%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO378^5 : TPTP v9.2.1. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n011.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 09:12:32 AM UTC 2026 % Result : Theorem 0.36s 0.58s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO378^5 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n011.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 : Wed Jun 3 00:05:50 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.36/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.58 % SZS status Theorem % 0.36/0.58 % SZS output start Proof % 0.36/0.58 ( % 0.36/0.58 (declare-sort $$unsorted 0) % 0.36/0.58 (declare-const tptp.c $$unsorted) % 0.36/0.58 (define tptp.cQDP0 () (let ((_let_1 (@var "Xz" $$unsorted))) (lambda (@list _let_1) (= _let_1 tptp.c)))) % 0.36/0.58 (define tptp.cQDP1 () (let ((_let_1 (@var "Xt" $$unsorted))) (let ((_let_2 (@var "Xz" (-> $$unsorted Bool)))) (lambda (@list _let_2) (and (= _let_2 tptp.cQDP0) (exists (@list _let_1) (_ _let_2 _let_1))))))) % 0.36/0.58 (define tptp.cQDP2 () (let ((_let_1 (@var "Xt" (-> $$unsorted Bool)))) (let ((_let_2 (@var "Xz" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_2) (and (= _let_2 tptp.cQDP1) (exists (@list _let_1) (_ _let_2 _let_1))))))) % 0.36/0.58 (define @t1 () (@var "Xs" (-> (-> $$unsorted Bool) Bool))) % 0.36/0.58 (define @t2 () (@list @t1)) % 0.36/0.58 (define @t3 () (exists @t2 (_ tptp.cQDP2 @t1))) % 0.36/0.58 (define @t4 () (not @t3)) % 0.36/0.58 (define @t5 () (@var "Xz" $$unsorted)) % 0.36/0.58 (define @t6 () (@list @t5)) % 0.36/0.58 (define @t7 () (lambda @t6 (= @t5 tptp.c))) % 0.36/0.58 (define @t8 () (@var "Xt" $$unsorted)) % 0.36/0.58 (define @t9 () (@var "Xz" (-> $$unsorted Bool))) % 0.36/0.58 (define @t10 () (_ @t9 @t8)) % 0.36/0.58 (define @t11 () (@list @t8)) % 0.36/0.58 (define @t12 () (exists @t11 @t10)) % 0.36/0.58 (define @t13 () (= @t9 tptp.cQDP0)) % 0.36/0.58 (define @t14 () (and @t13 @t12)) % 0.36/0.58 (define @t15 () (@list @t9)) % 0.36/0.58 (define @t16 () (lambda @t15 @t14)) % 0.36/0.58 (define @t17 () (@var "Xt" (-> $$unsorted Bool))) % 0.36/0.58 (define @t18 () (@var "Xz" (-> (-> $$unsorted Bool) Bool))) % 0.36/0.58 (define @t19 () (_ @t18 @t17)) % 0.36/0.58 (define @t20 () (@list @t17)) % 0.36/0.58 (define @t21 () (exists @t20 @t19)) % 0.36/0.58 (define @t22 () (= @t18 tptp.cQDP1)) % 0.36/0.58 (define @t23 () (and @t22 @t21)) % 0.36/0.58 (define @t24 () (@list @t18)) % 0.36/0.58 (define @t25 () (lambda @t24 @t23)) % 0.36/0.58 (define @t26 () (not (= tptp.c tptp.c))) % 0.36/0.58 (define @t27 () (@var "BOUND_VARIABLE_7541" $$unsorted)) % 0.36/0.58 (define @t28 () (= tptp.c @t27)) % 0.36/0.58 (define @t29 () (not @t28)) % 0.36/0.58 (define @t30 () (@list @t27)) % 0.36/0.58 (define @t31 () (or @t29 @t29)) % 0.36/0.58 (define @t32 () (lambda @t6 (= tptp.c @t5))) % 0.36/0.58 (define @t33 () (_ @t32 @t27)) % 0.36/0.58 (define @t34 () (not @t33)) % 0.36/0.58 (define @t35 () (not (= @t32 @t32))) % 0.36/0.58 (define @t36 () (or @t35 @t34)) % 0.36/0.58 (define @t37 () (@var "BOUND_VARIABLE_7516" (-> $$unsorted Bool))) % 0.36/0.58 (define @t38 () (not (_ @t37 @t27))) % 0.36/0.58 (define @t39 () (= @t32 @t37)) % 0.36/0.58 (define @t40 () (not @t39)) % 0.36/0.58 (define @t41 () (@list @t37)) % 0.36/0.58 (define @t42 () (or @t40 @t40 @t38)) % 0.36/0.58 (define @t43 () (or @t40 @t38)) % 0.36/0.58 (define @t44 () (forall @t41 @t43)) % 0.36/0.58 (define @t45 () (forall @t30 @t44)) % 0.36/0.58 (define @t46 () (forall (@list @t27 @t37) @t43)) % 0.36/0.58 (define @t47 () (forall (@list @t37 @t27) @t43)) % 0.36/0.58 (define @t48 () (forall @t30 @t43)) % 0.36/0.58 (define @t49 () (forall @t30 @t38)) % 0.36/0.58 (define @t50 () (or @t40 @t49)) % 0.36/0.58 (define @t51 () (forall @t11 (not (_ @t37 @t8)))) % 0.36/0.58 (define @t52 () (not @t51)) % 0.36/0.58 (define @t53 () (and @t39 @t52)) % 0.36/0.58 (define @t54 () (not @t53)) % 0.36/0.58 (define @t55 () (_ @t9 @t8)) % 0.36/0.58 (define @t56 () (lambda @t15 (and (= @t32 @t9) (not (forall @t11 (not @t55)))))) % 0.36/0.58 (define @t57 () (_ @t56 @t37)) % 0.36/0.58 (define @t58 () (not @t57)) % 0.36/0.58 (define @t59 () (not (= @t56 @t56))) % 0.36/0.58 (define @t60 () (or @t59 @t58)) % 0.36/0.58 (define @t61 () (not (_ @t1 @t37))) % 0.36/0.58 (define @t62 () (= @t56 @t1)) % 0.36/0.58 (define @t63 () (not @t62)) % 0.36/0.58 (define @t64 () (or @t63 @t63 @t61)) % 0.36/0.58 (define @t65 () (or @t63 @t61)) % 0.36/0.58 (define @t66 () (forall @t2 @t65)) % 0.36/0.58 (define @t67 () (forall @t41 @t66)) % 0.36/0.58 (define @t68 () (forall (@list @t37 @t1) @t65)) % 0.36/0.58 (define @t69 () (forall (@list @t1 @t37) @t65)) % 0.36/0.58 (define @t70 () (forall @t41 @t65)) % 0.36/0.58 (define @t71 () (forall @t41 @t61)) % 0.36/0.58 (define @t72 () (or @t63 @t71)) % 0.36/0.58 (define @t73 () (forall @t20 (not (_ @t1 @t17)))) % 0.36/0.58 (define @t74 () (not @t73)) % 0.36/0.58 (define @t75 () (and @t62 @t74)) % 0.36/0.58 (define @t76 () (forall @t2 (not @t75))) % 0.36/0.58 (define @t77 () (not @t76)) % 0.36/0.58 (define @t78 () (_ @t18 @t17)) % 0.36/0.58 (define @t79 () (_ (lambda @t24 (and (= @t56 @t18) (not (forall @t20 (not @t78))))) @t1)) % 0.36/0.58 (define @t80 () (exists @t2 @t79)) % 0.36/0.58 (define @t81 () (not @t19)) % 0.36/0.58 (define @t82 () (forall @t20 @t81)) % 0.36/0.58 (define @t83 () (not @t82)) % 0.36/0.58 (define @t84 () (not @t10)) % 0.36/0.58 (define @t85 () (forall @t11 @t84)) % 0.36/0.58 (define @t86 () (not @t85)) % 0.36/0.58 (assume @p1 @t4) % 0.36/0.58 (assume @p2 true) % 0.36/0.58 (step @p3 (= tptp.cQDP0 @t7) :rule refl :args (@t7)) % 0.36/0.58 (step @p4 (= tptp.cQDP1 @t16) :rule refl :args (@t16)) % 0.36/0.58 (step @p5 (= tptp.cQDP2 @t25) :rule refl :args (@t25)) % 0.36/0.58 (step @p6 :rule evaluate :args ((not true))) % 0.36/0.58 (step @p7 :rule evaluate :args ((not false))) % 0.36/0.58 (step @p8 :rule eq-refl :args (tptp.c)) % 0.36/0.58 (step @p9 :rule cong :premises (@p8) :args (@t26)) % 0.36/0.58 (step @p10 :rule trans :premises (@p9 @p6)) % 0.36/0.58 (step @p11 :rule quant-var-elim-eq :args ((= (forall @t30 (or (not (= @t27 tptp.c)) @t29)) @t26))) % 0.36/0.58 (step @p12 :rule refl :args (@t29)) % 0.36/0.58 (step @p13 :rule eq-symm :args (tptp.c @t27)) % 0.36/0.58 (step @p14 :rule cong :premises (@p13) :args (@t29)) % 0.36/0.58 (step @p15 :rule nary_cong :premises (@p14 @p12) :args (@t31)) % 0.36/0.58 (step @p16 :rule aci_norm :args ((= @t29 @t31))) % 0.36/0.58 (step @p17 :rule trans :premises (@p16 @p15)) % 0.36/0.58 (step @p18 :rule cong :premises (@p17) :args ((forall @t30 @t29))) % 0.36/0.58 (step @p19 :rule trans :premises (@p18 @p11)) % 0.36/0.58 (step @p20 :rule trans :premises (@p19 @p10)) % 0.36/0.58 (step @p21 :rule aci_norm :args ((= (or false @t29) @t29))) % 0.36/0.58 (step @p22 :rule beta-reduce :args ((= @t33 @t28))) % 0.36/0.58 (step @p23 :rule cong :premises (@p22) :args (@t34)) % 0.36/0.58 (step @p24 :rule eq-refl :args (@t32)) % 0.36/0.58 (step @p25 :rule cong :premises (@p24) :args (@t35)) % 0.36/0.58 (step @p26 :rule trans :premises (@p25 @p6)) % 0.36/0.58 (step @p27 :rule nary_cong :premises (@p26 @p23) :args (@t36)) % 0.36/0.58 (step @p28 :rule trans :premises (@p27 @p21)) % 0.36/0.58 (step @p29 :rule cong :premises (@p28) :args ((forall @t30 @t36))) % 0.36/0.58 (step @p30 :rule trans :premises (@p29 @p20)) % 0.36/0.58 (step @p31 :rule quant-var-elim-eq :args ((= (forall @t41 (or (not (= @t37 @t32)) @t40 @t38)) @t36))) % 0.36/0.58 (step @p32 :rule refl :args (@t38)) % 0.36/0.58 (step @p33 :rule refl :args (@t40)) % 0.36/0.58 (step @p34 :rule eq-symm :args (@t32 @t37)) % 0.36/0.58 (step @p35 :rule cong :premises (@p34) :args (@t40)) % 0.36/0.58 (step @p36 :rule nary_cong :premises (@p35 @p33 @p32) :args (@t42)) % 0.36/0.58 (step @p37 :rule aci_norm :args ((= @t43 @t42))) % 0.36/0.58 (step @p38 :rule trans :premises (@p37 @p36)) % 0.36/0.58 (step @p39 :rule cong :premises (@p38) :args (@t44)) % 0.36/0.58 (step @p40 :rule trans :premises (@p39 @p31)) % 0.36/0.58 (step @p41 :rule cong :premises (@p40) :args (@t45)) % 0.36/0.58 (step @p42 :rule quant-merge-prenex :args ((= @t45 @t46))) % 0.36/0.58 (step @p43 :rule symm :premises (@p42)) % 0.36/0.58 (step @p44 :rule quant_var_reordering :args ((= @t47 @t46))) % 0.36/0.58 (step @p45 :rule trans :premises (@p44 @p43 @p41)) % 0.36/0.58 (step @p46 :rule trans :premises (@p45 @p30)) % 0.36/0.58 (step @p47 :rule quant-merge-prenex :args ((= (forall @t41 @t48) @t47))) % 0.36/0.58 (step @p48 :rule alpha_equiv :args (@t49 (@list @t27) (@list @t8))) % 0.36/0.58 (step @p49 :rule nary_cong :premises (@p33 @p48) :args (@t50)) % 0.36/0.58 (step @p50 :rule quant-miniscope-or :args ((= @t48 @t50))) % 0.36/0.58 (step @p51 :rule trans :premises (@p50 @p49)) % 0.36/0.58 (step @p52 :rule symm :premises (@p51)) % 0.36/0.58 (step @p53 :rule cong :premises (@p52) :args ((forall @t41 (or @t40 @t51)))) % 0.36/0.58 (step @p54 :rule trans :premises (@p53 @p47)) % 0.36/0.58 (step @p55 :rule trans :premises (@p54 @p46)) % 0.36/0.58 (step @p56 :rule bool-double-not-elim :args (@t51)) % 0.36/0.58 (step @p57 :rule nary_cong :premises (@p33 @p56) :args ((or @t40 (not @t52)))) % 0.36/0.58 (step @p58 :rule bool-and-de-morgan :args (@t39 @t52 true)) % 0.36/0.58 (step @p59 :rule trans :premises (@p58 @p57)) % 0.36/0.58 (step @p60 :rule cong :premises (@p59) :args ((forall @t41 @t54))) % 0.36/0.58 (step @p61 :rule trans :premises (@p60 @p55)) % 0.36/0.58 (step @p62 :rule aci_norm :args ((= (or false @t54) @t54))) % 0.36/0.58 (step @p63 :rule beta-reduce :args ((= @t57 @t53))) % 0.36/0.58 (step @p64 :rule cong :premises (@p63) :args (@t58)) % 0.36/0.58 (step @p65 :rule eq-refl :args (@t56)) % 0.36/0.58 (step @p66 :rule cong :premises (@p65) :args (@t59)) % 0.36/0.58 (step @p67 :rule trans :premises (@p66 @p6)) % 0.36/0.58 (step @p68 :rule nary_cong :premises (@p67 @p64) :args (@t60)) % 0.36/0.58 (step @p69 :rule trans :premises (@p68 @p62)) % 0.36/0.58 (step @p70 :rule cong :premises (@p69) :args ((forall @t41 @t60))) % 0.36/0.58 (step @p71 :rule trans :premises (@p70 @p61)) % 0.36/0.58 (step @p72 :rule quant-var-elim-eq :args ((= (forall @t2 (or (not (= @t1 @t56)) @t63 @t61)) @t60))) % 0.36/0.58 (step @p73 :rule refl :args (@t61)) % 0.36/0.58 (step @p74 :rule refl :args (@t63)) % 0.36/0.58 (step @p75 :rule eq-symm :args (@t56 @t1)) % 0.36/0.58 (step @p76 :rule cong :premises (@p75) :args (@t63)) % 0.36/0.58 (step @p77 :rule nary_cong :premises (@p76 @p74 @p73) :args (@t64)) % 0.36/0.58 (step @p78 :rule aci_norm :args ((= @t65 @t64))) % 0.36/0.58 (step @p79 :rule trans :premises (@p78 @p77)) % 0.36/0.58 (step @p80 :rule cong :premises (@p79) :args (@t66)) % 0.36/0.58 (step @p81 :rule trans :premises (@p80 @p72)) % 0.36/0.58 (step @p82 :rule cong :premises (@p81) :args (@t67)) % 0.36/0.58 (step @p83 :rule quant-merge-prenex :args ((= @t67 @t68))) % 0.36/0.58 (step @p84 :rule symm :premises (@p83)) % 0.36/0.58 (step @p85 :rule quant_var_reordering :args ((= @t69 @t68))) % 0.36/0.58 (step @p86 :rule trans :premises (@p85 @p84 @p82)) % 0.36/0.58 (step @p87 :rule trans :premises (@p86 @p71)) % 0.36/0.58 (step @p88 :rule quant-merge-prenex :args ((= (forall @t2 @t70) @t69))) % 0.36/0.58 (step @p89 :rule alpha_equiv :args (@t71 (@list @t37) (@list @t17))) % 0.36/0.58 (step @p90 :rule nary_cong :premises (@p74 @p89) :args (@t72)) % 0.36/0.58 (step @p91 :rule quant-miniscope-or :args ((= @t70 @t72))) % 0.36/0.58 (step @p92 :rule trans :premises (@p91 @p90)) % 0.36/0.58 (step @p93 :rule symm :premises (@p92)) % 0.36/0.58 (step @p94 :rule cong :premises (@p93) :args ((forall @t2 (or @t63 @t73)))) % 0.36/0.58 (step @p95 :rule trans :premises (@p94 @p88)) % 0.36/0.58 (step @p96 :rule trans :premises (@p95 @p87)) % 0.36/0.58 (step @p97 :rule bool-double-not-elim :args (@t73)) % 0.36/0.58 (step @p98 :rule nary_cong :premises (@p74 @p97) :args ((or @t63 (not @t74)))) % 0.36/0.58 (step @p99 :rule bool-and-de-morgan :args (@t62 @t74 true)) % 0.36/0.58 (step @p100 :rule trans :premises (@p99 @p98)) % 0.36/0.58 (step @p101 :rule cong :premises (@p100) :args (@t76)) % 0.36/0.58 (step @p102 :rule trans :premises (@p101 @p96)) % 0.36/0.58 (step @p103 :rule cong :premises (@p102) :args (@t77)) % 0.36/0.58 (step @p104 :rule trans :premises (@p103 @p7)) % 0.36/0.58 (step @p105 :rule exists-elim :args ((= (exists @t2 @t75) @t77))) % 0.36/0.58 (step @p106 :rule trans :premises (@p105 @p104)) % 0.36/0.58 (step @p107 :rule beta-reduce :args ((= @t79 @t75))) % 0.36/0.58 (step @p108 :rule cong :premises (@p107) :args (@t80)) % 0.36/0.58 (step @p109 :rule trans :premises (@p108 @p106)) % 0.36/0.58 (step @p110 :rule cong :premises (@p109) :args ((not @t80))) % 0.36/0.58 (step @p111 :rule trans :premises (@p110 @p6)) % 0.36/0.58 (step @p112 :rule refl :args (@t1)) % 0.36/0.58 (step @p113 :rule refl :args (@t78)) % 0.36/0.58 (step @p114 :rule refl :args (@t19)) % 0.36/0.58 (step @p115 :rule cong :premises (@p114 @p113) :args ((= @t19 @t78))) % 0.36/0.58 (step @p116 :rule symm :premises (@p115)) % 0.36/0.58 (step @p117 :rule eq_resolve :premises (@p114 @p116)) % 0.36/0.58 (step @p118 :rule cong :premises (@p117) :args (@t81)) % 0.36/0.58 (step @p119 :rule cong :premises (@p118) :args (@t82)) % 0.36/0.58 (step @p120 :rule cong :premises (@p119) :args (@t83)) % 0.36/0.58 (step @p121 :rule exists-elim :args ((= @t21 @t83))) % 0.36/0.58 (step @p122 :rule trans :premises (@p121 @p120)) % 0.36/0.58 (step @p123 :rule eq-symm :args (@t18 @t56)) % 0.36/0.58 (step @p124 :rule nary_cong :premises (@p123 @p122) :args ((and (= @t18 @t56) @t21))) % 0.36/0.58 (step @p125 :rule refl :args (@t21)) % 0.36/0.58 (step @p126 :rule refl :args (@t55)) % 0.36/0.58 (step @p127 :rule refl :args (@t10)) % 0.36/0.58 (step @p128 :rule cong :premises (@p127 @p126) :args ((= @t10 @t55))) % 0.36/0.58 (step @p129 :rule symm :premises (@p128)) % 0.36/0.58 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 0.36/0.58 (step @p131 :rule cong :premises (@p130) :args (@t84)) % 0.36/0.58 (step @p132 :rule cong :premises (@p131) :args (@t85)) % 0.36/0.58 (step @p133 :rule cong :premises (@p132) :args (@t86)) % 0.36/0.58 (step @p134 :rule exists-elim :args ((= @t12 @t86))) % 0.36/0.58 (step @p135 :rule trans :premises (@p134 @p133)) % 0.36/0.58 (step @p136 :rule eq-symm :args (@t9 @t32)) % 0.36/0.58 (step @p137 :rule nary_cong :premises (@p136 @p135) :args ((and (= @t9 @t32) @t12))) % 0.36/0.58 (step @p138 :rule refl :args (@t12)) % 0.36/0.58 (step @p139 :rule eq-symm :args (@t5 tptp.c)) % 0.36/0.58 (step @p140 :rule cong :premises (@p139) :args (@t7)) % 0.36/0.58 (step @p141 :rule trans :premises (@p3 @p140)) % 0.36/0.58 (step @p142 :rule refl :args (@t9)) % 0.36/0.58 (step @p143 :rule cong :premises (@p142 @p141) :args (@t13)) % 0.36/0.58 (step @p144 :rule nary_cong :premises (@p143 @p138) :args (@t14)) % 0.36/0.58 (step @p145 :rule trans :premises (@p144 @p137)) % 0.36/0.58 (step @p146 :rule cong :premises (@p145) :args (@t16)) % 0.36/0.58 (step @p147 :rule trans :premises (@p4 @p146)) % 0.36/0.58 (step @p148 :rule refl :args (@t18)) % 0.36/0.58 (step @p149 :rule cong :premises (@p148 @p147) :args (@t22)) % 0.36/0.58 (step @p150 :rule nary_cong :premises (@p149 @p125) :args (@t23)) % 0.36/0.58 (step @p151 :rule trans :premises (@p150 @p124)) % 0.36/0.58 (step @p152 :rule cong :premises (@p151) :args (@t25)) % 0.36/0.58 (step @p153 :rule trans :premises (@p5 @p152)) % 0.36/0.58 (step @p154 :rule ho_cong :premises (@p153 @p112)) % 0.36/0.58 (step @p155 :rule cong :premises (@p154) :args (@t3)) % 0.36/0.58 (step @p156 :rule cong :premises (@p155) :args (@t4)) % 0.36/0.58 (step @p157 :rule trans :premises (@p156 @p111)) % 0.36/0.58 (step @p158 false :rule eq_resolve :premises (@p1 @p157)) % 0.36/0.58 ) % 0.36/0.58 % SZS output end Proof % 0.36/0.58 % cvc5 exiting %------------------------------------------------------------------------------