%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU461^1 : 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 : n023.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 08:51:53 AM UTC 2026 % Result : Theorem 0.71s 0.91s % Output : Proof 0.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU461^1 : 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 % 0.16/0.34 % Computer : n023.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 17:37:13 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.71/0.91 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.71/0.91 % SZS status Theorem % 0.71/0.91 % SZS output start Proof % 0.71/0.91 ( % 0.71/0.91 (declare-sort $$unsorted 0) % 0.71/0.91 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.71/0.91 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.71/0.91 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.71/0.91 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.71/0.91 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.71/0.91 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.71/0.91 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.71/0.91 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.71/0.91 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.71/0.91 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.71/0.91 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.71/0.91 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.71/0.91 (define tptp.trans () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "Y" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.71/0.91 (define tptp.tc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_1) (forall (@list _let_3) (=> (and (_ tptp.trans _let_3) (_ (_ tptp.subrel _let_4) _let_3)) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.71/0.91 (define tptp.trc () (let ((_let_1 (@var "__flatten_var_1" $$unsorted))) (let ((_let_2 (@var "__flatten_var_0" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.rc (_ tptp.tc _let_3)) _let_2) _let_1)))))) % 0.71/0.91 (define tptp.trsc () (let ((_let_1 (@var "__flatten_var_1" $$unsorted))) (let ((_let_2 (@var "__flatten_var_0" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.sc (_ tptp.rc (_ tptp.tc _let_3))) _let_2) _let_1)))))) % 0.71/0.91 (define tptp.po () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.refl _let_1) (_ tptp.antisymm _let_1) (_ tptp.trans _let_1))))) % 0.71/0.91 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.71/0.91 (define tptp.total () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (or (= _let_1 _let_2) (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.71/0.91 (define tptp.term () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.71/0.91 (define tptp.ind () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@list _let_1))) (let ((_let_5 (@var "Y" $$unsorted))) (let ((_let_6 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_6) (forall (@list _let_2) (=> (forall _let_4 (=> (forall (@list _let_5) (=> (_ (_ (_ tptp.tc _let_6) _let_1) _let_5) (_ _let_2 _let_5))) _let_3)) (forall _let_4 _let_3))))))))))) % 0.71/0.91 (define tptp.innf () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (not (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.71/0.91 (define tptp.nfof () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "Y" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (and (_ (_ (_ tptp.trc _let_2) _let_3) _let_1) (_ (_ tptp.innf _let_2) _let_1))))))) % 0.71/0.91 (define tptp.norm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1) (exists (@list _let_2) (_ (_ (_ tptp.nfof _let_3) _let_2) _let_1)))))))) % 0.71/0.91 (define tptp.join () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ tptp.trc _let_3))) (let ((_let_5 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.71/0.91 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))))) % 0.71/0.91 (define tptp.sconfl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.71/0.91 (define tptp.confl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (_ (_ tptp.trc _let_3) _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))))) % 0.71/0.91 (define tptp.cr () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ (_ tptp.trsc _let_3) _let_2) _let_1) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))) % 0.71/0.91 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.71/0.91 (define @t2 () (_ tptp.tc @t1)) % 0.71/0.91 (define @t3 () (@list @t1)) % 0.71/0.91 (define @t4 () (forall @t3 (_ tptp.trans @t2))) % 0.71/0.91 (define @t5 () (not @t4)) % 0.71/0.91 (define @t6 () (@var "Y" $$unsorted)) % 0.71/0.91 (define @t7 () (@var "X" $$unsorted)) % 0.71/0.91 (define @t8 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.71/0.91 (define @t9 () (_ (_ @t8 @t7) @t6)) % 0.71/0.91 (define @t10 () (_ @t1 @t7)) % 0.71/0.91 (define @t11 () (_ @t10 @t6)) % 0.71/0.91 (define @t12 () (@list @t7 @t6)) % 0.71/0.91 (define @t13 () (forall @t12 (=> @t11 @t9))) % 0.71/0.91 (define @t14 () (@list @t1 @t8)) % 0.71/0.91 (define @t15 () (lambda @t14 @t13)) % 0.71/0.91 (define @t16 () (_ @t1 @t6)) % 0.71/0.91 (define @t17 () (_ @t16 @t7)) % 0.71/0.91 (define @t18 () (@list @t1 @t7 @t6)) % 0.71/0.91 (define @t19 () (lambda @t18 @t17)) % 0.71/0.91 (define @t20 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.71/0.91 (define @t21 () (_ @t20 @t1)) % 0.71/0.91 (define @t22 () (@list @t20)) % 0.71/0.91 (define @t23 () (lambda @t22 (forall @t3 (= (_ @t20 @t21) @t21)))) % 0.71/0.91 (define @t24 () (_ tptp.subrel @t1)) % 0.71/0.91 (define @t25 () (lambda @t22 (forall @t3 (_ @t24 @t21)))) % 0.71/0.91 (define @t26 () (_ @t24 @t8)) % 0.71/0.91 (define @t27 () (lambda @t22 (forall @t14 (=> @t26 (_ (_ tptp.subrel @t21) (_ @t20 @t8)))))) % 0.71/0.91 (define @t28 () (_ @t10 @t7)) % 0.71/0.91 (define @t29 () (@list @t7)) % 0.71/0.91 (define @t30 () (lambda @t3 (forall @t29 @t28))) % 0.71/0.91 (define @t31 () (lambda @t3 (forall @t29 (not @t28)))) % 0.71/0.91 (define @t32 () (= @t7 @t6)) % 0.71/0.91 (define @t33 () (lambda @t18 (or @t32 @t11))) % 0.71/0.91 (define @t34 () (lambda @t3 (forall @t12 (=> @t11 @t17)))) % 0.71/0.91 (define @t35 () (lambda @t3 (forall @t12 (=> (and @t11 @t17) @t32)))) % 0.71/0.91 (define @t36 () (lambda @t3 (forall @t12 (=> @t11 (not @t17))))) % 0.71/0.91 (define @t37 () (lambda @t18 (or @t17 @t11))) % 0.71/0.91 (define @t38 () (@var "Z" $$unsorted)) % 0.71/0.91 (define @t39 () (_ @t10 @t38)) % 0.71/0.91 (define @t40 () (_ @t16 @t38)) % 0.71/0.91 (define @t41 () (and @t11 @t40)) % 0.71/0.91 (define @t42 () (@list @t7 @t6 @t38)) % 0.71/0.91 (define @t43 () (forall @t42 (=> @t41 @t39))) % 0.71/0.91 (define @t44 () (lambda @t3 @t43)) % 0.71/0.91 (define @t45 () (and (_ tptp.trans @t8) @t26)) % 0.71/0.91 (define @t46 () (=> @t45 @t9)) % 0.71/0.91 (define @t47 () (@list @t8)) % 0.71/0.91 (define @t48 () (forall @t47 @t46)) % 0.71/0.91 (define @t49 () (lambda @t18 @t48)) % 0.71/0.91 (define @t50 () (@var "__flatten_var_1" $$unsorted)) % 0.71/0.91 (define @t51 () (@var "__flatten_var_0" $$unsorted)) % 0.71/0.91 (define @t52 () (_ tptp.rc @t2)) % 0.71/0.91 (define @t53 () (@list @t1 @t51 @t50)) % 0.71/0.91 (define @t54 () (lambda @t53 (_ (_ @t52 @t51) @t50))) % 0.71/0.91 (define @t55 () (lambda @t53 (_ (_ (_ tptp.sc @t52) @t51) @t50))) % 0.71/0.91 (define @t56 () (_ tptp.trans @t1)) % 0.71/0.91 (define @t57 () (lambda @t3 (and (_ tptp.refl @t1) (_ tptp.antisymm @t1) @t56))) % 0.71/0.91 (define @t58 () (lambda @t3 (and (_ tptp.asymm @t1) @t56))) % 0.71/0.91 (define @t59 () (lambda @t3 (forall @t12 (or @t32 @t11 @t17)))) % 0.71/0.91 (define @t60 () (not @t11)) % 0.71/0.91 (define @t61 () (@var "A" (-> $$unsorted Bool))) % 0.71/0.91 (define @t62 () (@list @t6)) % 0.71/0.91 (define @t63 () (_ @t61 @t7)) % 0.71/0.91 (define @t64 () (lambda @t3 (forall (@list @t61) (=> (exists @t29 @t63) (exists @t29 (and @t63 (forall @t62 (=> (_ @t61 @t6) @t60)))))))) % 0.71/0.91 (define @t65 () (@var "P" (-> $$unsorted Bool))) % 0.71/0.91 (define @t66 () (_ @t65 @t7)) % 0.71/0.91 (define @t67 () (lambda @t3 (forall (@list @t65) (=> (forall @t29 (=> (forall @t62 (=> (_ (_ @t2 @t7) @t6) (_ @t65 @t6))) @t66)) (forall @t29 @t66))))) % 0.71/0.91 (define @t68 () (lambda (@list @t1 @t7) (not (exists @t62 @t11)))) % 0.71/0.91 (define @t69 () (_ tptp.trc @t1)) % 0.71/0.91 (define @t70 () (_ @t69 @t6)) % 0.71/0.91 (define @t71 () (lambda @t18 (and (_ @t70 @t7) (_ (_ tptp.innf @t1) @t7)))) % 0.71/0.91 (define @t72 () (lambda @t3 (forall @t29 (exists @t62 (_ (_ (_ tptp.nfof @t1) @t6) @t7))))) % 0.71/0.91 (define @t73 () (_ @t69 @t7)) % 0.71/0.91 (define @t74 () (_ @t73 @t38)) % 0.71/0.91 (define @t75 () (lambda @t18 (exists (@list @t38) (and @t74 (_ @t70 @t38))))) % 0.71/0.91 (define @t76 () (_ tptp.join @t1)) % 0.71/0.91 (define @t77 () (_ (_ @t76 @t38) @t6)) % 0.71/0.91 (define @t78 () (lambda @t3 (forall @t42 (=> (and @t39 @t11) @t77)))) % 0.71/0.91 (define @t79 () (_ @t73 @t6)) % 0.71/0.91 (define @t80 () (lambda @t3 (forall @t42 (=> (and @t39 @t79) @t77)))) % 0.71/0.91 (define @t81 () (lambda @t3 (forall @t42 (=> (and @t74 @t79) @t77)))) % 0.71/0.91 (define @t82 () (lambda @t3 (forall @t12 (=> (_ (_ (_ tptp.trsc @t1) @t7) @t6) (_ (_ @t76 @t7) @t6))))) % 0.71/0.91 (define @t83 () (@var "BOUND_VARIABLE_8884" (-> $$unsorted $$unsorted Bool))) % 0.71/0.91 (define @t84 () (_ @t83 @t7 @t38)) % 0.71/0.91 (define @t85 () (@var "BOUND_VARIABLE_7746" $$unsorted)) % 0.71/0.91 (define @t86 () (@var "BOUND_VARIABLE_7744" $$unsorted)) % 0.71/0.91 (define @t87 () (not (_ @t1 @t86 @t85))) % 0.71/0.91 (define @t88 () (@list @t86 @t85)) % 0.71/0.91 (define @t89 () (not (forall @t88 (or @t87 (_ @t83 @t86 @t85))))) % 0.71/0.91 (define @t90 () (@var "BOUND_VARIABLE_8853" $$unsorted)) % 0.71/0.91 (define @t91 () (@var "BOUND_VARIABLE_7755" $$unsorted)) % 0.71/0.91 (define @t92 () (@var "BOUND_VARIABLE_7757" $$unsorted)) % 0.71/0.91 (define @t93 () (@list @t91 @t92 @t90)) % 0.71/0.91 (define @t94 () (not (forall @t93 (or (not (_ @t83 @t91 @t92)) (not (_ @t83 @t92 @t90)) (_ @t83 @t91 @t90))))) % 0.71/0.91 (define @t95 () (_ @t8 @t6 @t38)) % 0.71/0.91 (define @t96 () (_ @t8 @t86 @t85)) % 0.71/0.91 (define @t97 () (not (forall @t88 (or @t87 @t96)))) % 0.71/0.91 (define @t98 () (@var "BOUND_VARIABLE_8837" $$unsorted)) % 0.71/0.91 (define @t99 () (not (_ @t8 @t91 @t92))) % 0.71/0.91 (define @t100 () (@list @t91 @t92 @t98)) % 0.71/0.91 (define @t101 () (not (forall @t100 (or @t99 (not (_ @t8 @t92 @t98)) (_ @t8 @t91 @t98))))) % 0.71/0.91 (define @t102 () (forall @t47 (or @t101 @t97 @t95))) % 0.71/0.91 (define @t103 () (not @t102)) % 0.71/0.91 (define @t104 () (_ @t8 @t7 @t6)) % 0.71/0.91 (define @t105 () (@var "BOUND_VARIABLE_8870" $$unsorted)) % 0.71/0.91 (define @t106 () (@list @t91 @t92 @t105)) % 0.71/0.91 (define @t107 () (not (forall @t106 (or @t99 (not (_ @t8 @t92 @t105)) (_ @t8 @t91 @t105))))) % 0.71/0.91 (define @t108 () (not (forall @t47 (or @t107 @t97 @t104)))) % 0.71/0.91 (define @t109 () (or @t108 @t103 @t94 @t89 @t84)) % 0.71/0.91 (define @t110 () (forall (@list @t1 @t7 @t6 @t38 @t83) @t109)) % 0.71/0.91 (define @t111 () (@list @t7 @t6 @t38 @t83)) % 0.71/0.91 (define @t112 () (or @t94 @t89 @t84)) % 0.71/0.91 (define @t113 () (or @t108 @t103 @t112)) % 0.71/0.91 (define @t114 () (forall @t111 @t113)) % 0.71/0.91 (define @t115 () (@list @t83)) % 0.71/0.91 (define @t116 () (forall @t115 @t113)) % 0.71/0.91 (define @t117 () (forall @t115 @t112)) % 0.71/0.91 (define @t118 () (or @t108 @t103 @t117)) % 0.71/0.91 (define @t119 () (_ @t8 @t7 @t38)) % 0.71/0.91 (define @t120 () (not (forall @t93 (or @t99 (not (_ @t8 @t92 @t90)) (_ @t8 @t91 @t90))))) % 0.71/0.91 (define @t121 () (forall @t47 (or @t120 @t97 @t119))) % 0.71/0.91 (define @t122 () (forall (@list @t91 @t92 @t38) (or @t99 (not (_ @t8 @t92 @t38)) (_ @t8 @t91 @t38)))) % 0.71/0.91 (define @t123 () (@list @t38)) % 0.71/0.91 (define @t124 () (not @t122)) % 0.71/0.91 (define @t125 () (or @t124 @t97 @t104)) % 0.71/0.91 (define @t126 () (forall @t47 @t125)) % 0.71/0.91 (define @t127 () (not @t126)) % 0.71/0.91 (define @t128 () (or @t127 @t103 @t121)) % 0.71/0.91 (define @t129 () (lambda @t12 @t126)) % 0.71/0.91 (define @t130 () (not (_ @t129 @t6 @t38))) % 0.71/0.91 (define @t131 () (_ @t129 @t7 @t6)) % 0.71/0.91 (define @t132 () (not @t131)) % 0.71/0.91 (define @t133 () (or @t132 @t130 (_ @t129 @t7 @t38))) % 0.71/0.91 (define @t134 () (forall @t42 @t133)) % 0.71/0.91 (define @t135 () (_ @t1 @t7 @t38)) % 0.71/0.91 (define @t136 () (_ @t1 @t6 @t38)) % 0.71/0.91 (define @t137 () (_ @t1 @t7 @t6)) % 0.71/0.91 (define @t138 () (not @t137)) % 0.71/0.91 (define @t139 () (lambda @t3 (forall @t42 (or @t138 (not @t136) @t135)))) % 0.71/0.91 (define @t140 () (lambda @t18 @t126)) % 0.71/0.91 (define @t141 () (forall @t12 (or @t138 @t104))) % 0.71/0.91 (define @t142 () (not @t141)) % 0.71/0.91 (define @t143 () (forall @t42 (or (not @t104) (not @t95) @t119))) % 0.71/0.91 (define @t144 () (not @t143)) % 0.71/0.91 (define @t145 () (lambda @t18 (forall @t47 (or @t144 @t142 @t104)))) % 0.71/0.91 (define @t146 () (forall @t3 (_ @t139 (_ @t145 @t1)))) % 0.71/0.91 (define @t147 () (or @t144 @t142 @t9)) % 0.71/0.91 (define @t148 () (and @t143 @t141)) % 0.71/0.91 (define @t149 () (lambda @t47 @t141)) % 0.71/0.91 (define @t150 () (_ (lambda @t14 @t141) @t1)) % 0.71/0.91 (define @t151 () (_ @t139 @t8)) % 0.71/0.91 (define @t152 () (and @t151 (_ @t150 @t8))) % 0.71/0.91 (define @t153 () (=> @t152 @t9)) % 0.71/0.91 (define @t154 () (or @t60 @t9)) % 0.71/0.91 (define @t155 () (not @t40)) % 0.71/0.91 (define @t156 () (or @t60 @t155 @t39)) % 0.71/0.91 (define @t157 () (@quantifiers_skolemize @t110 4)) % 0.71/0.91 (define @t158 () (not (_ (@quantifiers_skolemize @t110 0) @t86 @t85))) % 0.71/0.91 (define @t159 () (forall @t88 (or @t158 (_ @t157 @t86 @t85)))) % 0.71/0.91 (define @t160 () (@quantifiers_skolemize @t110 3)) % 0.71/0.91 (define @t161 () (@quantifiers_skolemize @t110 1)) % 0.71/0.91 (define @t162 () (_ @t157 @t161 @t160)) % 0.71/0.91 (define @t163 () (not @t159)) % 0.71/0.91 (define @t164 () (not (_ @t157 @t91 @t92))) % 0.71/0.91 (define @t165 () (forall @t93 (or @t164 (not (_ @t157 @t92 @t90)) (_ @t157 @t91 @t90)))) % 0.71/0.91 (define @t166 () (not @t165)) % 0.71/0.91 (define @t167 () (@quantifiers_skolemize @t110 2)) % 0.71/0.91 (define @t168 () (not (forall @t88 (or @t158 @t96)))) % 0.71/0.91 (define @t169 () (forall @t47 (or @t101 @t168 (_ @t8 @t167 @t160)))) % 0.71/0.91 (define @t170 () (not @t169)) % 0.71/0.91 (define @t171 () (forall @t47 (or @t107 @t168 (_ @t8 @t161 @t167)))) % 0.71/0.91 (define @t172 () (not @t171)) % 0.71/0.91 (define @t173 () (or @t172 @t170 @t166 @t163 @t162)) % 0.71/0.91 (define @t174 () (@list true)) % 0.71/0.91 (define @t175 () (@list @t173)) % 0.71/0.91 (define @t176 () (@list @t157)) % 0.71/0.91 (define @t177 () (@var "BOUND_VARIABLE_90093" $$unsorted)) % 0.71/0.91 (define @t178 () (@var "BOUND_VARIABLE_90091" $$unsorted)) % 0.71/0.91 (define @t179 () (@var "BOUND_VARIABLE_90092" $$unsorted)) % 0.71/0.91 (define @t180 () (@list @t178 @t179 @t177)) % 0.71/0.91 (define @t181 () (@list @t91 @t92 @t90)) % 0.71/0.91 (define @t182 () (forall @t106 (or @t164 (not (_ @t157 @t92 @t105)) (_ @t157 @t91 @t105)))) % 0.71/0.91 (define @t183 () (@list false)) % 0.71/0.91 (define @t184 () (@list @t165)) % 0.71/0.91 (define @t185 () (_ @t157 @t161 @t167)) % 0.71/0.91 (define @t186 () (not @t182)) % 0.71/0.91 (define @t187 () (or @t186 @t163 @t185)) % 0.71/0.91 (define @t188 () (_ @t157 @t167 @t160)) % 0.71/0.91 (define @t189 () (not @t188)) % 0.71/0.91 (define @t190 () (not @t185)) % 0.71/0.91 (define @t191 () (or @t190 @t189 @t162)) % 0.71/0.91 (define @t192 () (@var "BOUND_VARIABLE_90468" $$unsorted)) % 0.71/0.91 (define @t193 () (@var "BOUND_VARIABLE_90466" $$unsorted)) % 0.71/0.91 (define @t194 () (@var "BOUND_VARIABLE_90467" $$unsorted)) % 0.71/0.91 (define @t195 () (@list @t193 @t194 @t192)) % 0.71/0.91 (define @t196 () (forall @t100 (or @t164 (not (_ @t157 @t92 @t98)) (_ @t157 @t91 @t98)))) % 0.71/0.91 (define @t197 () (not @t196)) % 0.71/0.91 (define @t198 () (or @t197 @t163 @t188)) % 0.71/0.91 (assume @p1 @t5) % 0.71/0.91 (assume @p2 true) % 0.71/0.91 (step @p3 (= tptp.subrel @t15) :rule refl :args (@t15)) % 0.71/0.91 (step @p4 (= tptp.inv @t19) :rule refl :args (@t19)) % 0.71/0.91 (step @p5 (= tptp.idem @t23) :rule refl :args (@t23)) % 0.71/0.91 (step @p6 (= tptp.infl @t25) :rule refl :args (@t25)) % 0.71/0.91 (step @p7 (= tptp.mono @t27) :rule refl :args (@t27)) % 0.71/0.91 (step @p8 (= tptp.refl @t30) :rule refl :args (@t30)) % 0.71/0.91 (step @p9 (= tptp.irrefl @t31) :rule refl :args (@t31)) % 0.71/0.91 (step @p10 (= tptp.rc @t33) :rule refl :args (@t33)) % 0.71/0.91 (step @p11 (= tptp.symm @t34) :rule refl :args (@t34)) % 0.71/0.91 (step @p12 (= tptp.antisymm @t35) :rule refl :args (@t35)) % 0.71/0.91 (step @p13 (= tptp.asymm @t36) :rule refl :args (@t36)) % 0.71/0.91 (step @p14 (= tptp.sc @t37) :rule refl :args (@t37)) % 0.71/0.91 (step @p15 (= tptp.trans @t44) :rule refl :args (@t44)) % 0.71/0.91 (step @p16 (= tptp.tc @t49) :rule refl :args (@t49)) % 0.71/0.91 (step @p17 (= tptp.trc @t54) :rule refl :args (@t54)) % 0.71/0.91 (step @p18 (= tptp.trsc @t55) :rule refl :args (@t55)) % 0.71/0.91 (step @p19 (= tptp.po @t57) :rule refl :args (@t57)) % 0.71/0.91 (step @p20 (= tptp.so @t58) :rule refl :args (@t58)) % 0.71/0.91 (step @p21 (= tptp.total @t59) :rule refl :args (@t59)) % 0.71/0.91 (step @p22 (= tptp.term @t64) :rule refl :args (@t64)) % 0.71/0.91 (step @p23 (= tptp.ind @t67) :rule refl :args (@t67)) % 0.71/0.91 (step @p24 (= tptp.innf @t68) :rule refl :args (@t68)) % 0.71/0.91 (step @p25 (= tptp.nfof @t71) :rule refl :args (@t71)) % 0.71/0.91 (step @p26 (= tptp.norm @t72) :rule refl :args (@t72)) % 0.71/0.91 (step @p27 (= tptp.join @t75) :rule refl :args (@t75)) % 0.71/0.91 (step @p28 (= tptp.lconfl @t78) :rule refl :args (@t78)) % 0.71/0.91 (step @p29 (= tptp.sconfl @t80) :rule refl :args (@t80)) % 0.71/0.91 (step @p30 (= tptp.confl @t81) :rule refl :args (@t81)) % 0.71/0.91 (step @p31 (= tptp.cr @t82) :rule refl :args (@t82)) % 0.71/0.91 (step @p32 :rule quant-merge-prenex :args ((= (forall @t3 (forall @t111 @t109)) @t110))) % 0.71/0.91 (step @p33 :rule aci_norm :args ((= @t113 @t109))) % 0.71/0.91 (step @p34 :rule cong :premises (@p33) :args (@t114)) % 0.71/0.91 (step @p35 :rule quant-merge-prenex :args ((= (forall @t42 @t116) @t114))) % 0.71/0.91 (step @p36 :rule alpha_equiv :args (@t117 (@list @t83) (@list @t8))) % 0.71/0.91 (step @p37 :rule refl :args (@t103)) % 0.71/0.91 (step @p38 :rule refl :args (@t108)) % 0.71/0.91 (step @p39 :rule nary_cong :premises (@p38 @p37 @p36) :args (@t118)) % 0.71/0.91 (step @p40 :rule quant-miniscope-or :args ((= @t116 @t118))) % 0.71/0.91 (step @p41 :rule trans :premises (@p40 @p39)) % 0.71/0.91 (step @p42 :rule symm :premises (@p41)) % 0.71/0.91 (step @p43 :rule cong :premises (@p42) :args ((forall @t42 (or @t108 @t103 @t121)))) % 0.71/0.91 (step @p44 :rule trans :premises (@p43 @p35)) % 0.71/0.91 (step @p45 :rule trans :premises (@p44 @p34)) % 0.71/0.91 (step @p46 :rule refl :args (@t121)) % 0.71/0.91 (step @p47 :rule refl :args (@t104)) % 0.71/0.91 (step @p48 :rule refl :args (@t97)) % 0.71/0.91 (step @p49 :rule alpha_equiv :args (@t122 @t123 (@list @t105))) % 0.71/0.91 (step @p50 :rule cong :premises (@p49) :args (@t124)) % 0.71/0.91 (step @p51 :rule nary_cong :premises (@p50 @p48 @p47) :args (@t125)) % 0.71/0.91 (step @p52 :rule cong :premises (@p51) :args (@t126)) % 0.71/0.91 (step @p53 :rule cong :premises (@p52) :args (@t127)) % 0.71/0.91 (step @p54 :rule nary_cong :premises (@p53 @p37 @p46) :args (@t128)) % 0.71/0.91 (step @p55 :rule cong :premises (@p54) :args ((forall @t42 @t128))) % 0.71/0.91 (step @p56 :rule trans :premises (@p55 @p45)) % 0.71/0.91 (step @p57 :rule beta-reduce :args ((= (_ (lambda @t12 (forall @t47 (or @t120 @t97 @t104))) @t7 @t38) @t121))) % 0.71/0.91 (step @p58 :rule refl :args (@t38)) % 0.71/0.91 (step @p59 :rule refl :args (@t7)) % 0.71/0.91 (step @p60 :rule alpha_equiv :args (@t122 @t123 (@list @t90))) % 0.71/0.91 (step @p61 :rule cong :premises (@p60) :args (@t124)) % 0.71/0.91 (step @p62 :rule nary_cong :premises (@p61 @p48 @p47) :args (@t125)) % 0.71/0.91 (step @p63 :rule cong :premises (@p62) :args (@t126)) % 0.71/0.91 (step @p64 :rule cong :premises (@p63) :args (@t129)) % 0.71/0.91 (step @p65 :rule ho_cong :premises (@p64 @p59 @p58)) % 0.71/0.91 (step @p66 :rule trans :premises (@p65 @p57)) % 0.71/0.91 (step @p67 :rule beta-reduce :args ((= (_ (lambda @t12 (forall @t47 (or @t101 @t97 @t104))) @t6 @t38) @t102))) % 0.71/0.91 (step @p68 :rule refl :args (@t6)) % 0.71/0.91 (step @p69 :rule alpha_equiv :args (@t122 @t123 (@list @t98))) % 0.71/0.91 (step @p70 :rule cong :premises (@p69) :args (@t124)) % 0.71/0.91 (step @p71 :rule nary_cong :premises (@p70 @p48 @p47) :args (@t125)) % 0.71/0.91 (step @p72 :rule cong :premises (@p71) :args (@t126)) % 0.71/0.91 (step @p73 :rule cong :premises (@p72) :args (@t129)) % 0.71/0.91 (step @p74 :rule ho_cong :premises (@p73 @p68 @p58)) % 0.71/0.91 (step @p75 :rule trans :premises (@p74 @p67)) % 0.71/0.91 (step @p76 :rule cong :premises (@p75) :args (@t130)) % 0.71/0.91 (step @p77 :rule beta-reduce :args ((= @t131 @t126))) % 0.71/0.91 (step @p78 :rule cong :premises (@p77) :args (@t132)) % 0.71/0.91 (step @p79 :rule nary_cong :premises (@p78 @p76 @p66) :args (@t133)) % 0.71/0.91 (step @p80 :rule cong :premises (@p79) :args (@t134)) % 0.71/0.91 (step @p81 :rule trans :premises (@p80 @p56)) % 0.71/0.91 (step @p82 :rule beta-reduce :args ((= (_ @t139 @t129) @t134))) % 0.71/0.91 (step @p83 :rule trans :premises (@p82 @p81)) % 0.71/0.91 (step @p84 :rule beta-reduce :args ((= (_ @t140 @t1) @t129))) % 0.71/0.91 (step @p85 :rule refl :args (@t1)) % 0.71/0.91 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 0.71/0.91 ; trust TRUST_THEORY_REWRITE % 0.71/0.91 (step @p86 :rule trust :premises () :args ((= @t145 @t140))) % 0.71/0.91 (step @p87 :rule ho_cong :premises (@p86 @p85)) % 0.71/0.91 (step @p88 :rule trans :premises (@p87 @p84)) % 0.71/0.91 (step @p89 :rule refl :args (@t139)) % 0.71/0.91 (step @p90 :rule ho_cong :premises (@p89 @p88)) % 0.71/0.91 (step @p91 :rule trans :premises (@p90 @p83)) % 0.71/0.91 (step @p92 :rule cong :premises (@p91) :args (@t146)) % 0.71/0.91 (step @p93 :rule trans :premises (@p92 @p32)) % 0.71/0.91 (step @p94 :rule cong :premises (@p93) :args ((not @t146))) % 0.71/0.91 (step @p95 :rule refl :args (@t104)) % 0.71/0.91 (step @p96 :rule refl :args (@t9)) % 0.71/0.91 (step @p97 :rule cong :premises (@p96 @p95) :args ((= @t9 @t104))) % 0.71/0.91 (step @p98 :rule symm :premises (@p97)) % 0.71/0.91 (step @p99 :rule eq_resolve :premises (@p96 @p98)) % 0.71/0.91 (step @p100 :rule refl :args (@t142)) % 0.71/0.91 (step @p101 :rule refl :args (@t144)) % 0.71/0.91 (step @p102 :rule nary_cong :premises (@p101 @p100 @p99) :args (@t147)) % 0.71/0.91 (step @p103 :rule cong :premises (@p102) :args ((forall @t47 @t147))) % 0.71/0.91 (step @p104 :rule aci_norm :args ((= (or (or @t144 @t142) @t9) @t147))) % 0.71/0.91 (step @p105 :rule bool-and-de-morgan :args (@t143 @t141 true)) % 0.71/0.91 (step @p106 :rule nary_cong :premises (@p105 @p96) :args ((or (not @t148) @t9))) % 0.71/0.91 (step @p107 :rule trans :premises (@p106 @p104)) % 0.71/0.91 (step @p108 :rule bool-impl-elim :args (@t148 @t9)) % 0.71/0.91 (step @p109 :rule trans :premises (@p108 @p107)) % 0.71/0.91 (step @p110 :rule cong :premises (@p109) :args ((forall @t47 (=> @t148 @t9)))) % 0.71/0.91 (step @p111 :rule trans :premises (@p110 @p103)) % 0.71/0.91 (step @p112 :rule refl :args (@t9)) % 0.71/0.91 (step @p113 :rule beta-reduce :args ((= (_ @t149 @t8) @t141))) % 0.71/0.91 (step @p114 :rule refl :args (@t8)) % 0.71/0.91 (step @p115 :rule beta-reduce :args ((= @t150 @t149))) % 0.71/0.91 (step @p116 :rule ho_cong :premises (@p115 @p114)) % 0.71/0.91 (step @p117 :rule trans :premises (@p116 @p113)) % 0.71/0.91 (step @p118 :rule beta-reduce :args ((= @t151 @t143))) % 0.71/0.91 (step @p119 :rule nary_cong :premises (@p118 @p117) :args (@t152)) % 0.71/0.91 (step @p120 :rule cong :premises (@p119 @p112) :args (@t153)) % 0.71/0.91 (step @p121 :rule cong :premises (@p120) :args ((forall @t47 @t153))) % 0.71/0.91 (step @p122 :rule trans :premises (@p121 @p111)) % 0.71/0.91 (step @p123 :rule refl :args (@t137)) % 0.71/0.91 (step @p124 :rule refl :args (@t11)) % 0.71/0.91 (step @p125 :rule cong :premises (@p124 @p123) :args ((= @t11 @t137))) % 0.71/0.91 (step @p126 :rule symm :premises (@p125)) % 0.71/0.91 (step @p127 :rule eq_resolve :premises (@p124 @p126)) % 0.71/0.91 (step @p128 :rule cong :premises (@p127) :args (@t60)) % 0.71/0.91 (step @p129 :rule nary_cong :premises (@p128 @p99) :args (@t154)) % 0.71/0.91 (step @p130 :rule cong :premises (@p129) :args ((forall @t12 @t154))) % 0.71/0.91 (step @p131 :rule bool-impl-elim :args (@t11 @t9)) % 0.71/0.91 (step @p132 :rule cong :premises (@p131) :args (@t13)) % 0.71/0.91 (step @p133 :rule trans :premises (@p132 @p130)) % 0.71/0.91 (step @p134 :rule cong :premises (@p133) :args (@t15)) % 0.71/0.91 (step @p135 :rule trans :premises (@p3 @p134)) % 0.71/0.91 (step @p136 :rule ho_cong :premises (@p135 @p85)) % 0.71/0.91 (step @p137 :rule ho_cong :premises (@p136 @p114)) % 0.71/0.91 (step @p138 :rule refl :args (@t135)) % 0.71/0.91 (step @p139 :rule refl :args (@t39)) % 0.71/0.91 (step @p140 :rule cong :premises (@p139 @p138) :args ((= @t39 @t135))) % 0.71/0.91 (step @p141 :rule symm :premises (@p140)) % 0.71/0.91 (step @p142 :rule eq_resolve :premises (@p139 @p141)) % 0.71/0.91 (step @p143 :rule refl :args (@t136)) % 0.71/0.91 (step @p144 :rule refl :args (@t40)) % 0.71/0.91 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t40 @t136))) % 0.71/0.91 (step @p146 :rule symm :premises (@p145)) % 0.71/0.91 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 0.71/0.91 (step @p148 :rule cong :premises (@p147) :args (@t155)) % 0.71/0.91 (step @p149 :rule nary_cong :premises (@p128 @p148 @p142) :args (@t156)) % 0.71/0.91 (step @p150 :rule cong :premises (@p149) :args ((forall @t42 @t156))) % 0.71/0.91 (step @p151 :rule aci_norm :args ((= (or (or @t60 @t155) @t39) @t156))) % 0.71/0.91 (step @p152 :rule bool-and-de-morgan :args (@t11 @t40 true)) % 0.71/0.91 (step @p153 :rule nary_cong :premises (@p152 @p139) :args ((or (not @t41) @t39))) % 0.71/0.91 (step @p154 :rule trans :premises (@p153 @p151)) % 0.71/0.91 (step @p155 :rule bool-impl-elim :args (@t41 @t39)) % 0.71/0.91 (step @p156 :rule trans :premises (@p155 @p154)) % 0.71/0.91 (step @p157 :rule cong :premises (@p156) :args (@t43)) % 0.71/0.91 (step @p158 :rule trans :premises (@p157 @p150)) % 0.71/0.91 (step @p159 :rule cong :premises (@p158) :args (@t44)) % 0.71/0.91 (step @p160 :rule trans :premises (@p15 @p159)) % 0.71/0.91 (step @p161 :rule ho_cong :premises (@p160 @p114)) % 0.71/0.91 (step @p162 :rule nary_cong :premises (@p161 @p137) :args (@t45)) % 0.71/0.91 (step @p163 :rule cong :premises (@p162 @p112) :args (@t46)) % 0.71/0.91 (step @p164 :rule cong :premises (@p163) :args (@t48)) % 0.71/0.91 (step @p165 :rule trans :premises (@p164 @p122)) % 0.71/0.91 (step @p166 :rule cong :premises (@p165) :args (@t49)) % 0.71/0.91 (step @p167 :rule trans :premises (@p16 @p166)) % 0.71/0.91 (step @p168 :rule ho_cong :premises (@p167 @p85)) % 0.71/0.91 (step @p169 :rule ho_cong :premises (@p160 @p168)) % 0.71/0.91 (step @p170 :rule cong :premises (@p169) :args (@t4)) % 0.71/0.91 (step @p171 :rule cong :premises (@p170) :args (@t5)) % 0.71/0.91 (step @p172 :rule trans :premises (@p171 @p94)) % 0.71/0.91 (step @p173 :rule eq_resolve :premises (@p1 @p172)) % 0.71/0.91 (step @p174 :rule skolemize :premises (@p173)) % 0.71/0.91 (step @p175 :rule bool-double-not-elim :args (@t159)) % 0.71/0.91 (step @p176 :rule refl :args (@t173)) % 0.71/0.91 (step @p177 :rule nary_cong :premises (@p176 @p175) :args ((or @t173 (not @t163)))) % 0.71/0.91 (step @p178 :rule cnf_or_neg :args (@t173 3)) % 0.71/0.91 (step @p179 :rule eq_resolve :premises (@p178 @p177)) % 0.71/0.91 (step @p180 :rule reordering :premises (@p179) :args ((or @t159 @t173))) % 0.71/0.91 (step @p181 :rule chain_m_resolution :premises (@p180 @p174) :args (@t159 @t174 @t175)) % 0.71/0.91 (step @p182 :rule bool-double-not-elim :args (@t165)) % 0.71/0.91 (step @p183 :rule nary_cong :premises (@p176 @p182) :args ((or @t173 (not @t166)))) % 0.71/0.91 (step @p184 :rule cnf_or_neg :args (@t173 2)) % 0.71/0.91 (step @p185 :rule eq_resolve :premises (@p184 @p183)) % 0.71/0.91 (step @p186 :rule reordering :premises (@p185) :args ((or @t165 @t173))) % 0.71/0.91 (step @p187 :rule chain_m_resolution :premises (@p186 @p174) :args (@t165 @t174 @t175)) % 0.71/0.91 (step @p188 :rule instantiate :premises (@p187) :args ((@list @t161 @t167 @t160))) % 0.71/0.91 (step @p189 :rule bool-double-not-elim :args (@t171)) % 0.71/0.91 (step @p190 :rule nary_cong :premises (@p176 @p189) :args ((or @t173 (not @t172)))) % 0.71/0.91 (step @p191 :rule cnf_or_neg :args (@t173 0)) % 0.71/0.91 (step @p192 :rule eq_resolve :premises (@p191 @p190)) % 0.71/0.91 (step @p193 :rule reordering :premises (@p192) :args ((or @t171 @t173))) % 0.71/0.91 (step @p194 :rule chain_m_resolution :premises (@p193 @p174) :args (@t171 @t174 @t175)) % 0.71/0.91 (step @p195 :rule instantiate :premises (@p194) :args (@t176)) % 0.71/0.91 (step @p196 :rule alpha_equiv :args ((forall (@list @t178 @t179 @t177) (or (not (_ @t157 @t178 @t179)) (not (_ @t157 @t179 @t177)) (_ @t157 @t178 @t177))) @t180 (@list @t91 @t92 @t105))) % 0.71/0.91 (step @p197 :rule alpha_equiv :args (@t165 @t181 @t180)) % 0.71/0.91 (step @p198 :rule trans :premises (@p197 @p196)) % 0.71/0.91 (step @p199 :rule equiv_elim1 :premises (@p198)) % 0.71/0.91 (step @p200 :rule chain_m_resolution :premises (@p199 @p187) :args (@t182 @t183 @t184)) % 0.71/0.91 (step @p201 :rule cnf_or_pos :args (@t187)) % 0.71/0.91 (step @p202 :rule reordering :premises (@p201) :args ((or @t163 @t185 @t186 (not @t187)))) % 0.71/0.91 (step @p203 :rule chain_m_resolution :premises (@p202 @p181 @p200 @p195) :args (@t185 (@list false false false) (@list @t159 @t182 @t187))) % 0.71/0.91 (step @p204 :rule cnf_or_neg :args (@t173 4)) % 0.71/0.91 (step @p205 :rule chain_m_resolution :premises (@p204 @p174) :args ((not @t162) @t174 @t175)) % 0.71/0.91 (step @p206 :rule cnf_or_pos :args (@t191)) % 0.71/0.91 (step @p207 :rule reordering :premises (@p206) :args ((or @t162 @t190 @t189 (not @t191)))) % 0.71/0.91 (step @p208 :rule chain_m_resolution :premises (@p207 @p205 @p203 @p188) :args (@t189 (@list true false false) (@list @t162 @t185 @t191))) % 0.71/0.91 (step @p209 :rule alpha_equiv :args ((forall (@list @t193 @t194 @t192) (or (not (_ @t157 @t193 @t194)) (not (_ @t157 @t194 @t192)) (_ @t157 @t193 @t192))) @t195 (@list @t91 @t92 @t98))) % 0.71/0.91 (step @p210 :rule alpha_equiv :args (@t165 @t181 @t195)) % 0.71/0.91 (step @p211 :rule trans :premises (@p210 @p209)) % 0.71/0.91 (step @p212 :rule equiv_elim1 :premises (@p211)) % 0.71/0.91 (step @p213 :rule chain_m_resolution :premises (@p212 @p187) :args (@t196 @t183 @t184)) % 0.71/0.91 (step @p214 :rule bool-double-not-elim :args (@t169)) % 0.71/0.91 (step @p215 :rule nary_cong :premises (@p176 @p214) :args ((or @t173 (not @t170)))) % 0.71/0.91 (step @p216 :rule cnf_or_neg :args (@t173 1)) % 0.71/0.91 (step @p217 :rule eq_resolve :premises (@p216 @p215)) % 0.71/0.91 (step @p218 :rule reordering :premises (@p217) :args ((or @t169 @t173))) % 0.71/0.91 (step @p219 :rule chain_m_resolution :premises (@p218 @p174) :args (@t169 @t174 @t175)) % 0.71/0.91 (step @p220 :rule instantiate :premises (@p219) :args (@t176)) % 0.71/0.91 (step @p221 :rule cnf_or_pos :args (@t198)) % 0.71/0.91 (step @p222 :rule reordering :premises (@p221) :args ((or @t163 @t188 @t197 (not @t198)))) % 0.71/0.91 (step @p223 false :rule chain_m_resolution :premises (@p222 @p220 @p213 @p208 @p181) :args (false (@list false false true false) (@list @t198 @t196 @t188 @t159))) % 0.71/0.91 ) % 0.71/0.91 % SZS output end Proof % 0.71/0.91 % cvc5 exiting %------------------------------------------------------------------------------