%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU494^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : 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 08:51:56 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 : SEU494^1 : TPTP v9.2.1. Released v3.6.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n029.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 17:39:02 EDT 2026 % 0.18/0.35 % CPUTime : % 0.32/0.50 %----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 $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.38/0.63 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.38/0.63 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.38/0.63 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.63 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.38/0.63 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.63 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.63 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.38/0.63 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.38/0.63 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.63 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.38/0.63 (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))))))))) % 0.38/0.63 (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)))))) % 0.38/0.63 (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)))))) % 0.38/0.63 (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))))) % 0.38/0.63 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.38/0.63 (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)))))))) % 0.38/0.63 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.38/0.63 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 0.38/0.63 (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)))))))) % 0.38/0.63 (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))))))) % 0.38/0.63 (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)))))))) % 0.38/0.63 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.38/0.63 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.38/0.63 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.38/0.63 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.38/0.63 (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)))))))) % 0.38/0.63 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.63 (define @t2 () (=> (_ tptp.so @t1) (_ tptp.so (_ tptp.inv @t1)))) % 0.38/0.63 (define @t3 () (@list @t1)) % 0.38/0.63 (define @t4 () (forall @t3 @t2)) % 0.38/0.63 (define @t5 () (not @t4)) % 0.38/0.63 (define @t6 () (@var "Y" $$unsorted)) % 0.38/0.63 (define @t7 () (@var "X" $$unsorted)) % 0.38/0.63 (define @t8 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.38/0.63 (define @t9 () (_ (_ @t8 @t7) @t6)) % 0.38/0.63 (define @t10 () (_ @t1 @t7)) % 0.38/0.63 (define @t11 () (_ @t10 @t6)) % 0.38/0.63 (define @t12 () (@list @t7 @t6)) % 0.38/0.63 (define @t13 () (@list @t1 @t8)) % 0.38/0.63 (define @t14 () (lambda @t13 (forall @t12 (=> @t11 @t9)))) % 0.38/0.63 (define @t15 () (_ @t1 @t6)) % 0.38/0.63 (define @t16 () (_ @t15 @t7)) % 0.38/0.63 (define @t17 () (@list @t1 @t7 @t6)) % 0.38/0.63 (define @t18 () (lambda @t17 @t16)) % 0.38/0.63 (define @t19 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.38/0.63 (define @t20 () (_ @t19 @t1)) % 0.38/0.63 (define @t21 () (@list @t19)) % 0.38/0.63 (define @t22 () (lambda @t21 (forall @t3 (= (_ @t19 @t20) @t20)))) % 0.38/0.63 (define @t23 () (_ tptp.subrel @t1)) % 0.38/0.63 (define @t24 () (lambda @t21 (forall @t3 (_ @t23 @t20)))) % 0.38/0.63 (define @t25 () (_ @t23 @t8)) % 0.38/0.63 (define @t26 () (lambda @t21 (forall @t13 (=> @t25 (_ (_ tptp.subrel @t20) (_ @t19 @t8)))))) % 0.38/0.63 (define @t27 () (_ @t10 @t7)) % 0.38/0.63 (define @t28 () (@list @t7)) % 0.38/0.63 (define @t29 () (lambda @t3 (forall @t28 @t27))) % 0.38/0.63 (define @t30 () (lambda @t3 (forall @t28 (not @t27)))) % 0.38/0.63 (define @t31 () (= @t7 @t6)) % 0.38/0.63 (define @t32 () (lambda @t17 (or @t31 @t11))) % 0.38/0.63 (define @t33 () (lambda @t3 (forall @t12 (=> @t11 @t16)))) % 0.38/0.63 (define @t34 () (lambda @t3 (forall @t12 (=> (and @t11 @t16) @t31)))) % 0.38/0.63 (define @t35 () (not @t16)) % 0.38/0.63 (define @t36 () (forall @t12 (=> @t11 @t35))) % 0.38/0.63 (define @t37 () (lambda @t3 @t36)) % 0.38/0.63 (define @t38 () (lambda @t17 (or @t16 @t11))) % 0.38/0.63 (define @t39 () (@var "Z" $$unsorted)) % 0.38/0.63 (define @t40 () (_ @t10 @t39)) % 0.38/0.63 (define @t41 () (_ @t15 @t39)) % 0.38/0.63 (define @t42 () (and @t11 @t41)) % 0.38/0.63 (define @t43 () (@list @t7 @t6 @t39)) % 0.38/0.63 (define @t44 () (forall @t43 (=> @t42 @t40))) % 0.38/0.63 (define @t45 () (lambda @t3 @t44)) % 0.38/0.63 (define @t46 () (lambda @t17 (forall (@list @t8) (=> (and (_ tptp.trans @t8) @t25) @t9)))) % 0.38/0.63 (define @t47 () (@var "__flatten_var_1" $$unsorted)) % 0.38/0.63 (define @t48 () (@var "__flatten_var_0" $$unsorted)) % 0.38/0.63 (define @t49 () (_ tptp.tc @t1)) % 0.38/0.63 (define @t50 () (_ tptp.rc @t49)) % 0.38/0.63 (define @t51 () (@list @t1 @t48 @t47)) % 0.38/0.63 (define @t52 () (lambda @t51 (_ (_ @t50 @t48) @t47))) % 0.38/0.63 (define @t53 () (lambda @t51 (_ (_ (_ tptp.sc @t50) @t48) @t47))) % 0.38/0.63 (define @t54 () (_ tptp.trans @t1)) % 0.38/0.63 (define @t55 () (lambda @t3 (and (_ tptp.refl @t1) (_ tptp.antisymm @t1) @t54))) % 0.38/0.63 (define @t56 () (and (_ tptp.asymm @t1) @t54)) % 0.38/0.63 (define @t57 () (lambda @t3 @t56)) % 0.38/0.63 (define @t58 () (lambda @t3 (forall @t12 (or @t31 @t11 @t16)))) % 0.38/0.63 (define @t59 () (not @t11)) % 0.38/0.63 (define @t60 () (@var "A" (-> $$unsorted Bool))) % 0.38/0.63 (define @t61 () (@list @t6)) % 0.38/0.63 (define @t62 () (_ @t60 @t7)) % 0.38/0.63 (define @t63 () (lambda @t3 (forall (@list @t60) (=> (exists @t28 @t62) (exists @t28 (and @t62 (forall @t61 (=> (_ @t60 @t6) @t59)))))))) % 0.38/0.63 (define @t64 () (@var "P" (-> $$unsorted Bool))) % 0.38/0.63 (define @t65 () (_ @t64 @t7)) % 0.38/0.63 (define @t66 () (lambda @t3 (forall (@list @t64) (=> (forall @t28 (=> (forall @t61 (=> (_ (_ @t49 @t7) @t6) (_ @t64 @t6))) @t65)) (forall @t28 @t65))))) % 0.38/0.63 (define @t67 () (lambda (@list @t1 @t7) (not (exists @t61 @t11)))) % 0.38/0.63 (define @t68 () (_ tptp.trc @t1)) % 0.38/0.63 (define @t69 () (_ @t68 @t6)) % 0.38/0.63 (define @t70 () (lambda @t17 (and (_ @t69 @t7) (_ (_ tptp.innf @t1) @t7)))) % 0.38/0.63 (define @t71 () (lambda @t3 (forall @t28 (exists @t61 (_ (_ (_ tptp.nfof @t1) @t6) @t7))))) % 0.38/0.63 (define @t72 () (_ @t68 @t7)) % 0.38/0.63 (define @t73 () (_ @t72 @t39)) % 0.38/0.63 (define @t74 () (lambda @t17 (exists (@list @t39) (and @t73 (_ @t69 @t39))))) % 0.38/0.63 (define @t75 () (_ tptp.join @t1)) % 0.38/0.63 (define @t76 () (_ (_ @t75 @t39) @t6)) % 0.38/0.63 (define @t77 () (lambda @t3 (forall @t43 (=> (and @t40 @t11) @t76)))) % 0.38/0.63 (define @t78 () (_ @t72 @t6)) % 0.38/0.63 (define @t79 () (lambda @t3 (forall @t43 (=> (and @t40 @t78) @t76)))) % 0.38/0.63 (define @t80 () (lambda @t3 (forall @t43 (=> (and @t73 @t78) @t76)))) % 0.38/0.63 (define @t81 () (lambda @t3 (forall @t12 (=> (_ (_ (_ tptp.trsc @t1) @t7) @t6) (_ (_ @t75 @t7) @t6))))) % 0.38/0.63 (define @t82 () (@var "BOUND_VARIABLE_8883" $$unsorted)) % 0.38/0.63 (define @t83 () (@var "BOUND_VARIABLE_8887" $$unsorted)) % 0.38/0.63 (define @t84 () (@var "BOUND_VARIABLE_8885" $$unsorted)) % 0.38/0.63 (define @t85 () (or (not (_ @t1 @t84 @t82)) (not (_ @t1 @t83 @t84)) (_ @t1 @t83 @t82))) % 0.38/0.63 (define @t86 () (@var "BOUND_VARIABLE_8876" $$unsorted)) % 0.38/0.63 (define @t87 () (@var "BOUND_VARIABLE_8874" $$unsorted)) % 0.38/0.63 (define @t88 () (or (not (_ @t1 @t86 @t87)) (not (_ @t1 @t87 @t86)))) % 0.38/0.63 (define @t89 () (and @t88 @t85)) % 0.38/0.63 (define @t90 () (_ @t1 @t7 @t39)) % 0.38/0.63 (define @t91 () (_ @t1 @t6 @t39)) % 0.38/0.63 (define @t92 () (_ @t1 @t7 @t6)) % 0.38/0.63 (define @t93 () (not @t92)) % 0.38/0.63 (define @t94 () (forall @t43 (or @t93 (not @t91) @t90))) % 0.38/0.63 (define @t95 () (not @t94)) % 0.38/0.63 (define @t96 () (_ @t1 @t6 @t7)) % 0.38/0.63 (define @t97 () (not @t96)) % 0.38/0.63 (define @t98 () (forall @t12 (or @t93 @t97))) % 0.38/0.63 (define @t99 () (not @t98)) % 0.38/0.63 (define @t100 () (or @t99 @t95 @t89)) % 0.38/0.63 (define @t101 () (forall (@list @t1 @t87 @t86 @t82 @t84 @t83) @t100)) % 0.38/0.63 (define @t102 () (@list @t87 @t86 @t82 @t84 @t83)) % 0.38/0.63 (define @t103 () (forall @t102 @t100)) % 0.38/0.63 (define @t104 () (forall (@list @t82 @t84 @t83) @t85)) % 0.38/0.63 (define @t105 () (forall @t102 @t85)) % 0.38/0.63 (define @t106 () (forall (@list @t87 @t86) @t88)) % 0.38/0.63 (define @t107 () (forall @t102 @t88)) % 0.38/0.63 (define @t108 () (and @t107 @t105)) % 0.38/0.63 (define @t109 () (forall @t102 @t89)) % 0.38/0.63 (define @t110 () (or @t99 @t95 @t109)) % 0.38/0.63 (define @t111 () (_ @t1 @t39 @t7)) % 0.38/0.63 (define @t112 () (_ @t1 @t39 @t6)) % 0.38/0.63 (define @t113 () (and (forall @t12 (or @t97 @t93)) (forall @t43 (or @t97 (not @t112) @t111)))) % 0.38/0.63 (define @t114 () (or @t99 @t95 @t113)) % 0.38/0.63 (define @t115 () (and @t98 @t94)) % 0.38/0.63 (define @t116 () (_ @t1 @t39)) % 0.38/0.63 (define @t117 () (_ @t116 @t7)) % 0.38/0.63 (define @t118 () (_ @t116 @t6)) % 0.38/0.63 (define @t119 () (not @t118)) % 0.38/0.63 (define @t120 () (or @t35 @t119 @t117)) % 0.38/0.63 (define @t121 () (lambda @t12 @t16)) % 0.38/0.63 (define @t122 () (_ @t121 @t7 @t39)) % 0.38/0.63 (define @t123 () (_ @t121 @t6 @t39)) % 0.38/0.63 (define @t124 () (not @t123)) % 0.38/0.63 (define @t125 () (_ @t121 @t7 @t6)) % 0.38/0.63 (define @t126 () (not @t125)) % 0.38/0.63 (define @t127 () (or @t126 @t124 @t122)) % 0.38/0.63 (define @t128 () (forall @t43 @t127)) % 0.38/0.63 (define @t129 () (or @t35 @t59)) % 0.38/0.63 (define @t130 () (_ @t121 @t6 @t7)) % 0.38/0.63 (define @t131 () (not @t130)) % 0.38/0.63 (define @t132 () (or @t126 @t131)) % 0.38/0.63 (define @t133 () (forall @t12 @t132)) % 0.38/0.63 (define @t134 () (and @t133 @t128)) % 0.38/0.63 (define @t135 () (lambda @t3 @t115)) % 0.38/0.63 (define @t136 () (_ @t18 @t1)) % 0.38/0.63 (define @t137 () (_ @t135 @t1)) % 0.38/0.63 (define @t138 () (=> @t137 (_ @t135 @t136))) % 0.38/0.63 (define @t139 () (forall @t3 @t138)) % 0.38/0.63 (define @t140 () (_ (lambda @t3 @t94) @t1)) % 0.38/0.63 (define @t141 () (_ (lambda @t3 @t98) @t1)) % 0.38/0.63 (define @t142 () (not @t41)) % 0.38/0.63 (define @t143 () (or @t59 @t142 @t40)) % 0.38/0.63 (define @t144 () (or @t59 @t35)) % 0.38/0.63 (define @t145 () (@quantifiers_skolemize @t101 0)) % 0.38/0.63 (define @t146 () (not (_ @t145 @t7 @t6))) % 0.38/0.63 (define @t147 () (forall @t12 (or @t146 (not (_ @t145 @t6 @t7))))) % 0.38/0.63 (define @t148 () (@quantifiers_skolemize @t101 3)) % 0.38/0.63 (define @t149 () (@quantifiers_skolemize @t101 5)) % 0.38/0.63 (define @t150 () (_ @t145 @t149 @t148)) % 0.38/0.63 (define @t151 () (@quantifiers_skolemize @t101 4)) % 0.38/0.63 (define @t152 () (_ @t145 @t149 @t151)) % 0.38/0.63 (define @t153 () (not @t152)) % 0.38/0.63 (define @t154 () (_ @t145 @t151 @t148)) % 0.38/0.63 (define @t155 () (not @t154)) % 0.38/0.63 (define @t156 () (or @t155 @t153 @t150)) % 0.38/0.63 (define @t157 () (@quantifiers_skolemize @t101 2)) % 0.38/0.63 (define @t158 () (@quantifiers_skolemize @t101 1)) % 0.38/0.63 (define @t159 () (_ @t145 @t158 @t157)) % 0.38/0.63 (define @t160 () (not @t159)) % 0.38/0.63 (define @t161 () (_ @t145 @t157 @t158)) % 0.38/0.63 (define @t162 () (not @t161)) % 0.38/0.63 (define @t163 () (or @t162 @t160)) % 0.38/0.63 (define @t164 () (and @t163 @t156)) % 0.38/0.63 (define @t165 () (forall @t43 (or @t146 (not (_ @t145 @t6 @t39)) (_ @t145 @t7 @t39)))) % 0.38/0.63 (define @t166 () (not @t165)) % 0.38/0.63 (define @t167 () (not @t147)) % 0.38/0.63 (define @t168 () (or @t167 @t166 @t164)) % 0.38/0.63 (define @t169 () (@list true)) % 0.38/0.63 (define @t170 () (@list @t168)) % 0.38/0.63 (define @t171 () (or @t153 @t155 @t150)) % 0.38/0.63 (define @t172 () (@list @t163)) % 0.38/0.63 (define @t173 () (or @t160 @t162)) % 0.38/0.63 (assume @p1 @t5) % 0.38/0.63 (assume @p2 true) % 0.38/0.63 (step @p3 (= tptp.subrel @t14) :rule refl :args (@t14)) % 0.38/0.63 (step @p4 (= tptp.inv @t18) :rule refl :args (@t18)) % 0.38/0.63 (step @p5 (= tptp.idem @t22) :rule refl :args (@t22)) % 0.38/0.63 (step @p6 (= tptp.infl @t24) :rule refl :args (@t24)) % 0.38/0.63 (step @p7 (= tptp.mono @t26) :rule refl :args (@t26)) % 0.38/0.63 (step @p8 (= tptp.refl @t29) :rule refl :args (@t29)) % 0.38/0.63 (step @p9 (= tptp.irrefl @t30) :rule refl :args (@t30)) % 0.38/0.63 (step @p10 (= tptp.rc @t32) :rule refl :args (@t32)) % 0.38/0.63 (step @p11 (= tptp.symm @t33) :rule refl :args (@t33)) % 0.38/0.63 (step @p12 (= tptp.antisymm @t34) :rule refl :args (@t34)) % 0.38/0.63 (step @p13 (= tptp.asymm @t37) :rule refl :args (@t37)) % 0.38/0.63 (step @p14 (= tptp.sc @t38) :rule refl :args (@t38)) % 0.38/0.63 (step @p15 (= tptp.trans @t45) :rule refl :args (@t45)) % 0.38/0.63 (step @p16 (= tptp.tc @t46) :rule refl :args (@t46)) % 0.38/0.63 (step @p17 (= tptp.trc @t52) :rule refl :args (@t52)) % 0.38/0.63 (step @p18 (= tptp.trsc @t53) :rule refl :args (@t53)) % 0.38/0.63 (step @p19 (= tptp.po @t55) :rule refl :args (@t55)) % 0.38/0.63 (step @p20 (= tptp.so @t57) :rule refl :args (@t57)) % 0.38/0.63 (step @p21 (= tptp.total @t58) :rule refl :args (@t58)) % 0.38/0.63 (step @p22 (= tptp.term @t63) :rule refl :args (@t63)) % 0.38/0.63 (step @p23 (= tptp.ind @t66) :rule refl :args (@t66)) % 0.38/0.63 (step @p24 (= tptp.innf @t67) :rule refl :args (@t67)) % 0.38/0.63 (step @p25 (= tptp.nfof @t70) :rule refl :args (@t70)) % 0.38/0.63 (step @p26 (= tptp.norm @t71) :rule refl :args (@t71)) % 0.38/0.63 (step @p27 (= tptp.join @t74) :rule refl :args (@t74)) % 0.38/0.63 (step @p28 (= tptp.lconfl @t77) :rule refl :args (@t77)) % 0.38/0.63 (step @p29 (= tptp.sconfl @t79) :rule refl :args (@t79)) % 0.38/0.63 (step @p30 (= tptp.confl @t80) :rule refl :args (@t80)) % 0.38/0.63 (step @p31 (= tptp.cr @t81) :rule refl :args (@t81)) % 0.38/0.63 (step @p32 :rule quant-merge-prenex :args ((= (forall @t3 @t103) @t101))) % 0.38/0.63 (step @p33 :rule alpha_equiv :args (@t104 (@list @t82 @t84 @t83) (@list @t7 @t6 @t39))) % 0.38/0.63 (step @p34 :rule quant-unused-vars :args ((= @t105 @t104))) % 0.38/0.63 (step @p35 :rule trans :premises (@p34 @p33)) % 0.38/0.63 (step @p36 :rule alpha_equiv :args (@t106 (@list @t87 @t86) (@list @t7 @t6))) % 0.38/0.63 (step @p37 :rule quant-unused-vars :args ((= @t107 @t106))) % 0.38/0.63 (step @p38 :rule trans :premises (@p37 @p36)) % 0.38/0.63 (step @p39 :rule nary_cong :premises (@p38 @p35) :args (@t108)) % 0.38/0.63 (step @p40 :rule quant-miniscope-and :args ((= @t109 @t108))) % 0.38/0.63 (step @p41 :rule trans :premises (@p40 @p39)) % 0.38/0.63 (step @p42 :rule refl :args (@t95)) % 0.38/0.63 (step @p43 :rule refl :args (@t99)) % 0.38/0.63 (step @p44 :rule nary_cong :premises (@p43 @p42 @p41) :args (@t110)) % 0.38/0.63 (step @p45 :rule quant-miniscope-or :args ((= @t103 @t110))) % 0.38/0.63 (step @p46 :rule trans :premises (@p45 @p44)) % 0.38/0.63 (step @p47 :rule symm :premises (@p46)) % 0.38/0.63 (step @p48 :rule 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eq_resolve :premises (@p60 @p62)) % 0.38/0.63 (step @p64 :rule refl :args (@t112)) % 0.38/0.63 (step @p65 :rule refl :args (@t118)) % 0.38/0.63 (step @p66 :rule cong :premises (@p65 @p64) :args ((= @t118 @t112))) % 0.38/0.63 (step @p67 :rule symm :premises (@p66)) % 0.38/0.63 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.38/0.63 (step @p69 :rule cong :premises (@p68) :args (@t119)) % 0.38/0.63 (step @p70 :rule refl :args (@t96)) % 0.38/0.63 (step @p71 :rule refl :args (@t16)) % 0.38/0.63 (step @p72 :rule cong :premises (@p71 @p70) :args ((= @t16 @t96))) % 0.38/0.63 (step @p73 :rule symm :premises (@p72)) % 0.38/0.63 (step @p74 :rule eq_resolve :premises (@p71 @p73)) % 0.38/0.63 (step @p75 :rule cong :premises (@p74) :args (@t35)) % 0.38/0.63 (step @p76 :rule nary_cong :premises (@p75 @p69 @p63) :args (@t120)) % 0.38/0.63 (step @p77 :rule cong :premises (@p76) :args ((forall @t43 @t120))) % 0.38/0.63 (step @p78 :rule beta-reduce :args ((= @t122 @t117))) % 0.38/0.63 (step @p79 :rule beta-reduce :args ((= @t123 @t118))) % 0.38/0.63 (step @p80 :rule cong :premises (@p79) :args (@t124)) % 0.38/0.63 (step @p81 :rule beta-reduce :args ((= @t125 @t16))) % 0.38/0.63 (step @p82 :rule cong :premises (@p81) :args (@t126)) % 0.38/0.63 (step @p83 :rule nary_cong :premises (@p82 @p80 @p78) :args (@t127)) % 0.38/0.63 (step @p84 :rule cong :premises (@p83) :args (@t128)) % 0.38/0.63 (step @p85 :rule trans :premises (@p84 @p77)) % 0.38/0.63 (step @p86 :rule refl :args (@t92)) % 0.38/0.63 (step @p87 :rule refl :args (@t11)) % 0.38/0.63 (step @p88 :rule cong :premises (@p87 @p86) :args ((= @t11 @t92))) % 0.38/0.63 (step @p89 :rule symm :premises (@p88)) % 0.38/0.63 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 0.38/0.63 (step @p91 :rule cong :premises (@p90) :args (@t59)) % 0.38/0.63 (step @p92 :rule nary_cong :premises (@p75 @p91) :args (@t129)) % 0.38/0.63 (step @p93 :rule cong :premises (@p92) :args ((forall @t12 @t129))) % 0.38/0.63 (step @p94 :rule beta-reduce 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(@p138 @p111)) % 0.38/0.63 (step @p140 :rule nary_cong :premises (@p91 @p75) :args (@t144)) % 0.38/0.63 (step @p141 :rule cong :premises (@p140) :args ((forall @t12 @t144))) % 0.38/0.63 (step @p142 :rule bool-impl-elim :args (@t11 @t35)) % 0.38/0.63 (step @p143 :rule cong :premises (@p142) :args (@t36)) % 0.38/0.63 (step @p144 :rule trans :premises (@p143 @p141)) % 0.38/0.63 (step @p145 :rule cong :premises (@p144) :args (@t37)) % 0.38/0.63 (step @p146 :rule trans :premises (@p13 @p145)) % 0.38/0.63 (step @p147 :rule ho_cong :premises (@p146 @p111)) % 0.38/0.63 (step @p148 :rule nary_cong :premises (@p147 @p139) :args (@t56)) % 0.38/0.63 (step @p149 :rule trans :premises (@p148 @p115)) % 0.38/0.63 (step @p150 :rule cong :premises (@p149) :args (@t57)) % 0.38/0.63 (step @p151 :rule trans :premises (@p20 @p150)) % 0.38/0.63 (step @p152 :rule ho_cong :premises (@p151 @p112)) % 0.38/0.63 (step @p153 :rule ho_cong :premises (@p151 @p111)) % 0.38/0.63 (step @p154 :rule cong :premises (@p153 @p152) :args (@t2)) % 0.38/0.63 (step @p155 :rule cong :premises (@p154) :args (@t4)) % 0.38/0.63 (step @p156 :rule cong :premises (@p155) :args (@t5)) % 0.38/0.63 (step @p157 :rule trans :premises (@p156 @p110)) % 0.38/0.63 (step @p158 :rule eq_resolve :premises (@p1 @p157)) % 0.38/0.63 (step @p159 :rule skolemize :premises (@p158)) % 0.38/0.63 (step @p160 :rule bool-double-not-elim :args (@t147)) % 0.38/0.63 (step @p161 :rule refl :args (@t168)) % 0.38/0.63 (step @p162 :rule nary_cong :premises (@p161 @p160) :args ((or @t168 (not @t167)))) % 0.38/0.63 (step @p163 :rule cnf_or_neg :args (@t168 0)) % 0.38/0.63 (step @p164 :rule eq_resolve :premises (@p163 @p162)) % 0.38/0.63 (step @p165 :rule reordering :premises (@p164) :args ((or @t147 @t168))) % 0.38/0.63 (step @p166 :rule chain_m_resolution :premises (@p165 @p159) :args (@t147 @t169 @t170)) % 0.38/0.63 (step @p167 :rule instantiate :premises (@p166) :args ((@list @t158 @t157))) % 0.38/0.63 (step @p168 :rule bool-double-not-elim :args (@t154)) % 0.38/0.63 (step @p169 :rule refl :args (@t156)) % 0.38/0.63 (step @p170 :rule nary_cong :premises (@p169 @p168) :args ((or @t156 (not @t155)))) % 0.38/0.63 (step @p171 :rule cnf_or_neg :args (@t156 0)) % 0.38/0.63 (step @p172 :rule eq_resolve :premises (@p171 @p170)) % 0.38/0.63 (step @p173 :rule reordering :premises (@p172) :args ((or @t154 @t156))) % 0.38/0.63 (step @p174 :rule bool-double-not-elim :args (@t152)) % 0.38/0.63 (step @p175 :rule nary_cong :premises (@p169 @p174) :args ((or @t156 (not @t153)))) % 0.38/0.63 (step @p176 :rule cnf_or_neg :args (@t156 1)) % 0.38/0.63 (step @p177 :rule eq_resolve :premises (@p176 @p175)) % 0.38/0.63 (step @p178 :rule reordering :premises (@p177) :args ((or @t152 @t156))) % 0.38/0.63 (step @p179 :rule cnf_or_neg :args (@t156 2)) % 0.38/0.63 (step @p180 :rule bool-double-not-elim :args (@t165)) % 0.38/0.63 (step @p181 :rule nary_cong :premises (@p161 @p180) :args ((or @t168 (not @t166)))) % 0.38/0.63 (step @p182 :rule cnf_or_neg :args (@t168 1)) % 0.38/0.63 (step @p183 :rule eq_resolve :premises (@p182 @p181)) % 0.38/0.63 (step @p184 :rule reordering :premises (@p183) :args ((or @t165 @t168))) % 0.38/0.63 (step @p185 :rule chain_m_resolution :premises (@p184 @p159) :args (@t165 @t169 @t170)) % 0.38/0.63 (step @p186 :rule instantiate :premises (@p185) :args ((@list @t149 @t151 @t148))) % 0.38/0.63 (step @p187 :rule cnf_or_pos :args (@t171)) % 0.38/0.63 (step @p188 :rule reordering :premises (@p187) :args ((or @t155 @t153 @t150 (not @t171)))) % 0.38/0.63 (step @p189 :rule chain_m_resolution :premises (@p188 @p186 @p179 @p178 @p173) :args (@t156 (@list false true false false) (@list @t171 @t150 @t152 @t154))) % 0.38/0.63 (step @p190 :rule cnf_or_neg :args (@t168 2)) % 0.38/0.63 (step @p191 :rule chain_m_resolution :premises (@p190 @p159) :args ((not @t164) @t169 @t170)) % 0.38/0.63 (step @p192 :rule cnf_and_neg :args (@t164)) % 0.38/0.63 (step @p193 :rule chain_m_resolution :premises (@p192 @p191 @p189) :args ((not @t163) (@list true false) (@list @t164 @t156))) % 0.38/0.63 (step @p194 :rule bool-double-not-elim :args (@t161)) % 0.38/0.63 (step @p195 :rule refl :args (@t163)) % 0.38/0.63 (step @p196 :rule nary_cong :premises (@p195 @p194) :args ((or @t163 (not @t162)))) % 0.38/0.63 (step @p197 :rule cnf_or_neg :args (@t163 0)) % 0.38/0.63 (step @p198 :rule eq_resolve :premises (@p197 @p196)) % 0.38/0.63 (step @p199 :rule reordering :premises (@p198) :args ((or @t161 @t163))) % 0.38/0.63 (step @p200 :rule chain_m_resolution :premises (@p199 @p193) :args (@t161 @t169 @t172)) % 0.38/0.63 (step @p201 :rule bool-double-not-elim :args (@t159)) % 0.38/0.63 (step @p202 :rule nary_cong :premises (@p195 @p201) :args ((or @t163 (not @t160)))) % 0.38/0.63 (step @p203 :rule cnf_or_neg :args (@t163 1)) % 0.38/0.63 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.38/0.63 (step @p205 :rule reordering :premises (@p204) :args ((or @t159 @t163))) % 0.38/0.63 (step @p206 :rule chain_m_resolution :premises (@p205 @p193) :args (@t159 @t169 @t172)) % 0.38/0.63 (step @p207 :rule cnf_or_pos :args (@t173)) % 0.38/0.63 (step @p208 :rule reordering :premises (@p207) :args ((or @t162 @t160 (not @t173)))) % 0.38/0.63 (step @p209 false :rule chain_m_resolution :premises (@p208 @p206 @p200 @p167) :args (false (@list false false false) (@list @t159 @t161 @t173))) % 0.38/0.63 ) % 0.38/0.63 % SZS output end Proof % 0.35/0.63 % cvc5 exiting %------------------------------------------------------------------------------