%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU458^1 : 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 : n016.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 08:51:53 AM UTC 2026 % Result : Theorem 0.36s 0.62s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SEU458^1 : TPTP v9.2.1. Released v3.6.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n016.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 17:36:39 EDT 2026 % 0.16/0.35 % CPUTime : % 0.26/0.51 %----Proving TH0 % 0.36/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.62 % SZS status Theorem % 0.36/0.62 % SZS output start Proof % 0.36/0.62 ( % 0.36/0.62 (declare-sort $$unsorted 0) % 0.36/0.62 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.62 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.36/0.62 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.36/0.62 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.36/0.62 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.36/0.62 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.62 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.36/0.62 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.62 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.62 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.36/0.62 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.62 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.36/0.62 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.36/0.62 (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))))))))) % 0.36/0.62 (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)))))) % 0.36/0.62 (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)))))) % 0.36/0.62 (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))))) % 0.36/0.62 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.36/0.62 (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)))))))) % 0.36/0.62 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.36/0.62 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 0.36/0.62 (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)))))))) % 0.36/0.62 (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))))))) % 0.36/0.62 (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)))))))) % 0.36/0.62 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.36/0.62 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.36/0.62 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.36/0.62 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.36/0.62 (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)))))))) % 0.36/0.62 (define @t1 () (not (_ tptp.idem tptp.sc))) % 0.36/0.62 (define @t2 () (@var "Y" $$unsorted)) % 0.36/0.62 (define @t3 () (@var "X" $$unsorted)) % 0.36/0.62 (define @t4 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.36/0.62 (define @t5 () (_ (_ @t4 @t3) @t2)) % 0.36/0.62 (define @t6 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.62 (define @t7 () (_ @t6 @t3)) % 0.36/0.62 (define @t8 () (_ @t7 @t2)) % 0.36/0.62 (define @t9 () (@list @t3 @t2)) % 0.36/0.62 (define @t10 () (@list @t6 @t4)) % 0.36/0.62 (define @t11 () (lambda @t10 (forall @t9 (=> @t8 @t5)))) % 0.36/0.62 (define @t12 () (_ @t6 @t2)) % 0.36/0.62 (define @t13 () (_ @t12 @t3)) % 0.36/0.62 (define @t14 () (@list @t6 @t3 @t2)) % 0.36/0.62 (define @t15 () (lambda @t14 @t13)) % 0.36/0.62 (define @t16 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.36/0.62 (define @t17 () (_ @t16 @t6)) % 0.36/0.62 (define @t18 () (_ @t16 @t17)) % 0.36/0.62 (define @t19 () (@list @t6)) % 0.36/0.62 (define @t20 () (forall @t19 (= @t18 @t17))) % 0.36/0.62 (define @t21 () (@list @t16)) % 0.36/0.62 (define @t22 () (lambda @t21 @t20)) % 0.36/0.62 (define @t23 () (_ tptp.subrel @t6)) % 0.36/0.62 (define @t24 () (lambda @t21 (forall @t19 (_ @t23 @t17)))) % 0.36/0.62 (define @t25 () (_ @t23 @t4)) % 0.36/0.62 (define @t26 () (lambda @t21 (forall @t10 (=> @t25 (_ (_ tptp.subrel @t17) (_ @t16 @t4)))))) % 0.36/0.62 (define @t27 () (_ @t7 @t3)) % 0.36/0.62 (define @t28 () (@list @t3)) % 0.36/0.62 (define @t29 () (lambda @t19 (forall @t28 @t27))) % 0.36/0.62 (define @t30 () (lambda @t19 (forall @t28 (not @t27)))) % 0.36/0.62 (define @t31 () (= @t3 @t2)) % 0.36/0.62 (define @t32 () (lambda @t14 (or @t31 @t8))) % 0.36/0.62 (define @t33 () (lambda @t19 (forall @t9 (=> @t8 @t13)))) % 0.36/0.62 (define @t34 () (lambda @t19 (forall @t9 (=> (and @t8 @t13) @t31)))) % 0.36/0.62 (define @t35 () (lambda @t19 (forall @t9 (=> @t8 (not @t13))))) % 0.36/0.62 (define @t36 () (or @t13 @t8)) % 0.36/0.62 (define @t37 () (lambda @t14 @t36)) % 0.36/0.62 (define @t38 () (@var "Z" $$unsorted)) % 0.36/0.62 (define @t39 () (_ @t7 @t38)) % 0.36/0.62 (define @t40 () (@list @t3 @t2 @t38)) % 0.36/0.62 (define @t41 () (lambda @t19 (forall @t40 (=> (and @t8 (_ @t12 @t38)) @t39)))) % 0.36/0.62 (define @t42 () (lambda @t14 (forall (@list @t4) (=> (and (_ tptp.trans @t4) @t25) @t5)))) % 0.36/0.62 (define @t43 () (@var "__flatten_var_1" $$unsorted)) % 0.36/0.62 (define @t44 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.62 (define @t45 () (_ tptp.tc @t6)) % 0.36/0.62 (define @t46 () (_ tptp.rc @t45)) % 0.36/0.62 (define @t47 () (@list @t6 @t44 @t43)) % 0.36/0.62 (define @t48 () (lambda @t47 (_ (_ @t46 @t44) @t43))) % 0.36/0.62 (define @t49 () (lambda @t47 (_ (_ (_ tptp.sc @t46) @t44) @t43))) % 0.36/0.62 (define @t50 () (_ tptp.trans @t6)) % 0.36/0.62 (define @t51 () (lambda @t19 (and (_ tptp.refl @t6) (_ tptp.antisymm @t6) @t50))) % 0.36/0.62 (define @t52 () (lambda @t19 (and (_ tptp.asymm @t6) @t50))) % 0.36/0.62 (define @t53 () (lambda @t19 (forall @t9 (or @t31 @t8 @t13)))) % 0.36/0.62 (define @t54 () (@var "A" (-> $$unsorted Bool))) % 0.36/0.62 (define @t55 () (@list @t2)) % 0.36/0.62 (define @t56 () (_ @t54 @t3)) % 0.36/0.62 (define @t57 () (lambda @t19 (forall (@list @t54) (=> (exists @t28 @t56) (exists @t28 (and @t56 (forall @t55 (=> (_ @t54 @t2) (not @t8))))))))) % 0.36/0.62 (define @t58 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.62 (define @t59 () (_ @t58 @t3)) % 0.36/0.62 (define @t60 () (lambda @t19 (forall (@list @t58) (=> (forall @t28 (=> (forall @t55 (=> (_ (_ @t45 @t3) @t2) (_ @t58 @t2))) @t59)) (forall @t28 @t59))))) % 0.36/0.62 (define @t61 () (lambda (@list @t6 @t3) (not (exists @t55 @t8)))) % 0.36/0.62 (define @t62 () (_ tptp.trc @t6)) % 0.36/0.62 (define @t63 () (_ @t62 @t2)) % 0.36/0.62 (define @t64 () (lambda @t14 (and (_ @t63 @t3) (_ (_ tptp.innf @t6) @t3)))) % 0.36/0.62 (define @t65 () (lambda @t19 (forall @t28 (exists @t55 (_ (_ (_ tptp.nfof @t6) @t2) @t3))))) % 0.36/0.62 (define @t66 () (_ @t62 @t3)) % 0.36/0.62 (define @t67 () (_ @t66 @t38)) % 0.36/0.62 (define @t68 () (lambda @t14 (exists (@list @t38) (and @t67 (_ @t63 @t38))))) % 0.36/0.62 (define @t69 () (_ tptp.join @t6)) % 0.36/0.62 (define @t70 () (_ (_ @t69 @t38) @t2)) % 0.36/0.62 (define @t71 () (lambda @t19 (forall @t40 (=> (and @t39 @t8) @t70)))) % 0.36/0.62 (define @t72 () (_ @t66 @t2)) % 0.36/0.62 (define @t73 () (lambda @t19 (forall @t40 (=> (and @t39 @t72) @t70)))) % 0.36/0.62 (define @t74 () (lambda @t19 (forall @t40 (=> (and @t67 @t72) @t70)))) % 0.36/0.62 (define @t75 () (lambda @t19 (forall @t9 (=> (_ (_ (_ tptp.trsc @t6) @t3) @t2) (_ (_ @t69 @t3) @t2))))) % 0.36/0.62 (define @t76 () (_ @t6 @t2 @t3)) % 0.36/0.62 (define @t77 () (_ @t6 @t3 @t2)) % 0.36/0.62 (define @t78 () (or @t8 @t13)) % 0.36/0.62 (define @t79 () (lambda @t9 @t78)) % 0.36/0.62 (define @t80 () (lambda @t9 @t36)) % 0.36/0.62 (define @t81 () (= @t80 @t79)) % 0.36/0.62 (define @t82 () (lambda @t55 @t36)) % 0.36/0.62 (define @t83 () (_ @t80 @t3)) % 0.36/0.62 (define @t84 () (@var "BOUND_VARIABLE_8839" $$unsorted)) % 0.36/0.62 (define @t85 () (_ @t6 @t84)) % 0.36/0.62 (define @t86 () (lambda (@list @t84) (or (_ @t85 @t2) (_ @t12 @t84)))) % 0.36/0.62 (define @t87 () (or (_ (_ @t80 @t2) @t3) (_ @t83 @t2))) % 0.36/0.62 (define @t88 () (lambda @t9 @t87)) % 0.36/0.62 (define @t89 () (_ @t37 @t6)) % 0.36/0.62 (define @t90 () (= @t89 (_ @t37 @t89))) % 0.36/0.62 (define @t91 () (forall @t19 @t90)) % 0.36/0.62 (define @t92 () (_ (lambda @t21 (forall @t19 (= @t17 @t18))) @t37)) % 0.36/0.62 (define @t93 () (forall @t19 (= (lambda @t9 (or @t76 @t77)) (lambda @t9 (or @t77 @t76))))) % 0.36/0.62 (define @t94 () (@quantifiers_skolemize @t93 0)) % 0.36/0.62 (define @t95 () (_ @t94 @t3 @t2)) % 0.36/0.62 (define @t96 () (_ @t94 @t2 @t3)) % 0.36/0.62 (define @t97 () (lambda @t9 (or @t96 @t95))) % 0.36/0.62 (define @t98 () (@purify @t97)) % 0.36/0.62 (define @t99 () (lambda @t9 (or @t95 @t96))) % 0.36/0.62 (define @t100 () (@purify @t99)) % 0.36/0.62 (define @t101 () (= @t100 @t98)) % 0.36/0.62 (define @t102 () (not @t101)) % 0.36/0.62 (define @t103 () (not @t93)) % 0.36/0.62 (define @t104 () (= @t97 @t99)) % 0.36/0.62 (define @t105 () (not @t104)) % 0.36/0.62 (define @t106 () (@list true)) % 0.36/0.62 (define @t107 () (@const 0 $$unsorted)) % 0.36/0.62 (define @t108 () (@const 1 $$unsorted)) % 0.36/0.62 (define @t109 () (_ @t94 @t108 @t107)) % 0.36/0.62 (define @t110 () (_ @t94 @t107 @t108)) % 0.36/0.62 (define @t111 () (or @t110 @t109)) % 0.36/0.62 (define @t112 () (or @t109 @t110)) % 0.36/0.62 (define @t113 () (= @t112 @t111)) % 0.36/0.62 (define @t114 () (= (_ @t97 @t107 @t108) @t112)) % 0.36/0.62 (define @t115 () (_ @t98 @t107 @t108)) % 0.36/0.62 (define @t116 () (= (_ @t99 @t107 @t108) @t111)) % 0.36/0.62 (define @t117 () (_ @t100 @t107 @t108)) % 0.36/0.62 (define @t118 () (= @t117 @t115)) % 0.36/0.62 (define @t119 () (not @t118)) % 0.36/0.62 (define @t120 () (or @t101 @t119)) % 0.36/0.62 (define @t121 () (@list true false false)) % 0.36/0.62 (define @t122 () (@list @t113 @t111 @t112)) % 0.36/0.62 (define @t123 () (not @t112)) % 0.36/0.62 (define @t124 () (@list true true)) % 0.36/0.62 (define @t125 () (@list @t109 @t110)) % 0.36/0.62 (define @t126 () (not @t111)) % 0.36/0.62 (assume @p1 @t1) % 0.36/0.62 (assume @p2 true) % 0.36/0.62 (step @p3 (= tptp.subrel @t11) :rule refl :args (@t11)) % 0.36/0.62 (step @p4 (= tptp.inv @t15) :rule refl :args (@t15)) % 0.36/0.62 (step @p5 (= tptp.idem @t22) :rule refl :args (@t22)) % 0.36/0.62 (step @p6 (= tptp.infl @t24) :rule refl :args (@t24)) % 0.36/0.62 (step @p7 (= tptp.mono @t26) :rule refl :args (@t26)) % 0.36/0.62 (step @p8 (= tptp.refl @t29) :rule refl :args (@t29)) % 0.36/0.62 (step @p9 (= tptp.irrefl @t30) :rule refl :args (@t30)) % 0.36/0.62 (step @p10 (= tptp.rc @t32) :rule refl :args (@t32)) % 0.36/0.62 (step @p11 (= tptp.symm @t33) :rule refl :args (@t33)) % 0.36/0.62 (step @p12 (= tptp.antisymm @t34) :rule refl :args (@t34)) % 0.36/0.62 (step @p13 (= tptp.asymm @t35) :rule refl :args (@t35)) % 0.36/0.62 (step @p14 (= tptp.sc @t37) :rule refl :args (@t37)) % 0.36/0.62 (step @p15 (= tptp.trans @t41) :rule refl :args (@t41)) % 0.36/0.62 (step @p16 (= tptp.tc @t42) :rule refl :args (@t42)) % 0.36/0.62 (step @p17 (= tptp.trc @t48) :rule refl :args (@t48)) % 0.36/0.62 (step @p18 (= tptp.trsc @t49) :rule refl :args (@t49)) % 0.36/0.62 (step @p19 (= tptp.po @t51) :rule refl :args (@t51)) % 0.36/0.62 (step @p20 (= tptp.so @t52) :rule refl :args (@t52)) % 0.36/0.62 (step @p21 (= tptp.total @t53) :rule refl :args (@t53)) % 0.36/0.62 (step @p22 (= tptp.term @t57) :rule refl :args (@t57)) % 0.36/0.62 (step @p23 (= tptp.ind @t60) :rule refl :args (@t60)) % 0.36/0.62 (step @p24 (= tptp.innf @t61) :rule refl :args (@t61)) % 0.36/0.62 (step @p25 (= tptp.nfof @t64) :rule refl :args (@t64)) % 0.36/0.62 (step @p26 (= tptp.norm @t65) :rule refl :args (@t65)) % 0.36/0.62 (step @p27 (= tptp.join @t68) :rule refl :args (@t68)) % 0.36/0.62 (step @p28 (= tptp.lconfl @t71) :rule refl :args (@t71)) % 0.36/0.62 (step @p29 (= tptp.sconfl @t73) :rule refl :args (@t73)) % 0.36/0.62 (step @p30 (= tptp.confl @t74) :rule refl :args (@t74)) % 0.36/0.62 (step @p31 (= tptp.cr @t75) :rule refl :args (@t75)) % 0.36/0.62 (step @p32 :rule refl :args (@t76)) % 0.36/0.62 (step @p33 :rule refl :args (@t13)) % 0.36/0.62 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t13 @t76))) % 0.36/0.62 (step @p35 :rule symm :premises (@p34)) % 0.36/0.62 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 0.36/0.62 (step @p37 :rule refl :args (@t77)) % 0.36/0.62 (step @p38 :rule refl :args (@t8)) % 0.36/0.62 (step @p39 :rule cong :premises (@p38 @p37) :args ((= @t8 @t77))) % 0.36/0.62 (step @p40 :rule symm :premises (@p39)) % 0.36/0.62 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.36/0.62 (step @p42 :rule nary_cong :premises (@p41 @p36) :args (@t78)) % 0.36/0.62 (step @p43 :rule cong :premises (@p42) :args (@t79)) % 0.36/0.62 (step @p44 :rule nary_cong :premises (@p36 @p41) :args (@t36)) % 0.36/0.62 (step @p45 :rule cong :premises (@p44) :args (@t80)) % 0.36/0.62 (step @p46 :rule cong :premises (@p45 @p43) :args (@t81)) % 0.36/0.62 (step @p47 :rule cong :premises (@p46) :args ((forall @t19 @t81))) % 0.36/0.62 (step @p48 :rule aci_norm :args ((= (or @t78 @t36) @t78))) % 0.36/0.62 (step @p49 :rule beta-reduce :args ((= (_ @t82 @t2) @t36))) % 0.36/0.62 (step @p50 :rule refl :args (@t2)) % 0.36/0.62 (step @p51 :rule beta-reduce :args ((= @t83 @t82))) % 0.36/0.62 (step @p52 :rule ho_cong :premises (@p51 @p50)) % 0.36/0.62 (step @p53 :rule trans :premises (@p52 @p49)) % 0.36/0.62 (step @p54 :rule beta-reduce :args ((= (_ @t86 @t3) @t78))) % 0.36/0.62 (step @p55 :rule refl :args (@t3)) % 0.36/0.62 (step @p56 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t84) (or (_ @t85 @t3) (_ @t7 @t84))) @t2) @t86))) % 0.36/0.62 (step @p57 :rule refl :args (@t2)) % 0.36/0.62 (step @p58 :rule alpha_equiv :args (@t80 (@list @t2) (@list @t84))) % 0.36/0.62 (step @p59 :rule ho_cong :premises (@p58 @p57)) % 0.36/0.62 (step @p60 :rule trans :premises (@p59 @p56)) % 0.36/0.62 (step @p61 :rule ho_cong :premises (@p60 @p55)) % 0.36/0.62 (step @p62 :rule trans :premises (@p61 @p54)) % 0.36/0.62 (step @p63 :rule nary_cong :premises (@p62 @p53) :args (@t87)) % 0.36/0.62 (step @p64 :rule trans :premises (@p63 @p48)) % 0.36/0.62 (step @p65 :rule cong :premises (@p64) :args (@t88)) % 0.36/0.62 (step @p66 :rule beta-reduce :args ((= (_ @t37 @t80) @t88))) % 0.36/0.62 (step @p67 :rule trans :premises (@p66 @p65)) % 0.36/0.62 (step @p68 :rule beta-reduce :args ((= @t89 @t80))) % 0.36/0.62 (step @p69 :rule refl :args (@t37)) % 0.36/0.62 (step @p70 :rule ho_cong :premises (@p69 @p68)) % 0.36/0.62 (step @p71 :rule trans :premises (@p70 @p67)) % 0.36/0.62 (step @p72 :rule cong :premises (@p68 @p71) :args (@t90)) % 0.36/0.62 (step @p73 :rule cong :premises (@p72) :args (@t91)) % 0.36/0.62 (step @p74 :rule trans :premises (@p73 @p47)) % 0.36/0.62 (step @p75 :rule beta-reduce :args ((= @t92 @t91))) % 0.36/0.62 (step @p76 :rule trans :premises (@p75 @p74)) % 0.36/0.62 (step @p77 :rule cong :premises (@p76) :args ((not @t92))) % 0.36/0.62 (step @p78 :rule eq-symm :args (@t18 @t17)) % 0.36/0.62 (step @p79 :rule cong :premises (@p78) :args (@t20)) % 0.36/0.62 (step @p80 :rule cong :premises (@p79) :args (@t22)) % 0.36/0.62 (step @p81 :rule trans :premises (@p5 @p80)) % 0.36/0.62 (step @p82 :rule ho_cong :premises (@p81 @p14)) % 0.36/0.62 (step @p83 :rule cong :premises (@p82) :args (@t1)) % 0.36/0.62 (step @p84 :rule trans :premises (@p83 @p77)) % 0.36/0.62 (step @p85 :rule eq_resolve :premises (@p1 @p84)) % 0.36/0.62 (step @p86 :rule refl :args (@t102)) % 0.36/0.62 (step @p87 :rule bool-double-not-elim :args (@t93)) % 0.36/0.62 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((or (not @t103) @t102))) % 0.36/0.62 (step @p89 :rule eq-symm :args (@t98 @t100)) % 0.36/0.62 (step @p90 :rule eq-refl :args (@t99)) % 0.36/0.62 (step @p91 :rule skolem_intro :args (@t100)) % 0.36/0.62 (step @p92 :rule refl :args (@t99)) % 0.36/0.62 (step @p93 :rule cong :premises (@p92 @p91) :args ((= @t99 @t100))) % 0.36/0.62 (step @p94 :rule trans :premises (@p93 @p90)) % 0.36/0.62 (step @p95 :rule true_elim :premises (@p94)) % 0.36/0.62 (step @p96 :rule eq-refl :args (@t97)) % 0.36/0.62 (step @p97 :rule skolem_intro :args (@t98)) % 0.36/0.62 (step @p98 :rule refl :args (@t97)) % 0.36/0.62 (step @p99 :rule cong :premises (@p98 @p97) :args ((= @t97 @t98))) % 0.36/0.62 (step @p100 :rule trans :premises (@p99 @p96)) % 0.36/0.62 (step @p101 :rule true_elim :premises (@p100)) % 0.36/0.62 (step @p102 :rule cong :premises (@p101 @p95) :args (@t104)) % 0.36/0.62 (step @p103 :rule trans :premises (@p102 @p89)) % 0.36/0.62 (step @p104 :rule cong :premises (@p103) :args (@t105)) % 0.36/0.62 (step @p105 :rule refl :args (@t103)) % 0.36/0.62 (step @p106 :rule cong :premises (@p105 @p104) :args ((=> @t103 @t105))) % 0.36/0.62 (assume-push @p162 @t103) % 0.36/0.62 (step @p108 :rule skolemize :premises (@p85)) % 0.36/0.62 (step-pop @p163 :rule scope :premises (@p108)) % 0.36/0.62 (step @p109 :rule process_scope :premises (@p163) :args (@t105)) % 0.36/0.62 (step @p111 :rule eq_resolve :premises (@p109 @p106)) % 0.45/0.63 (step @p112 :rule implies_elim :premises (@p111)) % 0.45/0.63 (step @p113 :rule eq_resolve :premises (@p112 @p88)) % 0.45/0.63 (step @p114 :rule chain_m_resolution :premises (@p113 @p85) :args (@t102 @t106 (@list @t93))) % 0.45/0.63 (step @p115 :rule aci_norm :args (@t113)) % 0.45/0.63 (step @p116 :rule symm :premises (@p115)) % 0.45/0.63 (step @p117 :rule cong :premises (@p116 @p115) :args ((= @t111 @t112))) % 0.45/0.63 (step @p118 :rule eq-refl :args (@t112)) % 0.45/0.63 (step @p119 :rule refl :args (@t112)) % 0.45/0.63 (step @p120 :rule beta-reduce :args (@t114)) % 0.45/0.63 (step @p121 :rule cong :premises (@p120 @p119) :args (@t114)) % 0.45/0.63 (step @p122 :rule trans :premises (@p121 @p118)) % 0.45/0.63 (step @p123 :rule refl :args (@t108)) % 0.45/0.63 (step @p124 :rule refl :args (@t107)) % 0.45/0.63 (step @p125 :rule ho_cong :premises (@p97 @p124 @p123)) % 0.45/0.63 (step @p126 :rule cong :premises (@p125 @p119) :args ((= @t115 @t112))) % 0.45/0.63 (step @p127 :rule trans :premises (@p126 @p122)) % 0.45/0.63 (step @p128 :rule true_elim :premises (@p127)) % 0.45/0.63 (step @p129 :rule eq-refl :args (@t111)) % 0.45/0.63 (step @p130 :rule refl :args (@t111)) % 0.45/0.63 (step @p131 :rule beta-reduce :args (@t116)) % 0.45/0.63 (step @p132 :rule cong :premises (@p131 @p130) :args (@t116)) % 0.45/0.63 (step @p133 :rule trans :premises (@p132 @p129)) % 0.45/0.63 (step @p134 :rule ho_cong :premises (@p91 @p124 @p123)) % 0.45/0.63 (step @p135 :rule cong :premises (@p134 @p130) :args ((= @t117 @t111))) % 0.45/0.63 (step @p136 :rule trans :premises (@p135 @p133)) % 0.45/0.63 (step @p137 :rule true_elim :premises (@p136)) % 0.45/0.63 (step @p138 :rule cong :premises (@p137 @p128) :args (@t118)) % 0.45/0.63 (step @p139 :rule trans :premises (@p138 @p117)) % 0.45/0.63 (step @p140 :rule cong :premises (@p139) :args (@t119)) % 0.45/0.63 (step @p141 :rule refl :args (@t101)) % 0.45/0.63 (step @p142 :rule nary_cong :premises (@p141 @p140) :args (@t120)) % 0.45/0.63 ; WARNING: add trust step for TRUST % 0.45/0.63 ; trust TRUST THEORY_LEMMA % 0.45/0.63 (step @p143 :rule trust :premises () :args (@t120)) % 0.45/0.63 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.45/0.63 (step @p145 :rule chain_m_resolution :premises (@p144 @p114) :args ((not @t113) @t106 (@list @t101))) % 0.45/0.63 (step @p146 :rule cnf_or_neg :args (@t112 1)) % 0.45/0.63 (step @p147 :rule cnf_or_neg :args (@t111 0)) % 0.45/0.63 (step @p148 :rule cnf_equiv_neg2 :args (@t113)) % 0.45/0.63 (step @p149 :rule chain_m_resolution :premises (@p148 @p145 @p147 @p146) :args ((not @t110) @t121 @t122)) % 0.45/0.63 (step @p150 :rule cnf_or_neg :args (@t112 0)) % 0.45/0.63 (step @p151 :rule cnf_or_neg :args (@t111 1)) % 0.45/0.63 (step @p152 :rule chain_m_resolution :premises (@p148 @p145 @p151 @p150) :args ((not @t109) @t121 @t122)) % 0.45/0.63 (step @p153 :rule cnf_or_pos :args (@t112)) % 0.45/0.63 (step @p154 :rule reordering :premises (@p153) :args ((or @t109 @t110 @t123))) % 0.45/0.63 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p149) :args (@t123 @t124 @t125)) % 0.45/0.63 (step @p156 :rule cnf_or_pos :args (@t111)) % 0.45/0.63 (step @p157 :rule reordering :premises (@p156) :args ((or @t109 @t110 @t126))) % 0.45/0.63 (step @p158 :rule chain_m_resolution :premises (@p157 @p152 @p149) :args (@t126 @t124 @t125)) % 0.45/0.63 (step @p159 :rule cnf_equiv_neg1 :args (@t113)) % 0.45/0.63 (step @p160 :rule reordering :premises (@p159) :args ((or @t112 @t111 @t113))) % 0.45/0.63 (step @p161 false :rule chain_m_resolution :premises (@p160 @p158 @p155 @p145) :args (false (@list true true true) (@list @t111 @t112 @t113))) % 0.45/0.63 ) % 0.45/0.63 % SZS output end Proof % 0.45/0.63 % cvc5 exiting %------------------------------------------------------------------------------