%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV083^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n003.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 08:55:25 AM UTC 2026 % Result : Theorem 1.71s 1.98s % Output : Proof 1.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV083^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n003.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 18:11:59 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.49 %----Proving TH0 % 1.71/1.98 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.71/1.98 % SZS status Theorem % 1.71/1.98 % SZS output start Proof % 1.71/1.98 ( % 1.71/1.98 (declare-sort $$unsorted 0) % 1.71/1.98 (define @t1 () (@var "Xz" (-> $$unsorted Bool))) % 1.71/1.98 (define @t2 () (@var "Xx" (-> $$unsorted Bool))) % 1.71/1.98 (define @t3 () (@var "R" (-> (-> $$unsorted Bool) (-> $$unsorted Bool) Bool))) % 1.71/1.98 (define @t4 () (_ @t3 @t2)) % 1.71/1.98 (define @t5 () (_ @t4 @t1)) % 1.71/1.98 (define @t6 () (@var "Xy" (-> $$unsorted Bool))) % 1.71/1.98 (define @t7 () (_ (_ @t3 @t6) @t1)) % 1.71/1.98 (define @t8 () (_ @t4 @t6)) % 1.71/1.98 (define @t9 () (and @t8 @t7)) % 1.71/1.98 (define @t10 () (@list @t2 @t6 @t1)) % 1.71/1.98 (define @t11 () (forall @t10 (=> @t9 @t5))) % 1.71/1.98 (define @t12 () (_ @t4 @t2)) % 1.71/1.98 (define @t13 () (@list @t2)) % 1.71/1.98 (define @t14 () (forall @t13 @t12)) % 1.71/1.98 (define @t15 () (@var "Xx" $$unsorted)) % 1.71/1.98 (define @t16 () (@list @t15)) % 1.71/1.98 (define @t17 () (lambda @t16 false)) % 1.71/1.98 (define @t18 () (lambda @t16 true)) % 1.71/1.98 (define @t19 () (not (_ (_ @t3 @t18) @t17))) % 1.71/1.98 (define @t20 () (and @t19 @t14 @t11)) % 1.71/1.98 (define @t21 () (@list @t3)) % 1.71/1.98 (define @t22 () (exists @t21 @t20)) % 1.71/1.98 (define @t23 () (and @t22 true)) % 1.71/1.98 (define @t24 () (not @t23)) % 1.71/1.98 (define @t25 () (_ @t3 @t2 @t1)) % 1.71/1.98 (define @t26 () (_ @t3 @t6 @t1)) % 1.71/1.98 (define @t27 () (_ @t3 @t2 @t6)) % 1.71/1.98 (define @t28 () (forall @t10 (or (not @t27) (not @t26) @t25))) % 1.71/1.98 (define @t29 () (not @t28)) % 1.71/1.98 (define @t30 () (_ @t3 @t2 @t2)) % 1.71/1.98 (define @t31 () (forall @t13 @t30)) % 1.71/1.98 (define @t32 () (not @t31)) % 1.71/1.98 (define @t33 () (@var "BOUND_VARIABLE_7542" $$unsorted)) % 1.71/1.98 (define @t34 () (lambda (@list @t33) false)) % 1.71/1.98 (define @t35 () (@var "BOUND_VARIABLE_7546" $$unsorted)) % 1.71/1.98 (define @t36 () (lambda (@list @t35) true)) % 1.71/1.98 (define @t37 () (_ @t3 @t36 @t34)) % 1.71/1.98 (define @t38 () (forall @t21 (or @t37 @t32 @t29))) % 1.71/1.98 (define @t39 () (_ (_ @t3 @t36) @t34)) % 1.71/1.98 (define @t40 () (or @t39 @t32 @t29)) % 1.71/1.98 (define @t41 () (not @t39)) % 1.71/1.98 (define @t42 () (not @t41)) % 1.71/1.98 (define @t43 () (or @t42 @t32 @t29)) % 1.71/1.98 (define @t44 () (and @t41 @t31 @t28)) % 1.71/1.98 (define @t45 () (forall @t21 (not @t44))) % 1.71/1.98 (define @t46 () (not @t45)) % 1.71/1.98 (define @t47 () (not @t7)) % 1.71/1.98 (define @t48 () (not @t8)) % 1.71/1.98 (define @t49 () (or @t48 @t47 @t5)) % 1.71/1.98 (define @t50 () (@list @t15)) % 1.71/1.98 (define @t51 () (@list @t6 @t1)) % 1.71/1.98 (define @t52 () (= @t6 @t1)) % 1.71/1.98 (define @t53 () (not @t52)) % 1.71/1.98 (define @t54 () (or @t53 @t52)) % 1.71/1.98 (define @t55 () (not (= @t6 @t6))) % 1.71/1.98 (define @t56 () (or @t55 @t53 @t52)) % 1.71/1.98 (define @t57 () (= @t2 @t1)) % 1.71/1.98 (define @t58 () (= @t2 @t6)) % 1.71/1.98 (define @t59 () (not @t58)) % 1.71/1.98 (define @t60 () (or @t59 @t59 @t53 @t57)) % 1.71/1.98 (define @t61 () (or @t59 @t53 @t57)) % 1.71/1.98 (define @t62 () (forall @t13 @t61)) % 1.71/1.98 (define @t63 () (forall @t51 @t62)) % 1.71/1.98 (define @t64 () (forall (@list @t6 @t1 @t2) @t61)) % 1.71/1.98 (define @t65 () (@var "BOUND_VARIABLE_532560" (-> $$unsorted Bool))) % 1.71/1.98 (define @t66 () (@var "BOUND_VARIABLE_532559" (-> $$unsorted Bool))) % 1.71/1.98 (define @t67 () (lambda (@list @t66 @t65) (= @t66 @t65))) % 1.71/1.98 (define @t68 () (_ @t67 @t2 @t1)) % 1.71/1.98 (define @t69 () (_ @t67 @t6 @t1)) % 1.71/1.98 (define @t70 () (not @t69)) % 1.71/1.98 (define @t71 () (_ @t67 @t2 @t6)) % 1.71/1.98 (define @t72 () (not @t71)) % 1.71/1.98 (define @t73 () (or @t72 @t70 @t68)) % 1.71/1.98 (define @t74 () (forall @t10 @t73)) % 1.71/1.98 (define @t75 () (not @t74)) % 1.71/1.98 (define @t76 () (_ @t67 @t2 @t2)) % 1.71/1.98 (define @t77 () (forall @t13 @t76)) % 1.71/1.98 (define @t78 () (not @t77)) % 1.71/1.98 (define @t79 () (= @t36 @t34)) % 1.71/1.98 (define @t80 () (_ @t67 @t36 @t34)) % 1.71/1.98 (define @t81 () (or @t80 @t78 @t75)) % 1.71/1.98 (assume @p1 @t24) % 1.71/1.98 (assume @p2 true) % 1.71/1.98 (step @p3 :rule bool-double-not-elim :args (@t38)) % 1.71/1.98 (step @p4 :rule refl :args (@t29)) % 1.71/1.98 (step @p5 :rule refl :args (@t32)) % 1.71/1.98 (step @p6 :rule refl :args ((_ @t3 @t36 @t34))) % 1.71/1.98 (step @p7 :rule refl :args (@t34)) % 1.71/1.98 (step @p8 :rule refl :args (@t36)) % 1.71/1.98 (step @p9 :rule cong :premises (@p8 @p7) :args (@t37)) % 1.71/1.98 (step @p10 :rule trans :premises (@p9 @p6)) % 1.71/1.98 (step @p11 :rule refl :args (@t3)) % 1.71/1.98 (step @p12 :rule ho_cong :premises (@p11 @p8)) % 1.71/1.98 (step @p13 :rule ho_cong :premises (@p12 @p7)) % 1.71/1.98 (step @p14 :rule cong :premises (@p13 @p10) :args ((= @t39 @t37))) % 1.71/1.98 (step @p15 :rule symm :premises (@p14)) % 1.71/1.98 (step @p16 :rule refl :args ((_ (_ @t3 @t36) @t34))) % 1.71/1.98 (step @p17 :rule eq_resolve :premises (@p16 @p15)) % 1.71/1.98 (step @p18 :rule nary_cong :premises (@p17 @p5 @p4) :args (@t40)) % 1.71/1.98 (step @p19 :rule cong :premises (@p18) :args ((forall @t21 @t40))) % 1.71/1.98 (step @p20 :rule bool-double-not-elim :args (@t39)) % 1.71/1.98 (step @p21 :rule nary_cong :premises (@p20 @p5 @p4) :args (@t43)) % 1.71/1.98 (step @p22 :rule aci_norm :args ((= (or @t42 (or @t32 @t29)) @t43))) % 1.71/1.98 (step @p23 :rule trans :premises (@p22 @p21)) % 1.71/1.98 (step @p24 :rule bool-and-de-morgan :args (@t31 @t28 true)) % 1.71/1.98 (step @p25 :rule refl :args (@t42)) % 1.71/1.98 (step @p26 :rule nary_cong :premises (@p25 @p24) :args ((or @t42 (not (and @t31 @t28))))) % 1.71/1.98 (step @p27 :rule bool-and-de-morgan :args (@t41 @t31 (and @t28))) % 1.71/1.98 (step @p28 :rule trans :premises (@p27 @p26)) % 1.71/1.98 (step @p29 :rule trans :premises (@p28 @p23)) % 1.71/1.98 (step @p30 :rule cong :premises (@p29) :args (@t45)) % 1.71/1.98 (step @p31 :rule trans :premises (@p30 @p19)) % 1.71/1.98 (step @p32 :rule cong :premises (@p31) :args (@t46)) % 1.71/1.98 (step @p33 :rule exists-elim :args ((= (exists @t21 @t44) @t46))) % 1.71/1.98 (step @p34 :rule trans :premises (@p33 @p32)) % 1.71/1.98 (step @p35 :rule refl :args (@t25)) % 1.71/1.98 (step @p36 :rule refl :args (@t5)) % 1.71/1.98 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t5 @t25))) % 1.71/1.98 (step @p38 :rule symm :premises (@p37)) % 1.71/1.98 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 1.71/1.98 (step @p40 :rule refl :args (@t26)) % 1.71/1.98 (step @p41 :rule refl :args (@t7)) % 1.71/1.98 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t7 @t26))) % 1.71/1.98 (step @p43 :rule symm :premises (@p42)) % 1.71/1.98 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 1.71/1.98 (step @p45 :rule cong :premises (@p44) :args (@t47)) % 1.71/1.98 (step @p46 :rule refl :args (@t27)) % 1.71/1.98 (step @p47 :rule refl :args (@t8)) % 1.71/1.98 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t8 @t27))) % 1.71/1.98 (step @p49 :rule symm :premises (@p48)) % 1.71/1.98 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 1.71/1.98 (step @p51 :rule cong :premises (@p50) :args (@t48)) % 1.71/1.98 (step @p52 :rule nary_cong :premises (@p51 @p45 @p39) :args (@t49)) % 1.71/1.98 (step @p53 :rule cong :premises (@p52) :args ((forall @t10 @t49))) % 1.71/1.98 (step @p54 :rule aci_norm :args ((= (or (or @t48 @t47) @t5) @t49))) % 1.71/1.98 (step @p55 :rule bool-and-de-morgan :args (@t8 @t7 true)) % 1.71/1.98 (step @p56 :rule nary_cong :premises (@p55 @p36) :args ((or (not @t9) @t5))) % 1.71/1.98 (step @p57 :rule trans :premises (@p56 @p54)) % 1.71/1.98 (step @p58 :rule bool-impl-elim :args (@t9 @t5)) % 1.71/1.98 (step @p59 :rule trans :premises (@p58 @p57)) % 1.71/1.98 (step @p60 :rule cong :premises (@p59) :args (@t11)) % 1.71/1.98 (step @p61 :rule trans :premises (@p60 @p53)) % 1.71/1.98 (step @p62 :rule refl :args (@t30)) % 1.71/1.98 (step @p63 :rule refl :args (@t12)) % 1.71/1.98 (step @p64 :rule cong :premises (@p63 @p62) :args ((= @t12 @t30))) % 1.71/1.98 (step @p65 :rule symm :premises (@p64)) % 1.71/1.98 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 1.71/1.98 (step @p67 :rule cong :premises (@p66) :args (@t14)) % 1.71/1.98 (step @p68 :rule symm :premises (@p7)) % 1.71/1.98 (step @p69 :rule alpha_equiv :args (@t17 @t50 (@list @t33))) % 1.71/1.98 (step @p70 :rule trans :premises (@p69 @p68)) % 1.71/1.98 (step @p71 :rule symm :premises (@p8)) % 1.71/1.98 (step @p72 :rule alpha_equiv :args (@t18 @t50 (@list @t35))) % 1.71/1.98 (step @p73 :rule trans :premises (@p72 @p71)) % 1.71/1.98 (step @p74 :rule refl :args (@t3)) % 1.71/1.98 (step @p75 :rule ho_cong :premises (@p74 @p73)) % 1.71/1.98 (step @p76 :rule ho_cong :premises (@p75 @p70)) % 1.71/1.98 (step @p77 :rule cong :premises (@p76) :args (@t19)) % 1.71/1.98 (step @p78 :rule nary_cong :premises (@p77 @p67 @p61) :args (@t20)) % 1.71/1.98 (step @p79 :rule cong :premises (@p78) :args (@t22)) % 1.71/1.98 (step @p80 :rule trans :premises (@p79 @p34)) % 1.71/1.98 (step @p81 :rule aci_norm :args ((= @t23 @t22))) % 1.71/1.98 (step @p82 :rule trans :premises (@p81 @p80)) % 1.71/1.98 (step @p83 :rule cong :premises (@p82) :args (@t24)) % 1.71/1.98 (step @p84 :rule trans :premises (@p83 @p3)) % 1.71/1.98 (step @p85 :rule eq_resolve :premises (@p1 @p84)) % 1.71/1.98 (step @p86 :rule bool-impl-false1 :args (@t38)) % 1.71/1.98 (step @p87 :rule evaluate :args ((or false false false))) % 1.71/1.98 (step @p88 :rule evaluate :args ((not true))) % 1.71/1.98 (step @p89 :rule quant-unused-vars :args ((= (forall @t51 true) true))) % 1.71/1.98 (step @p90 :rule bool-or-taut2 :args (false @t52 false false)) % 1.71/1.98 (step @p91 :rule cong :premises (@p90) :args ((forall @t51 @t54))) % 1.71/1.98 (step @p92 :rule trans :premises (@p91 @p89)) % 1.71/1.98 (step @p93 :rule aci_norm :args ((= (or false @t53 @t52) @t54))) % 1.71/1.98 (step @p94 :rule refl :args (@t52)) % 1.71/1.98 (step @p95 :rule refl :args (@t53)) % 1.71/1.98 (step @p96 :rule eq-refl :args (@t6)) % 1.71/1.98 (step @p97 :rule cong :premises (@p96) :args (@t55)) % 1.71/1.98 (step @p98 :rule trans :premises (@p97 @p88)) % 1.71/1.98 (step @p99 :rule nary_cong :premises (@p98 @p95 @p94) :args (@t56)) % 1.71/1.99 (step @p100 :rule trans :premises (@p99 @p93)) % 1.71/1.99 (step @p101 :rule cong :premises (@p100) :args ((forall @t51 @t56))) % 1.71/1.99 (step @p102 :rule trans :premises (@p101 @p92)) % 1.71/1.99 (step @p103 :rule quant-var-elim-eq :args ((= (forall @t13 @t60) @t56))) % 1.71/1.99 (step @p104 :rule aci_norm :args ((= @t61 @t60))) % 1.71/1.99 (step @p105 :rule cong :premises (@p104) :args (@t62)) % 1.71/1.99 (step @p106 :rule trans :premises (@p105 @p103)) % 1.71/1.99 (step @p107 :rule cong :premises (@p106) :args (@t63)) % 1.71/1.99 (step @p108 :rule quant-merge-prenex :args ((= @t63 @t64))) % 1.71/1.99 (step @p109 :rule symm :premises (@p108)) % 1.71/1.99 (step @p110 :rule quant_var_reordering :args ((= (forall @t10 @t61) @t64))) % 1.71/1.99 (step @p111 :rule trans :premises (@p110 @p109 @p107)) % 1.71/1.99 (step @p112 :rule trans :premises (@p111 @p102)) % 1.71/1.99 (step @p113 :rule beta-reduce :args ((= @t68 @t57))) % 1.71/1.99 (step @p114 :rule beta-reduce :args ((= @t69 @t52))) % 1.71/1.99 (step @p115 :rule cong :premises (@p114) :args (@t70)) % 1.71/1.99 (step @p116 :rule beta-reduce :args ((= @t71 @t58))) % 1.71/1.99 (step @p117 :rule cong :premises (@p116) :args (@t72)) % 1.71/1.99 (step @p118 :rule nary_cong :premises (@p117 @p115 @p113) :args (@t73)) % 1.71/1.99 (step @p119 :rule cong :premises (@p118) :args (@t74)) % 1.71/1.99 (step @p120 :rule trans :premises (@p119 @p112)) % 1.71/1.99 (step @p121 :rule cong :premises (@p120) :args (@t75)) % 1.71/1.99 (step @p122 :rule trans :premises (@p121 @p88)) % 1.71/1.99 (step @p123 :rule quant-unused-vars :args ((= (forall @t13 true) true))) % 1.71/1.99 (step @p124 :rule eq-refl :args (@t2)) % 1.71/1.99 (step @p125 :rule beta-reduce :args ((= @t76 (= @t2 @t2)))) % 1.71/1.99 (step @p126 :rule trans :premises (@p125 @p124)) % 1.71/1.99 (step @p127 :rule cong :premises (@p126) :args (@t77)) % 1.71/1.99 (step @p128 :rule trans :premises (@p127 @p123)) % 1.71/1.99 (step @p129 :rule cong :premises (@p128) :args (@t78)) % 1.71/1.99 (step @p130 :rule trans :premises (@p129 @p88)) % 1.71/1.99 ; WARNING: add trust step for DISTINCT_VALUES % 1.71/1.99 ; trust DISTINCT_VALUES % 1.71/1.99 (step @p131 :rule trust :premises () :args ((not @t79))) % 1.71/1.99 (step @p132 :rule false_intro :premises (@p131)) % 1.71/1.99 (step @p133 :rule beta-reduce :args ((= @t80 @t79))) % 1.71/1.99 (step @p134 :rule trans :premises (@p133 @p132)) % 1.71/1.99 (step @p135 :rule nary_cong :premises (@p134 @p130 @p122) :args (@t81)) % 1.71/1.99 (step @p136 :rule trans :premises (@p135 @p87)) % 1.71/1.99 (step @p137 :rule refl :args (@t38)) % 1.71/1.99 (step @p138 :rule cong :premises (@p137 @p136) :args ((=> @t38 @t81))) % 1.71/1.99 (step @p139 :rule trans :premises (@p138 @p86)) % 1.71/1.99 (assume-push @p146 @t38) % 1.71/1.99 (step @p141 :rule instantiate :premises (@p85) :args ((@list @t67))) % 1.71/1.99 (step-pop @p147 :rule scope :premises (@p141)) % 1.71/1.99 (step @p142 :rule process_scope :premises (@p147) :args (@t81)) % 1.71/1.99 (step @p144 :rule eq_resolve :premises (@p142 @p139)) % 1.71/1.99 (step @p145 false :rule chain_m_resolution :premises (@p144 @p85) :args (false (@list false) (@list @t38))) % 1.71/1.99 ) % 1.71/1.99 % SZS output end Proof % 1.71/1.99 % cvc5 exiting %------------------------------------------------------------------------------