%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU456^1 : TPTP v9.2.1. Released v3.6.0. % 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 08:51:52 AM UTC 2026 % Result : Theorem 0.36s 0.65s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU456^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % 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 : Tue Jun 2 17:35:40 EDT 2026 % 0.17/0.35 % CPUTime : % 0.25/0.53 %----Proving TH0 % 0.36/0.65 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.65 % SZS status Theorem % 0.36/0.65 % SZS output start Proof % 0.36/0.65 ( % 0.36/0.65 (declare-sort $$unsorted 0) % 0.36/0.65 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.65 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.36/0.65 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.36/0.65 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.36/0.65 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.36/0.65 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.65 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.36/0.65 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.65 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.65 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.36/0.65 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.65 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.65 (define tptp.trans () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "Y" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.36/0.65 (define tptp.tc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_1) (forall (@list _let_3) (=> (and (_ tptp.trans _let_3) (_ (_ tptp.subrel _let_4) _let_3)) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.65 (define tptp.trc () (let ((_let_1 (@var "__flatten_var_1" $$unsorted))) (let ((_let_2 (@var "__flatten_var_0" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.rc (_ tptp.tc _let_3)) _let_2) _let_1)))))) % 0.36/0.65 (define tptp.trsc () (let ((_let_1 (@var "__flatten_var_1" $$unsorted))) (let ((_let_2 (@var "__flatten_var_0" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.sc (_ tptp.rc (_ tptp.tc _let_3))) _let_2) _let_1)))))) % 0.36/0.65 (define tptp.po () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.refl _let_1) (_ tptp.antisymm _let_1) (_ tptp.trans _let_1))))) % 0.36/0.65 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.36/0.65 (define tptp.total () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (or (= _let_1 _let_2) (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.65 (define tptp.term () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.36/0.65 (define tptp.ind () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@list _let_1))) (let ((_let_5 (@var "Y" $$unsorted))) (let ((_let_6 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_6) (forall (@list _let_2) (=> (forall _let_4 (=> (forall (@list _let_5) (=> (_ (_ (_ tptp.tc _let_6) _let_1) _let_5) (_ _let_2 _let_5))) _let_3)) (forall _let_4 _let_3))))))))))) % 0.36/0.65 (define tptp.innf () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (not (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.65 (define tptp.nfof () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "Y" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (and (_ (_ (_ tptp.trc _let_2) _let_3) _let_1) (_ (_ tptp.innf _let_2) _let_1))))))) % 0.36/0.65 (define tptp.norm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1) (exists (@list _let_2) (_ (_ (_ tptp.nfof _let_3) _let_2) _let_1)))))))) % 0.36/0.65 (define tptp.join () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ tptp.trc _let_3))) (let ((_let_5 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.36/0.65 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))))) % 0.36/0.65 (define tptp.sconfl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.36/0.65 (define tptp.confl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (_ (_ tptp.trc _let_3) _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))))) % 0.36/0.65 (define tptp.cr () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ (_ tptp.trsc _let_3) _let_2) _let_1) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))) % 0.36/0.65 (define @t1 () (not (_ tptp.mono tptp.rc))) % 0.36/0.65 (define @t2 () (@var "Y" $$unsorted)) % 0.36/0.65 (define @t3 () (@var "X" $$unsorted)) % 0.36/0.65 (define @t4 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.36/0.65 (define @t5 () (_ (_ @t4 @t3) @t2)) % 0.36/0.65 (define @t6 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.65 (define @t7 () (_ @t6 @t3)) % 0.36/0.65 (define @t8 () (_ @t7 @t2)) % 0.36/0.65 (define @t9 () (@list @t3 @t2)) % 0.36/0.65 (define @t10 () (forall @t9 (=> @t8 @t5))) % 0.36/0.65 (define @t11 () (@list @t6 @t4)) % 0.36/0.65 (define @t12 () (lambda @t11 @t10)) % 0.36/0.65 (define @t13 () (_ @t6 @t2)) % 0.36/0.65 (define @t14 () (_ @t13 @t3)) % 0.36/0.65 (define @t15 () (@list @t6 @t3 @t2)) % 0.36/0.65 (define @t16 () (lambda @t15 @t14)) % 0.36/0.65 (define @t17 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.36/0.65 (define @t18 () (_ @t17 @t6)) % 0.36/0.65 (define @t19 () (@list @t6)) % 0.36/0.65 (define @t20 () (@list @t17)) % 0.36/0.65 (define @t21 () (lambda @t20 (forall @t19 (= (_ @t17 @t18) @t18)))) % 0.36/0.65 (define @t22 () (_ tptp.subrel @t6)) % 0.36/0.65 (define @t23 () (lambda @t20 (forall @t19 (_ @t22 @t18)))) % 0.36/0.65 (define @t24 () (_ @t17 @t4)) % 0.36/0.65 (define @t25 () (_ @t22 @t4)) % 0.36/0.65 (define @t26 () (=> @t25 (_ (_ tptp.subrel @t18) @t24))) % 0.36/0.65 (define @t27 () (forall @t11 @t26)) % 0.36/0.65 (define @t28 () (lambda @t20 @t27)) % 0.36/0.65 (define @t29 () (_ @t7 @t3)) % 0.36/0.65 (define @t30 () (@list @t3)) % 0.36/0.65 (define @t31 () (lambda @t19 (forall @t30 @t29))) % 0.36/0.65 (define @t32 () (lambda @t19 (forall @t30 (not @t29)))) % 0.36/0.65 (define @t33 () (= @t3 @t2)) % 0.36/0.65 (define @t34 () (lambda @t15 (or @t33 @t8))) % 0.36/0.65 (define @t35 () (lambda @t19 (forall @t9 (=> @t8 @t14)))) % 0.36/0.65 (define @t36 () (lambda @t19 (forall @t9 (=> (and @t8 @t14) @t33)))) % 0.36/0.65 (define @t37 () (lambda @t19 (forall @t9 (=> @t8 (not @t14))))) % 0.36/0.65 (define @t38 () (lambda @t15 (or @t14 @t8))) % 0.36/0.65 (define @t39 () (@var "Z" $$unsorted)) % 0.36/0.65 (define @t40 () (_ @t7 @t39)) % 0.36/0.65 (define @t41 () (@list @t3 @t2 @t39)) % 0.36/0.65 (define @t42 () (lambda @t19 (forall @t41 (=> (and @t8 (_ @t13 @t39)) @t40)))) % 0.36/0.65 (define @t43 () (@list @t4)) % 0.36/0.65 (define @t44 () (lambda @t15 (forall @t43 (=> (and (_ tptp.trans @t4) @t25) @t5)))) % 0.36/0.65 (define @t45 () (@var "__flatten_var_1" $$unsorted)) % 0.36/0.65 (define @t46 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.65 (define @t47 () (_ tptp.tc @t6)) % 0.36/0.65 (define @t48 () (_ tptp.rc @t47)) % 0.36/0.65 (define @t49 () (@list @t6 @t46 @t45)) % 0.36/0.65 (define @t50 () (lambda @t49 (_ (_ @t48 @t46) @t45))) % 0.36/0.65 (define @t51 () (lambda @t49 (_ (_ (_ tptp.sc @t48) @t46) @t45))) % 0.36/0.65 (define @t52 () (_ tptp.trans @t6)) % 0.36/0.65 (define @t53 () (lambda @t19 (and (_ tptp.refl @t6) (_ tptp.antisymm @t6) @t52))) % 0.36/0.65 (define @t54 () (lambda @t19 (and (_ tptp.asymm @t6) @t52))) % 0.36/0.65 (define @t55 () (lambda @t19 (forall @t9 (or @t33 @t8 @t14)))) % 0.36/0.65 (define @t56 () (not @t8)) % 0.36/0.65 (define @t57 () (@var "A" (-> $$unsorted Bool))) % 0.36/0.65 (define @t58 () (@list @t2)) % 0.36/0.65 (define @t59 () (_ @t57 @t3)) % 0.36/0.65 (define @t60 () (lambda @t19 (forall (@list @t57) (=> (exists @t30 @t59) (exists @t30 (and @t59 (forall @t58 (=> (_ @t57 @t2) @t56)))))))) % 0.36/0.65 (define @t61 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.65 (define @t62 () (_ @t61 @t3)) % 0.36/0.65 (define @t63 () (lambda @t19 (forall (@list @t61) (=> (forall @t30 (=> (forall @t58 (=> (_ (_ @t47 @t3) @t2) (_ @t61 @t2))) @t62)) (forall @t30 @t62))))) % 0.36/0.65 (define @t64 () (lambda (@list @t6 @t3) (not (exists @t58 @t8)))) % 0.36/0.65 (define @t65 () (_ tptp.trc @t6)) % 0.36/0.65 (define @t66 () (_ @t65 @t2)) % 0.36/0.65 (define @t67 () (lambda @t15 (and (_ @t66 @t3) (_ (_ tptp.innf @t6) @t3)))) % 0.36/0.65 (define @t68 () (lambda @t19 (forall @t30 (exists @t58 (_ (_ (_ tptp.nfof @t6) @t2) @t3))))) % 0.36/0.65 (define @t69 () (_ @t65 @t3)) % 0.36/0.65 (define @t70 () (_ @t69 @t39)) % 0.36/0.65 (define @t71 () (lambda @t15 (exists (@list @t39) (and @t70 (_ @t66 @t39))))) % 0.36/0.65 (define @t72 () (_ tptp.join @t6)) % 0.36/0.65 (define @t73 () (_ (_ @t72 @t39) @t2)) % 0.36/0.65 (define @t74 () (lambda @t19 (forall @t41 (=> (and @t40 @t8) @t73)))) % 0.36/0.65 (define @t75 () (_ @t69 @t2)) % 0.36/0.65 (define @t76 () (lambda @t19 (forall @t41 (=> (and @t40 @t75) @t73)))) % 0.36/0.65 (define @t77 () (lambda @t19 (forall @t41 (=> (and @t70 @t75) @t73)))) % 0.36/0.65 (define @t78 () (lambda @t19 (forall @t9 (=> (_ (_ (_ tptp.trsc @t6) @t3) @t2) (_ (_ @t72 @t3) @t2))))) % 0.36/0.65 (define @t79 () (@var "BOUND_VARIABLE_7545" $$unsorted)) % 0.36/0.65 (define @t80 () (@var "BOUND_VARIABLE_7543" $$unsorted)) % 0.36/0.65 (define @t81 () (_ @t4 @t80 @t79)) % 0.36/0.65 (define @t82 () (_ (_ @t4 @t80) @t79)) % 0.36/0.65 (define @t83 () (= @t80 @t79)) % 0.36/0.65 (define @t84 () (_ @t6 @t80 @t79)) % 0.36/0.65 (define @t85 () (_ (_ @t6 @t80) @t79)) % 0.36/0.65 (define @t86 () (not @t85)) % 0.36/0.65 (define @t87 () (not @t83)) % 0.36/0.65 (define @t88 () (and @t87 @t86)) % 0.36/0.65 (define @t89 () (_ @t4 @t3 @t2)) % 0.36/0.65 (define @t90 () (_ @t6 @t3 @t2)) % 0.36/0.65 (define @t91 () (forall @t9 (or (not @t90) @t89))) % 0.36/0.65 (define @t92 () (not @t91)) % 0.36/0.65 (define @t93 () (or @t92 @t88 @t83 @t82)) % 0.36/0.65 (define @t94 () (@list @t6 @t4 @t80 @t79)) % 0.36/0.65 (define @t95 () (or @t83 @t85)) % 0.36/0.65 (define @t96 () (not @t95)) % 0.36/0.65 (define @t97 () (or @t92 @t96 @t83 @t82)) % 0.36/0.65 (define @t98 () (or @t83 @t82)) % 0.36/0.65 (define @t99 () (_ @t34 @t4 @t80 @t79)) % 0.36/0.65 (define @t100 () (_ @t34 @t6 @t80 @t79)) % 0.36/0.65 (define @t101 () (not @t100)) % 0.36/0.65 (define @t102 () (or @t92 @t101 @t99)) % 0.36/0.65 (define @t103 () (forall @t94 @t102)) % 0.36/0.65 (define @t104 () (_ @t17 @t4 @t80 @t79)) % 0.36/0.65 (define @t105 () (not (_ @t17 @t6 @t80 @t79))) % 0.36/0.65 (define @t106 () (or @t92 @t105 @t104)) % 0.36/0.65 (define @t107 () (_ (lambda @t20 (forall @t94 @t106)) @t34)) % 0.36/0.65 (define @t108 () (or @t105 @t104)) % 0.36/0.65 (define @t109 () (or @t92 @t108)) % 0.36/0.65 (define @t110 () (forall @t94 @t109)) % 0.36/0.65 (define @t111 () (@list @t80 @t79)) % 0.36/0.65 (define @t112 () (forall @t111 @t109)) % 0.36/0.65 (define @t113 () (forall @t111 @t108)) % 0.36/0.65 (define @t114 () (or @t92 @t113)) % 0.36/0.65 (define @t115 () (_ @t17 @t4 @t3 @t2)) % 0.36/0.65 (define @t116 () (_ @t17 @t6 @t3 @t2)) % 0.36/0.65 (define @t117 () (not @t116)) % 0.36/0.65 (define @t118 () (forall @t9 (or @t117 @t115))) % 0.36/0.65 (define @t119 () (_ (_ @t24 @t3) @t2)) % 0.36/0.65 (define @t120 () (or @t117 @t119)) % 0.36/0.65 (define @t121 () (_ @t24 @t3 @t2)) % 0.36/0.65 (define @t122 () (or @t117 @t121)) % 0.36/0.65 (define @t123 () (forall @t9 @t122)) % 0.36/0.65 (define @t124 () (_ (_ @t18 @t3) @t2)) % 0.36/0.65 (define @t125 () (not @t124)) % 0.36/0.65 (define @t126 () (or @t125 @t89)) % 0.36/0.65 (define @t127 () (_ @t18 @t3 @t2)) % 0.36/0.65 (define @t128 () (not @t127)) % 0.36/0.65 (define @t129 () (or @t128 @t89)) % 0.36/0.65 (define @t130 () (forall @t9 @t129)) % 0.36/0.65 (define @t131 () (lambda @t43 @t130)) % 0.36/0.65 (define @t132 () (lambda @t11 @t91)) % 0.36/0.65 (define @t133 () (_ @t132 @t18)) % 0.36/0.65 (define @t134 () (lambda @t43 @t91)) % 0.36/0.65 (define @t135 () (_ @t132 @t6)) % 0.36/0.65 (define @t136 () (=> (_ @t135 @t4) (_ @t133 @t24))) % 0.36/0.65 (define @t137 () (or @t56 @t5)) % 0.36/0.65 (define @t138 () (forall @t94 (or @t92 (and @t87 (not @t84)) @t83 @t81))) % 0.36/0.65 (define @t139 () (@quantifiers_skolemize @t138 1)) % 0.36/0.65 (define @t140 () (@quantifiers_skolemize @t138 0)) % 0.36/0.65 (define @t141 () (forall @t9 (or (not (_ @t140 @t3 @t2)) (_ @t139 @t3 @t2)))) % 0.36/0.65 (define @t142 () (@quantifiers_skolemize @t138 3)) % 0.36/0.65 (define @t143 () (@quantifiers_skolemize @t138 2)) % 0.36/0.65 (define @t144 () (_ @t139 @t143 @t142)) % 0.36/0.65 (define @t145 () (= @t143 @t142)) % 0.36/0.65 (define @t146 () (_ @t140 @t143 @t142)) % 0.36/0.65 (define @t147 () (not @t146)) % 0.36/0.65 (define @t148 () (not @t145)) % 0.36/0.65 (define @t149 () (and @t148 @t147)) % 0.36/0.65 (define @t150 () (not @t141)) % 0.36/0.65 (define @t151 () (or @t150 @t149 @t145 @t144)) % 0.36/0.65 (define @t152 () (@list true)) % 0.36/0.65 (define @t153 () (@list @t151)) % 0.36/0.65 (define @t154 () (or @t147 @t144)) % 0.36/0.65 (define @t155 () (not @t154)) % 0.36/0.65 (assume @p1 @t1) % 0.36/0.65 (assume @p2 true) % 0.36/0.65 (step @p3 (= tptp.subrel @t12) :rule refl :args (@t12)) % 0.36/0.65 (step @p4 (= tptp.inv @t16) :rule refl :args (@t16)) % 0.36/0.65 (step @p5 (= tptp.idem @t21) :rule refl :args (@t21)) % 0.36/0.65 (step @p6 (= tptp.infl @t23) :rule refl :args (@t23)) % 0.36/0.65 (step @p7 (= tptp.mono @t28) :rule refl :args (@t28)) % 0.36/0.65 (step @p8 (= tptp.refl @t31) :rule refl :args (@t31)) % 0.36/0.65 (step @p9 (= tptp.irrefl @t32) :rule refl :args (@t32)) % 0.36/0.65 (step @p10 (= tptp.rc @t34) :rule refl :args (@t34)) % 0.36/0.65 (step @p11 (= tptp.symm @t35) :rule refl :args (@t35)) % 0.36/0.65 (step @p12 (= tptp.antisymm @t36) :rule refl :args (@t36)) % 0.36/0.65 (step @p13 (= tptp.asymm @t37) :rule refl :args (@t37)) % 0.36/0.65 (step @p14 (= tptp.sc @t38) :rule refl :args (@t38)) % 0.36/0.65 (step @p15 (= tptp.trans @t42) :rule refl :args (@t42)) % 0.36/0.65 (step @p16 (= tptp.tc @t44) :rule refl :args (@t44)) % 0.36/0.65 (step @p17 (= tptp.trc @t50) :rule refl :args (@t50)) % 0.36/0.65 (step @p18 (= tptp.trsc @t51) :rule refl :args (@t51)) % 0.36/0.65 (step @p19 (= tptp.po @t53) :rule refl :args (@t53)) % 0.36/0.65 (step @p20 (= tptp.so @t54) :rule refl :args (@t54)) % 0.36/0.65 (step @p21 (= tptp.total @t55) :rule refl :args (@t55)) % 0.36/0.65 (step @p22 (= tptp.term @t60) :rule refl :args (@t60)) % 0.36/0.65 (step @p23 (= tptp.ind @t63) :rule refl :args (@t63)) % 0.36/0.65 (step @p24 (= tptp.innf @t64) :rule refl :args (@t64)) % 0.36/0.65 (step @p25 (= tptp.nfof @t67) :rule refl :args (@t67)) % 0.36/0.65 (step @p26 (= tptp.norm @t68) :rule refl :args (@t68)) % 0.36/0.65 (step @p27 (= tptp.join @t71) :rule refl :args (@t71)) % 0.36/0.65 (step @p28 (= tptp.lconfl @t74) :rule refl :args (@t74)) % 0.36/0.65 (step @p29 (= tptp.sconfl @t76) :rule refl :args (@t76)) % 0.36/0.65 (step @p30 (= tptp.confl @t77) :rule refl :args (@t77)) % 0.36/0.65 (step @p31 (= tptp.cr @t78) :rule refl :args (@t78)) % 0.36/0.65 (step @p32 :rule refl :args (@t81)) % 0.36/0.65 (step @p33 :rule refl :args (@t82)) % 0.36/0.65 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t82 @t81))) % 0.36/0.65 (step @p35 :rule symm :premises (@p34)) % 0.36/0.65 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 0.36/0.65 (step @p37 :rule refl :args (@t83)) % 0.36/0.65 (step @p38 :rule refl :args (@t84)) % 0.36/0.65 (step @p39 :rule refl :args (@t85)) % 0.36/0.65 (step @p40 :rule cong :premises (@p39 @p38) :args ((= @t85 @t84))) % 0.36/0.65 (step @p41 :rule symm :premises (@p40)) % 0.36/0.65 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 0.36/0.65 (step @p43 :rule cong :premises (@p42) :args (@t86)) % 0.36/0.65 (step @p44 :rule refl :args (@t87)) % 0.36/0.65 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t88)) % 0.36/0.65 (step @p46 :rule refl :args (@t92)) % 0.36/0.65 (step @p47 :rule nary_cong :premises (@p46 @p45 @p37 @p36) :args (@t93)) % 0.36/0.65 (step @p48 :rule cong :premises (@p47) :args ((forall @t94 @t93))) % 0.36/0.65 (step @p49 :rule bool-or-de-morgan :args (@t83 @t85 false)) % 0.36/0.65 (step @p50 :rule nary_cong :premises (@p46 @p49 @p37 @p33) :args (@t97)) % 0.36/0.65 (step @p51 :rule cong :premises (@p50) :args ((forall @t94 @t97))) % 0.36/0.65 (step @p52 :rule trans :premises (@p51 @p48)) % 0.36/0.65 (step @p53 :rule aci_norm :args ((= (or @t92 @t96 @t98) @t97))) % 0.36/0.65 (step @p54 :rule beta-reduce :args ((= @t99 @t98))) % 0.36/0.65 (step @p55 :rule beta-reduce :args ((= @t100 @t95))) % 0.36/0.65 (step @p56 :rule cong :premises (@p55) :args (@t101)) % 0.36/0.65 (step @p57 :rule refl :args (@t92)) % 0.36/0.65 (step @p58 :rule nary_cong :premises (@p57 @p56 @p54) :args (@t102)) % 0.36/0.65 (step @p59 :rule trans :premises (@p58 @p53)) % 0.36/0.65 (step @p60 :rule cong :premises (@p59) :args (@t103)) % 0.36/0.65 (step @p61 :rule trans :premises (@p60 @p52)) % 0.36/0.65 (step @p62 :rule beta-reduce :args ((= @t107 @t103))) % 0.36/0.65 (step @p63 :rule trans :premises (@p62 @p61)) % 0.36/0.65 (step @p64 :rule cong :premises (@p63) :args ((not @t107))) % 0.36/0.65 (step @p65 :rule aci_norm :args ((= @t109 @t106))) % 0.36/0.65 (step @p66 :rule cong :premises (@p65) :args (@t110)) % 0.36/0.65 (step @p67 :rule quant-merge-prenex :args ((= (forall @t11 @t112) @t110))) % 0.36/0.65 (step @p68 :rule alpha_equiv :args (@t113 (@list @t80 @t79) (@list @t3 @t2))) % 0.36/0.65 (step @p69 :rule nary_cong :premises (@p46 @p68) :args (@t114)) % 0.36/0.65 (step @p70 :rule quant-miniscope-or :args ((= @t112 @t114))) % 0.36/0.65 (step @p71 :rule trans :premises (@p70 @p69)) % 0.36/0.65 (step @p72 :rule symm :premises (@p71)) % 0.36/0.65 (step @p73 :rule cong :premises (@p72) :args ((forall @t11 (or @t92 @t118)))) % 0.36/0.65 (step @p74 :rule trans :premises (@p73 @p67)) % 0.36/0.65 (step @p75 :rule trans :premises (@p74 @p66)) % 0.36/0.65 (step @p76 :rule bool-impl-elim :args (@t91 @t118)) % 0.36/0.65 (step @p77 :rule cong :premises (@p76) :args ((forall @t11 (=> @t91 @t118)))) % 0.36/0.65 (step @p78 :rule trans :premises (@p77 @p75)) % 0.36/0.65 (step @p79 :rule refl :args (@t115)) % 0.36/0.65 (step @p80 :rule refl :args (@t119)) % 0.36/0.65 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t119 @t115))) % 0.36/0.65 (step @p82 :rule symm :premises (@p81)) % 0.36/0.65 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 0.36/0.65 (step @p84 :rule refl :args (@t117)) % 0.36/0.65 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t120)) % 0.36/0.65 (step @p86 :rule cong :premises (@p85) :args ((forall @t9 @t120))) % 0.36/0.65 (step @p87 :rule refl :args (@t121)) % 0.36/0.65 (step @p88 :rule refl :args (@t117)) % 0.36/0.65 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t122)) % 0.36/0.65 (step @p90 :rule cong :premises (@p89) :args (@t123)) % 0.36/0.65 (step @p91 :rule trans :premises (@p90 @p86)) % 0.36/0.65 (step @p92 :rule beta-reduce :args ((= (_ (lambda @t43 (forall @t9 (or @t117 @t89))) @t24) @t123))) % 0.36/0.65 (step @p93 :rule trans :premises (@p92 @p91)) % 0.36/0.65 (step @p94 :rule refl :args (@t24)) % 0.36/0.65 (step @p95 :rule refl :args (@t89)) % 0.36/0.65 (step @p96 :rule refl :args (@t116)) % 0.36/0.65 (step @p97 :rule refl :args (@t124)) % 0.36/0.65 (step @p98 :rule cong :premises (@p97 @p96) :args ((= @t124 @t116))) % 0.36/0.65 (step @p99 :rule symm :premises (@p98)) % 0.36/0.65 (step @p100 :rule eq_resolve :premises (@p97 @p99)) % 0.36/0.65 (step @p101 :rule cong :premises (@p100) :args (@t125)) % 0.36/0.65 (step @p102 :rule nary_cong :premises (@p101 @p95) :args (@t126)) % 0.36/0.65 (step @p103 :rule cong :premises (@p102) :args ((forall @t9 @t126))) % 0.36/0.65 (step @p104 :rule refl :args (@t89)) % 0.36/0.65 (step @p105 :rule refl :args (@t127)) % 0.36/0.65 (step @p106 :rule cong :premises (@p105) :args (@t128)) % 0.36/0.65 (step @p107 :rule nary_cong :premises (@p106 @p104) :args (@t129)) % 0.36/0.65 (step @p108 :rule cong :premises (@p107) :args (@t130)) % 0.36/0.65 (step @p109 :rule trans :premises (@p108 @p103)) % 0.36/0.65 (step @p110 :rule cong :premises (@p109) :args (@t131)) % 0.36/0.65 (step @p111 :rule beta-reduce :args ((= @t133 @t131))) % 0.36/0.65 (step @p112 :rule trans :premises (@p111 @p110)) % 0.36/0.65 (step @p113 :rule ho_cong :premises (@p112 @p94)) % 0.36/0.65 (step @p114 :rule trans :premises (@p113 @p93)) % 0.36/0.65 (step @p115 :rule beta-reduce :args ((= (_ @t134 @t4) @t91))) % 0.36/0.65 (step @p116 :rule refl :args (@t4)) % 0.36/0.65 (step @p117 :rule beta-reduce :args ((= @t135 @t134))) % 0.36/0.65 (step @p118 :rule ho_cong :premises (@p117 @p116)) % 0.36/0.65 (step @p119 :rule trans :premises (@p118 @p115)) % 0.36/0.65 (step @p120 :rule cong :premises (@p119 @p114) :args (@t136)) % 0.36/0.65 (step @p121 :rule cong :premises (@p120) :args ((forall @t11 @t136))) % 0.36/0.65 (step @p122 :rule trans :premises (@p121 @p78)) % 0.36/0.65 (step @p123 :rule refl :args (@t18)) % 0.36/0.65 (step @p124 :rule refl :args (@t89)) % 0.36/0.65 (step @p125 :rule refl :args (@t5)) % 0.36/0.65 (step @p126 :rule cong :premises (@p125 @p124) :args ((= @t5 @t89))) % 0.36/0.65 (step @p127 :rule symm :premises (@p126)) % 0.36/0.65 (step @p128 :rule eq_resolve :premises (@p125 @p127)) % 0.36/0.65 (step @p129 :rule refl :args (@t90)) % 0.36/0.65 (step @p130 :rule refl :args (@t8)) % 0.36/0.65 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t8 @t90))) % 0.36/0.65 (step @p132 :rule symm :premises (@p131)) % 0.36/0.65 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 0.36/0.65 (step @p134 :rule cong :premises (@p133) :args (@t56)) % 0.36/0.65 (step @p135 :rule nary_cong :premises (@p134 @p128) :args (@t137)) % 0.36/0.65 (step @p136 :rule cong :premises (@p135) :args ((forall @t9 @t137))) % 0.36/0.65 (step @p137 :rule bool-impl-elim :args (@t8 @t5)) % 0.36/0.65 (step @p138 :rule cong :premises (@p137) :args (@t10)) % 0.36/0.65 (step @p139 :rule trans :premises (@p138 @p136)) % 0.36/0.65 (step @p140 :rule cong :premises (@p139) :args (@t12)) % 0.36/0.65 (step @p141 :rule trans :premises (@p3 @p140)) % 0.36/0.65 (step @p142 :rule ho_cong :premises (@p141 @p123)) % 0.36/0.65 (step @p143 :rule ho_cong :premises (@p142 @p94)) % 0.36/0.65 (step @p144 :rule refl :args (@t6)) % 0.36/0.65 (step @p145 :rule ho_cong :premises (@p141 @p144)) % 0.36/0.65 (step @p146 :rule ho_cong :premises (@p145 @p116)) % 0.36/0.65 (step @p147 :rule cong :premises (@p146 @p143) :args (@t26)) % 0.36/0.65 (step @p148 :rule cong :premises (@p147) :args (@t27)) % 0.36/0.65 (step @p149 :rule trans :premises (@p148 @p122)) % 0.36/0.65 (step @p150 :rule cong :premises (@p149) :args (@t28)) % 0.36/0.65 (step @p151 :rule trans :premises (@p7 @p150)) % 0.36/0.65 (step @p152 :rule ho_cong :premises (@p151 @p10)) % 0.36/0.65 (step @p153 :rule cong :premises (@p152) :args (@t1)) % 0.36/0.65 (step @p154 :rule trans :premises (@p153 @p64)) % 0.36/0.65 (step @p155 :rule eq_resolve :premises (@p1 @p154)) % 0.36/0.65 (step @p156 :rule skolemize :premises (@p155)) % 0.36/0.65 (step @p157 :rule bool-double-not-elim :args (@t141)) % 0.36/0.65 (step @p158 :rule refl :args (@t151)) % 0.36/0.65 (step @p159 :rule nary_cong :premises (@p158 @p157) :args ((or @t151 (not @t150)))) % 0.36/0.65 (step @p160 :rule cnf_or_neg :args (@t151 0)) % 0.36/0.65 (step @p161 :rule eq_resolve :premises (@p160 @p159)) % 0.36/0.65 (step @p162 :rule reordering :premises (@p161) :args ((or @t141 @t151))) % 0.36/0.65 (step @p163 :rule chain_m_resolution :premises (@p162 @p156) :args (@t141 @t152 @t153)) % 0.36/0.65 (step @p164 :rule cnf_or_neg :args (@t151 3)) % 0.36/0.65 (step @p165 :rule chain_m_resolution :premises (@p164 @p156) :args ((not @t144) @t152 @t153)) % 0.36/0.65 (step @p166 :rule cnf_or_neg :args (@t151 1)) % 0.36/0.65 (step @p167 :rule chain_m_resolution :premises (@p166 @p156) :args ((not @t149) @t152 @t153)) % 0.36/0.65 (step @p168 :rule cnf_or_neg :args (@t151 2)) % 0.36/0.65 (step @p169 :rule reordering :premises (@p168) :args ((or @t148 @t151))) % 0.36/0.65 (step @p170 :rule chain_m_resolution :premises (@p169 @p156) :args (@t148 @t152 @t153)) % 0.36/0.65 (step @p171 :rule bool-double-not-elim :args (@t146)) % 0.36/0.65 (step @p172 :rule bool-double-not-elim :args (@t145)) % 0.36/0.65 (step @p173 :rule refl :args (@t149)) % 0.36/0.65 (step @p174 :rule nary_cong :premises (@p173 @p172 @p171) :args ((or @t149 (not @t148) (not @t147)))) % 0.36/0.65 (step @p175 :rule cnf_and_neg :args (@t149)) % 0.36/0.65 (step @p176 :rule eq_resolve :premises (@p175 @p174)) % 0.36/0.65 (step @p177 :rule reordering :premises (@p176) :args ((or @t145 @t146 @t149))) % 0.36/0.65 (step @p178 :rule chain_m_resolution :premises (@p177 @p170 @p167) :args (@t146 (@list true true) (@list @t145 @t149))) % 0.36/0.65 (step @p179 :rule cnf_or_pos :args (@t154)) % 0.36/0.65 (step @p180 :rule reordering :premises (@p179) :args ((or @t147 @t144 @t155))) % 0.36/0.65 (step @p181 :rule chain_m_resolution :premises (@p180 @p178 @p165) :args (@t155 (@list false true) (@list @t146 @t144))) % 0.36/0.65 (assume-push @p188 @t141) % 0.36/0.65 (step @p183 :rule instantiate :premises (@p163) :args ((@list @t143 @t142))) % 0.36/0.65 (step-pop @p189 :rule scope :premises (@p183)) % 0.36/0.65 (step @p184 :rule process_scope :premises (@p189) :args (@t154)) % 0.36/0.65 (step @p186 :rule implies_elim :premises (@p184)) % 0.36/0.65 (step @p187 false :rule chain_m_resolution :premises (@p186 @p181 @p163) :args (false (@list true false) (@list @t154 @t141))) % 0.36/0.65 ) % 0.36/0.65 % SZS output end Proof % 0.36/0.65 % cvc5 exiting %------------------------------------------------------------------------------