) % 16.10/16.31 (define @t61 () (tptp.cartesian_product2 @t60 @t59)) % 16.10/16.31 (define @t62 () (tptp.in @t8 @t61)) % 16.10/16.31 (define @t63 () (not (tptp.in @t5 @t59))) % 16.10/16.31 (define @t64 () (not (tptp.in @t6 @t60))) % 16.10/16.31 (define @t65 () (not (forall @t13 (or @t64 @t63 @t44)))) % 16.10/16.31 (define @t66 () (forall @t18 (= @t65 @t62))) % 16.10/16.31 (define @t67 () (forall @t18 (= @t62 @t65))) % 16.10/16.31 (define @t68 () (= (= @t61 @t61) @t67)) % 16.10/16.31 (define @t69 () (forall @t22 (= @t20 (forall @t18 (= @t16 (not (forall @t13 @t47))))))) % 16.10/16.31 (define @t70 () (@quantifiers_skolemize @t58 0)) % 16.10/16.31 (define @t71 () (@quantifiers_skolemize @t58 3)) % 16.10/16.31 (define @t72 () (forall @t13 (or @t64 @t63 (not (= @t7 @t71))))) % 16.10/16.31 (define @t73 () (not @t72)) % 16.10/16.31 (define @t74 () (tptp.in @t71 @t70)) % 16.10/16.31 (define @t75 () (not @t74)) % 16.10/16.31 (define @t76 () (tptp.subset @t70 @t61)) % 16.10/16.31 (define @t77 () (not @t76)) % 16.10/16.31 (define @t78 () (or @t77 @t75 @t73)) % 16.10/16.31 (define @t79 () (not @t78)) % 16.10/16.31 (define @t80 () (not @t58)) % 16.10/16.31 (define @t81 () (not (= @t71 @t7))) % 16.10/16.31 (define @t82 () (or @t64 @t63 @t81)) % 16.10/16.31 (define @t83 () (forall @t13 @t82)) % 16.10/16.31 (define @t84 () (not @t83)) % 16.10/16.31 (define @t85 () (or @t77 @t75 @t84)) % 16.10/16.31 (define @t86 () (not @t85)) % 16.10/16.31 (define @t87 () (@list true)) % 16.10/16.31 (define @t88 () (@list @t78)) % 16.10/16.31 (define @t89 () (forall @t26 (or (not (tptp.in @t15 @t70)) (tptp.in @t15 @t61)))) % 16.10/16.31 (define @t90 () (= @t76 @t89)) % 16.10/16.31 (define @t91 () (@list false false)) % 16.10/16.31 (define @t92 () (@list @t71)) % 16.10/16.31 (define @t93 () (tptp.in @t71 @t61)) % 16.10/16.31 (define @t94 () (or @t75 @t93)) % 16.10/16.31 (define @t95 () (= @t73 @t93)) % 16.10/16.31 (define @t96 () (not @t95)) % 16.10/16.31 (define @t97 () (= @t84 @t93)) % 16.10/16.31 (assume @p1 (forall @t3 (=> (tptp.in @t1 @t2) (not (tptp.in @t2 @t1))))) % 16.10/16.31 (assume @p2 (forall @t3 (= @t4 (tptp.unordered_pair @t2 @t1)))) % 16.10/16.31 (assume @p3 @t23) % 16.10/16.31 (assume @p4 @t30) % 16.10/16.31 (assume @p5 (forall @t3 (= @t31 (tptp.unordered_pair @t4 (tptp.singleton @t1))))) % 16.10/16.31 (assume @p6 (forall @t3 (not (tptp.empty @t31)))) % 16.10/16.31 (assume @p7 (exists @t33 @t32)) % 16.10/16.31 (assume @p8 (exists @t33 (not @t32))) % 16.10/16.31 (assume @p9 (forall @t3 (tptp.subset @t1 @t1))) % 16.10/16.31 (assume @p10 @t43) % 16.10/16.31 (assume @p11 true) % 16.10/16.31 (step @p12 :rule aci_norm :args ((= (or @t46 (or @t45 @t44)) @t47))) % 16.10/16.31 (step @p13 :rule bool-and-de-morgan :args (@t10 @t9 true)) % 16.10/16.31 (step @p14 :rule refl :args (@t46)) % 16.10/16.31 (step @p15 :rule nary_cong :premises (@p14 @p13) :args ((or @t46 (not (and @t10 @t9))))) % 16.10/16.31 (step @p16 :rule bool-and-de-morgan :args (@t11 @t10 (and @t9))) % 16.10/16.31 (step @p17 :rule trans :premises (@p16 @p15)) % 16.10/16.31 (step @p18 :rule trans :premises (@p17 @p12)) % 16.10/16.31 (step @p19 :rule cong :premises (@p18) :args (@t48)) % 16.10/16.31 (step @p20 :rule cong :premises (@p19) :args (@t49)) % 16.10/16.31 (step @p21 :rule exists-elim :args ((= @t14 @t49))) % 16.10/16.31 (step @p22 :rule trans :premises (@p21 @p20)) % 16.10/16.31 (step @p23 :rule refl :args (@t16)) % 16.10/16.31 (step @p24 :rule cong :premises (@p23 @p22) :args (@t17)) % 16.10/16.31 (step @p25 :rule cong :premises (@p24) :args (@t19)) % 16.10/16.31 (step @p26 :rule refl :args (@t20)) % 16.10/16.31 (step @p27 :rule cong :premises (@p26 @p25) :args (@t21)) % 16.10/16.31 (step @p28 :rule cong :premises (@p27) :args (@t23)) % 16.10/16.31 (step @p29 :rule eq_resolve :premises (@p3 @p28)) % 16.10/16.31 (step @p30 :rule bool-eq-true :args (@t66)) % 16.10/16.31 (step @p31 :rule eq-symm :args (true @t66)) % 16.10/16.31 (step @p32 :rule trans :premises (@p31 @p30)) % 16.10/16.31 (step @p33 :rule eq-symm :args (@t62 @t65)) % 16.10/16.31 (step @p34 :rule cong :premises (@p33) :args (@t67)) % 16.10/16.31 (step @p35 :rule eq-refl :args (@t61)) % 16.10/16.31 (step @p36 :rule cong :premises (@p35 @p34) :args (@t68)) % 16.10/16.31 (step @p37 :rule trans :premises (@p36 @p32)) % 16.10/16.31 (step @p38 :rule refl :args (@t69)) % 16.10/16.31 (step @p39 :rule cong :premises (@p38 @p37) :args ((=> @t69 @t68))) % 16.10/16.31 (assume-push @p142 @t69) % 16.10/16.31 (step @p41 :rule instantiate :premises (@p29) :args ((@list @t60 @t59 @t61))) % 16.10/16.31 (step-pop @p143 :rule scope :premises (@p41)) % 16.10/16.31 (step @p42 :rule process_scope :premises (@p143) :args (@t68)) % 16.10/16.31 (step @p44 :rule eq_resolve :premises (@p42 @p39)) % 16.10/16.31 (step @p45 :rule implies_elim :premises (@p44)) % 16.10/16.31 (step @p46 :rule chain_m_resolution :premises (@p45 @p29) :args (@t66 (@list false) (@list @t69))) % 16.10/16.31 (step @p47 :rule bool-impl-elim :args (@t25 @t24)) % 16.10/16.31 (step @p48 :rule cong :premises (@p47) :args (@t27)) % 16.10/16.31 (step @p49 :rule refl :args (@t28)) % 16.10/16.31 (step @p50 :rule cong :premises (@p49 @p48) :args (@t29)) % 16.10/16.31 (step @p51 :rule cong :premises (@p50) :args (@t30)) % 16.10/16.31 (step @p52 :rule eq_resolve :premises (@p4 @p51)) % 16.10/16.31 (step @p53 :rule instantiate :premises (@p52) :args ((@list @t70 @t61))) % 16.10/16.31 (step @p54 :rule aci_norm :args ((= (or @t56 (or @t55 @t54)) @t57))) % 16.10/16.31 (step @p55 :rule bool-and-de-morgan :args (@t37 @t53 true)) % 16.10/16.31 (step @p56 :rule refl :args (@t56)) % 16.10/16.31 (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((or @t56 (not (and @t37 @t53))))) % 16.10/16.31 (step @p58 :rule bool-and-de-morgan :args (@t38 @t37 (and @t53))) % 16.10/16.31 (step @p59 :rule trans :premises (@p58 @p57)) % 16.10/16.31 (step @p60 :rule trans :premises (@p59 @p54)) % 16.10/16.31 (step @p61 :rule cong :premises (@p60) :args ((forall @t41 (not (and @t38 @t37 @t53))))) % 16.10/16.31 (step @p62 :rule aci_norm :args ((= (or @t51 (or @t50 @t44)) @t52))) % 16.10/16.31 (step @p63 :rule bool-and-de-morgan :args (@t34 @t9 true)) % 16.10/16.31 (step @p64 :rule refl :args (@t51)) % 16.10/16.31 (step @p65 :rule nary_cong :premises (@p64 @p63) :args ((or @t51 (not (and @t34 @t9))))) % 16.10/16.31 (step @p66 :rule bool-and-de-morgan :args (@t35 @t34 (and @t9))) % 16.10/16.31 (step @p67 :rule trans :premises (@p66 @p65)) % 16.10/16.31 (step @p68 :rule trans :premises (@p67 @p62)) % 16.10/16.31 (step @p69 :rule cong :premises (@p68) :args (@t36)) % 16.10/16.31 (step @p70 :rule refl :args (@t37)) % 16.10/16.31 (step @p71 :rule refl :args (@t38)) % 16.10/16.31 (step @p72 :rule nary_cong :premises (@p71 @p70 @p69) :args (@t39)) % 16.10/16.31 (step @p73 :rule cong :premises (@p72) :args (@t40)) % 16.10/16.31 (step @p74 :rule cong :premises (@p73) :args (@t42)) % 16.10/16.31 (step @p75 :rule trans :premises (@p74 @p61)) % 16.10/16.31 (step @p76 :rule cong :premises (@p75) :args (@t43)) % 16.10/16.31 (step @p77 :rule eq_resolve :premises (@p10 @p76)) % 16.10/16.31 (step @p78 :rule refl :args (@t79)) % 16.10/16.31 (step @p79 :rule bool-double-not-elim :args (@t58)) % 16.10/16.31 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or (not @t80) @t79))) % 16.10/16.31 (step @p81 :rule eq-symm :args (@t71 @t7)) % 16.10/16.31 (step @p82 :rule cong :premises (@p81) :args (@t81)) % 16.10/16.31 (step @p83 :rule refl :args (@t63)) % 16.10/16.31 (step @p84 :rule refl :args (@t64)) % 16.10/16.31 (step @p85 :rule nary_cong :premises (@p84 @p83 @p82) :args (@t82)) % 16.10/16.31 (step @p86 :rule cong :premises (@p85) :args (@t83)) % 16.10/16.31 (step @p87 :rule cong :premises (@p86) :args (@t84)) % 16.10/16.31 (step @p88 :rule refl :args (@t75)) % 16.10/16.31 (step @p89 :rule refl :args (@t77)) % 16.10/16.31 (step @p90 :rule nary_cong :premises (@p89 @p88 @p87) :args (@t85)) % 16.10/16.31 (step @p91 :rule cong :premises (@p90) :args (@t86)) % 16.10/16.31 (step @p92 :rule refl :args (@t80)) % 16.10/16.31 (step @p93 :rule cong :premises (@p92 @p91) :args ((=> @t80 @t86))) % 16.10/16.31 (assume-push @p144 @t80) % 16.10/16.32 (step @p95 :rule skolemize :premises (@p77)) % 16.10/16.32 (step-pop @p145 :rule scope :premises (@p95)) % 16.10/16.32 (step @p96 :rule process_scope :premises (@p145) :args (@t86)) % 16.10/16.32 (step @p98 :rule eq_resolve :premises (@p96 @p93)) % 16.10/16.32 (step @p99 :rule implies_elim :premises (@p98)) % 16.10/16.32 (step @p100 :rule eq_resolve :premises (@p99 @p80)) % 16.10/16.32 (step @p101 :rule chain_m_resolution :premises (@p100 @p77) :args (@t79 @t87 (@list @t58))) % 16.10/16.32 (step @p102 :rule bool-double-not-elim :args (@t76)) % 16.10/16.32 (step @p103 :rule refl :args (@t78)) % 16.10/16.32 (step @p104 :rule nary_cong :premises (@p103 @p102) :args ((or @t78 (not @t77)))) % 16.10/16.32 (step @p105 :rule cnf_or_neg :args (@t78 0)) % 16.10/16.32 (step @p106 :rule eq_resolve :premises (@p105 @p104)) % 16.10/16.32 (step @p107 :rule reordering :premises (@p106) :args ((or @t76 @t78))) % 16.10/16.32 (step @p108 :rule chain_m_resolution :premises (@p107 @p101) :args (@t76 @t87 @t88)) % 16.10/16.32 (step @p109 :rule cnf_equiv_pos1 :args (@t90)) % 16.10/16.32 (step @p110 :rule reordering :premises (@p109) :args ((or @t77 @t89 (not @t90)))) % 16.10/16.32 (step @p111 :rule chain_m_resolution :premises (@p110 @p108 @p53) :args (@t89 @t91 (@list @t76 @t90))) % 16.10/16.32 (step @p112 :rule instantiate :premises (@p111) :args (@t92)) % 16.10/16.32 (step @p113 :rule bool-double-not-elim :args (@t74)) % 16.10/16.32 (step @p114 :rule nary_cong :premises (@p103 @p113) :args ((or @t78 (not @t75)))) % 16.10/16.32 (step @p115 :rule cnf_or_neg :args (@t78 1)) % 16.10/16.32 (step @p116 :rule eq_resolve :premises (@p115 @p114)) % 16.10/16.32 (step @p117 :rule reordering :premises (@p116) :args ((or @t74 @t78))) % 16.10/16.32 (step @p118 :rule chain_m_resolution :premises (@p117 @p101) :args (@t74 @t87 @t88)) % 16.10/16.32 (step @p119 :rule cnf_or_pos :args (@t94)) % 16.10/16.32 (step @p120 :rule reordering :premises (@p119) :args ((or @t75 @t93 (not @t94)))) % 16.10/16.32 (step @p121 :rule chain_m_resolution :premises (@p120 @p118 @p112) :args (@t93 @t91 (@list @t74 @t94))) % 16.10/16.32 (step @p122 :rule bool-double-not-elim :args (@t72)) % 16.10/16.32 (step @p123 :rule nary_cong :premises (@p103 @p122) :args ((or @t78 (not @t73)))) % 16.10/16.32 (step @p124 :rule cnf_or_neg :args (@t78 2)) % 16.10/16.32 (step @p125 :rule eq_resolve :premises (@p124 @p123)) % 16.10/16.32 (step @p126 :rule reordering :premises (@p125) :args ((or @t72 @t78))) % 16.10/16.32 (step @p127 :rule chain_m_resolution :premises (@p126 @p101) :args (@t72 @t87 @t88)) % 16.10/16.32 (step @p128 :rule cnf_equiv_pos2 :args (@t95)) % 16.10/16.32 (step @p129 :rule reordering :premises (@p128) :args ((or @t73 (not @t93) @t96))) % 16.10/16.32 (step @p130 :rule chain_m_resolution :premises (@p129 @p127 @p121) :args (@t96 @t91 (@list @t72 @t93))) % 16.10/16.32 (step @p131 :rule refl :args (@t93)) % 16.10/16.32 (step @p132 :rule cong :premises (@p87 @p131) :args (@t97)) % 16.10/16.32 (step @p133 :rule refl :args (@t66)) % 16.10/16.32 (step @p134 :rule cong :premises (@p133 @p132) :args ((=> @t66 @t97))) % 16.10/16.32 (assume-push @p146 @t66) % 16.10/16.32 (step @p136 :rule instantiate :premises (@p46) :args (@t92)) % 16.10/16.32 (step-pop @p147 :rule scope :premises (@p136)) % 16.10/16.32 (step @p137 :rule process_scope :premises (@p147) :args (@t97)) % 16.10/16.32 (step @p139 :rule eq_resolve :premises (@p137 @p134)) % 16.10/16.32 (step @p140 :rule implies_elim :premises (@p139)) % 16.10/16.32 (step @p141 false :rule chain_m_resolution :premises (@p140 @p130 @p46) :args (false (@list true false) (@list @t95 @t66))) % 16.10/16.32 ) % 16.10/16.32 % SZS output end Proof % 16.10/16.32 % cvc5 exiting %------------------------------------------------------------------------------