%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU466^1 : 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 : n009.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 0.62s 0.83s % Output : Proof 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU466^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n009.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 17:36:29 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.62/0.83 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.62/0.83 % SZS status Theorem % 0.62/0.83 % SZS output start Proof % 0.62/0.83 ( % 0.62/0.83 (declare-sort $$unsorted 0) % 0.62/0.83 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.62/0.83 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.62/0.83 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.62/0.83 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.62/0.83 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.62/0.83 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.62/0.83 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.62/0.83 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.62/0.83 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.62/0.83 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.62/0.83 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.62/0.83 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.62/0.83 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.62/0.83 (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))))))))) % 0.62/0.83 (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)))))) % 0.62/0.83 (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)))))) % 0.62/0.83 (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))))) % 0.62/0.83 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.62/0.83 (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)))))))) % 0.62/0.83 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.62/0.83 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 0.62/0.83 (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)))))))) % 0.62/0.83 (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))))))) % 0.62/0.83 (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)))))))) % 0.62/0.83 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.62/0.83 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.62/0.83 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.62/0.83 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.62/0.83 (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)))))))) % 0.62/0.83 (define @t1 () (not (_ tptp.idem tptp.tc))) % 0.62/0.83 (define @t2 () (@var "Y" $$unsorted)) % 0.62/0.83 (define @t3 () (@var "X" $$unsorted)) % 0.62/0.83 (define @t4 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.62/0.83 (define @t5 () (_ (_ @t4 @t3) @t2)) % 0.62/0.83 (define @t6 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.62/0.83 (define @t7 () (_ @t6 @t3)) % 0.62/0.83 (define @t8 () (_ @t7 @t2)) % 0.62/0.83 (define @t9 () (@list @t3 @t2)) % 0.62/0.83 (define @t10 () (forall @t9 (=> @t8 @t5))) % 0.62/0.83 (define @t11 () (@list @t6 @t4)) % 0.62/0.83 (define @t12 () (lambda @t11 @t10)) % 0.62/0.83 (define @t13 () (_ @t6 @t2)) % 0.62/0.83 (define @t14 () (_ @t13 @t3)) % 0.62/0.83 (define @t15 () (@list @t6 @t3 @t2)) % 0.62/0.83 (define @t16 () (lambda @t15 @t14)) % 0.62/0.83 (define @t17 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.62/0.83 (define @t18 () (_ @t17 @t6)) % 0.62/0.83 (define @t19 () (_ @t17 @t18)) % 0.62/0.83 (define @t20 () (@list @t6)) % 0.62/0.83 (define @t21 () (forall @t20 (= @t19 @t18))) % 0.62/0.83 (define @t22 () (@list @t17)) % 0.62/0.83 (define @t23 () (lambda @t22 @t21)) % 0.62/0.83 (define @t24 () (_ tptp.subrel @t6)) % 0.62/0.83 (define @t25 () (lambda @t22 (forall @t20 (_ @t24 @t18)))) % 0.62/0.83 (define @t26 () (_ @t24 @t4)) % 0.62/0.83 (define @t27 () (lambda @t22 (forall @t11 (=> @t26 (_ (_ tptp.subrel @t18) (_ @t17 @t4)))))) % 0.62/0.83 (define @t28 () (_ @t7 @t3)) % 0.62/0.83 (define @t29 () (@list @t3)) % 0.62/0.83 (define @t30 () (lambda @t20 (forall @t29 @t28))) % 0.62/0.83 (define @t31 () (lambda @t20 (forall @t29 (not @t28)))) % 0.62/0.83 (define @t32 () (= @t3 @t2)) % 0.62/0.83 (define @t33 () (lambda @t15 (or @t32 @t8))) % 0.62/0.83 (define @t34 () (lambda @t20 (forall @t9 (=> @t8 @t14)))) % 0.62/0.83 (define @t35 () (lambda @t20 (forall @t9 (=> (and @t8 @t14) @t32)))) % 0.62/0.83 (define @t36 () (lambda @t20 (forall @t9 (=> @t8 (not @t14))))) % 0.62/0.83 (define @t37 () (lambda @t15 (or @t14 @t8))) % 0.62/0.83 (define @t38 () (@var "Z" $$unsorted)) % 0.62/0.83 (define @t39 () (_ @t7 @t38)) % 0.62/0.83 (define @t40 () (_ @t13 @t38)) % 0.62/0.83 (define @t41 () (and @t8 @t40)) % 0.62/0.83 (define @t42 () (@list @t3 @t2 @t38)) % 0.62/0.83 (define @t43 () (forall @t42 (=> @t41 @t39))) % 0.62/0.83 (define @t44 () (lambda @t20 @t43)) % 0.62/0.83 (define @t45 () (and (_ tptp.trans @t4) @t26)) % 0.62/0.83 (define @t46 () (=> @t45 @t5)) % 0.62/0.83 (define @t47 () (@list @t4)) % 0.62/0.83 (define @t48 () (forall @t47 @t46)) % 0.62/0.83 (define @t49 () (lambda @t15 @t48)) % 0.62/0.83 (define @t50 () (@var "__flatten_var_1" $$unsorted)) % 0.62/0.83 (define @t51 () (@var "__flatten_var_0" $$unsorted)) % 0.62/0.83 (define @t52 () (_ tptp.tc @t6)) % 0.62/0.83 (define @t53 () (_ tptp.rc @t52)) % 0.62/0.83 (define @t54 () (@list @t6 @t51 @t50)) % 0.62/0.83 (define @t55 () (lambda @t54 (_ (_ @t53 @t51) @t50))) % 0.62/0.83 (define @t56 () (lambda @t54 (_ (_ (_ tptp.sc @t53) @t51) @t50))) % 0.62/0.83 (define @t57 () (_ tptp.trans @t6)) % 0.62/0.83 (define @t58 () (lambda @t20 (and (_ tptp.refl @t6) (_ tptp.antisymm @t6) @t57))) % 0.62/0.83 (define @t59 () (lambda @t20 (and (_ tptp.asymm @t6) @t57))) % 0.62/0.83 (define @t60 () (lambda @t20 (forall @t9 (or @t32 @t8 @t14)))) % 0.62/0.83 (define @t61 () (not @t8)) % 0.62/0.83 (define @t62 () (@var "A" (-> $$unsorted Bool))) % 0.62/0.83 (define @t63 () (@list @t2)) % 0.62/0.83 (define @t64 () (_ @t62 @t3)) % 0.62/0.83 (define @t65 () (lambda @t20 (forall (@list @t62) (=> (exists @t29 @t64) (exists @t29 (and @t64 (forall @t63 (=> (_ @t62 @t2) @t61)))))))) % 0.62/0.83 (define @t66 () (@var "P" (-> $$unsorted Bool))) % 0.62/0.83 (define @t67 () (_ @t66 @t3)) % 0.62/0.83 (define @t68 () (lambda @t20 (forall (@list @t66) (=> (forall @t29 (=> (forall @t63 (=> (_ (_ @t52 @t3) @t2) (_ @t66 @t2))) @t67)) (forall @t29 @t67))))) % 0.62/0.83 (define @t69 () (lambda (@list @t6 @t3) (not (exists @t63 @t8)))) % 0.62/0.83 (define @t70 () (_ tptp.trc @t6)) % 0.62/0.83 (define @t71 () (_ @t70 @t2)) % 0.62/0.83 (define @t72 () (lambda @t15 (and (_ @t71 @t3) (_ (_ tptp.innf @t6) @t3)))) % 0.62/0.83 (define @t73 () (lambda @t20 (forall @t29 (exists @t63 (_ (_ (_ tptp.nfof @t6) @t2) @t3))))) % 0.62/0.83 (define @t74 () (_ @t70 @t3)) % 0.62/0.83 (define @t75 () (_ @t74 @t38)) % 0.62/0.83 (define @t76 () (lambda @t15 (exists (@list @t38) (and @t75 (_ @t71 @t38))))) % 0.62/0.83 (define @t77 () (_ tptp.join @t6)) % 0.62/0.83 (define @t78 () (_ (_ @t77 @t38) @t2)) % 0.62/0.83 (define @t79 () (lambda @t20 (forall @t42 (=> (and @t39 @t8) @t78)))) % 0.62/0.83 (define @t80 () (_ @t74 @t2)) % 0.62/0.83 (define @t81 () (lambda @t20 (forall @t42 (=> (and @t39 @t80) @t78)))) % 0.62/0.83 (define @t82 () (lambda @t20 (forall @t42 (=> (and @t75 @t80) @t78)))) % 0.62/0.83 (define @t83 () (lambda @t20 (forall @t9 (=> (_ (_ (_ tptp.trsc @t6) @t3) @t2) (_ (_ @t77 @t3) @t2))))) % 0.62/0.83 (define @t84 () (_ @t4 @t3 @t2)) % 0.62/0.83 (define @t85 () (@var "BOUND_VARIABLE_7746" $$unsorted)) % 0.62/0.83 (define @t86 () (@var "BOUND_VARIABLE_7744" $$unsorted)) % 0.62/0.83 (define @t87 () (_ @t4 @t86 @t85)) % 0.62/0.83 (define @t88 () (@var "BOUND_VARIABLE_8842" $$unsorted)) % 0.62/0.83 (define @t89 () (@var "BOUND_VARIABLE_8840" $$unsorted)) % 0.62/0.83 (define @t90 () (not (_ @t6 @t89 @t88))) % 0.62/0.83 (define @t91 () (@list @t89 @t88)) % 0.62/0.83 (define @t92 () (not (forall @t91 (or @t90 (_ @t4 @t89 @t88))))) % 0.62/0.83 (define @t93 () (@var "BOUND_VARIABLE_7755" $$unsorted)) % 0.62/0.83 (define @t94 () (@var "BOUND_VARIABLE_7757" $$unsorted)) % 0.62/0.83 (define @t95 () (@list @t93 @t94 @t38)) % 0.62/0.83 (define @t96 () (not (forall @t95 (or (not (_ @t4 @t93 @t94)) (not (_ @t4 @t94 @t38)) (_ @t4 @t93 @t38))))) % 0.62/0.83 (define @t97 () (forall @t47 (or @t96 @t92 @t87))) % 0.62/0.83 (define @t98 () (@var "BOUND_VARIABLE_8863" (-> $$unsorted $$unsorted Bool))) % 0.62/0.83 (define @t99 () (not @t97)) % 0.62/0.83 (define @t100 () (or @t99 @t87)) % 0.62/0.83 (define @t101 () (@list @t86 @t85)) % 0.62/0.83 (define @t102 () (forall @t101 @t100)) % 0.62/0.83 (define @t103 () (not @t102)) % 0.62/0.83 (define @t104 () (or @t96 @t103 @t84)) % 0.62/0.83 (define @t105 () (forall @t101 (or (not (_ @t6 @t86 @t85)) @t87))) % 0.62/0.83 (define @t106 () (@list @t86 @t85)) % 0.62/0.83 (define @t107 () (@list @t89 @t88)) % 0.62/0.83 (define @t108 () (not @t105)) % 0.62/0.83 (define @t109 () (or @t96 @t108 @t84)) % 0.62/0.83 (define @t110 () (forall @t47 @t109)) % 0.62/0.83 (define @t111 () (lambda @t9 @t110)) % 0.62/0.83 (define @t112 () (not (_ @t111 @t86 @t85))) % 0.62/0.83 (define @t113 () (or @t112 @t87)) % 0.62/0.83 (define @t114 () (forall @t101 @t113)) % 0.62/0.83 (define @t115 () (not @t114)) % 0.62/0.83 (define @t116 () (or @t96 @t115 @t84)) % 0.62/0.83 (define @t117 () (forall @t47 @t116)) % 0.62/0.83 (define @t118 () (lambda @t9 @t117)) % 0.62/0.83 (define @t119 () (lambda @t15 @t110)) % 0.62/0.83 (define @t120 () (_ @t119 @t6)) % 0.62/0.83 (define @t121 () (= @t120 (_ @t119 @t120))) % 0.62/0.83 (define @t122 () (forall @t20 @t121)) % 0.62/0.83 (define @t123 () (lambda @t22 (forall @t20 (= @t18 @t19)))) % 0.62/0.83 (define @t124 () (_ @t6 @t3 @t2)) % 0.62/0.83 (define @t125 () (not @t124)) % 0.62/0.83 (define @t126 () (forall @t9 (or @t125 @t84))) % 0.62/0.83 (define @t127 () (not @t126)) % 0.62/0.83 (define @t128 () (forall @t42 (or (not @t84) (not (_ @t4 @t2 @t38)) (_ @t4 @t3 @t38)))) % 0.62/0.83 (define @t129 () (not @t128)) % 0.62/0.83 (define @t130 () (lambda @t15 (forall @t47 (or @t129 @t127 @t84)))) % 0.62/0.83 (define @t131 () (or @t129 @t127 @t5)) % 0.62/0.83 (define @t132 () (and @t128 @t126)) % 0.62/0.83 (define @t133 () (lambda @t47 @t126)) % 0.62/0.83 (define @t134 () (_ (lambda @t11 @t126) @t6)) % 0.62/0.83 (define @t135 () (_ @t6 @t3 @t38)) % 0.62/0.83 (define @t136 () (_ @t6 @t2 @t38)) % 0.62/0.83 (define @t137 () (_ (lambda @t20 (forall @t42 (or @t125 (not @t136) @t135))) @t4)) % 0.62/0.83 (define @t138 () (and @t137 (_ @t134 @t4))) % 0.62/0.83 (define @t139 () (=> @t138 @t5)) % 0.62/0.83 (define @t140 () (or @t61 @t5)) % 0.62/0.83 (define @t141 () (not @t40)) % 0.62/0.83 (define @t142 () (or @t61 @t141 @t39)) % 0.62/0.83 (define @t143 () (_ @t98 @t86 @t85)) % 0.62/0.83 (define @t144 () (_ @t98 @t89 @t88)) % 0.62/0.83 (define @t145 () (not (forall @t95 (or (not (_ @t98 @t93 @t94)) (not (_ @t98 @t94 @t38)) (_ @t98 @t93 @t38))))) % 0.62/0.83 (define @t146 () (@list @t98)) % 0.62/0.83 (define @t147 () (forall @t20 (= @t111 (lambda @t9 (forall @t47 (or @t96 (not (forall @t101 (or (not (forall @t146 (or @t145 (not (forall @t91 (or @t90 @t144))) @t143))) @t87))) @t84)))))) % 0.62/0.83 (define @t148 () (@quantifiers_skolemize @t147 0)) % 0.62/0.83 (define @t149 () (not (_ @t148 @t86 @t85))) % 0.62/0.83 (define @t150 () (not (forall @t101 (or @t149 @t87)))) % 0.62/0.83 (define @t151 () (lambda @t9 (forall @t47 (or @t96 @t150 @t84)))) % 0.62/0.83 (define @t152 () (@purify @t151)) % 0.62/0.83 (define @t153 () (not (_ @t148 @t89 @t88))) % 0.62/0.83 (define @t154 () (not (forall @t91 (or @t153 @t144)))) % 0.62/0.83 (define @t155 () (not (forall @t146 (or @t145 @t154 @t143)))) % 0.62/0.83 (define @t156 () (not (forall @t101 (or @t155 @t87)))) % 0.62/0.83 (define @t157 () (lambda @t9 (forall @t47 (or @t96 @t156 @t84)))) % 0.62/0.83 (define @t158 () (@purify @t157)) % 0.62/0.83 (define @t159 () (= @t158 @t152)) % 0.62/0.83 (define @t160 () (not @t159)) % 0.62/0.83 (define @t161 () (not @t147)) % 0.62/0.83 (define @t162 () (= @t151 @t157)) % 0.62/0.83 (define @t163 () (not @t162)) % 0.62/0.83 (define @t164 () (@list true)) % 0.62/0.83 (define @t165 () (@const 0 $$unsorted)) % 0.62/0.83 (define @t166 () (@const 1 $$unsorted)) % 0.62/0.83 (define @t167 () (_ @t4 @t166 @t165)) % 0.62/0.83 (define @t168 () (forall @t47 (or @t96 @t156 @t167))) % 0.62/0.83 (define @t169 () (forall @t47 (or @t96 @t150 @t167))) % 0.62/0.83 (define @t170 () (_ @t151 @t166 @t165)) % 0.62/0.83 (define @t171 () (_ @t152 @t166 @t165)) % 0.62/0.83 (define @t172 () (_ @t157 @t166 @t165)) % 0.62/0.83 (define @t173 () (_ @t158 @t166 @t165)) % 0.62/0.83 (define @t174 () (= @t173 @t171)) % 0.62/0.83 (define @t175 () (not @t174)) % 0.62/0.83 (define @t176 () (or @t159 @t175)) % 0.62/0.83 (define @t177 () (= @t169 @t168)) % 0.62/0.83 (define @t178 () (@quantifiers_skolemize @t168 0)) % 0.62/0.83 (define @t179 () (_ @t178 @t166 @t165)) % 0.62/0.83 (define @t180 () (forall @t101 (or @t155 (_ @t178 @t86 @t85)))) % 0.62/0.83 (define @t181 () (not @t180)) % 0.62/0.83 (define @t182 () (or (not (forall @t95 (or (not (_ @t178 @t93 @t94)) (not (_ @t178 @t94 @t38)) (_ @t178 @t93 @t38)))) @t181 @t179)) % 0.62/0.83 (define @t183 () (not @t182)) % 0.62/0.83 (define @t184 () (not @t168)) % 0.62/0.83 (define @t185 () (forall @t146 (or @t145 @t154 (_ @t98 @t166 @t165)))) % 0.62/0.83 (define @t186 () (not @t185)) % 0.62/0.83 (define @t187 () (or @t186 @t179)) % 0.62/0.83 (define @t188 () (@quantifiers_skolemize @t185 0)) % 0.62/0.83 (define @t189 () (_ @t188 @t166 @t165)) % 0.62/0.83 (define @t190 () (forall @t91 (or @t153 (_ @t188 @t89 @t88)))) % 0.62/0.83 (define @t191 () (not @t190)) % 0.62/0.83 (define @t192 () (forall @t95 (or (not (_ @t188 @t93 @t94)) (not (_ @t188 @t94 @t38)) (_ @t188 @t93 @t38)))) % 0.62/0.83 (define @t193 () (not @t192)) % 0.62/0.83 (define @t194 () (or @t193 @t191 @t189)) % 0.62/0.83 (define @t195 () (not @t194)) % 0.62/0.83 (define @t196 () (forall @t101 (or @t149 (_ @t188 @t86 @t85)))) % 0.62/0.83 (define @t197 () (not @t196)) % 0.62/0.83 (define @t198 () (or @t193 @t197 @t189)) % 0.62/0.83 (define @t199 () (not @t169)) % 0.62/0.83 (define @t200 () (@quantifiers_skolemize @t169 0)) % 0.62/0.83 (define @t201 () (@list @t200)) % 0.62/0.83 (define @t202 () (_ @t200 @t166 @t165)) % 0.62/0.83 (define @t203 () (_ @t200 @t86 @t85)) % 0.62/0.83 (define @t204 () (forall @t101 (or @t155 @t203))) % 0.62/0.83 (define @t205 () (not @t204)) % 0.62/0.83 (define @t206 () (forall @t95 (or (not (_ @t200 @t93 @t94)) (not (_ @t200 @t94 @t38)) (_ @t200 @t93 @t38)))) % 0.62/0.83 (define @t207 () (not @t206)) % 0.62/0.83 (define @t208 () (or @t207 @t205 @t202)) % 0.62/0.83 (define @t209 () (@list false)) % 0.62/0.83 (define @t210 () (forall @t101 (or @t149 @t203))) % 0.62/0.83 (define @t211 () (not @t210)) % 0.62/0.83 (define @t212 () (or @t207 @t211 @t202)) % 0.62/0.83 (define @t213 () (not @t212)) % 0.62/0.83 (define @t214 () (@list @t212)) % 0.62/0.83 (define @t215 () (@quantifiers_skolemize @t204 1)) % 0.62/0.83 (define @t216 () (@quantifiers_skolemize @t204 0)) % 0.62/0.83 (define @t217 () (_ @t200 @t216 @t215)) % 0.62/0.83 (define @t218 () (forall @t146 (or @t145 @t154 (_ @t98 @t216 @t215)))) % 0.62/0.83 (define @t219 () (not @t218)) % 0.62/0.83 (define @t220 () (or @t219 @t217)) % 0.62/0.83 (define @t221 () (not @t220)) % 0.62/0.83 (define @t222 () (@list @t220)) % 0.62/0.83 (define @t223 () (forall @t91 (or @t153 (_ @t200 @t89 @t88)))) % 0.62/0.83 (define @t224 () (not @t223)) % 0.62/0.83 (define @t225 () (or @t207 @t224 @t217)) % 0.62/0.83 (define @t226 () (not @t225)) % 0.62/0.83 (assume @p1 @t1) % 0.62/0.83 (assume @p2 true) % 0.62/0.83 (step @p3 (= tptp.subrel @t12) :rule refl :args (@t12)) % 0.62/0.83 (step @p4 (= tptp.inv @t16) :rule refl :args (@t16)) % 0.62/0.83 (step @p5 (= tptp.idem @t23) :rule refl :args (@t23)) % 0.62/0.83 (step @p6 (= tptp.infl @t25) :rule refl :args (@t25)) % 0.62/0.83 (step @p7 (= tptp.mono @t27) :rule refl :args (@t27)) % 0.62/0.83 (step @p8 (= tptp.refl @t30) :rule refl :args (@t30)) % 0.62/0.83 (step @p9 (= tptp.irrefl @t31) :rule refl :args (@t31)) % 0.62/0.83 (step @p10 (= tptp.rc @t33) :rule refl :args (@t33)) % 0.62/0.83 (step @p11 (= tptp.symm @t34) :rule refl :args (@t34)) % 0.62/0.83 (step @p12 (= tptp.antisymm @t35) :rule refl :args (@t35)) % 0.62/0.83 (step @p13 (= tptp.asymm @t36) :rule refl :args (@t36)) % 0.62/0.83 (step @p14 (= tptp.sc @t37) :rule refl :args (@t37)) % 0.62/0.83 (step @p15 (= tptp.trans @t44) :rule refl :args (@t44)) % 0.62/0.83 (step @p16 (= tptp.tc @t49) :rule refl :args (@t49)) % 0.62/0.83 (step @p17 (= tptp.trc @t55) :rule refl :args (@t55)) % 0.62/0.83 (step @p18 (= tptp.trsc @t56) :rule refl :args (@t56)) % 0.62/0.83 (step @p19 (= tptp.po @t58) :rule refl :args (@t58)) % 0.62/0.83 (step @p20 (= tptp.so @t59) :rule refl :args (@t59)) % 0.62/0.83 (step @p21 (= tptp.total @t60) :rule refl :args (@t60)) % 0.62/0.83 (step @p22 (= tptp.term @t65) :rule refl :args (@t65)) % 0.62/0.83 (step @p23 (= tptp.ind @t68) :rule refl :args (@t68)) % 0.62/0.83 (step @p24 (= tptp.innf @t69) :rule refl :args (@t69)) % 0.62/0.83 (step @p25 (= tptp.nfof @t72) :rule refl :args (@t72)) % 0.62/0.83 (step @p26 (= tptp.norm @t73) :rule refl :args (@t73)) % 0.62/0.83 (step @p27 (= tptp.join @t76) :rule refl :args (@t76)) % 0.62/0.83 (step @p28 (= tptp.lconfl @t79) :rule refl :args (@t79)) % 0.62/0.83 (step @p29 (= tptp.sconfl @t81) :rule refl :args (@t81)) % 0.62/0.83 (step @p30 (= tptp.confl @t82) :rule refl :args (@t82)) % 0.62/0.83 (step @p31 (= tptp.cr @t83) :rule refl :args (@t83)) % 0.62/0.83 (step @p32 :rule refl :args (@t84)) % 0.62/0.83 (step @p33 :rule refl :args (@t87)) % 0.62/0.83 (step @p34 :rule alpha_equiv :args (@t97 (@list @t4) (@list @t98))) % 0.62/0.83 (step @p35 :rule cong :premises (@p34) :args (@t99)) % 0.62/0.83 (step @p36 :rule nary_cong :premises (@p35 @p33) :args (@t100)) % 0.62/0.83 (step @p37 :rule cong :premises (@p36) :args (@t102)) % 0.62/0.83 (step @p38 :rule cong :premises (@p37) :args (@t103)) % 0.62/0.83 (step @p39 :rule refl :args (@t96)) % 0.62/0.83 (step @p40 :rule nary_cong :premises (@p39 @p38 @p32) :args (@t104)) % 0.62/0.83 (step @p41 :rule cong :premises (@p40) :args ((forall @t47 @t104))) % 0.62/0.83 (step @p42 :rule refl :args (@t84)) % 0.62/0.83 (step @p43 :rule refl :args (@t87)) % 0.62/0.83 (step @p44 :rule beta-reduce :args ((= (_ (lambda @t9 (forall @t47 (or @t96 @t92 @t84))) @t86 @t85) @t97))) % 0.62/0.83 (step @p45 :rule refl :args (@t85)) % 0.62/0.83 (step @p46 :rule refl :args (@t86)) % 0.62/0.83 (step @p47 :rule alpha_equiv :args (@t105 @t106 @t107)) % 0.62/0.83 (step @p48 :rule cong :premises (@p47) :args (@t108)) % 0.62/0.83 (step @p49 :rule nary_cong :premises (@p39 @p48 @p32) :args (@t109)) % 0.62/0.83 (step @p50 :rule cong :premises (@p49) :args (@t110)) % 0.62/0.83 (step @p51 :rule cong :premises (@p50) :args (@t111)) % 0.62/0.83 (step @p52 :rule ho_cong :premises (@p51 @p46 @p45)) % 0.62/0.83 (step @p53 :rule trans :premises (@p52 @p44)) % 0.62/0.83 (step @p54 :rule cong :premises (@p53) :args (@t112)) % 0.62/0.83 (step @p55 :rule nary_cong :premises (@p54 @p43) :args (@t113)) % 0.62/0.83 (step @p56 :rule cong :premises (@p55) :args (@t114)) % 0.62/0.83 (step @p57 :rule cong :premises (@p56) :args (@t115)) % 0.62/0.83 (step @p58 :rule refl :args (@t96)) % 0.62/0.83 (step @p59 :rule nary_cong :premises (@p58 @p57 @p42) :args (@t116)) % 0.62/0.83 (step @p60 :rule cong :premises (@p59) :args (@t117)) % 0.62/0.83 (step @p61 :rule trans :premises (@p60 @p41)) % 0.62/0.83 (step @p62 :rule cong :premises (@p61) :args (@t118)) % 0.62/0.83 (step @p63 :rule beta-reduce :args ((= (_ @t119 @t111) @t118))) % 0.62/0.83 (step @p64 :rule trans :premises (@p63 @p62)) % 0.62/0.83 (step @p65 :rule beta-reduce :args ((= @t120 @t111))) % 0.62/0.83 (step @p66 :rule refl :args (@t119)) % 0.62/0.83 (step @p67 :rule ho_cong :premises (@p66 @p65)) % 0.62/0.83 (step @p68 :rule trans :premises (@p67 @p64)) % 0.62/0.83 (step @p69 :rule cong :premises (@p65 @p68) :args (@t121)) % 0.62/0.83 (step @p70 :rule cong :premises (@p69) :args (@t122)) % 0.62/0.83 (step @p71 :rule beta-reduce :args ((= (_ @t123 @t119) @t122))) % 0.62/0.83 (step @p72 :rule trans :premises (@p71 @p70)) % 0.62/0.83 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 0.62/0.83 ; trust TRUST_THEORY_REWRITE % 0.62/0.83 (step @p73 :rule trust :premises () :args ((= @t130 @t119))) % 0.62/0.83 (step @p74 :rule refl :args (@t123)) % 0.62/0.83 (step @p75 :rule ho_cong :premises (@p74 @p73)) % 0.62/0.83 (step @p76 :rule trans :premises (@p75 @p72)) % 0.62/0.83 (step @p77 :rule cong :premises (@p76) :args ((not (_ @t123 @t130)))) % 0.62/0.83 (step @p78 :rule refl :args (@t84)) % 0.62/0.83 (step @p79 :rule refl :args (@t5)) % 0.62/0.83 (step @p80 :rule cong :premises (@p79 @p78) :args ((= @t5 @t84))) % 0.62/0.83 (step @p81 :rule symm :premises (@p80)) % 0.62/0.83 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.62/0.83 (step @p83 :rule refl :args (@t127)) % 0.62/0.83 (step @p84 :rule refl :args (@t129)) % 0.62/0.83 (step @p85 :rule nary_cong :premises (@p84 @p83 @p82) :args (@t131)) % 0.62/0.83 (step @p86 :rule cong :premises (@p85) :args ((forall @t47 @t131))) % 0.62/0.83 (step @p87 :rule aci_norm :args ((= (or (or @t129 @t127) @t5) @t131))) % 0.62/0.83 (step @p88 :rule bool-and-de-morgan 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output end Proof % 0.62/0.84 % cvc5 exiting %------------------------------------------------------------------------------