%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU468^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:51:54 AM UTC 2026 % Result : Theorem 0.45s 0.68s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU468^1 : TPTP v9.2.1. Released v3.6.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n029.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 17:36:47 EDT 2026 % 0.16/0.35 % CPUTime : % 0.30/0.51 %----Proving TH0 % 0.45/0.68 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.68 % SZS status Theorem % 0.45/0.68 % SZS output start Proof % 0.45/0.68 ( % 0.45/0.68 (declare-sort $$unsorted 0) % 0.45/0.68 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.45/0.68 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.45/0.68 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.45/0.68 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.45/0.68 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.45/0.68 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.45/0.68 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.45/0.68 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.45/0.68 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.45/0.68 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.45/0.68 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.45/0.68 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.45/0.68 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.45/0.68 (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))))))))) % 0.45/0.68 (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)))))) % 0.45/0.68 (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)))))) % 0.45/0.68 (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))))) % 0.45/0.68 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.45/0.68 (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)))))))) % 0.45/0.68 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.45/0.68 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 0.45/0.68 (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)))))))) % 0.45/0.68 (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))))))) % 0.45/0.68 (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)))))))) % 0.45/0.68 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.45/0.68 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.45/0.68 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.45/0.68 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.45/0.68 (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)))))))) % 0.45/0.68 (define @t1 () (not (_ tptp.mono tptp.tc))) % 0.45/0.68 (define @t2 () (@var "Y" $$unsorted)) % 0.45/0.68 (define @t3 () (@var "X" $$unsorted)) % 0.45/0.68 (define @t4 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.45/0.68 (define @t5 () (_ (_ @t4 @t3) @t2)) % 0.45/0.68 (define @t6 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.45/0.68 (define @t7 () (_ @t6 @t3)) % 0.45/0.68 (define @t8 () (_ @t7 @t2)) % 0.45/0.68 (define @t9 () (@list @t3 @t2)) % 0.45/0.68 (define @t10 () (forall @t9 (=> @t8 @t5))) % 0.45/0.68 (define @t11 () (@list @t6 @t4)) % 0.45/0.68 (define @t12 () (lambda @t11 @t10)) % 0.45/0.68 (define @t13 () (_ @t6 @t2)) % 0.45/0.68 (define @t14 () (_ @t13 @t3)) % 0.45/0.68 (define @t15 () (@list @t6 @t3 @t2)) % 0.45/0.68 (define @t16 () (lambda @t15 @t14)) % 0.45/0.68 (define @t17 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.45/0.68 (define @t18 () (_ @t17 @t6)) % 0.45/0.68 (define @t19 () (@list @t6)) % 0.45/0.68 (define @t20 () (@list @t17)) % 0.45/0.68 (define @t21 () (lambda @t20 (forall @t19 (= (_ @t17 @t18) @t18)))) % 0.45/0.68 (define @t22 () (_ tptp.subrel @t6)) % 0.45/0.68 (define @t23 () (lambda @t20 (forall @t19 (_ @t22 @t18)))) % 0.45/0.68 (define @t24 () (_ @t17 @t4)) % 0.45/0.68 (define @t25 () (_ @t22 @t4)) % 0.45/0.68 (define @t26 () (=> @t25 (_ (_ tptp.subrel @t18) @t24))) % 0.45/0.68 (define @t27 () (forall @t11 @t26)) % 0.45/0.68 (define @t28 () (lambda @t20 @t27)) % 0.45/0.68 (define @t29 () (_ @t7 @t3)) % 0.45/0.68 (define @t30 () (@list @t3)) % 0.45/0.68 (define @t31 () (lambda @t19 (forall @t30 @t29))) % 0.45/0.68 (define @t32 () (lambda @t19 (forall @t30 (not @t29)))) % 0.45/0.68 (define @t33 () (= @t3 @t2)) % 0.45/0.68 (define @t34 () (lambda @t15 (or @t33 @t8))) % 0.45/0.68 (define @t35 () (lambda @t19 (forall @t9 (=> @t8 @t14)))) % 0.45/0.68 (define @t36 () (lambda @t19 (forall @t9 (=> (and @t8 @t14) @t33)))) % 0.45/0.68 (define @t37 () (lambda @t19 (forall @t9 (=> @t8 (not @t14))))) % 0.45/0.68 (define @t38 () (lambda @t15 (or @t14 @t8))) % 0.45/0.68 (define @t39 () (@var "Z" $$unsorted)) % 0.45/0.68 (define @t40 () (_ @t7 @t39)) % 0.45/0.68 (define @t41 () (_ @t13 @t39)) % 0.45/0.68 (define @t42 () (and @t8 @t41)) % 0.45/0.68 (define @t43 () (@list @t3 @t2 @t39)) % 0.45/0.68 (define @t44 () (forall @t43 (=> @t42 @t40))) % 0.45/0.68 (define @t45 () (lambda @t19 @t44)) % 0.45/0.68 (define @t46 () (and (_ tptp.trans @t4) @t25)) % 0.45/0.68 (define @t47 () (=> @t46 @t5)) % 0.45/0.68 (define @t48 () (@list @t4)) % 0.45/0.68 (define @t49 () (forall @t48 @t47)) % 0.45/0.68 (define @t50 () (lambda @t15 @t49)) % 0.45/0.68 (define @t51 () (@var "__flatten_var_1" $$unsorted)) % 0.45/0.68 (define @t52 () (@var "__flatten_var_0" $$unsorted)) % 0.45/0.68 (define @t53 () (_ tptp.tc @t6)) % 0.45/0.68 (define @t54 () (_ tptp.rc @t53)) % 0.45/0.68 (define @t55 () (@list @t6 @t52 @t51)) % 0.45/0.68 (define @t56 () (lambda @t55 (_ (_ @t54 @t52) @t51))) % 0.45/0.68 (define @t57 () (lambda @t55 (_ (_ (_ tptp.sc @t54) @t52) @t51))) % 0.45/0.68 (define @t58 () (_ tptp.trans @t6)) % 0.45/0.68 (define @t59 () (lambda @t19 (and (_ tptp.refl @t6) (_ tptp.antisymm @t6) @t58))) % 0.45/0.68 (define @t60 () (lambda @t19 (and (_ tptp.asymm @t6) @t58))) % 0.45/0.68 (define @t61 () (lambda @t19 (forall @t9 (or @t33 @t8 @t14)))) % 0.45/0.68 (define @t62 () (not @t8)) % 0.45/0.68 (define @t63 () (@var "A" (-> $$unsorted Bool))) % 0.45/0.68 (define @t64 () (@list @t2)) % 0.45/0.68 (define @t65 () (_ @t63 @t3)) % 0.45/0.68 (define @t66 () (lambda @t19 (forall (@list @t63) (=> (exists @t30 @t65) (exists @t30 (and @t65 (forall @t64 (=> (_ @t63 @t2) @t62)))))))) % 0.45/0.68 (define @t67 () (@var "P" (-> $$unsorted Bool))) % 0.45/0.68 (define @t68 () (_ @t67 @t3)) % 0.45/0.68 (define @t69 () (lambda @t19 (forall (@list @t67) (=> (forall @t30 (=> (forall @t64 (=> (_ (_ @t53 @t3) @t2) (_ @t67 @t2))) @t68)) (forall @t30 @t68))))) % 0.45/0.68 (define @t70 () (lambda (@list @t6 @t3) (not (exists @t64 @t8)))) % 0.45/0.68 (define @t71 () (_ tptp.trc @t6)) % 0.45/0.68 (define @t72 () (_ @t71 @t2)) % 0.45/0.68 (define @t73 () (lambda @t15 (and (_ @t72 @t3) (_ (_ tptp.innf @t6) @t3)))) % 0.45/0.68 (define @t74 () (lambda @t19 (forall @t30 (exists @t64 (_ (_ (_ tptp.nfof @t6) @t2) @t3))))) % 0.45/0.68 (define @t75 () (_ @t71 @t3)) % 0.45/0.68 (define @t76 () (_ @t75 @t39)) % 0.45/0.68 (define @t77 () (lambda @t15 (exists (@list @t39) (and @t76 (_ @t72 @t39))))) % 0.45/0.68 (define @t78 () (_ tptp.join @t6)) % 0.45/0.68 (define @t79 () (_ (_ @t78 @t39) @t2)) % 0.45/0.68 (define @t80 () (lambda @t19 (forall @t43 (=> (and @t40 @t8) @t79)))) % 0.45/0.68 (define @t81 () (_ @t75 @t2)) % 0.45/0.68 (define @t82 () (lambda @t19 (forall @t43 (=> (and @t40 @t81) @t79)))) % 0.45/0.68 (define @t83 () (lambda @t19 (forall @t43 (=> (and @t76 @t81) @t79)))) % 0.45/0.68 (define @t84 () (lambda @t19 (forall @t9 (=> (_ (_ (_ tptp.trsc @t6) @t3) @t2) (_ (_ @t78 @t3) @t2))))) % 0.45/0.68 (define @t85 () (@var "BOUND_VARIABLE_7545" $$unsorted)) % 0.45/0.68 (define @t86 () (@var "BOUND_VARIABLE_7543" $$unsorted)) % 0.45/0.68 (define @t87 () (@var "BOUND_VARIABLE_8887" (-> $$unsorted $$unsorted Bool))) % 0.45/0.68 (define @t88 () (_ @t87 @t86 @t85)) % 0.45/0.68 (define @t89 () (@var "BOUND_VARIABLE_7746" $$unsorted)) % 0.45/0.68 (define @t90 () (@var "BOUND_VARIABLE_7744" $$unsorted)) % 0.45/0.68 (define @t91 () (_ @t4 @t90 @t89)) % 0.45/0.68 (define @t92 () (not @t91)) % 0.45/0.68 (define @t93 () (@list @t90 @t89)) % 0.45/0.68 (define @t94 () (not (forall @t93 (or @t92 (_ @t87 @t90 @t89))))) % 0.45/0.68 (define @t95 () (@var "BOUND_VARIABLE_7755" $$unsorted)) % 0.45/0.68 (define @t96 () (@var "BOUND_VARIABLE_7757" $$unsorted)) % 0.45/0.68 (define @t97 () (@list @t95 @t96 @t39)) % 0.45/0.68 (define @t98 () (not (forall @t97 (or (not (_ @t87 @t95 @t96)) (not (_ @t87 @t96 @t39)) (_ @t87 @t95 @t39))))) % 0.45/0.68 (define @t99 () (@var "BOUND_VARIABLE_8866" (-> $$unsorted $$unsorted Bool))) % 0.45/0.68 (define @t100 () (_ @t99 @t90 @t89)) % 0.45/0.68 (define @t101 () (not (_ @t6 @t90 @t89))) % 0.45/0.68 (define @t102 () (not (forall @t97 (or (not (_ @t99 @t95 @t96)) (not (_ @t99 @t96 @t39)) (_ @t99 @t95 @t39))))) % 0.45/0.68 (define @t103 () (@list @t99)) % 0.45/0.68 (define @t104 () (not (forall @t103 (or @t102 (not (forall @t93 (or @t101 @t100))) (_ @t99 @t86 @t85))))) % 0.45/0.68 (define @t105 () (_ @t4 @t3 @t2)) % 0.45/0.68 (define @t106 () (_ @t6 @t3 @t2)) % 0.45/0.68 (define @t107 () (not @t106)) % 0.45/0.68 (define @t108 () (forall @t9 (or @t107 @t105))) % 0.45/0.68 (define @t109 () (not @t108)) % 0.45/0.68 (define @t110 () (or @t109 @t104 @t98 @t94 @t88)) % 0.45/0.68 (define @t111 () (or @t98 @t94 @t88)) % 0.45/0.68 (define @t112 () (or @t109 @t104 @t111)) % 0.45/0.68 (define @t113 () (@list @t6 @t4 @t86 @t85 @t87)) % 0.45/0.68 (define @t114 () (forall @t113 @t112)) % 0.45/0.68 (define @t115 () (@list @t87)) % 0.45/0.68 (define @t116 () (forall @t115 @t112)) % 0.45/0.68 (define @t117 () (@list @t6 @t4 @t86 @t85)) % 0.45/0.68 (define @t118 () (forall @t115 @t111)) % 0.45/0.68 (define @t119 () (@var "BOUND_VARIABLE_8837" (-> $$unsorted $$unsorted Bool))) % 0.45/0.68 (define @t120 () (@list @t119)) % 0.45/0.68 (define @t121 () (or @t109 @t104 @t118)) % 0.45/0.68 (define @t122 () (_ @t119 @t90 @t89)) % 0.45/0.68 (define @t123 () (not (forall @t97 (or (not (_ @t119 @t95 @t96)) (not (_ @t119 @t96 @t39)) (_ @t119 @t95 @t39))))) % 0.45/0.68 (define @t124 () (@list @t119)) % 0.45/0.68 (define @t125 () (forall @t124 (or @t123 (not (forall @t93 (or @t92 @t122))) (_ @t119 @t86 @t85)))) % 0.45/0.68 (define @t126 () (not (forall @t93 (or @t101 @t91)))) % 0.45/0.68 (define @t127 () (not (forall @t97 (or (not (_ @t4 @t95 @t96)) (not (_ @t4 @t96 @t39)) (_ @t4 @t95 @t39))))) % 0.45/0.68 (define @t128 () (forall @t48 (or @t127 @t126 (_ @t4 @t86 @t85)))) % 0.45/0.68 (define @t129 () (@list @t4)) % 0.45/0.68 (define @t130 () (not @t128)) % 0.45/0.68 (define @t131 () (or @t109 @t130 @t125)) % 0.45/0.68 (define @t132 () (forall @t48 (or @t127 @t126 @t105))) % 0.45/0.68 (define @t133 () (lambda @t15 @t132)) % 0.45/0.68 (define @t134 () (_ @t133 @t6 @t86 @t85)) % 0.45/0.68 (define @t135 () (not @t134)) % 0.45/0.68 (define @t136 () (or @t109 @t135 (_ @t133 @t4 @t86 @t85))) % 0.45/0.68 (define @t137 () (forall @t117 @t136)) % 0.45/0.68 (define @t138 () (_ @t17 @t4 @t86 @t85)) % 0.45/0.68 (define @t139 () (not (_ @t17 @t6 @t86 @t85))) % 0.45/0.68 (define @t140 () (or @t109 @t139 @t138)) % 0.45/0.68 (define @t141 () (lambda @t20 (forall @t117 @t140))) % 0.45/0.68 (define @t142 () (forall @t43 (or (not @t105) (not (_ @t4 @t2 @t39)) (_ @t4 @t3 @t39)))) % 0.45/0.68 (define @t143 () (not @t142)) % 0.45/0.68 (define @t144 () (lambda @t15 (forall @t48 (or @t143 @t109 @t105)))) % 0.45/0.68 (define @t145 () (or @t143 @t109 @t5)) % 0.45/0.68 (define @t146 () (and @t142 @t108)) % 0.45/0.68 (define @t147 () (lambda @t48 @t108)) % 0.45/0.68 (define @t148 () (lambda @t11 @t108)) % 0.45/0.68 (define @t149 () (_ @t148 @t6)) % 0.45/0.68 (define @t150 () (_ @t6 @t3 @t39)) % 0.45/0.68 (define @t151 () (_ @t6 @t2 @t39)) % 0.45/0.68 (define @t152 () (_ (lambda @t19 (forall @t43 (or @t107 (not @t151) @t150))) @t4)) % 0.45/0.68 (define @t153 () (_ @t149 @t4)) % 0.45/0.68 (define @t154 () (and @t152 @t153)) % 0.45/0.68 (define @t155 () (=> @t154 @t5)) % 0.45/0.68 (define @t156 () (or @t62 @t5)) % 0.45/0.68 (define @t157 () (not @t41)) % 0.45/0.68 (define @t158 () (or @t62 @t157 @t40)) % 0.45/0.68 (define @t159 () (or @t139 @t138)) % 0.45/0.68 (define @t160 () (or @t109 @t159)) % 0.45/0.68 (define @t161 () (forall @t117 @t160)) % 0.45/0.68 (define @t162 () (@list @t86 @t85)) % 0.45/0.68 (define @t163 () (forall @t162 @t160)) % 0.45/0.68 (define @t164 () (forall @t162 @t159)) % 0.45/0.68 (define @t165 () (or @t109 @t164)) % 0.45/0.68 (define @t166 () (_ @t17 @t4 @t3 @t2)) % 0.45/0.68 (define @t167 () (_ @t17 @t6 @t3 @t2)) % 0.45/0.68 (define @t168 () (not @t167)) % 0.45/0.68 (define @t169 () (forall @t9 (or @t168 @t166))) % 0.45/0.68 (define @t170 () (_ (_ @t24 @t3) @t2)) % 0.45/0.68 (define @t171 () (or @t168 @t170)) % 0.45/0.68 (define @t172 () (_ @t24 @t3 @t2)) % 0.45/0.68 (define @t173 () (or @t168 @t172)) % 0.45/0.68 (define @t174 () (forall @t9 @t173)) % 0.45/0.68 (define @t175 () (_ (_ @t18 @t3) @t2)) % 0.45/0.68 (define @t176 () (not @t175)) % 0.45/0.68 (define @t177 () (or @t176 @t105)) % 0.45/0.68 (define @t178 () (_ @t18 @t3 @t2)) % 0.45/0.68 (define @t179 () (not @t178)) % 0.45/0.68 (define @t180 () (or @t179 @t105)) % 0.45/0.68 (define @t181 () (forall @t9 @t180)) % 0.45/0.68 (define @t182 () (lambda @t48 @t181)) % 0.45/0.68 (define @t183 () (_ @t148 @t18)) % 0.45/0.68 (define @t184 () (=> @t153 (_ @t183 @t24))) % 0.45/0.68 (define @t185 () (forall @t113 @t110)) % 0.45/0.68 (define @t186 () (@quantifiers_skolemize @t185 1)) % 0.45/0.68 (define @t187 () (@quantifiers_skolemize @t185 0)) % 0.45/0.68 (define @t188 () (forall @t9 (or (not (_ @t187 @t3 @t2)) (_ @t186 @t3 @t2)))) % 0.45/0.68 (define @t189 () (@quantifiers_skolemize @t185 3)) % 0.45/0.68 (define @t190 () (@quantifiers_skolemize @t185 2)) % 0.45/0.68 (define @t191 () (@quantifiers_skolemize @t185 4)) % 0.45/0.68 (define @t192 () (_ @t191 @t190 @t189)) % 0.45/0.68 (define @t193 () (_ @t191 @t90 @t89)) % 0.45/0.68 (define @t194 () (forall @t93 (or (not (_ @t186 @t90 @t89)) @t193))) % 0.45/0.68 (define @t195 () (not @t194)) % 0.45/0.68 (define @t196 () (forall @t97 (or (not (_ @t191 @t95 @t96)) (not (_ @t191 @t96 @t39)) (_ @t191 @t95 @t39)))) % 0.45/0.68 (define @t197 () (not @t196)) % 0.45/0.68 (define @t198 () (not (_ @t187 @t90 @t89))) % 0.45/0.68 (define @t199 () (forall @t103 (or @t102 (not (forall @t93 (or @t198 @t100))) (_ @t99 @t190 @t189)))) % 0.45/0.68 (define @t200 () (not @t199)) % 0.45/0.68 (define @t201 () (not @t188)) % 0.45/0.68 (define @t202 () (or @t201 @t200 @t197 @t195 @t192)) % 0.45/0.68 (define @t203 () (@list true)) % 0.45/0.68 (define @t204 () (@list @t202)) % 0.45/0.68 (define @t205 () (forall @t93 (or @t198 @t193))) % 0.45/0.68 (define @t206 () (@quantifiers_skolemize @t205 1)) % 0.45/0.68 (define @t207 () (@quantifiers_skolemize @t205 0)) % 0.45/0.68 (define @t208 () (@list @t207 @t206)) % 0.45/0.68 (define @t209 () (not @t205)) % 0.45/0.68 (define @t210 () (or @t197 @t209 @t192)) % 0.45/0.68 (define @t211 () (_ @t191 @t207 @t206)) % 0.45/0.68 (define @t212 () (_ @t187 @t207 @t206)) % 0.45/0.68 (define @t213 () (not @t212)) % 0.45/0.68 (define @t214 () (or @t213 @t211)) % 0.45/0.68 (define @t215 () (@list @t214)) % 0.45/0.68 (define @t216 () (_ @t186 @t207 @t206)) % 0.45/0.68 (define @t217 () (not @t216)) % 0.45/0.68 (define @t218 () (or @t217 @t211)) % 0.45/0.68 (define @t219 () (@list true false)) % 0.45/0.68 (define @t220 () (or @t213 @t216)) % 0.45/0.68 (define @t221 () (not @t220)) % 0.45/0.68 (assume @p1 @t1) % 0.45/0.68 (assume @p2 true) % 0.45/0.68 (step @p3 (= tptp.subrel @t12) :rule refl :args (@t12)) % 0.45/0.68 (step @p4 (= tptp.inv @t16) :rule refl :args (@t16)) % 0.45/0.68 (step @p5 (= tptp.idem @t21) :rule refl :args (@t21)) % 0.45/0.68 (step @p6 (= tptp.infl @t23) :rule refl :args (@t23)) % 0.45/0.68 (step @p7 (= tptp.mono @t28) :rule refl :args (@t28)) % 0.45/0.68 (step @p8 (= tptp.refl @t31) :rule refl :args (@t31)) % 0.45/0.68 (step @p9 (= tptp.irrefl @t32) :rule refl :args (@t32)) % 0.45/0.68 (step @p10 (= tptp.rc @t34) :rule refl :args (@t34)) % 0.45/0.68 (step @p11 (= tptp.symm @t35) :rule refl :args (@t35)) % 0.45/0.68 (step @p12 (= tptp.antisymm @t36) :rule refl :args (@t36)) % 0.45/0.68 (step @p13 (= tptp.asymm @t37) :rule refl :args (@t37)) % 0.45/0.68 (step @p14 (= tptp.sc @t38) :rule refl :args (@t38)) % 0.45/0.68 (step @p15 (= tptp.trans @t45) :rule refl :args (@t45)) % 0.45/0.68 (step @p16 (= tptp.tc @t50) :rule refl :args (@t50)) % 0.45/0.68 (step @p17 (= tptp.trc @t56) :rule refl :args (@t56)) % 0.45/0.68 (step @p18 (= tptp.trsc @t57) :rule refl :args (@t57)) % 0.45/0.68 (step @p19 (= tptp.po @t59) :rule refl :args (@t59)) % 0.45/0.68 (step @p20 (= tptp.so @t60) :rule refl :args (@t60)) % 0.45/0.68 (step @p21 (= tptp.total @t61) :rule refl :args (@t61)) % 0.45/0.68 (step @p22 (= tptp.term @t66) :rule refl :args (@t66)) % 0.45/0.68 (step @p23 (= tptp.ind @t69) :rule refl :args (@t69)) % 0.45/0.68 (step @p24 (= tptp.innf @t70) :rule refl :args (@t70)) % 0.45/0.68 (step @p25 (= tptp.nfof @t73) :rule refl :args (@t73)) % 0.45/0.68 (step @p26 (= tptp.norm @t74) :rule refl :args (@t74)) % 0.45/0.68 (step @p27 (= tptp.join @t77) :rule refl :args (@t77)) % 0.45/0.68 (step @p28 (= tptp.lconfl @t80) :rule refl :args (@t80)) % 0.45/0.68 (step @p29 (= tptp.sconfl @t82) :rule refl :args (@t82)) % 0.45/0.68 (step @p30 (= tptp.confl @t83) :rule refl :args (@t83)) % 0.45/0.68 (step @p31 (= tptp.cr @t84) :rule refl :args (@t84)) % 0.45/0.68 (step @p32 :rule aci_norm :args ((= @t112 @t110))) % 0.45/0.68 (step @p33 :rule cong :premises (@p32) :args (@t114)) % 0.45/0.68 (step @p34 :rule quant-merge-prenex :args ((= (forall @t117 @t116) @t114))) % 0.45/0.68 (step @p35 :rule alpha_equiv :args (@t118 (@list @t87) @t120)) % 0.45/0.68 (step @p36 :rule refl :args (@t104)) % 0.45/0.68 (step @p37 :rule refl :args (@t109)) % 0.45/0.68 (step @p38 :rule nary_cong :premises (@p37 @p36 @p35) :args (@t121)) % 0.45/0.68 (step @p39 :rule quant-miniscope-or :args ((= @t116 @t121))) % 0.45/0.68 (step @p40 :rule trans :premises (@p39 @p38)) % 0.45/0.68 (step @p41 :rule symm :premises (@p40)) % 0.45/0.68 (step @p42 :rule cong :premises (@p41) :args ((forall @t117 (or @t109 @t104 @t125)))) % 0.45/0.68 (step @p43 :rule trans :premises (@p42 @p34)) % 0.45/0.68 (step @p44 :rule trans :premises (@p43 @p33)) % 0.45/0.68 (step @p45 :rule refl :args (@t125)) % 0.45/0.68 (step @p46 :rule alpha_equiv :args (@t128 @t129 (@list @t99))) % 0.45/0.68 (step @p47 :rule cong :premises (@p46) :args (@t130)) % 0.45/0.68 (step @p48 :rule nary_cong :premises (@p37 @p47 @p45) :args (@t131)) % 0.45/0.68 (step @p49 :rule cong :premises (@p48) :args ((forall @t117 @t131))) % 0.45/0.68 (step @p50 :rule trans :premises (@p49 @p44)) % 0.45/0.68 (step @p51 :rule beta-reduce :args ((= (_ (lambda @t15 (forall @t124 (or @t123 (not (forall @t93 (or @t101 @t122))) (_ @t119 @t3 @t2)))) @t4 @t86 @t85) @t125))) % 0.45/0.68 (step @p52 :rule refl :args (@t85)) % 0.45/0.68 (step @p53 :rule refl :args (@t86)) % 0.45/0.68 (step @p54 :rule refl :args (@t4)) % 0.45/0.68 (step @p55 :rule alpha_equiv :args (@t132 @t129 @t120)) % 0.45/0.68 (step @p56 :rule cong :premises (@p55) :args (@t133)) % 0.45/0.68 (step @p57 :rule ho_cong :premises (@p56 @p54 @p53 @p52)) % 0.45/0.68 (step @p58 :rule trans :premises (@p57 @p51)) % 0.45/0.68 (step @p59 :rule beta-reduce :args ((= @t134 @t128))) % 0.45/0.68 (step @p60 :rule cong :premises (@p59) :args (@t135)) % 0.45/0.68 (step @p61 :rule refl :args (@t109)) % 0.45/0.68 (step @p62 :rule nary_cong :premises (@p61 @p60 @p58) :args (@t136)) % 0.45/0.68 (step @p63 :rule cong :premises (@p62) :args (@t137)) % 0.45/0.68 (step @p64 :rule trans :premises (@p63 @p50)) % 0.45/0.68 (step @p65 :rule beta-reduce :args ((= (_ @t141 @t133) @t137))) % 0.45/0.68 (step @p66 :rule trans :premises (@p65 @p64)) % 0.45/0.68 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 0.45/0.68 ; trust TRUST_THEORY_REWRITE % 0.45/0.68 (step @p67 :rule trust :premises () :args ((= @t144 @t133))) % 0.45/0.68 (step @p68 :rule refl :args (@t141)) % 0.45/0.68 (step @p69 :rule ho_cong :premises (@p68 @p67)) % 0.45/0.68 (step @p70 :rule trans :premises (@p69 @p66)) % 0.45/0.68 (step @p71 :rule cong :premises (@p70) :args ((not (_ @t141 @t144)))) % 0.45/0.68 (step @p72 :rule refl :args (@t105)) % 0.45/0.68 (step @p73 :rule refl :args (@t5)) % 0.45/0.68 (step @p74 :rule cong :premises (@p73 @p72) :args ((= @t5 @t105))) % 0.45/0.68 (step @p75 :rule symm :premises (@p74)) % 0.45/0.68 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 0.45/0.68 (step @p77 :rule refl :args (@t143)) % 0.45/0.68 (step @p78 :rule nary_cong :premises (@p77 @p37 @p76) :args (@t145)) % 0.45/0.68 (step @p79 :rule cong :premises (@p78) :args ((forall @t48 @t145))) % 0.45/0.68 (step @p80 :rule aci_norm :args ((= (or (or @t143 @t109) @t5) @t145))) % 0.45/0.68 (step @p81 :rule bool-and-de-morgan :args (@t142 @t108 true)) % 0.45/0.68 (step @p82 :rule nary_cong :premises (@p81 @p73) :args ((or (not @t146) @t5))) % 0.45/0.68 (step @p83 :rule trans :premises (@p82 @p80)) % 0.45/0.68 (step @p84 :rule bool-impl-elim :args (@t146 @t5)) % 0.45/0.68 (step @p85 :rule trans :premises (@p84 @p83)) % 0.45/0.68 (step @p86 :rule cong :premises (@p85) :args ((forall @t48 (=> @t146 @t5)))) % 0.45/0.68 (step @p87 :rule trans :premises (@p86 @p79)) % 0.45/0.68 (step @p88 :rule refl :args (@t5)) % 0.45/0.68 (step @p89 :rule beta-reduce :args ((= (_ @t147 @t4) @t108))) % 0.45/0.68 (step @p90 :rule refl :args (@t4)) % 0.45/0.68 (step @p91 :rule beta-reduce :args ((= @t149 @t147))) % 0.45/0.68 (step @p92 :rule ho_cong :premises (@p91 @p90)) % 0.45/0.68 (step @p93 :rule trans :premises (@p92 @p89)) % 0.45/0.68 (step @p94 :rule beta-reduce :args ((= @t152 @t142))) % 0.45/0.68 (step @p95 :rule nary_cong :premises (@p94 @p93) :args (@t154)) % 0.45/0.68 (step @p96 :rule cong :premises (@p95 @p88) :args (@t155)) % 0.45/0.68 (step @p97 :rule cong :premises (@p96) :args ((forall @t48 @t155))) % 0.45/0.68 (step @p98 :rule trans :premises (@p97 @p87)) % 0.45/0.68 (step @p99 :rule refl :args (@t6)) % 0.45/0.68 (step @p100 :rule refl :args (@t106)) % 0.45/0.68 (step @p101 :rule refl :args (@t8)) % 0.45/0.68 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t8 @t106))) % 0.45/0.68 (step @p103 :rule symm :premises (@p102)) % 0.45/0.68 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 0.45/0.68 (step @p105 :rule cong :premises (@p104) :args (@t62)) % 0.45/0.68 (step @p106 :rule nary_cong :premises (@p105 @p76) :args (@t156)) % 0.45/0.68 (step @p107 :rule cong :premises (@p106) :args ((forall @t9 @t156))) % 0.45/0.68 (step @p108 :rule bool-impl-elim :args (@t8 @t5)) % 0.45/0.68 (step @p109 :rule cong :premises (@p108) :args (@t10)) % 0.45/0.68 (step @p110 :rule trans :premises (@p109 @p107)) % 0.45/0.68 (step @p111 :rule cong :premises (@p110) :args (@t12)) % 0.45/0.68 (step @p112 :rule trans :premises (@p3 @p111)) % 0.45/0.68 (step @p113 :rule ho_cong :premises (@p112 @p99)) % 0.45/0.68 (step @p114 :rule ho_cong :premises (@p113 @p90)) % 0.45/0.68 (step @p115 :rule refl :args (@t150)) % 0.45/0.68 (step @p116 :rule refl :args (@t40)) % 0.45/0.68 (step @p117 :rule cong :premises (@p116 @p115) :args ((= @t40 @t150))) % 0.45/0.68 (step @p118 :rule symm :premises (@p117)) % 0.45/0.68 (step @p119 :rule eq_resolve :premises (@p116 @p118)) % 0.45/0.68 (step @p120 :rule refl :args (@t151)) % 0.45/0.68 (step @p121 :rule refl :args (@t41)) % 0.45/0.68 (step @p122 :rule cong :premises (@p121 @p120) :args ((= @t41 @t151))) % 0.45/0.68 (step @p123 :rule symm :premises (@p122)) % 0.45/0.68 (step @p124 :rule eq_resolve :premises (@p121 @p123)) % 0.45/0.68 (step @p125 :rule cong :premises (@p124) :args (@t157)) % 0.45/0.68 (step @p126 :rule nary_cong :premises (@p105 @p125 @p119) :args (@t158)) % 0.45/0.68 (step @p127 :rule cong :premises (@p126) :args ((forall @t43 @t158))) % 0.45/0.68 (step @p128 :rule aci_norm :args ((= (or (or @t62 @t157) @t40) @t158))) % 0.45/0.68 (step @p129 :rule bool-and-de-morgan :args (@t8 @t41 true)) % 0.45/0.68 (step @p130 :rule nary_cong :premises (@p129 @p116) :args ((or (not @t42) @t40))) % 0.45/0.68 (step @p131 :rule trans :premises (@p130 @p128)) % 0.45/0.68 (step @p132 :rule bool-impl-elim :args (@t42 @t40)) % 0.45/0.68 (step @p133 :rule trans :premises (@p132 @p131)) % 0.45/0.68 (step @p134 :rule cong :premises (@p133) :args (@t44)) % 0.45/0.68 (step @p135 :rule trans :premises (@p134 @p127)) % 0.45/0.68 (step @p136 :rule cong :premises (@p135) :args (@t45)) % 0.45/0.68 (step @p137 :rule trans :premises (@p15 @p136)) % 0.45/0.68 (step @p138 :rule ho_cong :premises (@p137 @p90)) % 0.45/0.68 (step @p139 :rule nary_cong :premises (@p138 @p114) :args (@t46)) % 0.45/0.68 (step @p140 :rule cong :premises (@p139 @p88) :args (@t47)) % 0.45/0.68 (step @p141 :rule cong :premises (@p140) :args (@t49)) % 0.45/0.68 (step @p142 :rule trans :premises (@p141 @p98)) % 0.45/0.68 (step @p143 :rule cong :premises (@p142) :args (@t50)) % 0.45/0.68 (step @p144 :rule trans :premises (@p16 @p143)) % 0.45/0.68 (step @p145 :rule aci_norm :args ((= @t160 @t140))) % 0.45/0.68 (step @p146 :rule cong :premises (@p145) :args (@t161)) % 0.45/0.68 (step @p147 :rule quant-merge-prenex :args ((= (forall @t11 @t163) @t161))) % 0.45/0.68 (step @p148 :rule alpha_equiv :args (@t164 (@list @t86 @t85) (@list @t3 @t2))) % 0.45/0.68 (step @p149 :rule nary_cong :premises (@p37 @p148) :args (@t165)) % 0.45/0.68 (step @p150 :rule quant-miniscope-or :args ((= @t163 @t165))) % 0.45/0.68 (step @p151 :rule trans :premises (@p150 @p149)) % 0.45/0.68 (step @p152 :rule symm :premises (@p151)) % 0.45/0.68 (step @p153 :rule cong :premises (@p152) :args ((forall @t11 (or @t109 @t169)))) % 0.45/0.68 (step @p154 :rule trans :premises (@p153 @p147)) % 0.45/0.68 (step @p155 :rule trans :premises (@p154 @p146)) % 0.45/0.68 (step @p156 :rule bool-impl-elim :args (@t108 @t169)) % 0.45/0.68 (step @p157 :rule cong :premises (@p156) :args ((forall @t11 (=> @t108 @t169)))) % 0.45/0.68 (step @p158 :rule trans :premises (@p157 @p155)) % 0.45/0.68 (step @p159 :rule refl :args (@t166)) % 0.45/0.68 (step @p160 :rule refl :args (@t170)) % 0.45/0.68 (step @p161 :rule cong :premises (@p160 @p159) :args ((= @t170 @t166))) % 0.45/0.68 (step @p162 :rule symm :premises (@p161)) % 0.45/0.68 (step @p163 :rule eq_resolve :premises (@p160 @p162)) % 0.45/0.68 (step @p164 :rule refl :args (@t168)) % 0.45/0.68 (step @p165 :rule nary_cong :premises (@p164 @p163) :args (@t171)) % 0.45/0.68 (step @p166 :rule cong :premises (@p165) :args ((forall @t9 @t171))) % 0.45/0.68 (step @p167 :rule refl :args (@t172)) % 0.45/0.68 (step @p168 :rule refl :args (@t168)) % 0.45/0.68 (step @p169 :rule nary_cong :premises (@p168 @p167) :args (@t173)) % 0.45/0.68 (step @p170 :rule cong :premises (@p169) :args (@t174)) % 0.45/0.68 (step @p171 :rule trans :premises (@p170 @p166)) % 0.45/0.68 (step @p172 :rule beta-reduce :args ((= (_ (lambda @t48 (forall @t9 (or @t168 @t105))) @t24) @t174))) % 0.45/0.68 (step @p173 :rule trans :premises (@p172 @p171)) % 0.45/0.68 (step @p174 :rule refl :args (@t24)) % 0.45/0.68 (step @p175 :rule refl :args (@t105)) % 0.45/0.68 (step @p176 :rule refl :args (@t167)) % 0.45/0.68 (step @p177 :rule refl :args (@t175)) % 0.45/0.68 (step @p178 :rule cong :premises (@p177 @p176) :args ((= @t175 @t167))) % 0.45/0.68 (step @p179 :rule symm :premises (@p178)) % 0.45/0.68 (step @p180 :rule eq_resolve :premises (@p177 @p179)) % 0.45/0.68 (step @p181 :rule cong :premises (@p180) :args (@t176)) % 0.45/0.68 (step @p182 :rule nary_cong :premises (@p181 @p175) :args (@t177)) % 0.45/0.68 (step @p183 :rule cong :premises (@p182) :args ((forall @t9 @t177))) % 0.45/0.68 (step @p184 :rule refl :args (@t105)) % 0.45/0.68 (step @p185 :rule refl :args (@t178)) % 0.45/0.68 (step @p186 :rule cong :premises (@p185) :args (@t179)) % 0.45/0.68 (step @p187 :rule nary_cong :premises (@p186 @p184) :args (@t180)) % 0.45/0.68 (step @p188 :rule cong :premises (@p187) :args (@t181)) % 0.45/0.68 (step @p189 :rule trans :premises (@p188 @p183)) % 0.45/0.68 (step @p190 :rule cong :premises (@p189) :args (@t182)) % 0.45/0.68 (step @p191 :rule beta-reduce :args ((= @t183 @t182))) % 0.45/0.68 (step @p192 :rule trans :premises (@p191 @p190)) % 0.45/0.68 (step @p193 :rule ho_cong :premises (@p192 @p174)) % 0.45/0.68 (step @p194 :rule trans :premises (@p193 @p173)) % 0.45/0.68 (step @p195 :rule cong :premises (@p93 @p194) :args (@t184)) % 0.45/0.68 (step @p196 :rule cong :premises (@p195) :args ((forall @t11 @t184))) % 0.45/0.68 (step @p197 :rule trans :premises (@p196 @p158)) % 0.45/0.68 (step @p198 :rule refl :args (@t18)) % 0.45/0.68 (step @p199 :rule ho_cong :premises (@p112 @p198)) % 0.45/0.68 (step @p200 :rule ho_cong :premises (@p199 @p174)) % 0.45/0.68 (step @p201 :rule cong :premises (@p114 @p200) :args (@t26)) % 0.45/0.68 (step @p202 :rule cong :premises (@p201) :args (@t27)) % 0.45/0.68 (step @p203 :rule trans :premises (@p202 @p197)) % 0.45/0.68 (step @p204 :rule cong :premises (@p203) :args (@t28)) % 0.45/0.68 (step @p205 :rule trans :premises (@p7 @p204)) % 0.45/0.68 (step @p206 :rule ho_cong :premises (@p205 @p144)) % 0.45/0.68 (step @p207 :rule cong :premises (@p206) :args (@t1)) % 0.45/0.68 (step @p208 :rule trans :premises (@p207 @p71)) % 0.45/0.68 (step @p209 :rule eq_resolve :premises (@p1 @p208)) % 0.45/0.68 (step @p210 :rule skolemize :premises (@p209)) % 0.45/0.68 (step @p211 :rule bool-double-not-elim :args (@t188)) % 0.45/0.68 (step @p212 :rule refl :args (@t202)) % 0.45/0.68 (step @p213 :rule nary_cong :premises (@p212 @p211) :args ((or @t202 (not @t201)))) % 0.45/0.68 (step @p214 :rule cnf_or_neg :args (@t202 0)) % 0.45/0.68 (step @p215 :rule eq_resolve :premises (@p214 @p213)) % 0.45/0.68 (step @p216 :rule reordering :premises (@p215) :args ((or @t188 @t202))) % 0.45/0.68 (step @p217 :rule chain_m_resolution :premises (@p216 @p210) :args (@t188 @t203 @t204)) % 0.45/0.68 (step @p218 :rule bool-double-not-elim :args (@t194)) % 0.45/0.68 (step @p219 :rule nary_cong :premises (@p212 @p218) :args ((or @t202 (not @t195)))) % 0.45/0.68 (step @p220 :rule cnf_or_neg :args (@t202 3)) % 0.45/0.68 (step @p221 :rule eq_resolve :premises (@p220 @p219)) % 0.45/0.68 (step @p222 :rule reordering :premises (@p221) :args ((or @t194 @t202))) % 0.45/0.68 (step @p223 :rule chain_m_resolution :premises (@p222 @p210) :args (@t194 @t203 @t204)) % 0.45/0.68 (step @p224 :rule instantiate :premises (@p223) :args (@t208)) % 0.45/0.68 (step @p225 :rule bool-double-not-elim :args (@t199)) % 0.45/0.68 (step @p226 :rule nary_cong :premises (@p212 @p225) :args ((or @t202 (not @t200)))) % 0.45/0.68 (step @p227 :rule cnf_or_neg :args (@t202 1)) % 0.45/0.68 (step @p228 :rule eq_resolve :premises (@p227 @p226)) % 0.45/0.68 (step @p229 :rule reordering :premises (@p228) :args ((or @t199 @t202))) % 0.45/0.68 (step @p230 :rule chain_m_resolution :premises (@p229 @p210) :args (@t199 @t203 @t204)) % 0.45/0.68 (step @p231 :rule instantiate :premises (@p230) :args ((@list @t191))) % 0.45/0.68 (step @p232 :rule cnf_or_neg :args (@t202 4)) % 0.45/0.68 (step @p233 :rule chain_m_resolution :premises (@p232 @p210) :args ((not @t192) @t203 @t204)) % 0.45/0.68 (step @p234 :rule bool-double-not-elim :args (@t196)) % 0.45/0.68 (step @p235 :rule nary_cong :premises (@p212 @p234) :args ((or @t202 (not @t197)))) % 0.45/0.68 (step @p236 :rule cnf_or_neg :args (@t202 2)) % 0.45/0.68 (step @p237 :rule eq_resolve :premises (@p236 @p235)) % 0.45/0.68 (step @p238 :rule reordering :premises (@p237) :args ((or @t196 @t202))) % 0.45/0.68 (step @p239 :rule chain_m_resolution :premises (@p238 @p210) :args (@t196 @t203 @t204)) % 0.45/0.68 (step @p240 :rule cnf_or_pos :args (@t210)) % 0.45/0.68 (step @p241 :rule reordering :premises (@p240) :args ((or @t197 @t192 @t209 (not @t210)))) % 0.45/0.68 (step @p242 :rule chain_m_resolution :premises (@p241 @p239 @p233 @p231) :args (@t209 (@list false true false) (@list @t196 @t192 @t210))) % 0.45/0.69 (step @p243 :rule skolemize :premises (@p242)) % 0.45/0.69 (step @p244 :rule cnf_or_neg :args (@t214 1)) % 0.45/0.69 (step @p245 :rule chain_m_resolution :premises (@p244 @p243) :args ((not @t211) @t203 @t215)) % 0.45/0.69 (step @p246 :rule cnf_or_pos :args (@t218)) % 0.45/0.69 (step @p247 :rule reordering :premises (@p246) :args ((or @t211 @t217 (not @t218)))) % 0.45/0.69 (step @p248 :rule chain_m_resolution :premises (@p247 @p245 @p224) :args (@t217 @t219 (@list @t211 @t218))) % 0.45/0.69 (step @p249 :rule bool-double-not-elim :args (@t212)) % 0.45/0.69 (step @p250 :rule refl :args (@t214)) % 0.45/0.69 (step @p251 :rule nary_cong :premises (@p250 @p249) :args ((or @t214 (not @t213)))) % 0.45/0.69 (step @p252 :rule cnf_or_neg :args (@t214 0)) % 0.45/0.69 (step @p253 :rule eq_resolve :premises (@p252 @p251)) % 0.45/0.69 (step @p254 :rule reordering :premises (@p253) :args ((or @t212 @t214))) % 0.45/0.69 (step @p255 :rule chain_m_resolution :premises (@p254 @p243) :args (@t212 @t203 @t215)) % 0.45/0.69 (step @p256 :rule cnf_or_pos :args (@t220)) % 0.45/0.69 (step @p257 :rule reordering :premises (@p256) :args ((or @t213 @t216 @t221))) % 0.45/0.69 (step @p258 :rule chain_m_resolution :premises (@p257 @p255 @p248) :args (@t221 (@list false true) (@list @t212 @t216))) % 0.45/0.69 (assume-push @p265 @t188) % 0.45/0.69 (step @p260 :rule instantiate :premises (@p217) :args (@t208)) % 0.45/0.69 (step-pop @p266 :rule scope :premises (@p260)) % 0.45/0.69 (step @p261 :rule process_scope :premises (@p266) :args (@t220)) % 0.45/0.69 (step @p263 :rule implies_elim :premises (@p261)) % 0.45/0.69 (step @p264 false :rule chain_m_resolution :premises (@p263 @p258 @p217) :args (false @t219 (@list @t220 @t188))) % 0.45/0.69 ) % 0.45/0.69 % SZS output end Proof % 0.45/0.69 % cvc5 exiting %------------------------------------------------------------------------------