%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU496^1 : 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 : n028.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 08:51:56 AM UTC 2026 % Result : Theorem 34.72s 34.91s % Output : Proof 34.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU496^1 : 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 % 0.18/0.34 % Computer : n028.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 17:39:20 EDT 2026 % 0.18/0.34 % CPUTime : % 0.30/0.51 %----Proving TH0 % 34.72/34.91 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 34.72/34.91 % SZS status Theorem % 34.72/34.91 % SZS output start Proof % 34.72/34.91 ( % 34.72/34.91 (declare-sort $$unsorted 0) % 34.72/34.91 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 34.72/34.91 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 34.72/34.91 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 34.72/34.91 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 34.72/34.91 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 34.72/34.91 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 34.72/34.91 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 34.72/34.91 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 34.72/34.91 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 34.72/34.91 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 34.72/34.91 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 34.72/34.91 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 34.72/34.91 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 34.72/34.91 (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))))))))) % 34.72/34.91 (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)))))) % 34.72/34.91 (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)))))) % 34.72/34.91 (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))))) % 34.72/34.91 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 34.72/34.91 (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)))))))) % 34.72/34.91 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 34.72/34.91 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 34.72/34.91 (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)))))))) % 34.72/34.91 (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))))))) % 34.72/34.91 (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)))))))) % 34.72/34.91 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 34.72/34.91 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 34.72/34.91 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 34.72/34.91 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 34.72/34.91 (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)))))))) % 34.72/34.91 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 34.72/34.91 (define @t2 () (_ tptp.tc @t1)) % 34.72/34.91 (define @t3 () (=> (_ tptp.so @t1) (_ tptp.so @t2))) % 34.72/34.91 (define @t4 () (@list @t1)) % 34.72/34.91 (define @t5 () (forall @t4 @t3)) % 34.72/34.91 (define @t6 () (not @t5)) % 34.72/34.91 (define @t7 () (@var "Y" $$unsorted)) % 34.72/34.91 (define @t8 () (@var "X" $$unsorted)) % 34.72/34.91 (define @t9 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 34.72/34.91 (define @t10 () (_ (_ @t9 @t8) @t7)) % 34.72/34.91 (define @t11 () (_ @t1 @t8)) % 34.72/34.91 (define @t12 () (_ @t11 @t7)) % 34.72/34.91 (define @t13 () (@list @t8 @t7)) % 34.72/34.91 (define @t14 () (forall @t13 (=> @t12 @t10))) % 34.72/34.91 (define @t15 () (@list @t1 @t9)) % 34.72/34.91 (define @t16 () (lambda @t15 @t14)) % 34.72/34.91 (define @t17 () (_ @t1 @t7)) % 34.72/34.91 (define @t18 () (_ @t17 @t8)) % 34.72/34.91 (define @t19 () (@list @t1 @t8 @t7)) % 34.72/34.91 (define @t20 () (lambda @t19 @t18)) % 34.72/34.91 (define @t21 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 34.72/34.91 (define @t22 () (_ @t21 @t1)) % 34.72/34.91 (define @t23 () (@list @t21)) % 34.72/34.91 (define @t24 () (lambda @t23 (forall @t4 (= (_ @t21 @t22) @t22)))) % 34.72/34.91 (define @t25 () (_ tptp.subrel @t1)) % 34.72/34.91 (define @t26 () (lambda @t23 (forall @t4 (_ @t25 @t22)))) % 34.72/34.91 (define @t27 () (_ @t25 @t9)) % 34.72/34.91 (define @t28 () (lambda @t23 (forall @t15 (=> @t27 (_ (_ tptp.subrel @t22) (_ @t21 @t9)))))) % 34.72/34.91 (define @t29 () (_ @t11 @t8)) % 34.72/34.91 (define @t30 () (@list @t8)) % 34.72/34.91 (define @t31 () (lambda @t4 (forall @t30 @t29))) % 34.72/34.91 (define @t32 () (lambda @t4 (forall @t30 (not @t29)))) % 34.72/34.91 (define @t33 () (= @t8 @t7)) % 34.72/34.91 (define @t34 () (lambda @t19 (or @t33 @t12))) % 34.72/34.91 (define @t35 () (lambda @t4 (forall @t13 (=> @t12 @t18)))) % 34.72/34.91 (define @t36 () (lambda @t4 (forall @t13 (=> (and @t12 @t18) @t33)))) % 34.72/34.91 (define @t37 () (not @t18)) % 34.72/34.91 (define @t38 () (forall @t13 (=> @t12 @t37))) % 34.72/34.91 (define @t39 () (lambda @t4 @t38)) % 34.72/34.91 (define @t40 () (lambda @t19 (or @t18 @t12))) % 34.72/34.91 (define @t41 () (@var "Z" $$unsorted)) % 34.72/34.91 (define @t42 () (_ @t11 @t41)) % 34.72/34.91 (define @t43 () (_ @t17 @t41)) % 34.72/34.91 (define @t44 () (and @t12 @t43)) % 34.72/34.91 (define @t45 () (@list @t8 @t7 @t41)) % 34.72/34.91 (define @t46 () (forall @t45 (=> @t44 @t42))) % 34.72/34.91 (define @t47 () (lambda @t4 @t46)) % 34.72/34.91 (define @t48 () (and (_ tptp.trans @t9) @t27)) % 34.72/34.91 (define @t49 () (=> @t48 @t10)) % 34.72/34.91 (define @t50 () (@list @t9)) % 34.72/34.91 (define @t51 () (forall @t50 @t49)) % 34.72/34.91 (define @t52 () (lambda @t19 @t51)) % 34.72/34.91 (define @t53 () (@var "__flatten_var_1" $$unsorted)) % 34.72/34.91 (define @t54 () (@var "__flatten_var_0" $$unsorted)) % 34.72/34.91 (define @t55 () (_ tptp.rc @t2)) % 34.72/34.91 (define @t56 () (@list @t1 @t54 @t53)) % 34.72/34.91 (define @t57 () (lambda @t56 (_ (_ @t55 @t54) @t53))) % 34.72/34.91 (define @t58 () (lambda @t56 (_ (_ (_ tptp.sc @t55) @t54) @t53))) % 34.72/34.91 (define @t59 () (_ tptp.trans @t1)) % 34.72/34.91 (define @t60 () (lambda @t4 (and (_ tptp.refl @t1) (_ tptp.antisymm @t1) @t59))) % 34.72/34.91 (define @t61 () (and (_ tptp.asymm @t1) @t59)) % 34.72/34.91 (define @t62 () (lambda @t4 @t61)) % 34.72/34.91 (define @t63 () (lambda @t4 (forall @t13 (or @t33 @t12 @t18)))) % 34.72/34.91 (define @t64 () (not @t12)) % 34.72/34.91 (define @t65 () (@var "A" (-> $$unsorted Bool))) % 34.72/34.91 (define @t66 () (@list @t7)) % 34.72/34.91 (define @t67 () (_ @t65 @t8)) % 34.72/34.91 (define @t68 () (lambda @t4 (forall (@list @t65) (=> (exists @t30 @t67) (exists @t30 (and @t67 (forall @t66 (=> (_ @t65 @t7) @t64)))))))) % 34.72/34.91 (define @t69 () (@var "P" (-> $$unsorted Bool))) % 34.72/34.91 (define @t70 () (_ @t69 @t8)) % 34.72/34.91 (define @t71 () (lambda @t4 (forall (@list @t69) (=> (forall @t30 (=> (forall @t66 (=> (_ (_ @t2 @t8) @t7) (_ @t69 @t7))) @t70)) (forall @t30 @t70))))) % 34.72/34.91 (define @t72 () (lambda (@list @t1 @t8) (not (exists @t66 @t12)))) % 34.72/34.91 (define @t73 () (_ tptp.trc @t1)) % 34.72/34.91 (define @t74 () (_ @t73 @t7)) % 34.72/34.91 (define @t75 () (lambda @t19 (and (_ @t74 @t8) (_ (_ tptp.innf @t1) @t8)))) % 34.72/34.91 (define @t76 () (lambda @t4 (forall @t30 (exists @t66 (_ (_ (_ tptp.nfof @t1) @t7) @t8))))) % 34.72/34.91 (define @t77 () (_ @t73 @t8)) % 34.72/34.91 (define @t78 () (_ @t77 @t41)) % 34.72/34.91 (define @t79 () (lambda @t19 (exists (@list @t41) (and @t78 (_ @t74 @t41))))) % 34.72/34.91 (define @t80 () (_ tptp.join @t1)) % 34.72/34.91 (define @t81 () (_ (_ @t80 @t41) @t7)) % 34.72/34.91 (define @t82 () (lambda @t4 (forall @t45 (=> (and @t42 @t12) @t81)))) % 34.72/34.91 (define @t83 () (_ @t77 @t7)) % 34.72/34.91 (define @t84 () (lambda @t4 (forall @t45 (=> (and @t42 @t83) @t81)))) % 34.72/34.91 (define @t85 () (lambda @t4 (forall @t45 (=> (and @t78 @t83) @t81)))) % 34.72/34.91 (define @t86 () (lambda @t4 (forall @t13 (=> (_ (_ (_ tptp.trsc @t1) @t8) @t7) (_ (_ @t80 @t8) @t7))))) % 34.72/34.91 (define @t87 () (@var "BOUND_VARIABLE_8942" $$unsorted)) % 34.72/34.91 (define @t88 () (@var "BOUND_VARIABLE_8938" $$unsorted)) % 34.72/34.91 (define @t89 () (@var "BOUND_VARIABLE_8944" (-> $$unsorted $$unsorted Bool))) % 34.72/34.91 (define @t90 () (@var "BOUND_VARIABLE_7746" $$unsorted)) % 34.72/34.91 (define @t91 () (@var "BOUND_VARIABLE_7744" $$unsorted)) % 34.72/34.91 (define @t92 () (not (_ @t1 @t91 @t90))) % 34.72/34.91 (define @t93 () (@list @t91 @t90)) % 34.72/34.91 (define @t94 () (@var "BOUND_VARIABLE_8864" $$unsorted)) % 34.72/34.91 (define @t95 () (@var "BOUND_VARIABLE_7755" $$unsorted)) % 34.72/34.91 (define @t96 () (@var "BOUND_VARIABLE_7757" $$unsorted)) % 34.72/34.91 (define @t97 () (@list @t95 @t96 @t94)) % 34.72/34.91 (define @t98 () (@var "BOUND_VARIABLE_8940" $$unsorted)) % 34.72/34.91 (define @t99 () (_ @t9 @t91 @t90)) % 34.72/34.91 (define @t100 () (not (forall @t93 (or @t92 @t99)))) % 34.72/34.91 (define @t101 () (@var "BOUND_VARIABLE_8848" $$unsorted)) % 34.72/34.91 (define @t102 () (not (_ @t9 @t95 @t96))) % 34.72/34.91 (define @t103 () (@list @t95 @t96 @t101)) % 34.72/34.91 (define @t104 () (not (forall @t103 (or @t102 (not (_ @t9 @t96 @t101)) (_ @t9 @t95 @t101))))) % 34.72/34.91 (define @t105 () (@var "BOUND_VARIABLE_8881" $$unsorted)) % 34.72/34.91 (define @t106 () (@list @t95 @t96 @t105)) % 34.72/34.91 (define @t107 () (not (forall @t106 (or @t102 (not (_ @t9 @t96 @t105)) (_ @t9 @t95 @t105))))) % 34.72/34.91 (define @t108 () (or (not (forall @t50 (or @t107 @t100 (_ @t9 @t88 @t98)))) (not (forall @t50 (or @t104 @t100 (_ @t9 @t98 @t87)))) (not (forall @t97 (or (not (_ @t89 @t95 @t96)) (not (_ @t89 @t96 @t94)) (_ @t89 @t95 @t94)))) (not (forall @t93 (or @t92 (_ @t89 @t91 @t90)))) (_ @t89 @t88 @t87))) % 34.72/34.91 (define @t109 () (@var "BOUND_VARIABLE_8925" $$unsorted)) % 34.72/34.91 (define @t110 () (@var "BOUND_VARIABLE_8927" $$unsorted)) % 34.72/34.91 (define @t111 () (@list @t95 @t96 @t41)) % 34.72/34.91 (define @t112 () (forall @t111 (or @t102 (not (_ @t9 @t96 @t41)) (_ @t9 @t95 @t41)))) % 34.72/34.91 (define @t113 () (not @t112)) % 34.72/34.91 (define @t114 () (or (not (forall @t50 (or @t113 @t100 (_ @t9 @t109 @t110)))) (not (forall @t50 (or @t113 @t100 (_ @t9 @t110 @t109)))))) % 34.72/34.91 (define @t115 () (and @t114 @t108)) % 34.72/34.91 (define @t116 () (_ @t1 @t8 @t41)) % 34.72/34.91 (define @t117 () (_ @t1 @t7 @t41)) % 34.72/34.91 (define @t118 () (_ @t1 @t8 @t7)) % 34.72/34.91 (define @t119 () (not @t118)) % 34.72/34.91 (define @t120 () (forall @t45 (or @t119 (not @t117) @t116))) % 34.72/34.91 (define @t121 () (not @t120)) % 34.72/34.91 (define @t122 () (_ @t1 @t7 @t8)) % 34.72/34.91 (define @t123 () (forall @t13 (or @t119 (not @t122)))) % 34.72/34.91 (define @t124 () (not @t123)) % 34.72/34.91 (define @t125 () (or @t124 @t121 @t115)) % 34.72/34.91 (define @t126 () (forall (@list @t1 @t109 @t110 @t88 @t98 @t87 @t89) @t125)) % 34.72/34.91 (define @t127 () (@list @t109 @t110 @t88 @t98 @t87 @t89)) % 34.72/34.91 (define @t128 () (forall @t127 @t125)) % 34.72/34.91 (define @t129 () (forall (@list @t88 @t98 @t87 @t89) @t108)) % 34.72/34.91 (define @t130 () (@var "BOUND_VARIABLE_8895" (-> $$unsorted $$unsorted Bool))) % 34.72/34.91 (define @t131 () (forall @t127 @t108)) % 34.72/34.91 (define @t132 () (forall (@list @t109 @t110) @t114)) % 34.72/34.91 (define @t133 () (forall @t127 @t114)) % 34.72/34.91 (define @t134 () (and @t133 @t131)) % 34.72/34.91 (define @t135 () (forall @t127 @t115)) % 34.72/34.91 (define @t136 () (or @t124 @t121 @t135)) % 34.72/34.91 (define @t137 () (_ @t130 @t8 @t41)) % 34.72/34.91 (define @t138 () (not (forall @t93 (or @t92 (_ @t130 @t91 @t90))))) % 34.72/34.91 (define @t139 () (not (forall @t97 (or (not (_ @t130 @t95 @t96)) (not (_ @t130 @t96 @t94)) (_ @t130 @t95 @t94))))) % 34.72/34.91 (define @t140 () (_ @t9 @t7 @t41)) % 34.72/34.91 (define @t141 () (forall @t50 (or @t104 @t100 @t140))) % 34.72/34.91 (define @t142 () (not @t141)) % 34.72/34.91 (define @t143 () (_ @t9 @t8 @t7)) % 34.72/34.91 (define @t144 () (not (forall @t50 (or @t107 @t100 @t143)))) % 34.72/34.91 (define @t145 () (or @t144 @t142 @t139 @t138 @t137)) % 34.72/34.91 (define @t146 () (@list @t8 @t7 @t41 @t130)) % 34.72/34.91 (define @t147 () (forall @t50 (or @t113 @t100 (_ @t9 @t7 @t8)))) % 34.72/34.91 (define @t148 () (or @t113 @t100 @t143)) % 34.72/34.91 (define @t149 () (forall @t50 @t148)) % 34.72/34.91 (define @t150 () (not @t149)) % 34.72/34.91 (define @t151 () (and (forall @t13 (or @t150 (not @t147))) (forall @t146 @t145))) % 34.72/34.91 (define @t152 () (or @t124 @t121 @t151)) % 34.72/34.91 (define @t153 () (and @t123 @t120)) % 34.72/34.91 (define @t154 () (or @t139 @t138 @t137)) % 34.72/34.91 (define @t155 () (or @t144 @t142 @t154)) % 34.72/34.91 (define @t156 () (forall @t146 @t155)) % 34.72/34.91 (define @t157 () (@list @t130)) % 34.72/34.91 (define @t158 () (forall @t157 @t155)) % 34.72/34.91 (define @t159 () (forall @t157 @t154)) % 34.72/34.91 (define @t160 () (or @t144 @t142 @t159)) % 34.72/34.91 (define @t161 () (_ @t9 @t8 @t41)) % 34.72/34.91 (define @t162 () (not (forall @t97 (or @t102 (not (_ @t9 @t96 @t94)) (_ @t9 @t95 @t94))))) % 34.72/34.91 (define @t163 () (forall @t50 (or @t162 @t100 @t161))) % 34.72/34.91 (define @t164 () (@list @t41)) % 34.72/34.91 (define @t165 () (or @t150 @t142 @t163)) % 34.72/34.91 (define @t166 () (lambda @t13 @t149)) % 34.72/34.91 (define @t167 () (not (_ @t166 @t7 @t41))) % 34.72/34.91 (define @t168 () (_ @t166 @t8 @t7)) % 34.72/34.91 (define @t169 () (not @t168)) % 34.72/34.91 (define @t170 () (or @t169 @t167 (_ @t166 @t8 @t41))) % 34.72/34.91 (define @t171 () (forall @t45 @t170)) % 34.72/34.91 (define @t172 () (_ @t166 @t7 @t8)) % 34.72/34.91 (define @t173 () (not @t172)) % 34.72/34.91 (define @t174 () (or @t169 @t173)) % 34.72/34.91 (define @t175 () (forall @t13 @t174)) % 34.72/34.91 (define @t176 () (and @t175 @t171)) % 34.72/34.91 (define @t177 () (lambda @t4 @t153)) % 34.72/34.91 (define @t178 () (lambda @t19 @t149)) % 34.72/34.91 (define @t179 () (forall @t13 (or @t119 @t143))) % 34.72/34.91 (define @t180 () (not @t179)) % 34.72/34.91 (define @t181 () (forall @t45 (or (not @t143) (not @t140) @t161))) % 34.72/34.91 (define @t182 () (not @t181)) % 34.72/34.91 (define @t183 () (lambda @t19 (forall @t50 (or @t182 @t180 @t143)))) % 34.72/34.91 (define @t184 () (_ @t177 @t1)) % 34.72/34.91 (define @t185 () (=> @t184 (_ @t177 (_ @t183 @t1)))) % 34.72/34.91 (define @t186 () (forall @t4 @t185)) % 34.72/34.91 (define @t187 () (or @t182 @t180 @t10)) % 34.72/34.91 (define @t188 () (and @t181 @t179)) % 34.72/34.91 (define @t189 () (lambda @t50 @t179)) % 34.72/34.91 (define @t190 () (_ (lambda @t15 @t179) @t1)) % 34.72/34.91 (define @t191 () (lambda @t4 @t120)) % 34.72/34.91 (define @t192 () (_ @t191 @t9)) % 34.72/34.91 (define @t193 () (and @t192 (_ @t190 @t9))) % 34.72/34.91 (define @t194 () (=> @t193 @t10)) % 34.72/34.91 (define @t195 () (or @t64 @t10)) % 34.72/34.91 (define @t196 () (not @t43)) % 34.72/34.91 (define @t197 () (or @t64 @t196 @t42)) % 34.72/34.91 (define @t198 () (_ @t191 @t1)) % 34.72/34.91 (define @t199 () (_ (lambda @t4 @t123) @t1)) % 34.72/34.91 (define @t200 () (or @t64 @t37)) % 34.72/34.91 (define @t201 () (@quantifiers_skolemize @t126 0)) % 34.72/34.91 (define @t202 () (not (_ @t201 @t8 @t7))) % 34.72/34.91 (define @t203 () (forall @t13 (or @t202 (not (_ @t201 @t7 @t8))))) % 34.72/34.91 (define @t204 () (@quantifiers_skolemize @t126 5)) % 34.72/34.91 (define @t205 () (@quantifiers_skolemize @t126 3)) % 34.72/34.91 (define @t206 () (@quantifiers_skolemize @t126 6)) % 34.72/34.91 (define @t207 () (_ @t206 @t205 @t204)) % 34.72/34.91 (define @t208 () (_ @t201 @t91 @t90)) % 34.72/34.91 (define @t209 () (not @t208)) % 34.72/34.91 (define @t210 () (forall @t93 (or @t209 (_ @t206 @t91 @t90)))) % 34.72/34.91 (define @t211 () (not @t210)) % 34.72/34.91 (define @t212 () (@quantifiers_skolemize @t126 4)) % 34.72/34.91 (define @t213 () (not (forall @t93 (or @t209 @t99)))) % 34.72/34.91 (define @t214 () (forall @t50 (or @t104 @t213 (_ @t9 @t212 @t204)))) % 34.72/34.91 (define @t215 () (not @t214)) % 34.72/34.91 (define @t216 () (forall @t50 (or @t107 @t213 (_ @t9 @t205 @t212)))) % 34.72/34.91 (define @t217 () (not @t216)) % 34.72/34.91 (define @t218 () (or @t217 @t215 (not (forall @t97 (or (not (_ @t206 @t95 @t96)) (not (_ @t206 @t96 @t94)) (_ @t206 @t95 @t94)))) @t211 @t207)) % 34.72/34.91 (define @t219 () (@quantifiers_skolemize @t126 1)) % 34.72/34.91 (define @t220 () (@quantifiers_skolemize @t126 2)) % 34.72/34.91 (define @t221 () (forall @t50 (or @t113 @t213 (_ @t9 @t220 @t219)))) % 34.72/34.91 (define @t222 () (not @t221)) % 34.72/34.91 (define @t223 () (forall @t50 (or @t113 @t213 (_ @t9 @t219 @t220)))) % 34.72/34.91 (define @t224 () (not @t223)) % 34.72/34.91 (define @t225 () (or @t224 @t222)) % 34.72/34.91 (define @t226 () (and @t225 @t218)) % 34.72/34.91 (define @t227 () (forall @t45 (or @t202 (not (_ @t201 @t7 @t41)) (_ @t201 @t8 @t41)))) % 34.72/34.91 (define @t228 () (not @t227)) % 34.72/34.91 (define @t229 () (not @t203)) % 34.72/34.91 (define @t230 () (or @t229 @t228 @t226)) % 34.72/34.91 (define @t231 () (@list true)) % 34.72/34.91 (define @t232 () (@list @t230)) % 34.72/34.91 (define @t233 () (_ @t201 @t205 @t212)) % 34.72/34.91 (define @t234 () (_ @t201 @t95 @t105)) % 34.72/34.91 (define @t235 () (_ @t201 @t96 @t105)) % 34.72/34.91 (define @t236 () (_ @t201 @t95 @t96)) % 34.72/34.91 (define @t237 () (not @t236)) % 34.72/34.92 (define @t238 () (forall @t106 (or @t237 (not @t235) @t234))) % 34.72/34.92 (define @t239 () (not @t238)) % 34.72/34.92 (define @t240 () (or @t239 @t233)) % 34.72/34.92 (define @t241 () (@var "BOUND_VARIABLE_590400" $$unsorted)) % 34.72/34.92 (define @t242 () (@var "BOUND_VARIABLE_590399" $$unsorted)) % 34.72/34.92 (define @t243 () (lambda (@list @t242 @t241) (_ @t201 @t242 @t241))) % 34.72/34.92 (define @t244 () (_ @t243 @t205 @t212)) % 34.72/34.92 (define @t245 () (_ @t243 @t91 @t90)) % 34.72/34.92 (define @t246 () (or @t209 @t245)) % 34.72/34.92 (define @t247 () (forall @t93 @t246)) % 34.72/34.92 (define @t248 () (not @t247)) % 34.72/34.92 (define @t249 () (_ @t243 @t95 @t105)) % 34.72/34.92 (define @t250 () (_ @t243 @t96 @t105)) % 34.72/34.92 (define @t251 () (not @t250)) % 34.72/34.92 (define @t252 () (_ @t243 @t95 @t96)) % 34.72/34.92 (define @t253 () (not @t252)) % 34.72/34.92 (define @t254 () (or @t253 @t251 @t249)) % 34.72/34.92 (define @t255 () (forall @t106 @t254)) % 34.72/34.92 (define @t256 () (not @t255)) % 34.72/34.92 (define @t257 () (or @t256 @t248 @t244)) % 34.72/34.92 (define @t258 () (_ @t201 @t212 @t204)) % 34.72/34.92 (define @t259 () (_ @t201 @t95 @t101)) % 34.72/34.92 (define @t260 () (_ @t201 @t96 @t101)) % 34.72/34.92 (define @t261 () (forall @t103 (or @t237 (not @t260) @t259))) % 34.72/34.92 (define @t262 () (not @t261)) % 34.72/34.92 (define @t263 () (or @t262 @t258)) % 34.72/34.92 (define @t264 () (@var "BOUND_VARIABLE_2212727" $$unsorted)) % 34.72/34.92 (define @t265 () (@var "BOUND_VARIABLE_2212726" $$unsorted)) % 34.72/34.92 (define @t266 () (lambda (@list @t265 @t264) (_ @t201 @t265 @t264))) % 34.72/34.92 (define @t267 () (_ @t266 @t212 @t204)) % 34.72/34.92 (define @t268 () (_ @t266 @t91 @t90)) % 34.72/34.92 (define @t269 () (or @t209 @t268)) % 34.72/34.92 (define @t270 () (forall @t93 @t269)) % 34.72/34.92 (define @t271 () (not @t270)) % 34.72/34.92 (define @t272 () (_ @t266 @t95 @t101)) % 34.72/34.92 (define @t273 () (_ @t266 @t96 @t101)) % 34.72/34.92 (define @t274 () (not @t273)) % 34.72/34.92 (define @t275 () (_ @t266 @t95 @t96)) % 34.72/34.92 (define @t276 () (not @t275)) % 34.72/34.92 (define @t277 () (or @t276 @t274 @t272)) % 34.72/34.92 (define @t278 () (forall @t103 @t277)) % 34.72/34.92 (define @t279 () (not @t278)) % 34.72/34.92 (define @t280 () (or @t279 @t271 @t267)) % 34.72/34.92 (define @t281 () (@list @t8 @t7 @t41)) % 34.72/34.92 (define @t282 () (@list false)) % 34.72/34.92 (define @t283 () (@list @t227)) % 34.72/34.92 (define @t284 () (_ @t201 @t205 @t204)) % 34.72/34.92 (define @t285 () (not @t258)) % 34.72/34.92 (define @t286 () (not @t233)) % 34.72/34.92 (define @t287 () (or @t286 @t285 @t284)) % 34.72/34.92 (define @t288 () (not @t284)) % 34.72/34.92 (define @t289 () (or @t288 @t207)) % 34.72/34.92 (define @t290 () (@list @t225)) % 34.72/34.92 (define @t291 () (_ @t201 @t219 @t220)) % 34.72/34.92 (define @t292 () (_ @t201 @t95 @t41)) % 34.72/34.92 (define @t293 () (_ @t201 @t96 @t41)) % 34.72/34.92 (define @t294 () (forall @t111 (or @t237 (not @t293) @t292))) % 34.72/34.92 (define @t295 () (not @t294)) % 34.72/34.92 (define @t296 () (or @t295 @t291)) % 34.72/34.92 (define @t297 () (@var "BOUND_VARIABLE_52964" $$unsorted)) % 34.72/34.92 (define @t298 () (@var "BOUND_VARIABLE_52963" $$unsorted)) % 34.72/34.92 (define @t299 () (lambda (@list @t298 @t297) (_ @t201 @t298 @t297))) % 34.72/34.92 (define @t300 () (_ @t299 @t219 @t220)) % 34.72/34.92 (define @t301 () (_ @t299 @t91 @t90)) % 34.72/34.92 (define @t302 () (or @t209 @t301)) % 34.72/34.92 (define @t303 () (forall @t93 @t302)) % 34.72/34.92 (define @t304 () (not @t303)) % 34.72/34.92 (define @t305 () (_ @t299 @t95 @t41)) % 34.72/34.92 (define @t306 () (_ @t299 @t96 @t41)) % 34.72/34.92 (define @t307 () (not @t306)) % 34.72/34.92 (define @t308 () (_ @t299 @t95 @t96)) % 34.72/34.92 (define @t309 () (not @t308)) % 34.72/34.92 (define @t310 () (or @t309 @t307 @t305)) % 34.72/34.92 (define @t311 () (forall @t111 @t310)) % 34.72/34.92 (define @t312 () (not @t311)) % 34.72/34.92 (define @t313 () (or @t312 @t304 @t300)) % 34.72/34.92 (define @t314 () (@var "BOUND_VARIABLE_435265" $$unsorted)) % 34.72/34.92 (define @t315 () (@var "BOUND_VARIABLE_435263" $$unsorted)) % 34.72/34.92 (define @t316 () (@var "BOUND_VARIABLE_435264" $$unsorted)) % 34.72/34.92 (define @t317 () (@list @t315 @t316 @t314)) % 34.72/34.92 (define @t318 () (@list false false)) % 34.72/34.92 (define @t319 () (_ @t201 @t220 @t219)) % 34.72/34.92 (define @t320 () (or @t295 @t319)) % 34.72/34.92 (define @t321 () (@var "BOUND_VARIABLE_142069" $$unsorted)) % 34.72/34.92 (define @t322 () (@var "BOUND_VARIABLE_142068" $$unsorted)) % 34.72/34.92 (define @t323 () (lambda (@list @t322 @t321) (_ @t201 @t322 @t321))) % 34.72/34.92 (define @t324 () (_ @t323 @t220 @t219)) % 34.72/34.92 (define @t325 () (_ @t323 @t91 @t90)) % 34.72/34.92 (define @t326 () (or @t209 @t325)) % 34.72/34.92 (define @t327 () (forall @t93 @t326)) % 34.72/34.92 (define @t328 () (not @t327)) % 34.72/34.92 (define @t329 () (_ @t323 @t95 @t41)) % 34.72/34.92 (define @t330 () (_ @t323 @t96 @t41)) % 34.72/34.92 (define @t331 () (not @t330)) % 34.72/34.92 (define @t332 () (_ @t323 @t95 @t96)) % 34.72/34.92 (define @t333 () (not @t332)) % 34.72/34.92 (define @t334 () (or @t333 @t331 @t329)) % 34.72/34.92 (define @t335 () (forall @t111 @t334)) % 34.72/34.92 (define @t336 () (not @t335)) % 34.72/34.92 (define @t337 () (or @t336 @t328 @t324)) % 34.72/34.92 (define @t338 () (not @t319)) % 34.72/34.92 (define @t339 () (not @t291)) % 34.72/34.92 (define @t340 () (or @t339 @t338)) % 34.72/34.92 (assume @p1 @t6) % 34.72/34.92 (assume @p2 true) % 34.72/34.92 (step @p3 (= tptp.subrel @t16) :rule refl :args (@t16)) % 34.72/34.92 (step @p4 (= tptp.inv @t20) :rule refl :args (@t20)) % 34.72/34.92 (step @p5 (= tptp.idem @t24) :rule refl :args (@t24)) % 34.72/34.92 (step @p6 (= tptp.infl @t26) :rule refl :args (@t26)) % 34.72/34.92 (step @p7 (= tptp.mono @t28) :rule refl :args (@t28)) % 34.72/34.92 (step @p8 (= tptp.refl @t31) :rule refl :args (@t31)) % 34.72/34.92 (step @p9 (= tptp.irrefl @t32) :rule refl :args (@t32)) % 34.72/34.92 (step @p10 (= tptp.rc @t34) :rule refl :args (@t34)) % 34.72/34.92 (step @p11 (= tptp.symm @t35) :rule refl :args (@t35)) % 34.72/34.92 (step @p12 (= tptp.antisymm @t36) :rule refl :args (@t36)) % 34.72/34.92 (step @p13 (= tptp.asymm @t39) :rule refl :args (@t39)) % 34.72/34.92 (step @p14 (= tptp.sc @t40) :rule refl :args (@t40)) % 34.72/34.92 (step @p15 (= tptp.trans @t47) :rule refl :args (@t47)) % 34.72/34.92 (step @p16 (= tptp.tc @t52) :rule refl :args (@t52)) % 34.72/34.92 (step @p17 (= tptp.trc @t57) :rule refl :args (@t57)) % 34.72/34.92 (step @p18 (= tptp.trsc @t58) :rule refl :args (@t58)) % 34.72/34.92 (step @p19 (= tptp.po @t60) :rule refl :args (@t60)) % 34.72/34.92 (step @p20 (= tptp.so @t62) :rule refl :args (@t62)) % 34.72/34.92 (step @p21 (= tptp.total @t63) :rule refl :args (@t63)) % 34.72/34.92 (step @p22 (= tptp.term @t68) :rule refl :args (@t68)) % 34.72/34.92 (step @p23 (= tptp.ind @t71) :rule refl :args 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34.72/34.92 (step @p66 :rule quant-miniscope-or :args ((= @t158 @t160))) % 34.72/34.92 (step @p67 :rule trans :premises (@p66 @p65)) % 34.72/34.92 (step @p68 :rule symm :premises (@p67)) % 34.72/34.92 (step @p69 :rule cong :premises (@p68) :args ((forall @t45 (or @t144 @t142 @t163)))) % 34.72/34.92 (step @p70 :rule trans :premises (@p69 @p61)) % 34.72/34.92 (step @p71 :rule trans :premises (@p70 @p60)) % 34.72/34.92 (step @p72 :rule refl :args (@t163)) % 34.72/34.92 (step @p73 :rule refl :args (@t143)) % 34.72/34.92 (step @p74 :rule refl :args (@t100)) % 34.72/34.92 (step @p75 :rule alpha_equiv :args (@t112 @t164 (@list @t105))) % 34.72/34.92 (step @p76 :rule cong :premises (@p75) :args (@t113)) % 34.72/34.92 (step @p77 :rule nary_cong :premises (@p76 @p74 @p73) :args (@t148)) % 34.72/34.92 (step @p78 :rule cong :premises (@p77) :args (@t149)) % 34.72/34.92 (step @p79 :rule cong :premises (@p78) :args (@t150)) % 34.72/34.92 (step @p80 :rule nary_cong :premises (@p79 @p63 @p72) :args 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34.72/34.92 (step @p94 :rule refl :args (@t7)) % 34.72/34.92 (step @p95 :rule alpha_equiv :args (@t112 @t164 (@list @t101))) % 34.72/34.92 (step @p96 :rule cong :premises (@p95) :args (@t113)) % 34.72/34.92 (step @p97 :rule nary_cong :premises (@p96 @p74 @p73) :args (@t148)) % 34.72/34.92 (step @p98 :rule cong :premises (@p97) :args (@t149)) % 34.72/34.92 (step @p99 :rule cong :premises (@p98) :args (@t166)) % 34.72/34.92 (step @p100 :rule ho_cong :premises (@p99 @p94 @p84)) % 34.72/34.92 (step @p101 :rule trans :premises (@p100 @p93)) % 34.72/34.92 (step @p102 :rule cong :premises (@p101) :args (@t167)) % 34.72/34.92 (step @p103 :rule beta-reduce :args ((= @t168 @t149))) % 34.72/34.92 (step @p104 :rule cong :premises (@p103) :args (@t169)) % 34.72/34.92 (step @p105 :rule nary_cong :premises (@p104 @p102 @p92) :args (@t170)) % 34.72/34.92 (step @p106 :rule cong :premises (@p105) :args (@t171)) % 34.72/34.92 (step @p107 :rule trans :premises (@p106 @p82)) % 34.72/34.92 (step @p108 :rule 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:args (@t62)) % 34.72/34.92 (step @p223 :rule trans :premises (@p20 @p222)) % 34.72/34.92 (step @p224 :rule ho_cong :premises (@p223 @p201)) % 34.72/34.92 (step @p225 :rule ho_cong :premises (@p223 @p116)) % 34.72/34.92 (step @p226 :rule cong :premises (@p225 @p224) :args (@t3)) % 34.72/34.92 (step @p227 :rule cong :premises (@p226) :args (@t5)) % 34.72/34.92 (step @p228 :rule cong :premises (@p227) :args (@t6)) % 34.72/34.92 (step @p229 :rule trans :premises (@p228 @p127)) % 34.72/34.92 (step @p230 :rule eq_resolve :premises (@p1 @p229)) % 34.72/34.92 (step @p231 :rule skolemize :premises (@p230)) % 34.72/34.92 (step @p232 :rule bool-double-not-elim :args (@t203)) % 34.72/34.92 (step @p233 :rule refl :args (@t230)) % 34.72/34.92 (step @p234 :rule nary_cong :premises (@p233 @p232) :args ((or @t230 (not @t229)))) % 34.72/34.92 (step @p235 :rule cnf_or_neg :args (@t230 0)) % 34.72/34.92 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 34.72/34.92 (step @p237 :rule reordering 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reordering :premises (@p249) :args ((or @t214 @t218))) % 34.72/34.92 (step @p251 :rule bool-double-not-elim :args (@t210)) % 34.72/34.92 (step @p252 :rule nary_cong :premises (@p241 @p251) :args ((or @t218 (not @t211)))) % 34.72/34.92 (step @p253 :rule cnf_or_neg :args (@t218 3)) % 34.72/34.92 (step @p254 :rule eq_resolve :premises (@p253 @p252)) % 34.72/34.92 (step @p255 :rule reordering :premises (@p254) :args ((or @t210 @t218))) % 34.72/34.92 (step @p256 :rule cnf_or_neg :args (@t218 4)) % 34.72/34.92 (step @p257 :rule aci_norm :args ((= (or @t239 false @t233) @t240))) % 34.72/34.92 (step @p258 :rule beta-reduce :args ((= @t244 @t233))) % 34.72/34.92 (step @p259 :rule evaluate :args ((not true))) % 34.72/34.92 (step @p260 :rule quant-unused-vars :args ((= (forall @t93 true) true))) % 34.72/34.92 (step @p261 :rule bool-or-taut2 :args (false @t208 false false)) % 34.72/34.92 (step @p262 :rule cong :premises (@p261) :args ((forall @t93 (or @t209 @t208)))) % 34.72/34.92 (step @p263 :rule trans :premises (@p262 @p260)) % 34.72/34.92 (step @p264 :rule beta-reduce :args ((= @t245 @t208))) % 34.72/34.92 (step @p265 :rule refl :args (@t209)) % 34.72/34.92 (step @p266 :rule nary_cong :premises (@p265 @p264) :args (@t246)) % 34.72/34.92 (step @p267 :rule cong :premises (@p266) :args (@t247)) % 34.72/34.92 (step @p268 :rule trans :premises (@p267 @p263)) % 34.72/34.92 (step @p269 :rule cong :premises (@p268) :args (@t248)) % 34.72/34.92 (step @p270 :rule trans :premises (@p269 @p259)) % 34.72/34.92 (step @p271 :rule beta-reduce :args ((= @t249 @t234))) % 34.72/34.92 (step @p272 :rule beta-reduce :args ((= @t250 @t235))) % 34.72/34.92 (step @p273 :rule cong :premises (@p272) :args (@t251)) % 34.72/34.92 (step @p274 :rule beta-reduce :args ((= @t252 @t236))) % 34.72/34.92 (step @p275 :rule cong :premises (@p274) :args (@t253)) % 34.72/34.92 (step @p276 :rule nary_cong :premises (@p275 @p273 @p271) :args (@t254)) % 34.72/34.92 (step @p277 :rule cong :premises (@p276) :args (@t255)) % 34.72/34.92 (step @p278 :rule cong :premises (@p277) :args (@t256)) % 34.72/34.92 (step @p279 :rule nary_cong :premises (@p278 @p270 @p258) :args (@t257)) % 34.72/34.92 (step @p280 :rule trans :premises (@p279 @p257)) % 34.72/34.92 (step @p281 :rule refl :args (@t216)) % 34.72/34.92 (step @p282 :rule cong :premises (@p281 @p280) :args ((=> @t216 @t257))) % 34.72/34.92 (assume-push @p427 @t216) % 34.72/34.92 (step @p284 :rule instantiate :premises (@p427) :args ((@list @t243))) % 34.72/34.92 (step-pop @p428 :rule scope :premises (@p284)) % 34.72/34.92 (step @p285 :rule process_scope :premises (@p428) :args (@t257)) % 34.72/34.92 (step @p287 :rule eq_resolve :premises (@p285 @p282)) % 34.72/34.92 (step @p288 :rule implies_elim :premises (@p287)) % 34.72/34.92 (step @p289 :rule aci_norm :args ((= (or @t262 false @t258) @t263))) % 34.72/34.92 (step @p290 :rule beta-reduce :args ((= @t267 @t258))) % 34.72/34.92 (step @p291 :rule beta-reduce :args ((= @t268 @t208))) % 34.72/34.92 (step @p292 :rule nary_cong :premises (@p265 @p291) :args (@t269)) % 34.72/34.92 (step @p293 :rule cong :premises (@p292) :args (@t270)) % 34.72/34.92 (step @p294 :rule trans :premises (@p293 @p263)) % 34.72/34.92 (step @p295 :rule cong :premises (@p294) :args (@t271)) % 34.72/34.92 (step @p296 :rule trans :premises (@p295 @p259)) % 34.72/34.92 (step @p297 :rule beta-reduce :args ((= @t272 @t259))) % 34.72/34.92 (step @p298 :rule beta-reduce :args ((= @t273 @t260))) % 34.72/34.92 (step @p299 :rule cong :premises (@p298) :args (@t274)) % 34.72/34.92 (step @p300 :rule beta-reduce :args ((= @t275 @t236))) % 34.72/34.92 (step @p301 :rule cong :premises (@p300) :args (@t276)) % 34.72/34.92 (step @p302 :rule nary_cong :premises (@p301 @p299 @p297) :args (@t277)) % 34.72/34.92 (step @p303 :rule cong :premises (@p302) :args (@t278)) % 34.72/34.92 (step @p304 :rule cong :premises (@p303) :args (@t279)) % 34.72/34.92 (step @p305 :rule nary_cong :premises (@p304 @p296 @p290) :args (@t280)) % 34.72/34.92 (step @p306 :rule trans :premises (@p305 @p289)) % 34.72/34.92 (step @p307 :rule refl :args (@t214)) % 34.72/34.92 (step @p308 :rule cong :premises (@p307 @p306) :args ((=> @t214 @t280))) % 34.72/34.92 (assume-push @p429 @t214) % 34.72/34.92 (step @p310 :rule instantiate :premises (@p429) :args ((@list @t266))) % 34.72/34.92 (step-pop @p430 :rule scope :premises (@p310)) % 34.72/34.92 (step @p311 :rule process_scope :premises (@p430) :args (@t280)) % 34.72/34.92 (step @p313 :rule eq_resolve :premises (@p311 @p308)) % 34.72/34.92 (step @p314 :rule implies_elim :premises (@p313)) % 34.72/34.92 (step @p315 :rule bool-double-not-elim :args (@t227)) % 34.72/34.92 (step @p316 :rule nary_cong :premises (@p233 @p315) :args ((or @t230 (not @t228)))) % 34.72/34.92 (step @p317 :rule cnf_or_neg :args (@t230 1)) % 34.72/34.92 (step @p318 :rule eq_resolve :premises (@p317 @p316)) % 34.72/34.92 (step @p319 :rule reordering :premises (@p318) :args ((or @t227 @t230))) % 34.72/34.92 (step @p320 :rule chain_m_resolution :premises (@p319 @p231) :args (@t227 @t231 @t232)) % 34.72/34.92 (step @p321 :rule alpha_equiv :args (@t227 @t281 (@list @t95 @t96 @t105))) % 34.72/34.92 (step @p322 :rule equiv_elim1 :premises (@p321)) % 34.72/34.92 (step @p323 :rule chain_m_resolution :premises (@p322 @p320) :args (@t238 @t282 @t283)) % 34.72/34.92 (step @p324 :rule cnf_or_pos :args (@t240)) % 34.72/34.92 (step @p325 :rule reordering :premises (@p324) :args ((or @t233 @t239 (not @t240)))) % 34.72/34.92 (step @p326 :rule alpha_equiv :args (@t227 @t281 (@list @t95 @t96 @t101))) % 34.72/34.92 (step @p327 :rule equiv_elim1 :premises (@p326)) % 34.72/34.92 (step @p328 :rule chain_m_resolution :premises (@p327 @p320) :args (@t261 @t282 @t283)) % 34.72/34.92 (step @p329 :rule cnf_or_pos :args (@t263)) % 34.72/34.92 (step @p330 :rule reordering :premises (@p329) :args ((or @t258 @t262 (not @t263)))) % 34.72/34.92 (step @p331 :rule instantiate :premises (@p320) :args ((@list @t205 @t212 @t204))) % 34.72/34.92 (step @p332 :rule cnf_or_pos :args (@t287)) % 34.72/34.92 (step @p333 :rule reordering :premises (@p332) :args ((or @t284 @t286 @t285 (not @t287)))) % 34.72/34.92 (step @p334 :rule cnf_or_pos :args (@t289)) % 34.72/34.92 (step @p335 :rule reordering :premises (@p334) :args ((or @t207 @t288 (not @t289)))) % 34.72/34.92 (assume-push @p431 @t210) % 34.72/34.92 (step @p337 :rule instantiate :premises (@p431) :args ((@list @t205 @t204))) % 34.72/34.92 (step-pop @p432 :rule scope :premises (@p337)) % 34.72/34.92 (step @p338 :rule process_scope :premises (@p432) :args (@t289)) % 34.72/34.92 (step @p340 :rule implies_elim :premises (@p338)) % 34.72/34.92 (step @p341 :rule chain_m_resolution :premises (@p340 @p335 @p333 @p331 @p330 @p328 @p325 @p323 @p314 @p288 @p256 @p255 @p250 @p245) :args (@t218 (@list true false false false false false false false false true false false false) (@list @t289 @t284 @t287 @t258 @t261 @t233 @t238 @t263 @t240 @t207 @t210 @t214 @t216))) % 34.72/34.92 (step @p342 :rule cnf_or_neg :args (@t230 2)) % 34.72/34.92 (step @p343 :rule chain_m_resolution :premises (@p342 @p231) :args ((not @t226) @t231 @t232)) % 34.72/34.92 (step @p344 :rule cnf_and_neg :args (@t226)) % 34.72/34.92 (step @p345 :rule chain_m_resolution :premises (@p344 @p343 @p341) :args ((not @t225) (@list true false) (@list @t226 @t218))) % 34.72/34.92 (step @p346 :rule bool-double-not-elim :args (@t223)) % 34.72/34.92 (step @p347 :rule refl :args (@t225)) % 34.72/34.92 (step @p348 :rule nary_cong :premises (@p347 @p346) :args ((or @t225 (not @t224)))) % 34.72/34.92 (step @p349 :rule cnf_or_neg :args (@t225 0)) % 34.72/34.92 (step @p350 :rule eq_resolve :premises (@p349 @p348)) % 34.72/34.92 (step @p351 :rule reordering :premises (@p350) :args ((or @t223 @t225))) % 34.72/34.92 (step @p352 :rule chain_m_resolution :premises (@p351 @p345) :args (@t223 @t231 @t290)) % 34.72/34.92 (step @p353 :rule aci_norm :args ((= (or @t295 false @t291) @t296))) % 34.72/34.92 (step @p354 :rule beta-reduce :args ((= @t300 @t291))) % 34.72/34.92 (step @p355 :rule beta-reduce :args ((= @t301 @t208))) % 34.72/34.92 (step @p356 :rule nary_cong :premises (@p265 @p355) :args (@t302)) % 34.72/34.92 (step @p357 :rule cong :premises (@p356) :args (@t303)) % 34.72/34.92 (step @p358 :rule trans :premises (@p357 @p263)) % 34.72/34.92 (step @p359 :rule cong :premises (@p358) :args (@t304)) % 34.72/34.92 (step @p360 :rule trans :premises (@p359 @p259)) % 34.72/34.92 (step @p361 :rule beta-reduce :args ((= @t305 @t292))) % 34.72/34.92 (step @p362 :rule beta-reduce :args ((= @t306 @t293))) % 34.72/34.92 (step @p363 :rule cong :premises (@p362) :args (@t307)) % 34.72/34.92 (step @p364 :rule beta-reduce :args ((= @t308 @t236))) % 34.72/34.92 (step @p365 :rule cong :premises (@p364) :args (@t309)) % 34.72/34.92 (step @p366 :rule nary_cong :premises (@p365 @p363 @p361) :args (@t310)) % 34.72/34.92 (step @p367 :rule cong :premises (@p366) :args (@t311)) % 34.72/34.92 (step @p368 :rule cong :premises (@p367) :args (@t312)) % 34.72/34.92 (step @p369 :rule nary_cong :premises (@p368 @p360 @p354) :args (@t313)) % 34.72/34.92 (step @p370 :rule trans :premises (@p369 @p353)) % 34.72/34.92 (step @p371 :rule refl :args (@t223)) % 34.72/34.92 (step @p372 :rule cong :premises (@p371 @p370) :args ((=> @t223 @t313))) % 34.72/34.92 (assume-push @p433 @t223) % 34.72/34.92 (step @p374 :rule instantiate :premises (@p433) :args ((@list @t299))) % 34.72/34.92 (step-pop @p434 :rule scope :premises (@p374)) % 34.72/34.92 (step @p375 :rule process_scope :premises (@p434) :args (@t313)) % 34.72/34.92 (step @p377 :rule eq_resolve :premises (@p375 @p372)) % 34.72/34.92 (step @p378 :rule implies_elim :premises (@p377)) % 34.72/34.92 (step @p379 :rule chain_m_resolution :premises (@p378 @p352) :args (@t296 @t282 (@list @t223))) % 34.72/34.92 (step @p380 :rule alpha_equiv :args ((forall (@list @t315 @t316 @t314) (or (not (_ @t201 @t315 @t316)) (not (_ @t201 @t316 @t314)) (_ @t201 @t315 @t314))) @t317 (@list @t95 @t96 @t41))) % 34.72/34.92 (step @p381 :rule alpha_equiv :args (@t227 @t281 @t317)) % 34.72/34.92 (step @p382 :rule trans :premises (@p381 @p380)) % 34.72/34.92 (step @p383 :rule equiv_elim1 :premises (@p382)) % 34.72/34.92 (step @p384 :rule chain_m_resolution :premises (@p383 @p320) :args (@t294 @t282 @t283)) % 34.72/34.92 (step @p385 :rule cnf_or_pos :args (@t296)) % 34.72/34.92 (step @p386 :rule reordering :premises (@p385) :args ((or @t291 @t295 (not @t296)))) % 34.72/34.92 (step @p387 :rule chain_m_resolution :premises (@p386 @p384 @p379) :args (@t291 @t318 (@list @t294 @t296))) % 34.72/34.92 (step @p388 :rule bool-double-not-elim :args (@t221)) % 34.72/34.92 (step @p389 :rule nary_cong :premises (@p347 @p388) :args ((or @t225 (not @t222)))) % 34.72/34.92 (step @p390 :rule cnf_or_neg :args (@t225 1)) % 34.72/34.92 (step @p391 :rule eq_resolve :premises (@p390 @p389)) % 34.72/34.92 (step @p392 :rule reordering :premises (@p391) :args ((or @t221 @t225))) % 34.72/34.92 (step @p393 :rule chain_m_resolution :premises (@p392 @p345) :args (@t221 @t231 @t290)) % 34.72/34.92 (step @p394 :rule aci_norm :args ((= (or @t295 false @t319) @t320))) % 34.72/34.92 (step @p395 :rule beta-reduce :args ((= @t324 @t319))) % 34.72/34.92 (step @p396 :rule beta-reduce :args ((= @t325 @t208))) % 34.72/34.92 (step @p397 :rule nary_cong :premises (@p265 @p396) :args (@t326)) % 34.72/34.92 (step @p398 :rule cong :premises (@p397) :args (@t327)) % 34.72/34.92 (step @p399 :rule trans :premises (@p398 @p263)) % 34.72/34.92 (step @p400 :rule cong :premises (@p399) :args (@t328)) % 34.72/34.92 (step @p401 :rule trans :premises (@p400 @p259)) % 34.72/34.92 (step @p402 :rule beta-reduce :args ((= @t329 @t292))) % 34.72/34.92 (step @p403 :rule beta-reduce :args ((= @t330 @t293))) % 34.72/34.92 (step @p404 :rule cong :premises (@p403) :args (@t331)) % 34.72/34.92 (step @p405 :rule beta-reduce :args ((= @t332 @t236))) % 34.72/34.92 (step @p406 :rule cong :premises (@p405) :args (@t333)) % 34.72/34.92 (step @p407 :rule nary_cong :premises (@p406 @p404 @p402) :args (@t334)) % 34.72/34.92 (step @p408 :rule cong :premises (@p407) :args (@t335)) % 34.72/34.92 (step @p409 :rule cong :premises (@p408) :args (@t336)) % 34.72/34.92 (step @p410 :rule nary_cong :premises (@p409 @p401 @p395) :args (@t337)) % 34.72/34.92 (step @p411 :rule trans :premises (@p410 @p394)) % 34.72/34.92 (step @p412 :rule refl :args (@t221)) % 34.72/34.92 (step @p413 :rule cong :premises (@p412 @p411) :args ((=> @t221 @t337))) % 34.72/34.92 (assume-push @p435 @t221) % 34.72/34.92 (step @p415 :rule instantiate :premises (@p435) :args ((@list @t323))) % 34.72/34.92 (step-pop @p436 :rule scope :premises (@p415)) % 34.72/34.92 (step @p416 :rule process_scope :premises (@p436) :args (@t337)) % 34.72/34.92 (step @p418 :rule eq_resolve :premises (@p416 @p413)) % 34.72/34.92 (step @p419 :rule implies_elim :premises (@p418)) % 34.72/34.92 (step @p420 :rule chain_m_resolution :premises (@p419 @p393) :args (@t320 @t282 (@list @t221))) % 34.72/34.92 (step @p421 :rule cnf_or_pos :args (@t320)) % 34.72/34.92 (step @p422 :rule reordering :premises (@p421) :args ((or @t319 @t295 (not @t320)))) % 34.72/34.92 (step @p423 :rule chain_m_resolution :premises (@p422 @p384 @p420) :args (@t319 @t318 (@list @t294 @t320))) % 34.72/34.92 (step @p424 :rule cnf_or_pos :args (@t340)) % 34.72/34.92 (step @p425 :rule reordering :premises (@p424) :args ((or @t339 @t338 (not @t340)))) % 34.72/34.92 (step @p426 false :rule chain_m_resolution :premises (@p425 @p423 @p387 @p239) :args (false (@list false false false) (@list @t319 @t291 @t340))) % 34.72/34.92 ) % 34.72/34.92 % SZS output end Proof % 34.72/34.92 % cvc5 exiting %------------------------------------------------------------------------------