%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU472^1 : 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 0.38s 0.62s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU472^1 : 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 % 0.17/0.34 % Computer : n029.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:37:02 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.38/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.62 % SZS status Theorem % 0.38/0.62 % SZS output start Proof % 0.38/0.62 ( % 0.38/0.62 (declare-sort $$unsorted 0) % 0.38/0.62 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.38/0.62 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.38/0.62 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.38/0.62 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.38/0.62 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.38/0.62 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.62 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.38/0.62 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.62 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.62 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.38/0.62 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.38/0.62 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.62 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.38/0.62 (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))))))))) % 0.38/0.62 (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)))))) % 0.38/0.62 (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)))))) % 0.38/0.62 (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))))) % 0.38/0.62 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.38/0.62 (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)))))))) % 0.38/0.62 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.38/0.62 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 0.38/0.62 (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)))))))) % 0.38/0.62 (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))))))) % 0.38/0.62 (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)))))))) % 0.38/0.62 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.38/0.62 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.38/0.62 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.38/0.62 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.38/0.62 (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)))))))) % 0.38/0.62 (define @t1 () (not (_ tptp.infl tptp.trsc))) % 0.38/0.62 (define @t2 () (@var "Y" $$unsorted)) % 0.38/0.62 (define @t3 () (@var "X" $$unsorted)) % 0.38/0.62 (define @t4 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.38/0.62 (define @t5 () (_ (_ @t4 @t3) @t2)) % 0.38/0.62 (define @t6 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.62 (define @t7 () (_ @t6 @t3)) % 0.38/0.62 (define @t8 () (_ @t7 @t2)) % 0.38/0.62 (define @t9 () (@list @t3 @t2)) % 0.38/0.62 (define @t10 () (forall @t9 (=> @t8 @t5))) % 0.38/0.62 (define @t11 () (@list @t6 @t4)) % 0.38/0.62 (define @t12 () (lambda @t11 @t10)) % 0.38/0.62 (define @t13 () (_ @t6 @t2)) % 0.38/0.62 (define @t14 () (_ @t13 @t3)) % 0.38/0.62 (define @t15 () (@list @t6 @t3 @t2)) % 0.38/0.62 (define @t16 () (lambda @t15 @t14)) % 0.38/0.62 (define @t17 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.38/0.62 (define @t18 () (_ @t17 @t6)) % 0.38/0.62 (define @t19 () (@list @t6)) % 0.38/0.62 (define @t20 () (@list @t17)) % 0.38/0.62 (define @t21 () (lambda @t20 (forall @t19 (= (_ @t17 @t18) @t18)))) % 0.38/0.62 (define @t22 () (_ tptp.subrel @t6)) % 0.38/0.62 (define @t23 () (forall @t19 (_ @t22 @t18))) % 0.38/0.62 (define @t24 () (lambda @t20 @t23)) % 0.38/0.62 (define @t25 () (_ @t22 @t4)) % 0.38/0.62 (define @t26 () (lambda @t20 (forall @t11 (=> @t25 (_ (_ tptp.subrel @t18) (_ @t17 @t4)))))) % 0.38/0.62 (define @t27 () (_ @t7 @t3)) % 0.38/0.62 (define @t28 () (@list @t3)) % 0.38/0.62 (define @t29 () (lambda @t19 (forall @t28 @t27))) % 0.38/0.62 (define @t30 () (lambda @t19 (forall @t28 (not @t27)))) % 0.38/0.62 (define @t31 () (= @t3 @t2)) % 0.38/0.62 (define @t32 () (lambda @t15 (or @t31 @t8))) % 0.38/0.62 (define @t33 () (lambda @t19 (forall @t9 (=> @t8 @t14)))) % 0.38/0.62 (define @t34 () (lambda @t19 (forall @t9 (=> (and @t8 @t14) @t31)))) % 0.38/0.62 (define @t35 () (lambda @t19 (forall @t9 (=> @t8 (not @t14))))) % 0.38/0.62 (define @t36 () (lambda @t15 (or @t14 @t8))) % 0.38/0.62 (define @t37 () (@var "Z" $$unsorted)) % 0.38/0.62 (define @t38 () (_ @t7 @t37)) % 0.38/0.62 (define @t39 () (_ @t13 @t37)) % 0.38/0.62 (define @t40 () (and @t8 @t39)) % 0.38/0.62 (define @t41 () (@list @t3 @t2 @t37)) % 0.38/0.62 (define @t42 () (forall @t41 (=> @t40 @t38))) % 0.38/0.62 (define @t43 () (lambda @t19 @t42)) % 0.38/0.62 (define @t44 () (and (_ tptp.trans @t4) @t25)) % 0.38/0.62 (define @t45 () (=> @t44 @t5)) % 0.38/0.62 (define @t46 () (@list @t4)) % 0.38/0.62 (define @t47 () (forall @t46 @t45)) % 0.38/0.62 (define @t48 () (lambda @t15 @t47)) % 0.38/0.62 (define @t49 () (@var "__flatten_var_1" $$unsorted)) % 0.38/0.62 (define @t50 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.62 (define @t51 () (_ tptp.tc @t6)) % 0.38/0.62 (define @t52 () (_ tptp.rc @t51)) % 0.38/0.62 (define @t53 () (@list @t6 @t50 @t49)) % 0.38/0.62 (define @t54 () (lambda @t53 (_ (_ @t52 @t50) @t49))) % 0.38/0.62 (define @t55 () (lambda @t53 (_ (_ (_ tptp.sc @t52) @t50) @t49))) % 0.38/0.62 (define @t56 () (_ tptp.trans @t6)) % 0.38/0.62 (define @t57 () (lambda @t19 (and (_ tptp.refl @t6) (_ tptp.antisymm @t6) @t56))) % 0.38/0.62 (define @t58 () (lambda @t19 (and (_ tptp.asymm @t6) @t56))) % 0.38/0.62 (define @t59 () (lambda @t19 (forall @t9 (or @t31 @t8 @t14)))) % 0.38/0.62 (define @t60 () (not @t8)) % 0.38/0.62 (define @t61 () (@var "A" (-> $$unsorted Bool))) % 0.38/0.62 (define @t62 () (@list @t2)) % 0.38/0.62 (define @t63 () (_ @t61 @t3)) % 0.38/0.62 (define @t64 () (lambda @t19 (forall (@list @t61) (=> (exists @t28 @t63) (exists @t28 (and @t63 (forall @t62 (=> (_ @t61 @t2) @t60)))))))) % 0.38/0.62 (define @t65 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.62 (define @t66 () (_ @t65 @t3)) % 0.38/0.62 (define @t67 () (lambda @t19 (forall (@list @t65) (=> (forall @t28 (=> (forall @t62 (=> (_ (_ @t51 @t3) @t2) (_ @t65 @t2))) @t66)) (forall @t28 @t66))))) % 0.38/0.62 (define @t68 () (lambda (@list @t6 @t3) (not (exists @t62 @t8)))) % 0.38/0.62 (define @t69 () (_ tptp.trc @t6)) % 0.38/0.62 (define @t70 () (_ @t69 @t2)) % 0.38/0.62 (define @t71 () (lambda @t15 (and (_ @t70 @t3) (_ (_ tptp.innf @t6) @t3)))) % 0.38/0.62 (define @t72 () (lambda @t19 (forall @t28 (exists @t62 (_ (_ (_ tptp.nfof @t6) @t2) @t3))))) % 0.38/0.62 (define @t73 () (_ @t69 @t3)) % 0.38/0.62 (define @t74 () (_ @t73 @t37)) % 0.38/0.62 (define @t75 () (lambda @t15 (exists (@list @t37) (and @t74 (_ @t70 @t37))))) % 0.38/0.62 (define @t76 () (_ tptp.join @t6)) % 0.38/0.62 (define @t77 () (_ (_ @t76 @t37) @t2)) % 0.38/0.62 (define @t78 () (lambda @t19 (forall @t41 (=> (and @t38 @t8) @t77)))) % 0.38/0.62 (define @t79 () (_ @t73 @t2)) % 0.38/0.62 (define @t80 () (lambda @t19 (forall @t41 (=> (and @t38 @t79) @t77)))) % 0.38/0.62 (define @t81 () (lambda @t19 (forall @t41 (=> (and @t74 @t79) @t77)))) % 0.38/0.62 (define @t82 () (lambda @t19 (forall @t9 (=> (_ (_ (_ tptp.trsc @t6) @t3) @t2) (_ (_ @t76 @t3) @t2))))) % 0.38/0.62 (define @t83 () (@var "BOUND_VARIABLE_8849" (-> $$unsorted $$unsorted Bool))) % 0.38/0.62 (define @t84 () (_ @t83 @t3 @t2)) % 0.38/0.62 (define @t85 () (@var "BOUND_VARIABLE_7746" $$unsorted)) % 0.38/0.62 (define @t86 () (@var "BOUND_VARIABLE_7744" $$unsorted)) % 0.38/0.62 (define @t87 () (not (_ @t6 @t86 @t85))) % 0.38/0.62 (define @t88 () (@list @t86 @t85)) % 0.38/0.62 (define @t89 () (not (forall @t88 (or @t87 (_ @t83 @t86 @t85))))) % 0.38/0.62 (define @t90 () (@var "BOUND_VARIABLE_7755" $$unsorted)) % 0.38/0.62 (define @t91 () (@var "BOUND_VARIABLE_7757" $$unsorted)) % 0.38/0.62 (define @t92 () (@list @t90 @t91 @t37)) % 0.38/0.62 (define @t93 () (not (forall @t92 (or (not (_ @t83 @t90 @t91)) (not (_ @t83 @t91 @t37)) (_ @t83 @t90 @t37))))) % 0.38/0.62 (define @t94 () (@var "BOUND_VARIABLE_8833" (-> $$unsorted $$unsorted Bool))) % 0.38/0.62 (define @t95 () (_ @t94 @t2 @t3)) % 0.38/0.62 (define @t96 () (not (forall @t88 (or @t87 (_ @t94 @t86 @t85))))) % 0.38/0.62 (define @t97 () (not (forall @t92 (or (not (_ @t94 @t90 @t91)) (not (_ @t94 @t91 @t37)) (_ @t94 @t90 @t37))))) % 0.38/0.62 (define @t98 () (_ @t6 @t3 @t2)) % 0.38/0.62 (define @t99 () (not @t98)) % 0.38/0.62 (define @t100 () (or @t99 @t31 @t97 @t96 @t95 @t93 @t89 @t84)) % 0.38/0.62 (define @t101 () (or @t93 @t89 @t84)) % 0.38/0.62 (define @t102 () (or @t97 @t96 @t95)) % 0.38/0.62 (define @t103 () (or @t99 @t31 @t102 @t101)) % 0.38/0.62 (define @t104 () (@list @t6 @t3 @t2 @t94 @t83)) % 0.38/0.62 (define @t105 () (forall @t104 @t103)) % 0.38/0.62 (define @t106 () (forall (@list @t94 @t83) @t103)) % 0.38/0.62 (define @t107 () (forall (@list @t83) @t101)) % 0.38/0.62 (define @t108 () (@list @t4)) % 0.38/0.62 (define @t109 () (forall (@list @t94) @t102)) % 0.38/0.62 (define @t110 () (or @t99 @t31 @t109 @t107)) % 0.38/0.62 (define @t111 () (_ @t4 @t3 @t2)) % 0.38/0.62 (define @t112 () (not (forall @t88 (or @t87 (_ @t4 @t86 @t85))))) % 0.38/0.62 (define @t113 () (not (forall @t92 (or (not (_ @t4 @t90 @t91)) (not (_ @t4 @t91 @t37)) (_ @t4 @t90 @t37))))) % 0.38/0.62 (define @t114 () (forall @t46 (or @t113 @t112 @t111))) % 0.38/0.62 (define @t115 () (forall @t46 (or @t113 @t112 (_ @t4 @t2 @t3)))) % 0.38/0.62 (define @t116 () (or @t99 @t31 @t115 @t114)) % 0.38/0.62 (define @t117 () (or @t31 @t115 @t114)) % 0.38/0.62 (define @t118 () (forall @t46 (or @t113 @t112 (_ @t4 @t50 @t49)))) % 0.38/0.62 (define @t119 () (forall @t46 (or @t113 @t112 (_ @t4 @t49 @t50)))) % 0.38/0.62 (define @t120 () (lambda @t53 (or (= @t50 @t49) @t119 @t118))) % 0.38/0.62 (define @t121 () (_ @t120 @t6 @t3 @t2)) % 0.38/0.62 (define @t122 () (or @t99 @t121)) % 0.38/0.62 (define @t123 () (forall @t15 @t122)) % 0.38/0.62 (define @t124 () (_ @t17 @t6 @t3 @t2)) % 0.38/0.62 (define @t125 () (or @t99 @t124)) % 0.38/0.62 (define @t126 () (forall @t15 @t125)) % 0.38/0.62 (define @t127 () (_ (lambda @t20 @t126) @t120)) % 0.38/0.62 (define @t128 () (or (= @t49 @t50) @t119 @t118)) % 0.38/0.62 (define @t129 () (forall @t46 (or @t113 @t112 (_ @t4 @t50 @t2)))) % 0.38/0.62 (define @t130 () (forall @t46 (or @t113 @t112 (_ @t4 @t2 @t50)))) % 0.38/0.62 (define @t131 () (or (= @t50 @t2) @t130 @t129)) % 0.38/0.62 (define @t132 () (lambda @t62 @t131)) % 0.38/0.62 (define @t133 () (or @t31 @t114)) % 0.38/0.62 (define @t134 () (lambda @t62 @t133)) % 0.38/0.62 (define @t135 () (lambda @t9 @t133)) % 0.38/0.62 (define @t136 () (_ @t135 @t3)) % 0.38/0.62 (define @t137 () (or (= @t2 @t3) @t115)) % 0.38/0.62 (define @t138 () (@var "BOUND_VARIABLE_7826" $$unsorted)) % 0.38/0.62 (define @t139 () (lambda (@list @t138) (or (= @t2 @t138) (forall @t46 (or @t113 @t112 (_ @t4 @t2 @t138)))))) % 0.38/0.62 (define @t140 () (or (_ (_ @t135 @t2) @t3) (_ @t136 @t2))) % 0.38/0.62 (define @t141 () (lambda @t9 @t140)) % 0.38/0.62 (define @t142 () (lambda @t62 @t114)) % 0.38/0.62 (define @t143 () (lambda @t9 @t114)) % 0.38/0.62 (define @t144 () (_ @t143 @t3)) % 0.38/0.62 (define @t145 () (or @t31 (_ @t144 @t2))) % 0.38/0.62 (define @t146 () (lambda @t9 @t145)) % 0.38/0.62 (define @t147 () (lambda @t15 @t114)) % 0.38/0.62 (define @t148 () (forall @t9 (or @t99 @t111))) % 0.38/0.62 (define @t149 () (not @t148)) % 0.38/0.62 (define @t150 () (forall @t41 (or (not @t111) (not (_ @t4 @t2 @t37)) (_ @t4 @t3 @t37)))) % 0.38/0.62 (define @t151 () (not @t150)) % 0.38/0.62 (define @t152 () (or @t151 @t149 @t5)) % 0.38/0.62 (define @t153 () (and @t150 @t148)) % 0.38/0.62 (define @t154 () (lambda @t46 @t148)) % 0.38/0.62 (define @t155 () (_ (lambda @t11 @t148) @t6)) % 0.38/0.62 (define @t156 () (_ @t6 @t3 @t37)) % 0.38/0.62 (define @t157 () (_ @t6 @t2 @t37)) % 0.38/0.62 (define @t158 () (_ (lambda @t19 (forall @t41 (or @t99 (not @t157) @t156))) @t4)) % 0.38/0.62 (define @t159 () (and @t158 (_ @t155 @t4))) % 0.38/0.62 (define @t160 () (=> @t159 @t5)) % 0.38/0.62 (define @t161 () (or @t60 @t5)) % 0.38/0.62 (define @t162 () (not @t39)) % 0.38/0.62 (define @t163 () (or @t60 @t162 @t38)) % 0.38/0.62 (define @t164 () (_ (_ @t18 @t3) @t2)) % 0.38/0.62 (define @t165 () (or @t99 @t164)) % 0.38/0.62 (define @t166 () (_ @t18 @t3 @t2)) % 0.38/0.62 (define @t167 () (or @t99 @t166)) % 0.38/0.62 (define @t168 () (forall @t9 @t167)) % 0.38/0.62 (define @t169 () (forall @t104 @t100)) % 0.38/0.62 (define @t170 () (@quantifiers_skolemize @t169 4)) % 0.38/0.62 (define @t171 () (@quantifiers_skolemize @t169 0)) % 0.38/0.62 (define @t172 () (not (_ @t171 @t86 @t85))) % 0.38/0.62 (define @t173 () (forall @t88 (or @t172 (_ @t170 @t86 @t85)))) % 0.38/0.62 (define @t174 () (@quantifiers_skolemize @t169 2)) % 0.38/0.62 (define @t175 () (@quantifiers_skolemize @t169 1)) % 0.38/0.62 (define @t176 () (_ @t170 @t175 @t174)) % 0.38/0.62 (define @t177 () (not @t173)) % 0.38/0.62 (define @t178 () (@quantifiers_skolemize @t169 3)) % 0.38/0.62 (define @t179 () (_ @t171 @t175 @t174)) % 0.38/0.62 (define @t180 () (not @t179)) % 0.38/0.62 (define @t181 () (or @t180 (= @t175 @t174) (not (forall @t92 (or (not (_ @t178 @t90 @t91)) (not (_ @t178 @t91 @t37)) (_ @t178 @t90 @t37)))) (not (forall @t88 (or @t172 (_ @t178 @t86 @t85)))) (_ @t178 @t174 @t175) (not (forall @t92 (or (not (_ @t170 @t90 @t91)) (not (_ @t170 @t91 @t37)) (_ @t170 @t90 @t37)))) @t177 @t176)) % 0.38/0.62 (define @t182 () (@list true)) % 0.38/0.62 (define @t183 () (@list @t181)) % 0.38/0.62 (define @t184 () (or @t180 @t176)) % 0.38/0.62 (define @t185 () (not @t184)) % 0.38/0.62 (assume @p1 @t1) % 0.38/0.62 (assume @p2 true) % 0.38/0.62 (step @p3 (= tptp.subrel @t12) :rule refl :args (@t12)) % 0.38/0.62 (step @p4 (= tptp.inv @t16) :rule refl :args (@t16)) % 0.38/0.62 (step @p5 (= tptp.idem @t21) :rule refl :args (@t21)) % 0.38/0.62 (step @p6 (= tptp.infl @t24) :rule refl :args (@t24)) % 0.38/0.62 (step @p7 (= tptp.mono @t26) :rule refl :args (@t26)) % 0.38/0.62 (step @p8 (= tptp.refl @t29) :rule refl :args (@t29)) % 0.38/0.62 (step @p9 (= tptp.irrefl @t30) :rule refl :args (@t30)) % 0.38/0.62 (step @p10 (= tptp.rc @t32) :rule refl :args (@t32)) % 0.38/0.62 (step @p11 (= tptp.symm @t33) :rule refl :args (@t33)) % 0.38/0.62 (step @p12 (= tptp.antisymm @t34) :rule refl :args (@t34)) % 0.38/0.62 (step @p13 (= tptp.asymm @t35) :rule refl :args (@t35)) % 0.38/0.62 (step @p14 (= tptp.sc @t36) :rule refl :args (@t36)) % 0.38/0.62 (step @p15 (= tptp.trans @t43) :rule refl :args (@t43)) % 0.38/0.62 (step @p16 (= tptp.tc @t48) :rule refl :args (@t48)) % 0.38/0.62 (step @p17 (= tptp.trc @t54) :rule refl :args (@t54)) % 0.38/0.62 (step @p18 (= tptp.trsc @t55) :rule refl :args (@t55)) % 0.38/0.62 (step @p19 (= tptp.po @t57) :rule refl :args (@t57)) % 0.38/0.62 (step @p20 (= tptp.so @t58) :rule refl :args (@t58)) % 0.38/0.62 (step @p21 (= tptp.total @t59) :rule refl :args (@t59)) % 0.38/0.62 (step @p22 (= tptp.term @t64) :rule refl :args (@t64)) % 0.38/0.62 (step @p23 (= tptp.ind @t67) :rule refl :args (@t67)) % 0.38/0.62 (step @p24 (= tptp.innf @t68) :rule refl :args (@t68)) % 0.38/0.62 (step @p25 (= tptp.nfof @t71) :rule refl :args (@t71)) % 0.38/0.62 (step @p26 (= tptp.norm @t72) :rule refl :args (@t72)) % 0.38/0.62 (step @p27 (= tptp.join @t75) :rule refl :args (@t75)) % 0.38/0.62 (step @p28 (= tptp.lconfl @t78) :rule refl :args (@t78)) % 0.38/0.62 (step @p29 (= tptp.sconfl @t80) :rule refl :args (@t80)) % 0.38/0.62 (step @p30 (= tptp.confl @t81) :rule refl :args (@t81)) % 0.38/0.62 (step @p31 (= tptp.cr @t82) :rule refl :args (@t82)) % 0.38/0.62 (step @p32 :rule aci_norm :args ((= @t103 @t100))) % 0.38/0.62 (step @p33 :rule cong :premises (@p32) :args (@t105)) % 0.38/0.62 (step @p34 :rule quant-merge-prenex :args ((= (forall @t15 @t106) @t105))) % 0.38/0.62 (step @p35 :rule alpha_equiv :args (@t107 (@list @t83) @t108)) % 0.38/0.62 (step @p36 :rule alpha_equiv :args (@t109 (@list @t94) @t108)) % 0.38/0.62 (step @p37 :rule refl :args (@t31)) % 0.38/0.62 (step @p38 :rule refl :args (@t99)) % 0.38/0.62 (step @p39 :rule nary_cong :premises (@p38 @p37 @p36 @p35) :args (@t110)) % 0.38/0.62 (step @p40 :rule quant-miniscope-or :args ((= @t106 @t110))) % 0.38/0.62 (step @p41 :rule trans :premises (@p40 @p39)) % 0.38/0.62 (step @p42 :rule symm :premises (@p41)) % 0.38/0.62 (step @p43 :rule cong :premises (@p42) :args ((forall @t15 @t116))) % 0.38/0.62 (step @p44 :rule trans :premises (@p43 @p34)) % 0.38/0.62 (step @p45 :rule trans :premises (@p44 @p33)) % 0.38/0.62 (step @p46 :rule aci_norm :args ((= (or @t99 @t117) @t116))) % 0.38/0.62 (step @p47 :rule beta-reduce :args ((= @t121 @t117))) % 0.38/0.62 (step @p48 :rule refl :args (@t99)) % 0.38/0.62 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t122)) % 0.38/0.62 (step @p50 :rule trans :premises (@p49 @p46)) % 0.38/0.62 (step @p51 :rule cong :premises (@p50) :args (@t123)) % 0.38/0.62 (step @p52 :rule trans :premises (@p51 @p45)) % 0.38/0.62 (step @p53 :rule beta-reduce :args ((= @t127 @t123))) % 0.38/0.62 (step @p54 :rule trans :premises (@p53 @p52)) % 0.38/0.62 (step @p55 :rule cong :premises (@p54) :args ((not @t127))) % 0.38/0.62 (step @p56 :rule refl :args (@t118)) % 0.38/0.62 (step @p57 :rule refl :args (@t119)) % 0.38/0.62 (step @p58 :rule eq-symm :args (@t49 @t50)) % 0.38/0.62 (step @p59 :rule nary_cong :premises (@p58 @p57 @p56) :args (@t128)) % 0.38/0.62 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t62 (or (= @t2 @t50) @t130 @t129)) @t49) @t128))) % 0.38/0.62 (step @p61 :rule trans :premises (@p60 @p59)) % 0.38/0.62 (step @p62 :rule refl :args (@t49)) % 0.38/0.62 (step @p63 :rule refl :args (@t129)) % 0.38/0.62 (step @p64 :rule refl :args (@t130)) % 0.38/0.62 (step @p65 :rule eq-symm :args (@t50 @t2)) % 0.38/0.62 (step @p66 :rule nary_cong :premises (@p65 @p64 @p63) :args (@t131)) % 0.38/0.62 (step @p67 :rule cong :premises (@p66) :args (@t132)) % 0.38/0.62 (step @p68 :rule beta-reduce :args ((= (_ (lambda @t9 @t117) @t50) @t132))) % 0.38/0.62 (step @p69 :rule trans :premises (@p68 @p67)) % 0.38/0.62 (step @p70 :rule refl :args (@t50)) % 0.38/0.62 (step @p71 :rule aci_norm :args ((= (or (or @t31 @t115) @t133) @t117))) % 0.38/0.62 (step @p72 :rule beta-reduce :args ((= (_ @t134 @t2) @t133))) % 0.38/0.62 (step @p73 :rule refl :args (@t2)) % 0.38/0.62 (step @p74 :rule beta-reduce :args ((= @t136 @t134))) % 0.38/0.62 (step @p75 :rule ho_cong :premises (@p74 @p73)) % 0.38/0.62 (step @p76 :rule trans :premises (@p75 @p72)) % 0.38/0.62 (step @p77 :rule refl :args (@t115)) % 0.38/0.62 (step @p78 :rule eq-symm :args (@t2 @t3)) % 0.38/0.62 (step @p79 :rule nary_cong :premises (@p78 @p77) :args (@t137)) % 0.38/0.62 (step @p80 :rule beta-reduce :args ((= (_ @t139 @t3) @t137))) % 0.38/0.62 (step @p81 :rule trans :premises (@p80 @p79)) % 0.38/0.62 (step @p82 :rule refl :args (@t3)) % 0.38/0.62 (step @p83 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t138) (or (= @t3 @t138) (forall @t46 (or @t113 @t112 (_ @t4 @t3 @t138))))) @t2) @t139))) % 0.38/0.62 (step @p84 :rule refl :args (@t2)) % 0.38/0.62 (step @p85 :rule alpha_equiv :args (@t135 (@list @t2) (@list @t138))) % 0.38/0.62 (step @p86 :rule ho_cong :premises (@p85 @p84)) % 0.38/0.62 (step @p87 :rule trans :premises (@p86 @p83)) % 0.38/0.62 (step @p88 :rule ho_cong :premises (@p87 @p82)) % 0.38/0.62 (step @p89 :rule trans :premises (@p88 @p81)) % 0.38/0.62 (step @p90 :rule nary_cong :premises (@p89 @p76) :args (@t140)) % 0.38/0.62 (step @p91 :rule trans :premises (@p90 @p71)) % 0.38/0.62 (step @p92 :rule cong :premises (@p91) :args (@t141)) % 0.38/0.62 (step @p93 :rule beta-reduce :args ((= (_ @t36 @t135) @t141))) % 0.38/0.62 (step @p94 :rule trans :premises (@p93 @p92)) % 0.38/0.62 (step @p95 :rule beta-reduce :args ((= (_ @t142 @t2) @t114))) % 0.38/0.62 (step @p96 :rule beta-reduce :args ((= @t144 @t142))) % 0.38/0.62 (step @p97 :rule ho_cong :premises (@p96 @p73)) % 0.38/0.62 (step @p98 :rule trans :premises (@p97 @p95)) % 0.38/0.62 (step @p99 :rule refl :args (@t31)) % 0.38/0.62 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t145)) % 0.38/0.62 (step @p101 :rule cong :premises (@p100) :args (@t146)) % 0.38/0.62 (step @p102 :rule beta-reduce :args ((= (_ @t32 @t143) @t146))) % 0.38/0.62 (step @p103 :rule trans :premises (@p102 @p101)) % 0.38/0.62 (step @p104 :rule beta-reduce :args ((= (_ @t147 @t6) @t143))) % 0.38/0.62 (step @p105 :rule refl :args (@t6)) % 0.38/0.62 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 0.38/0.62 ; trust TRUST_THEORY_REWRITE % 0.38/0.62 (step @p106 :rule trust :premises () :args ((= (lambda @t15 (forall @t46 (or @t151 @t149 @t111))) @t147))) % 0.38/0.62 (step @p107 :rule ho_cong :premises (@p106 @p105)) % 0.38/0.62 (step @p108 :rule trans :premises (@p107 @p104)) % 0.38/0.62 (step @p109 :rule refl :args (@t32)) % 0.38/0.62 (step @p110 :rule ho_cong :premises (@p109 @p108)) % 0.38/0.62 (step @p111 :rule trans :premises (@p110 @p103)) % 0.38/0.62 (step @p112 :rule refl :args (@t36)) % 0.38/0.62 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 0.38/0.62 (step @p114 :rule trans :premises (@p113 @p94)) % 0.38/0.62 (step @p115 :rule ho_cong :premises (@p114 @p70)) % 0.38/0.62 (step @p116 :rule trans :premises (@p115 @p69)) % 0.38/0.62 (step @p117 :rule ho_cong :premises (@p116 @p62)) % 0.38/0.62 (step @p118 :rule trans :premises (@p117 @p61)) % 0.38/0.62 (step @p119 :rule refl :args (@t111)) % 0.38/0.62 (step @p120 :rule refl :args (@t5)) % 0.38/0.62 (step @p121 :rule cong :premises (@p120 @p119) :args ((= @t5 @t111))) % 0.38/0.62 (step @p122 :rule symm :premises (@p121)) % 0.38/0.62 (step @p123 :rule eq_resolve :premises (@p120 @p122)) % 0.38/0.62 (step @p124 :rule refl :args (@t149)) % 0.38/0.62 (step @p125 :rule refl :args (@t151)) % 0.38/0.62 (step @p126 :rule nary_cong :premises (@p125 @p124 @p123) :args (@t152)) % 0.38/0.62 (step @p127 :rule cong :premises (@p126) :args ((forall @t46 @t152))) % 0.38/0.62 (step @p128 :rule aci_norm :args ((= (or (or @t151 @t149) @t5) @t152))) % 0.38/0.62 (step @p129 :rule bool-and-de-morgan :args (@t150 @t148 true)) % 0.38/0.62 (step @p130 :rule nary_cong :premises (@p129 @p120) :args ((or (not @t153) @t5))) % 0.38/0.62 (step @p131 :rule trans :premises (@p130 @p128)) % 0.38/0.62 (step @p132 :rule bool-impl-elim :args (@t153 @t5)) % 0.38/0.62 (step @p133 :rule trans :premises (@p132 @p131)) % 0.38/0.62 (step @p134 :rule cong :premises (@p133) :args ((forall @t46 (=> @t153 @t5)))) % 0.38/0.62 (step @p135 :rule trans :premises (@p134 @p127)) % 0.38/0.62 (step @p136 :rule refl :args (@t5)) % 0.38/0.62 (step @p137 :rule beta-reduce :args ((= (_ @t154 @t4) @t148))) % 0.38/0.62 (step @p138 :rule refl :args (@t4)) % 0.38/0.62 (step @p139 :rule beta-reduce :args ((= @t155 @t154))) % 0.38/0.62 (step @p140 :rule ho_cong :premises (@p139 @p138)) % 0.38/0.62 (step @p141 :rule trans :premises (@p140 @p137)) % 0.38/0.62 (step @p142 :rule beta-reduce :args ((= @t158 @t150))) % 0.38/0.62 (step @p143 :rule nary_cong :premises (@p142 @p141) :args (@t159)) % 0.38/0.62 (step @p144 :rule cong :premises (@p143 @p136) :args (@t160)) % 0.38/0.62 (step @p145 :rule cong :premises (@p144) :args ((forall @t46 @t160))) % 0.38/0.62 (step @p146 :rule trans :premises (@p145 @p135)) % 0.38/0.62 (step @p147 :rule refl :args (@t98)) % 0.38/0.62 (step @p148 :rule refl :args (@t8)) % 0.38/0.62 (step @p149 :rule cong :premises (@p148 @p147) :args ((= @t8 @t98))) % 0.38/0.62 (step @p150 :rule symm :premises (@p149)) % 0.38/0.62 (step @p151 :rule eq_resolve :premises (@p148 @p150)) % 0.38/0.62 (step @p152 :rule cong :premises (@p151) :args (@t60)) % 0.38/0.62 (step @p153 :rule nary_cong :premises (@p152 @p123) :args (@t161)) % 0.38/0.62 (step @p154 :rule cong :premises (@p153) :args ((forall @t9 @t161))) % 0.38/0.62 (step @p155 :rule bool-impl-elim :args (@t8 @t5)) % 0.38/0.62 (step @p156 :rule cong :premises (@p155) :args (@t10)) % 0.38/0.62 (step @p157 :rule trans :premises (@p156 @p154)) % 0.38/0.62 (step @p158 :rule cong :premises (@p157) :args (@t12)) % 0.38/0.62 (step @p159 :rule trans :premises (@p3 @p158)) % 0.38/0.62 (step @p160 :rule ho_cong :premises (@p159 @p105)) % 0.38/0.62 (step @p161 :rule ho_cong :premises (@p160 @p138)) % 0.38/0.62 (step @p162 :rule refl :args (@t156)) % 0.38/0.62 (step @p163 :rule refl :args (@t38)) % 0.38/0.62 (step @p164 :rule cong :premises (@p163 @p162) :args ((= @t38 @t156))) % 0.38/0.62 (step @p165 :rule symm :premises (@p164)) % 0.38/0.62 (step @p166 :rule eq_resolve :premises (@p163 @p165)) % 0.38/0.62 (step @p167 :rule refl :args (@t157)) % 0.38/0.62 (step @p168 :rule refl :args (@t39)) % 0.38/0.62 (step @p169 :rule cong :premises (@p168 @p167) :args ((= @t39 @t157))) % 0.38/0.62 (step @p170 :rule symm :premises (@p169)) % 0.38/0.62 (step @p171 :rule eq_resolve :premises (@p168 @p170)) % 0.38/0.62 (step @p172 :rule cong :premises (@p171) :args (@t162)) % 0.38/0.62 (step @p173 :rule nary_cong :premises (@p152 @p172 @p166) :args (@t163)) % 0.38/0.62 (step @p174 :rule cong :premises (@p173) :args ((forall @t41 @t163))) % 0.38/0.62 (step @p175 :rule aci_norm :args ((= (or (or @t60 @t162) @t38) @t163))) % 0.38/0.62 (step @p176 :rule bool-and-de-morgan :args (@t8 @t39 true)) % 0.38/0.62 (step @p177 :rule nary_cong :premises (@p176 @p163) :args ((or (not @t40) @t38))) % 0.38/0.62 (step @p178 :rule trans :premises (@p177 @p175)) % 0.38/0.62 (step @p179 :rule bool-impl-elim :args (@t40 @t38)) % 0.38/0.62 (step @p180 :rule trans :premises (@p179 @p178)) % 0.38/0.62 (step @p181 :rule cong :premises (@p180) :args (@t42)) % 0.38/0.62 (step @p182 :rule trans :premises (@p181 @p174)) % 0.38/0.62 (step @p183 :rule cong :premises (@p182) :args (@t43)) % 0.38/0.62 (step @p184 :rule trans :premises (@p15 @p183)) % 0.38/0.62 (step @p185 :rule ho_cong :premises (@p184 @p138)) % 0.38/0.62 (step @p186 :rule nary_cong :premises (@p185 @p161) :args (@t44)) % 0.38/0.62 (step @p187 :rule cong :premises (@p186 @p136) :args (@t45)) % 0.38/0.62 (step @p188 :rule cong :premises (@p187) :args (@t47)) % 0.38/0.62 (step @p189 :rule trans :premises (@p188 @p146)) % 0.38/0.62 (step @p190 :rule cong :premises (@p189) :args (@t48)) % 0.38/0.62 (step @p191 :rule trans :premises (@p16 @p190)) % 0.38/0.62 (step @p192 :rule ho_cong :premises (@p191 @p105)) % 0.38/0.62 (step @p193 :rule ho_cong :premises (@p10 @p192)) % 0.38/0.62 (step @p194 :rule ho_cong :premises (@p14 @p193)) % 0.38/0.62 (step @p195 :rule ho_cong :premises (@p194 @p70)) % 0.38/0.62 (step @p196 :rule ho_cong :premises (@p195 @p62)) % 0.38/0.62 (step @p197 :rule trans :premises (@p196 @p118)) % 0.38/0.62 (step @p198 :rule cong :premises (@p197) :args (@t55)) % 0.38/0.62 (step @p199 :rule trans :premises (@p18 @p198)) % 0.38/0.62 (step @p200 :rule quant-merge-prenex :args ((= (forall @t19 (forall @t9 @t125)) @t126))) % 0.38/0.62 (step @p201 :rule refl :args (@t124)) % 0.38/0.62 (step @p202 :rule refl :args (@t164)) % 0.38/0.62 (step @p203 :rule cong :premises (@p202 @p201) :args ((= @t164 @t124))) % 0.38/0.62 (step @p204 :rule symm :premises (@p203)) % 0.38/0.62 (step @p205 :rule eq_resolve :premises (@p202 @p204)) % 0.38/0.62 (step @p206 :rule nary_cong :premises (@p38 @p205) :args (@t165)) % 0.38/0.62 (step @p207 :rule cong :premises (@p206) :args ((forall @t9 @t165))) % 0.38/0.62 (step @p208 :rule refl :args (@t166)) % 0.38/0.62 (step @p209 :rule nary_cong :premises (@p48 @p208) :args (@t167)) % 0.38/0.62 (step @p210 :rule cong :premises (@p209) :args (@t168)) % 0.38/0.62 (step @p211 :rule trans :premises (@p210 @p207)) % 0.38/0.62 (step @p212 :rule beta-reduce :args ((= (_ @t154 @t18) @t168))) % 0.38/0.62 (step @p213 :rule trans :premises (@p212 @p211)) % 0.38/0.62 (step @p214 :rule refl :args (@t18)) % 0.38/0.62 (step @p215 :rule ho_cong :premises (@p139 @p214)) % 0.38/0.62 (step @p216 :rule trans :premises (@p215 @p213)) % 0.38/0.62 (step @p217 :rule cong :premises (@p216) :args ((forall @t19 (_ @t155 @t18)))) % 0.38/0.62 (step @p218 :rule trans :premises (@p217 @p200)) % 0.38/0.62 (step @p219 :rule ho_cong :premises (@p160 @p214)) % 0.38/0.62 (step @p220 :rule cong :premises (@p219) :args (@t23)) % 0.38/0.62 (step @p221 :rule trans :premises (@p220 @p218)) % 0.38/0.62 (step @p222 :rule cong :premises (@p221) :args (@t24)) % 0.38/0.62 (step @p223 :rule trans :premises (@p6 @p222)) % 0.38/0.62 (step @p224 :rule ho_cong :premises (@p223 @p199)) % 0.38/0.62 (step @p225 :rule cong :premises (@p224) :args (@t1)) % 0.38/0.62 (step @p226 :rule trans :premises (@p225 @p55)) % 0.38/0.62 (step @p227 :rule eq_resolve :premises (@p1 @p226)) % 0.38/0.62 (step @p228 :rule skolemize :premises (@p227)) % 0.38/0.62 (step @p229 :rule bool-double-not-elim :args (@t173)) % 0.38/0.62 (step @p230 :rule refl :args (@t181)) % 0.38/0.62 (step @p231 :rule nary_cong :premises (@p230 @p229) :args ((or @t181 (not @t177)))) % 0.38/0.62 (step @p232 :rule cnf_or_neg :args (@t181 6)) % 0.38/0.62 (step @p233 :rule eq_resolve :premises (@p232 @p231)) % 0.38/0.62 (step @p234 :rule reordering :premises (@p233) :args ((or @t173 @t181))) % 0.38/0.62 (step @p235 :rule chain_m_resolution :premises (@p234 @p228) :args (@t173 @t182 @t183)) % 0.38/0.62 (step @p236 :rule cnf_or_neg :args (@t181 7)) % 0.38/0.62 (step @p237 :rule chain_m_resolution :premises (@p236 @p228) :args ((not @t176) @t182 @t183)) % 0.38/0.62 (step @p238 :rule bool-double-not-elim :args (@t179)) % 0.38/0.62 (step @p239 :rule nary_cong :premises (@p230 @p238) :args ((or @t181 (not @t180)))) % 0.38/0.62 (step @p240 :rule cnf_or_neg :args (@t181 0)) % 0.38/0.62 (step @p241 :rule eq_resolve :premises (@p240 @p239)) % 0.38/0.62 (step @p242 :rule reordering :premises (@p241) :args ((or @t179 @t181))) % 0.38/0.62 (step @p243 :rule chain_m_resolution :premises (@p242 @p228) :args (@t179 @t182 @t183)) % 0.38/0.62 (step @p244 :rule cnf_or_pos :args (@t184)) % 0.38/0.62 (step @p245 :rule reordering :premises (@p244) :args ((or @t180 @t176 @t185))) % 0.38/0.62 (step @p246 :rule chain_m_resolution :premises (@p245 @p243 @p237) :args (@t185 (@list false true) (@list @t179 @t176))) % 0.38/0.62 (assume-push @p253 @t173) % 0.38/0.62 (step @p248 :rule instantiate :premises (@p235) :args ((@list @t175 @t174))) % 0.38/0.62 (step-pop @p254 :rule scope :premises (@p248)) % 0.38/0.62 (step @p249 :rule process_scope :premises (@p254) :args (@t184)) % 0.38/0.62 (step @p251 :rule implies_elim :premises (@p249)) % 0.38/0.62 (step @p252 false :rule chain_m_resolution :premises (@p251 @p246 @p235) :args (false (@list true false) (@list @t184 @t173))) % 0.38/0.62 ) % 0.38/0.62 % SZS output end Proof % 0.38/0.62 % cvc5 exiting %------------------------------------------------------------------------------