%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO894^8 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n024.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 09:13:43 AM UTC 2026 % Result : Theorem 0.13s 0.38s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SYO894^8 : TPTP v9.2.1. Released v8.1.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 20:08:45 EDT 2026 % 0.07/0.25 % CPUTime : % 0.13/0.34 %----Proving TH0 % 0.13/0.38 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.13/0.38 % SZS status Theorem % 0.13/0.38 % SZS output start Proof % 0.13/0.38 ( % 0.13/0.38 (declare-sort tptp.mworld 0) % 0.13/0.38 (declare-const tptp.mactual tptp.mworld) % 0.13/0.38 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.13/0.38 (declare-const tptp.p (-> tptp.mworld Bool)) % 0.13/0.38 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.13/0.38 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.13/0.38 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.13/0.38 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.13/0.38 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.13/0.38 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.13/0.38 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.13/0.38 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (and (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.13/0.38 (define @t1 () (@var "W" tptp.mworld)) % 0.13/0.38 (define @t2 () (_ tptp.mrel @t1)) % 0.13/0.38 (define @t3 () (@list @t1)) % 0.13/0.38 (define @t4 () (not (_ tptp.mlocal (_ (_ tptp.mequiv (_ tptp.mbox (_ (_ tptp.mimplies tptp.p) (_ tptp.mnot tptp.p)))) (_ tptp.mnot (_ tptp.mdia tptp.p)))))) % 0.13/0.38 (define @t5 () (@var "Phi" (-> tptp.mworld Bool))) % 0.13/0.38 (define @t6 () (lambda (@list @t5) (_ @t5 tptp.mactual))) % 0.13/0.38 (define @t7 () (@var "A" (-> tptp.mworld Bool))) % 0.13/0.38 (define @t8 () (_ @t7 @t1)) % 0.13/0.38 (define @t9 () (lambda (@list @t7 @t1) (not @t8))) % 0.13/0.38 (define @t10 () (@var "B" (-> tptp.mworld Bool))) % 0.13/0.38 (define @t11 () (_ @t10 @t1)) % 0.13/0.38 (define @t12 () (@list @t7 @t10 @t1)) % 0.13/0.38 (define @t13 () (lambda @t12 (and @t8 @t11))) % 0.13/0.38 (define @t14 () (lambda @t12 (or @t8 @t11))) % 0.13/0.38 (define @t15 () (lambda @t12 (=> @t8 @t11))) % 0.13/0.38 (define @t16 () (lambda @t12 (= @t8 @t11))) % 0.13/0.38 (define @t17 () (@var "V" tptp.mworld)) % 0.13/0.38 (define @t18 () (_ @t5 @t17)) % 0.13/0.38 (define @t19 () (_ @t2 @t17)) % 0.13/0.38 (define @t20 () (@list @t17)) % 0.13/0.38 (define @t21 () (forall @t20 (=> @t19 @t18))) % 0.13/0.38 (define @t22 () (@list @t5 @t1)) % 0.13/0.38 (define @t23 () (lambda @t22 @t21)) % 0.13/0.38 (define @t24 () (and @t19 @t18)) % 0.13/0.38 (define @t25 () (exists @t20 @t24)) % 0.13/0.38 (define @t26 () (lambda @t22 @t25)) % 0.13/0.38 (define @t27 () (@var "BOUND_VARIABLE_7609" tptp.mworld)) % 0.13/0.38 (define @t28 () (lambda (@list @t27) true)) % 0.13/0.38 (define @t29 () (_ @t28 tptp.mactual)) % 0.13/0.38 (define @t30 () (tptp.p @t17)) % 0.13/0.38 (define @t31 () (tptp.mrel @t1 @t17)) % 0.13/0.38 (define @t32 () (not @t31)) % 0.13/0.38 (define @t33 () (forall @t20 (or @t32 (not @t30)))) % 0.13/0.38 (define @t34 () (lambda @t3 @t33)) % 0.13/0.38 (define @t35 () (_ @t34 @t1)) % 0.13/0.38 (define @t36 () (= @t35 @t33)) % 0.13/0.38 (define @t37 () (lambda @t3 @t36)) % 0.13/0.38 (define @t38 () (@list @t10 @t1)) % 0.13/0.38 (define @t39 () (not @t33)) % 0.13/0.38 (define @t40 () (lambda @t3 @t39)) % 0.13/0.38 (define @t41 () (_ @t40 @t1)) % 0.13/0.38 (define @t42 () (not @t41)) % 0.13/0.38 (define @t43 () (lambda @t3 @t42)) % 0.13/0.38 (define @t44 () (_ @t5 @t17)) % 0.13/0.38 (define @t45 () (_ (lambda @t22 (not (forall @t20 (or @t32 (not @t44))))) tptp.p)) % 0.13/0.38 (define @t46 () (lambda @t38 (= @t35 @t11))) % 0.13/0.38 (define @t47 () (_ tptp.p @t17)) % 0.13/0.38 (define @t48 () (not @t47)) % 0.13/0.38 (define @t49 () (or @t32 @t48)) % 0.13/0.38 (define @t50 () (=> @t47 @t48)) % 0.13/0.38 (define @t51 () (or @t32 @t50)) % 0.13/0.38 (define @t52 () (_ tptp.p @t1)) % 0.13/0.38 (define @t53 () (not @t52)) % 0.13/0.38 (define @t54 () (lambda @t3 (=> @t52 @t53))) % 0.13/0.38 (define @t55 () (_ @t54 @t17)) % 0.13/0.38 (define @t56 () (or @t32 @t55)) % 0.13/0.38 (define @t57 () (forall @t20 @t56)) % 0.13/0.38 (define @t58 () (lambda @t3 @t57)) % 0.13/0.38 (define @t59 () (lambda @t22 (forall @t20 (or @t32 @t44)))) % 0.13/0.38 (define @t60 () (lambda @t3 @t53)) % 0.13/0.38 (define @t61 () (_ @t60 @t1)) % 0.13/0.38 (define @t62 () (=> @t52 @t61)) % 0.13/0.38 (define @t63 () (lambda @t3 @t62)) % 0.13/0.38 (define @t64 () (lambda @t38 (=> @t52 @t11))) % 0.13/0.38 (define @t65 () (_ @t9 tptp.p)) % 0.13/0.38 (define @t66 () (_ @t15 tptp.p)) % 0.13/0.38 (define @t67 () (not @t18)) % 0.13/0.38 (define @t68 () (not @t19)) % 0.13/0.38 (define @t69 () (or @t68 @t67)) % 0.13/0.38 (define @t70 () (forall @t20 (not @t24))) % 0.13/0.38 (define @t71 () (not @t70)) % 0.13/0.38 (define @t72 () (or @t68 @t18)) % 0.13/0.38 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.13/0.38 (assume @p2 @t4) % 0.13/0.38 (assume @p3 true) % 0.13/0.38 (step @p4 (= tptp.mlocal @t6) :rule refl :args (@t6)) % 0.13/0.38 (step @p5 (= tptp.mnot @t9) :rule refl :args (@t9)) % 0.13/0.38 (step @p6 (= tptp.mand @t13) :rule refl :args (@t13)) % 0.13/0.38 (step @p7 (= tptp.mor @t14) :rule refl :args (@t14)) % 0.13/0.38 (step @p8 (= tptp.mimplies @t15) :rule refl :args (@t15)) % 0.13/0.38 (step @p9 (= tptp.mequiv @t16) :rule refl :args (@t16)) % 0.13/0.38 (step @p10 (= tptp.mbox @t23) :rule refl :args (@t23)) % 0.13/0.38 (step @p11 (= tptp.mdia @t26) :rule refl :args (@t26)) % 0.13/0.38 (step @p12 :rule evaluate :args ((not true))) % 0.13/0.38 (step @p13 :rule beta-reduce :args ((= @t29 true))) % 0.13/0.38 (step @p14 :rule beta-reduce :args ((= (_ @t6 @t28) @t29))) % 0.13/0.38 (step @p15 :rule trans :premises (@p14 @p13)) % 0.13/0.38 (step @p16 :rule refl :args (@t28)) % 0.13/0.38 (step @p17 :rule symm :premises (@p16)) % 0.13/0.38 (step @p18 :rule alpha_equiv :args ((lambda @t3 true) (@list @t1) (@list @t27))) % 0.13/0.38 (step @p19 :rule trans :premises (@p18 @p17)) % 0.13/0.38 (step @p20 :rule eq-refl :args (@t33)) % 0.13/0.38 (step @p21 :rule beta-reduce :args (@t36)) % 0.13/0.38 (step @p22 :rule refl :args (@t33)) % 0.13/0.38 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t33 @t35))) % 0.13/0.38 (step @p24 :rule trans :premises (@p23 @p20)) % 0.13/0.38 (step @p25 :rule eq-symm :args (@t35 @t33)) % 0.13/0.38 (step @p26 :rule trans :premises (@p25 @p24)) % 0.13/0.38 (step @p27 :rule cong :premises (@p26) :args (@t37)) % 0.13/0.38 (step @p28 :rule trans :premises (@p27 @p19)) % 0.13/0.38 (step @p29 :rule beta-reduce :args ((= (_ (lambda @t38 (= @t11 @t33)) @t34) @t37))) % 0.13/0.38 (step @p30 :rule trans :premises (@p29 @p28)) % 0.13/0.38 (step @p31 :rule bool-double-not-elim :args (@t33)) % 0.13/0.38 (step @p32 :rule beta-reduce :args ((= @t41 @t39))) % 0.13/0.38 (step @p33 :rule cong :premises (@p32) :args (@t42)) % 0.13/0.38 (step @p34 :rule trans :premises (@p33 @p31)) % 0.13/0.38 (step @p35 :rule cong :premises (@p34) :args (@t43)) % 0.13/0.38 (step @p36 :rule beta-reduce :args ((= (_ @t9 @t40) @t43))) % 0.13/0.38 (step @p37 :rule trans :premises (@p36 @p35)) % 0.13/0.38 (step @p38 :rule beta-reduce :args ((= @t45 @t40))) % 0.13/0.38 (step @p39 :rule refl :args (@t9)) % 0.13/0.38 (step @p40 :rule ho_cong :premises (@p39 @p38)) % 0.13/0.38 (step @p41 :rule trans :premises (@p40 @p37)) % 0.13/0.38 (step @p42 :rule refl :args (@t11)) % 0.13/0.38 (step @p43 :rule cong :premises (@p42 @p21) :args ((= @t11 @t35))) % 0.13/0.38 (step @p44 :rule eq-symm :args (@t35 @t11)) % 0.13/0.38 (step @p45 :rule trans :premises (@p44 @p43)) % 0.13/0.38 (step @p46 :rule cong :premises (@p45) :args (@t46)) % 0.13/0.38 (step @p47 :rule beta-reduce :args ((= (_ @t16 @t34) @t46))) % 0.13/0.38 (step @p48 :rule trans :premises (@p47 @p46)) % 0.13/0.38 (step @p49 :rule refl :args (@t30)) % 0.13/0.38 (step @p50 :rule refl :args (@t47)) % 0.13/0.38 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t47 @t30))) % 0.13/0.38 (step @p52 :rule symm :premises (@p51)) % 0.13/0.38 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.13/0.38 (step @p54 :rule cong :premises (@p53) :args (@t48)) % 0.13/0.38 (step @p55 :rule refl :args (@t32)) % 0.13/0.38 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t49)) % 0.13/0.38 (step @p57 :rule cong :premises (@p56) :args ((forall @t20 @t49))) % 0.13/0.38 (step @p58 :rule aci_norm :args ((= (or @t48 @t48) @t48))) % 0.13/0.38 (step @p59 :rule bool-impl-elim :args (@t47 @t48)) % 0.13/0.38 (step @p60 :rule trans :premises (@p59 @p58)) % 0.13/0.38 (step @p61 :rule nary_cong :premises (@p55 @p60) :args (@t51)) % 0.13/0.38 (step @p62 :rule cong :premises (@p61) :args ((forall @t20 @t51))) % 0.13/0.38 (step @p63 :rule trans :premises (@p62 @p57)) % 0.13/0.38 (step @p64 :rule beta-reduce :args ((= @t55 @t50))) % 0.13/0.38 (step @p65 :rule refl :args (@t32)) % 0.13/0.38 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t56)) % 0.13/0.38 (step @p67 :rule cong :premises (@p66) :args (@t57)) % 0.13/0.38 (step @p68 :rule trans :premises (@p67 @p63)) % 0.13/0.38 (step @p69 :rule cong :premises (@p68) :args (@t58)) % 0.13/0.38 (step @p70 :rule beta-reduce :args ((= (_ @t59 @t54) @t58))) % 0.13/0.38 (step @p71 :rule trans :premises (@p70 @p69)) % 0.13/0.38 (step @p72 :rule beta-reduce :args ((= @t61 @t53))) % 0.13/0.38 (step @p73 :rule refl :args (@t52)) % 0.13/0.38 (step @p74 :rule cong :premises (@p73 @p72) :args (@t62)) % 0.13/0.38 (step @p75 :rule cong :premises (@p74) :args (@t63)) % 0.13/0.38 (step @p76 :rule beta-reduce :args ((= (_ @t64 @t60) @t63))) % 0.13/0.38 (step @p77 :rule trans :premises (@p76 @p75)) % 0.13/0.38 (step @p78 :rule beta-reduce :args ((= @t65 @t60))) % 0.13/0.38 (step @p79 :rule beta-reduce :args ((= @t66 @t64))) % 0.13/0.38 (step @p80 :rule ho_cong :premises (@p79 @p78)) % 0.13/0.38 (step @p81 :rule trans :premises (@p80 @p77)) % 0.13/0.38 (step @p82 :rule refl :args (@t59)) % 0.13/0.38 (step @p83 :rule ho_cong :premises (@p82 @p81)) % 0.13/0.38 (step @p84 :rule trans :premises (@p83 @p71)) % 0.13/0.38 (step @p85 :rule refl :args (@t16)) % 0.13/0.38 (step @p86 :rule ho_cong :premises (@p85 @p84)) % 0.13/0.38 (step @p87 :rule trans :premises (@p86 @p48)) % 0.13/0.38 (step @p88 :rule ho_cong :premises (@p87 @p41)) % 0.13/0.38 (step @p89 :rule trans :premises (@p88 @p30)) % 0.13/0.38 (step @p90 :rule refl :args (@t6)) % 0.13/0.38 (step @p91 :rule ho_cong :premises (@p90 @p89)) % 0.13/0.38 (step @p92 :rule trans :premises (@p91 @p15)) % 0.13/0.38 (step @p93 :rule cong :premises (@p92) :args ((not (_ @t6 (_ (_ @t16 (_ @t59 (_ @t66 @t65))) (_ @t9 @t45)))))) % 0.13/0.38 (step @p94 :rule trans :premises (@p93 @p12)) % 0.13/0.38 (step @p95 :rule refl :args (tptp.p)) % 0.13/0.38 (step @p96 :rule refl :args (@t44)) % 0.13/0.38 (step @p97 :rule refl :args (@t18)) % 0.13/0.38 (step @p98 :rule cong :premises (@p97 @p96) :args ((= @t18 @t44))) % 0.13/0.38 (step @p99 :rule symm :premises (@p98)) % 0.13/0.38 (step @p100 :rule eq_resolve :premises (@p97 @p99)) % 0.13/0.38 (step @p101 :rule cong :premises (@p100) :args (@t67)) % 0.13/0.38 (step @p102 :rule refl :args (@t31)) % 0.13/0.38 (step @p103 :rule refl :args (@t19)) % 0.13/0.38 (step @p104 :rule cong :premises (@p103 @p102) :args ((= @t19 @t31))) % 0.13/0.38 (step @p105 :rule symm :premises (@p104)) % 0.13/0.38 (step @p106 :rule eq_resolve :premises (@p103 @p105)) % 0.13/0.38 (step @p107 :rule cong :premises (@p106) :args (@t68)) % 0.13/0.38 (step @p108 :rule nary_cong :premises (@p107 @p101) :args (@t69)) % 0.13/0.38 (step @p109 :rule cong :premises (@p108) :args ((forall @t20 @t69))) % 0.13/0.38 (step @p110 :rule bool-and-de-morgan :args (@t19 @t18 true)) % 0.13/0.38 (step @p111 :rule cong :premises (@p110) :args (@t70)) % 0.13/0.38 (step @p112 :rule trans :premises (@p111 @p109)) % 0.13/0.38 (step @p113 :rule cong :premises (@p112) :args (@t71)) % 0.13/0.38 (step @p114 :rule exists-elim :args ((= @t25 @t71))) % 0.13/0.38 (step @p115 :rule trans :premises (@p114 @p113)) % 0.13/0.38 (step @p116 :rule cong :premises (@p115) :args (@t26)) % 0.13/0.38 (step @p117 :rule trans :premises (@p11 @p116)) % 0.13/0.38 (step @p118 :rule ho_cong :premises (@p117 @p95)) % 0.13/0.38 (step @p119 :rule ho_cong :premises (@p5 @p118)) % 0.13/0.38 (step @p120 :rule ho_cong :premises (@p5 @p95)) % 0.13/0.38 (step @p121 :rule ho_cong :premises (@p8 @p95)) % 0.13/0.38 (step @p122 :rule ho_cong :premises (@p121 @p120)) % 0.13/0.38 (step @p123 :rule nary_cong :premises (@p107 @p100) :args (@t72)) % 0.13/0.38 (step @p124 :rule cong :premises (@p123) :args ((forall @t20 @t72))) % 0.13/0.38 (step @p125 :rule bool-impl-elim :args (@t19 @t18)) % 0.13/0.38 (step @p126 :rule cong :premises (@p125) :args (@t21)) % 0.13/0.38 (step @p127 :rule trans :premises (@p126 @p124)) % 0.13/0.38 (step @p128 :rule cong :premises (@p127) :args (@t23)) % 0.13/0.38 (step @p129 :rule trans :premises (@p10 @p128)) % 0.13/0.38 (step @p130 :rule ho_cong :premises (@p129 @p122)) % 0.13/0.38 (step @p131 :rule ho_cong :premises (@p9 @p130)) % 0.13/0.38 (step @p132 :rule ho_cong :premises (@p131 @p119)) % 0.13/0.38 (step @p133 :rule ho_cong :premises (@p4 @p132)) % 0.13/0.38 (step @p134 :rule cong :premises (@p133) :args (@t4)) % 0.13/0.38 (step @p135 :rule trans :premises (@p134 @p94)) % 0.13/0.38 (step @p136 false :rule eq_resolve :premises (@p2 @p135)) % 0.13/0.38 ) % 0.13/0.38 % SZS output end Proof % 0.13/0.38 % cvc5 exiting %------------------------------------------------------------------------------