%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU476^1 : 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 : n024.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 08:51:55 AM UTC 2026 % Result : Theorem 208.00s 208.81s % Output : Proof 208.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SEU476^1 : TPTP v9.2.1. Released v3.6.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 12:36:45 EDT 2026 % 0.07/0.25 % CPUTime : % 0.07/0.33 %----Proving TH0 % 208.00/208.81 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 208.00/208.81 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 208.00/208.81 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 208.00/208.81 --- Run --ho-elim --full-saturate-quant at 18s... % 208.00/208.81 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 208.00/208.81 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 208.00/208.81 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 9s... % 208.00/208.81 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 6s... % 208.00/208.81 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 21s... % 208.00/208.81 % SZS status Theorem % 208.00/208.81 % SZS output start Proof % 208.00/208.81 ( % 208.00/208.81 (declare-sort $$unsorted 0) % 208.00/208.81 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 208.00/208.81 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 208.00/208.81 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 208.00/208.81 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 208.00/208.81 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 208.00/208.81 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 208.00/208.81 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 208.00/208.81 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 208.00/208.81 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 208.00/208.81 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 208.00/208.81 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 208.00/208.81 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 208.00/208.81 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 208.00/208.81 (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))))))))) % 208.00/208.81 (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)))))) % 208.00/208.81 (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)))))) % 208.00/208.81 (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))))) % 208.00/208.81 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 208.00/208.81 (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)))))))) % 208.00/208.81 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 208.00/208.81 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 208.00/208.81 (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)))))))) % 208.00/208.81 (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))))))) % 208.00/208.81 (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)))))))) % 208.00/208.81 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 208.00/208.81 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 208.00/208.81 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 208.00/208.81 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 208.00/208.81 (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)))))))) % 208.00/208.81 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 208.00/208.81 (define @t2 () (_ tptp.tc @t1)) % 208.00/208.81 (define @t3 () (_ tptp.rc @t2)) % 208.00/208.81 (define @t4 () (= (_ tptp.tc (_ tptp.rc @t1)) @t3)) % 208.00/208.81 (define @t5 () (@list @t1)) % 208.00/208.81 (define @t6 () (forall @t5 @t4)) % 208.00/208.81 (define @t7 () (not @t6)) % 208.00/208.81 (define @t8 () (@var "Y" $$unsorted)) % 208.00/208.81 (define @t9 () (@var "X" $$unsorted)) % 208.00/208.81 (define @t10 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 208.00/208.81 (define @t11 () (_ (_ @t10 @t9) @t8)) % 208.00/208.81 (define @t12 () (_ @t1 @t9)) % 208.00/208.81 (define @t13 () (_ @t12 @t8)) % 208.00/208.81 (define @t14 () (@list @t9 @t8)) % 208.00/208.81 (define @t15 () (forall @t14 (=> @t13 @t11))) % 208.00/208.81 (define @t16 () (@list @t1 @t10)) % 208.00/208.81 (define @t17 () (lambda @t16 @t15)) % 208.00/208.81 (define @t18 () (_ @t1 @t8)) % 208.00/208.81 (define @t19 () (_ @t18 @t9)) % 208.00/208.81 (define @t20 () (@list @t1 @t9 @t8)) % 208.00/208.81 (define @t21 () (lambda @t20 @t19)) % 208.00/208.81 (define @t22 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 208.00/208.81 (define @t23 () (_ @t22 @t1)) % 208.00/208.81 (define @t24 () (@list @t22)) % 208.00/208.81 (define @t25 () (lambda @t24 (forall @t5 (= (_ @t22 @t23) @t23)))) % 208.00/208.81 (define @t26 () (_ tptp.subrel @t1)) % 208.00/208.81 (define @t27 () (lambda @t24 (forall @t5 (_ @t26 @t23)))) % 208.00/208.81 (define @t28 () (_ @t26 @t10)) % 208.00/208.81 (define @t29 () (lambda @t24 (forall @t16 (=> @t28 (_ (_ tptp.subrel @t23) (_ @t22 @t10)))))) % 208.00/208.81 (define @t30 () (_ @t12 @t9)) % 208.00/208.81 (define @t31 () (@list @t9)) % 208.00/208.81 (define @t32 () (lambda @t5 (forall @t31 @t30))) % 208.00/208.81 (define @t33 () (lambda @t5 (forall @t31 (not @t30)))) % 208.00/208.81 (define @t34 () (= @t9 @t8)) % 208.00/208.81 (define @t35 () (or @t34 @t13)) % 208.00/208.81 (define @t36 () (lambda @t20 @t35)) % 208.00/208.81 (define @t37 () (lambda @t5 (forall @t14 (=> @t13 @t19)))) % 208.00/208.81 (define @t38 () (lambda @t5 (forall @t14 (=> (and @t13 @t19) @t34)))) % 208.00/208.81 (define @t39 () (lambda @t5 (forall @t14 (=> @t13 (not @t19))))) % 208.00/208.81 (define @t40 () (lambda @t20 (or @t19 @t13))) % 208.00/208.81 (define @t41 () (@var "Z" $$unsorted)) % 208.00/208.81 (define @t42 () (_ @t12 @t41)) % 208.00/208.81 (define @t43 () (_ @t18 @t41)) % 208.00/208.81 (define @t44 () (and @t13 @t43)) % 208.00/208.81 (define @t45 () (@list @t9 @t8 @t41)) % 208.00/208.81 (define @t46 () (forall @t45 (=> @t44 @t42))) % 208.00/208.81 (define @t47 () (lambda @t5 @t46)) % 208.00/208.81 (define @t48 () (and (_ tptp.trans @t10) @t28)) % 208.00/208.81 (define @t49 () (=> @t48 @t11)) % 208.00/208.81 (define @t50 () (@list @t10)) % 208.00/208.81 (define @t51 () (forall @t50 @t49)) % 208.00/208.81 (define @t52 () (lambda @t20 @t51)) % 208.00/208.81 (define @t53 () (@var "__flatten_var_1" $$unsorted)) % 208.00/208.81 (define @t54 () (@var "__flatten_var_0" $$unsorted)) % 208.00/208.81 (define @t55 () (@list @t1 @t54 @t53)) % 208.00/208.81 (define @t56 () (lambda @t55 (_ (_ @t3 @t54) @t53))) % 208.00/208.81 (define @t57 () (lambda @t55 (_ (_ (_ tptp.sc @t3) @t54) @t53))) % 208.00/208.81 (define @t58 () (_ tptp.trans @t1)) % 208.00/208.81 (define @t59 () (lambda @t5 (and (_ tptp.refl @t1) (_ tptp.antisymm @t1) @t58))) % 208.00/208.81 (define @t60 () (lambda @t5 (and (_ tptp.asymm @t1) @t58))) % 208.00/208.81 (define @t61 () (lambda @t5 (forall @t14 (or @t34 @t13 @t19)))) % 208.00/208.81 (define @t62 () (not @t13)) % 208.00/208.81 (define @t63 () (@var "A" (-> $$unsorted Bool))) % 208.00/208.81 (define @t64 () (@list @t8)) % 208.00/208.81 (define @t65 () (_ @t63 @t9)) % 208.00/208.81 (define @t66 () (lambda @t5 (forall (@list @t63) (=> (exists @t31 @t65) (exists @t31 (and @t65 (forall @t64 (=> (_ @t63 @t8) @t62)))))))) % 208.00/208.81 (define @t67 () (@var "P" (-> $$unsorted Bool))) % 208.00/208.81 (define @t68 () (_ @t67 @t9)) % 208.00/208.81 (define @t69 () (lambda @t5 (forall (@list @t67) (=> (forall @t31 (=> (forall @t64 (=> (_ (_ @t2 @t9) @t8) (_ @t67 @t8))) @t68)) (forall @t31 @t68))))) % 208.00/208.81 (define @t70 () (lambda (@list @t1 @t9) (not (exists @t64 @t13)))) % 208.00/208.81 (define @t71 () (_ tptp.trc @t1)) % 208.00/208.81 (define @t72 () (_ @t71 @t8)) % 208.00/208.81 (define @t73 () (lambda @t20 (and (_ @t72 @t9) (_ (_ tptp.innf @t1) @t9)))) % 208.00/208.81 (define @t74 () (lambda @t5 (forall @t31 (exists @t64 (_ (_ (_ tptp.nfof @t1) @t8) @t9))))) % 208.00/208.81 (define @t75 () (_ @t71 @t9)) % 208.00/208.81 (define @t76 () (_ @t75 @t41)) % 208.00/208.81 (define @t77 () (lambda @t20 (exists (@list @t41) (and @t76 (_ @t72 @t41))))) % 208.00/208.81 (define @t78 () (_ tptp.join @t1)) % 208.00/208.81 (define @t79 () (_ (_ @t78 @t41) @t8)) % 208.00/208.81 (define @t80 () (lambda @t5 (forall @t45 (=> (and @t42 @t13) @t79)))) % 208.00/208.81 (define @t81 () (_ @t75 @t8)) % 208.00/208.81 (define @t82 () (lambda @t5 (forall @t45 (=> (and @t42 @t81) @t79)))) % 208.00/208.81 (define @t83 () (lambda @t5 (forall @t45 (=> (and @t76 @t81) @t79)))) % 208.00/208.81 (define @t84 () (lambda @t5 (forall @t14 (=> (_ (_ (_ tptp.trsc @t1) @t9) @t8) (_ (_ @t78 @t9) @t8))))) % 208.00/208.81 (define @t85 () (_ @t10 @t9 @t8)) % 208.00/208.81 (define @t86 () (@var "BOUND_VARIABLE_8873" $$unsorted)) % 208.00/208.81 (define @t87 () (@var "BOUND_VARIABLE_8871" $$unsorted)) % 208.00/208.81 (define @t88 () (_ @t10 @t87 @t86)) % 208.00/208.81 (define @t89 () (@list @t87 @t86)) % 208.00/208.81 (define @t90 () (forall @t89 (or (not (_ @t1 @t87 @t86)) @t88))) % 208.00/208.81 (define @t91 () (not @t90)) % 208.00/208.81 (define @t92 () (@var "BOUND_VARIABLE_8863" $$unsorted)) % 208.00/208.81 (define @t93 () (_ @t10 @t92 @t92)) % 208.00/208.81 (define @t94 () (@list @t92)) % 208.00/208.81 (define @t95 () (forall @t94 @t93)) % 208.00/208.81 (define @t96 () (not @t95)) % 208.00/208.81 (define @t97 () (@var "BOUND_VARIABLE_7756" $$unsorted)) % 208.00/208.81 (define @t98 () (@var "BOUND_VARIABLE_7758" $$unsorted)) % 208.00/208.81 (define @t99 () (@list @t97 @t98 @t41)) % 208.00/208.81 (define @t100 () (not (forall @t99 (or (not (_ @t10 @t97 @t98)) (not (_ @t10 @t98 @t41)) (_ @t10 @t97 @t41))))) % 208.00/208.81 (define @t101 () (or @t100 @t96 @t91 @t85)) % 208.00/208.81 (define @t102 () (lambda @t14 (forall @t50 @t101))) % 208.00/208.81 (define @t103 () (@var "BOUND_VARIABLE_7747" $$unsorted)) % 208.00/208.81 (define @t104 () (@var "BOUND_VARIABLE_7745" $$unsorted)) % 208.00/208.81 (define @t105 () (_ @t10 @t104 @t103)) % 208.00/208.81 (define @t106 () (_ @t1 @t104 @t103)) % 208.00/208.81 (define @t107 () (not @t106)) % 208.00/208.81 (define @t108 () (or @t107 @t105)) % 208.00/208.81 (define @t109 () (@list @t104 @t103)) % 208.00/208.81 (define @t110 () (forall @t109 @t108)) % 208.00/208.81 (define @t111 () (forall @t50 (or @t100 (not @t110) @t85))) % 208.00/208.81 (define @t112 () (lambda @t14 (or @t34 @t111))) % 208.00/208.81 (define @t113 () (lambda @t64 @t111)) % 208.00/208.81 (define @t114 () (lambda @t14 @t111)) % 208.00/208.81 (define @t115 () (_ @t114 @t9)) % 208.00/208.81 (define @t116 () (or @t34 (_ @t115 @t8))) % 208.00/208.81 (define @t117 () (lambda @t14 @t116)) % 208.00/208.81 (define @t118 () (lambda @t20 @t111)) % 208.00/208.81 (define @t119 () (_ @t1 @t9 @t8)) % 208.00/208.81 (define @t120 () (not @t119)) % 208.00/208.81 (define @t121 () (forall @t14 (or @t120 @t85))) % 208.00/208.81 (define @t122 () (not @t121)) % 208.00/208.81 (define @t123 () (forall @t45 (or (not @t85) (not (_ @t10 @t8 @t41)) (_ @t10 @t9 @t41)))) % 208.00/208.81 (define @t124 () (not @t123)) % 208.00/208.81 (define @t125 () (lambda @t20 (forall @t50 (or @t124 @t122 @t85)))) % 208.00/208.81 (define @t126 () (or @t100 (not (and @t95 @t90)) @t85)) % 208.00/208.81 (define @t127 () (not (= @t92 @t92))) % 208.00/208.81 (define @t128 () (or @t127 @t93)) % 208.00/208.81 (define @t129 () (@var "BOUND_VARIABLE_8861" $$unsorted)) % 208.00/208.81 (define @t130 () (_ @t10 @t129 @t92)) % 208.00/208.81 (define @t131 () (not (= @t129 @t92))) % 208.00/208.81 (define @t132 () (or @t131 @t131 @t130)) % 208.00/208.81 (define @t133 () (@list @t129)) % 208.00/208.81 (define @t134 () (or @t131 @t130)) % 208.00/208.81 (define @t135 () (forall @t133 @t134)) % 208.00/208.81 (define @t136 () (forall @t94 @t135)) % 208.00/208.81 (define @t137 () (forall (@list @t92 @t129) @t134)) % 208.00/208.81 (define @t138 () (forall (@list @t129 @t92) @t134)) % 208.00/208.81 (define @t139 () (@list @t104 @t103)) % 208.00/208.81 (define @t140 () (@list @t87 @t86)) % 208.00/208.81 (define @t141 () (= @t104 @t103)) % 208.00/208.81 (define @t142 () (not @t141)) % 208.00/208.81 (define @t143 () (or @t142 @t105)) % 208.00/208.81 (define @t144 () (forall @t109 @t143)) % 208.00/208.81 (define @t145 () (and @t144 @t110)) % 208.00/208.81 (define @t146 () (_ (_ @t1 @t104) @t103)) % 208.00/208.81 (define @t147 () (not @t146)) % 208.00/208.81 (define @t148 () (and @t142 @t147)) % 208.00/208.81 (define @t149 () (or @t148 @t105)) % 208.00/208.81 (define @t150 () (or @t141 @t146)) % 208.00/208.81 (define @t151 () (or (not @t150) @t105)) % 208.00/208.81 (define @t152 () (lambda @t14 @t35)) % 208.00/208.81 (define @t153 () (_ @t152 @t104 @t103)) % 208.00/208.81 (define @t154 () (not @t153)) % 208.00/208.81 (define @t155 () (or @t154 @t105)) % 208.00/208.81 (define @t156 () (forall @t109 @t155)) % 208.00/208.81 (define @t157 () (not @t156)) % 208.00/208.81 (define @t158 () (or @t100 @t157 @t85)) % 208.00/208.81 (define @t159 () (forall @t50 @t158)) % 208.00/208.81 (define @t160 () (lambda @t14 @t159)) % 208.00/208.81 (define @t161 () (_ @t36 @t1)) % 208.00/208.81 (define @t162 () (= (_ @t125 @t161) (_ @t36 (_ @t125 @t1)))) % 208.00/208.81 (define @t163 () (forall @t5 @t162)) % 208.00/208.81 (define @t164 () (or @t124 @t122 @t11)) % 208.00/208.81 (define @t165 () (and @t123 @t121)) % 208.00/208.81 (define @t166 () (lambda @t50 @t121)) % 208.00/208.81 (define @t167 () (_ (lambda @t16 @t121) @t1)) % 208.00/208.81 (define @t168 () (_ @t1 @t9 @t41)) % 208.00/208.81 (define @t169 () (_ @t1 @t8 @t41)) % 208.00/208.81 (define @t170 () (_ (lambda @t5 (forall @t45 (or @t120 (not @t169) @t168))) @t10)) % 208.00/208.81 (define @t171 () (and @t170 (_ @t167 @t10))) % 208.00/208.81 (define @t172 () (=> @t171 @t11)) % 208.00/208.81 (define @t173 () (or @t62 @t11)) % 208.00/208.81 (define @t174 () (not @t43)) % 208.00/208.81 (define @t175 () (or @t62 @t174 @t42)) % 208.00/208.81 (define @t176 () (forall @t5 (= @t112 @t102))) % 208.00/208.81 (define @t177 () (@quantifiers_skolemize @t176 0)) % 208.00/208.81 (define @t178 () (not (_ @t177 @t104 @t103))) % 208.00/208.81 (define @t179 () (not (forall @t109 (or @t178 @t105)))) % 208.00/208.81 (define @t180 () (lambda @t14 (or @t34 (forall @t50 (or @t100 @t179 @t85))))) % 208.00/208.81 (define @t181 () (@purify @t180)) % 208.00/208.81 (define @t182 () (not (_ @t177 @t87 @t86))) % 208.00/208.81 (define @t183 () (not (forall @t89 (or @t182 @t88)))) % 208.00/208.81 (define @t184 () (lambda @t14 (forall @t50 (or @t100 @t96 @t183 @t85)))) % 208.00/208.81 (define @t185 () (@purify @t184)) % 208.00/208.81 (define @t186 () (= @t185 @t181)) % 208.00/208.81 (define @t187 () (not @t186)) % 208.00/208.81 (define @t188 () (not @t176)) % 208.00/208.81 (define @t189 () (= @t180 @t184)) % 208.00/208.81 (define @t190 () (not @t189)) % 208.00/208.81 (define @t191 () (@list true)) % 208.00/208.81 (define @t192 () (@const 0 $$unsorted)) % 208.00/208.81 (define @t193 () (@const 1 $$unsorted)) % 208.00/208.81 (define @t194 () (_ @t10 @t193 @t192)) % 208.00/208.81 (define @t195 () (forall @t50 (or @t100 @t96 @t183 @t194))) % 208.00/208.81 (define @t196 () (forall @t50 (or @t100 @t179 @t194))) % 208.00/208.81 (define @t197 () (= @t193 @t192)) % 208.00/208.81 (define @t198 () (or @t197 @t196)) % 208.00/208.81 (define @t199 () (_ @t180 @t193 @t192)) % 208.00/208.81 (define @t200 () (_ @t181 @t193 @t192)) % 208.00/208.81 (define @t201 () (_ @t184 @t193 @t192)) % 208.00/208.81 (define @t202 () (_ @t185 @t193 @t192)) % 208.00/208.81 (define @t203 () (= @t202 @t200)) % 208.00/208.81 (define @t204 () (not @t203)) % 208.00/208.81 (define @t205 () (or @t186 @t204)) % 208.00/208.81 (define @t206 () (= @t198 @t195)) % 208.00/208.81 (define @t207 () (@quantifiers_skolemize @t195 0)) % 208.00/208.81 (define @t208 () (_ @t207 @t193 @t192)) % 208.00/208.81 (define @t209 () (forall @t89 (or @t182 (_ @t207 @t87 @t86)))) % 208.00/208.81 (define @t210 () (not @t209)) % 208.00/208.81 (define @t211 () (forall @t94 (_ @t207 @t92 @t92))) % 208.00/208.81 (define @t212 () (not @t211)) % 208.00/208.81 (define @t213 () (forall @t99 (or (not (_ @t207 @t97 @t98)) (not (_ @t207 @t98 @t41)) (_ @t207 @t97 @t41)))) % 208.00/208.81 (define @t214 () (not @t213)) % 208.00/208.81 (define @t215 () (or @t214 @t212 @t210 @t208)) % 208.00/208.81 (define @t216 () (not @t215)) % 208.00/208.81 (define @t217 () (not @t195)) % 208.00/208.81 (define @t218 () (forall @t109 (or @t178 (_ @t207 @t104 @t103)))) % 208.00/208.81 (define @t219 () (not @t218)) % 208.00/208.81 (define @t220 () (or @t214 @t219 @t208)) % 208.00/208.81 (define @t221 () (_ @t207 @t193 @t193)) % 208.00/208.81 (define @t222 () (not @t221)) % 208.00/208.81 (define @t223 () (not @t197)) % 208.00/208.81 (define @t224 () (not @t208)) % 208.00/208.81 (define @t225 () (and @t197 @t224)) % 208.00/208.81 (define @t226 () (not @t198)) % 208.00/208.81 (define @t227 () (@list true true)) % 208.00/208.81 (define @t228 () (forall @t89 (or @t182 (_ @t181 @t87 @t86)))) % 208.00/208.81 (define @t229 () (not @t228)) % 208.00/208.81 (define @t230 () (forall @t94 (_ @t181 @t92 @t92))) % 208.00/208.81 (define @t231 () (not @t230)) % 208.00/208.81 (define @t232 () (forall @t99 (or (not (_ @t181 @t97 @t98)) (not (_ @t181 @t98 @t41)) (_ @t181 @t97 @t41)))) % 208.00/208.81 (define @t233 () (not @t232)) % 208.00/208.81 (define @t234 () (or @t233 @t231 @t229 @t197 @t196)) % 208.00/208.81 (define @t235 () (or @t233 @t231 @t229 @t200)) % 208.00/208.81 (define @t236 () (@list false)) % 208.00/208.81 (define @t237 () (@quantifiers_skolemize @t230 0)) % 208.00/208.81 (define @t238 () (forall @t50 (or @t100 @t179 (_ @t10 @t237 @t237)))) % 208.00/208.81 (define @t239 () (or (= @t237 @t237) @t238)) % 208.00/208.81 (define @t240 () (_ @t181 @t237 @t237)) % 208.00/208.81 (define @t241 () (not @t240)) % 208.00/208.81 (define @t242 () (@quantifiers_skolemize @t232 1)) % 208.00/208.81 (define @t243 () (@quantifiers_skolemize @t232 0)) % 208.00/208.81 (define @t244 () (forall @t50 (or @t100 @t179 (_ @t10 @t243 @t242)))) % 208.00/208.81 (define @t245 () (= @t243 @t242)) % 208.00/208.81 (define @t246 () (or @t245 @t244)) % 208.00/208.81 (define @t247 () (@quantifiers_skolemize @t232 2)) % 208.00/208.81 (define @t248 () (forall @t50 (or @t100 @t179 (_ @t10 @t243 @t247)))) % 208.00/208.81 (define @t249 () (= @t243 @t247)) % 208.00/208.81 (define @t250 () (forall @t50 (or @t100 @t179 (_ @t10 @t242 @t247)))) % 208.00/208.81 (define @t251 () (= @t242 @t247)) % 208.00/208.81 (define @t252 () (or @t251 @t250)) % 208.00/208.81 (define @t253 () (not @t252)) % 208.00/208.81 (define @t254 () (not @t246)) % 208.00/208.81 (define @t255 () (or @t254 @t253 @t249 @t248)) % 208.00/208.81 (define @t256 () (@quantifiers_skolemize @t248 0)) % 208.00/208.81 (define @t257 () (_ @t256 @t243 @t247)) % 208.00/208.81 (define @t258 () (forall @t109 (or @t178 (_ @t256 @t104 @t103)))) % 208.00/208.81 (define @t259 () (not @t258)) % 208.00/208.81 (define @t260 () (forall @t99 (or (not (_ @t256 @t97 @t98)) (not (_ @t256 @t98 @t41)) (_ @t256 @t97 @t41)))) % 208.00/208.81 (define @t261 () (not @t260)) % 208.00/208.81 (define @t262 () (or @t261 @t259 @t257)) % 208.00/208.81 (define @t263 () (not @t262)) % 208.00/208.81 (define @t264 () (not @t248)) % 208.00/208.81 (define @t265 () (not @t251)) % 208.00/208.81 (define @t266 () (not @t245)) % 208.00/208.81 (define @t267 () (not @t249)) % 208.00/208.81 (define @t268 () (and @t245 @t267)) % 208.00/208.81 (define @t269 () (_ @t256 @t242 @t247)) % 208.00/208.81 (define @t270 () (not @t269)) % 208.00/208.81 (define @t271 () (not @t257)) % 208.00/208.81 (define @t272 () (not @t271)) % 208.00/208.81 (define @t273 () (and @t245 @t271)) % 208.00/208.81 (define @t274 () (or @t261 @t259 @t269)) % 208.00/208.81 (define @t275 () (@list @t256)) % 208.00/208.81 (define @t276 () (_ @t256 @t243 @t242)) % 208.00/208.81 (define @t277 () (or @t261 @t259 @t276)) % 208.00/208.81 (define @t278 () (not @t276)) % 208.00/208.81 (define @t279 () (and @t276 @t251 @t271)) % 208.00/208.81 (define @t280 () (or @t278 @t270 @t257)) % 208.00/208.81 (define @t281 () (not @t255)) % 208.00/208.81 (define @t282 () (or @t249 @t248)) % 208.00/208.81 (define @t283 () (_ @t180 @t243 @t247)) % 208.00/208.81 (define @t284 () (_ @t181 @t243 @t247)) % 208.00/208.81 (define @t285 () (_ @t180 @t242 @t247)) % 208.00/208.81 (define @t286 () (_ @t181 @t242 @t247)) % 208.00/208.81 (define @t287 () (not @t286)) % 208.00/208.81 (define @t288 () (_ @t180 @t243 @t242)) % 208.00/208.81 (define @t289 () (_ @t181 @t243 @t242)) % 208.00/208.81 (define @t290 () (not @t289)) % 208.00/208.81 (define @t291 () (or @t290 @t287 @t284)) % 208.00/208.81 (define @t292 () (not @t291)) % 208.00/208.81 (define @t293 () (@quantifiers_skolemize @t228 1)) % 208.00/208.81 (define @t294 () (@quantifiers_skolemize @t228 0)) % 208.00/208.81 (define @t295 () (forall @t50 (or @t100 @t179 (_ @t10 @t294 @t293)))) % 208.00/208.81 (define @t296 () (= @t294 @t293)) % 208.00/208.81 (define @t297 () (_ @t177 @t294 @t293)) % 208.00/208.81 (define @t298 () (not @t297)) % 208.00/208.81 (define @t299 () (or @t298 @t296 @t295)) % 208.00/208.81 (define @t300 () (not @t299)) % 208.00/208.81 (define @t301 () (or @t296 @t295)) % 208.00/208.81 (define @t302 () (= (_ @t180 @t294 @t293) @t301)) % 208.00/208.81 (define @t303 () (_ @t181 @t294 @t293)) % 208.00/208.81 (define @t304 () (or @t298 @t303)) % 208.00/208.81 (define @t305 () (not @t304)) % 208.00/208.81 (define @t306 () (not @t295)) % 208.00/208.81 (define @t307 () (@list @t299)) % 208.00/208.81 (define @t308 () (@quantifiers_skolemize @t295 0)) % 208.00/208.81 (define @t309 () (_ @t308 @t294 @t293)) % 208.00/208.81 (define @t310 () (forall @t109 (or @t178 (_ @t308 @t104 @t103)))) % 208.00/208.81 (define @t311 () (not @t310)) % 208.00/208.81 (define @t312 () (or (not (forall @t99 (or (not (_ @t308 @t97 @t98)) (not (_ @t308 @t98 @t41)) (_ @t308 @t97 @t41)))) @t311 @t309)) % 208.00/208.81 (define @t313 () (not @t312)) % 208.00/208.81 (define @t314 () (@list @t312)) % 208.00/208.81 (define @t315 () (or @t298 @t309)) % 208.00/208.81 (define @t316 () (not @t315)) % 208.00/208.81 (assume @p1 @t7) % 208.00/208.81 (assume @p2 true) % 208.00/208.81 (step @p3 (= tptp.subrel @t17) :rule refl :args (@t17)) % 208.00/208.81 (step @p4 (= tptp.inv @t21) :rule refl :args (@t21)) % 208.00/208.81 (step @p5 (= tptp.idem @t25) :rule refl :args (@t25)) % 208.00/208.81 (step @p6 (= tptp.infl @t27) :rule refl :args (@t27)) % 208.00/208.81 (step @p7 (= tptp.mono @t29) :rule refl :args (@t29)) % 208.00/208.81 (step @p8 (= tptp.refl @t32) :rule refl :args (@t32)) % 208.00/208.81 (step @p9 (= tptp.irrefl @t33) :rule refl :args (@t33)) % 208.00/208.81 (step @p10 (= tptp.rc @t36) :rule refl :args (@t36)) % 208.00/208.81 (step @p11 (= tptp.symm @t37) :rule refl :args (@t37)) % 208.00/208.81 (step @p12 (= tptp.antisymm @t38) :rule refl :args (@t38)) % 208.00/208.81 (step @p13 (= tptp.asymm @t39) :rule refl :args (@t39)) % 208.00/208.81 (step @p14 (= tptp.sc @t40) :rule refl :args (@t40)) % 208.00/208.81 (step @p15 (= tptp.trans @t47) :rule refl :args (@t47)) % 208.00/208.81 (step @p16 (= tptp.tc @t52) :rule refl :args (@t52)) % 208.00/208.81 (step @p17 (= tptp.trc @t56) :rule refl :args (@t56)) % 208.00/208.81 (step @p18 (= tptp.trsc @t57) :rule refl :args (@t57)) % 208.00/208.81 (step @p19 (= tptp.po @t59) :rule refl :args (@t59)) % 208.00/208.81 (step @p20 (= tptp.so @t60) :rule refl :args (@t60)) % 208.00/208.81 (step @p21 (= tptp.total @t61) :rule refl :args (@t61)) % 208.00/208.81 (step @p22 (= tptp.term @t66) :rule refl :args (@t66)) % 208.00/208.81 (step @p23 (= tptp.ind @t69) :rule refl :args (@t69)) % 208.00/208.81 (step @p24 (= tptp.innf @t70) :rule refl :args (@t70)) % 208.00/208.81 (step @p25 (= tptp.nfof @t73) :rule refl :args (@t73)) % 208.00/208.81 (step @p26 (= tptp.norm @t74) :rule refl :args (@t74)) % 208.00/208.81 (step @p27 (= tptp.join @t77) :rule refl :args (@t77)) % 208.00/208.81 (step @p28 (= tptp.lconfl @t80) :rule refl :args (@t80)) % 208.00/208.81 (step @p29 (= tptp.sconfl @t82) :rule refl :args (@t82)) % 208.00/208.81 (step @p30 (= tptp.confl @t83) :rule refl :args (@t83)) % 208.00/208.81 (step @p31 (= tptp.cr @t84) :rule refl :args (@t84)) % 208.00/208.81 (step @p32 :rule eq-symm :args (@t102 @t112)) % 208.00/208.81 (step @p33 :rule beta-reduce :args ((= (_ @t113 @t8) @t111))) % 208.00/208.81 (step @p34 :rule refl :args (@t8)) % 208.00/208.81 (step @p35 :rule beta-reduce :args ((= @t115 @t113))) % 208.00/208.81 (step @p36 :rule ho_cong :premises (@p35 @p34)) % 208.00/208.81 (step @p37 :rule trans :premises (@p36 @p33)) % 208.00/208.81 (step @p38 :rule refl :args (@t34)) % 208.00/208.81 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t116)) % 208.00/208.81 (step @p40 :rule cong :premises (@p39) :args (@t117)) % 208.00/208.81 (step @p41 :rule beta-reduce :args ((= (_ @t36 @t114) @t117))) % 208.00/208.81 (step @p42 :rule trans :premises (@p41 @p40)) % 208.00/208.81 (step @p43 :rule beta-reduce :args ((= (_ @t118 @t1) @t114))) % 208.00/208.81 (step @p44 :rule refl :args (@t1)) % 208.00/208.81 ; WARNING: add trust step for 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:rule and_intro :premises (@p695 @p693 @p694)) % 208.00/208.81 (step-pop @p696 :rule scope :premises (@p508)) % 208.00/208.81 (step-pop @p697 :rule scope :premises (@p696)) % 208.00/208.81 (step-pop @p698 :rule scope :premises (@p697)) % 208.00/208.81 (step @p509 :rule process_scope :premises (@p698) :args (@t279)) % 208.00/208.81 (step @p513 :rule implies_elim :premises (@p509)) % 208.00/208.81 (step @p514 :rule resolution :premises (@p513 @p501) :args (true @t279)) % 208.00/208.81 (step @p515 :rule not_and :premises (@p514)) % 208.00/208.81 (step @p516 :rule eq_resolve :premises (@p515 @p488)) % 208.00/208.81 (step @p517 :rule cnf_or_pos :args (@t280)) % 208.00/208.81 (step @p518 :rule reordering :premises (@p517) :args ((or @t257 @t270 @t278 (not @t280)))) % 208.00/208.81 (assume-push @p699 @t260) % 208.00/208.81 (step @p520 :rule instantiate :premises (@p699) :args ((@list @t243 @t242 @t247))) % 208.00/208.81 (step-pop @p700 :rule scope :premises (@p520)) % 208.00/208.81 (step @p521 :rule process_scope :premises (@p700) :args (@t280)) % 208.00/208.81 (step @p523 :rule implies_elim :premises (@p521)) % 208.00/208.81 (step @p524 :rule chain_m_resolution :premises (@p523 @p518 @p471 @p476 @p469 @p516 @p486 @p484 @p479 @p477 @p416 @p415 @p410 @p404 @p395 @p394 @p393 @p388) :args (@t255 (@list true false false false true false false false true true false false true true true false false) (@list @t280 @t269 @t274 @t250 @t251 @t276 @t277 @t244 @t245 @t257 @t258 @t260 @t262 @t248 @t249 @t252 @t246))) % 208.00/208.81 (step @p525 :rule refl :args (@t281)) % 208.00/208.81 (step @p526 :rule bool-double-not-elim :args (@t232)) % 208.00/208.81 (step @p527 :rule nary_cong :premises (@p526 @p525) :args ((or (not @t233) @t281))) % 208.00/208.81 (step @p528 :rule aci_norm :args ((= (or @t254 @t253 @t282) @t255))) % 208.00/208.81 (step @p529 :rule eq-refl :args (@t282)) % 208.00/208.81 (step @p530 :rule beta-reduce :args ((= @t283 @t282))) % 208.00/208.81 (step @p531 :rule refl :args (@t282)) % 208.00/208.81 (step @p532 :rule cong :premises (@p531 @p530) :args ((= @t282 @t283))) % 208.00/208.81 (step @p533 :rule trans :premises (@p532 @p529)) % 208.00/208.81 (step @p534 :rule eq-symm :args (@t283 @t282)) % 208.00/208.81 (step @p535 :rule trans :premises (@p534 @p533)) % 208.00/208.81 (step @p426 :rule refl :args (@t247)) % 208.00/208.81 (step @p495 :rule refl :args (@t243)) % 208.00/208.81 (step @p536 :rule ho_cong :premises (@p219 @p495 @p426)) % 208.00/208.81 (step @p537 :rule cong :premises (@p536 @p531) :args ((= @t284 @t282))) % 208.00/208.81 (step @p538 :rule trans :premises (@p537 @p535)) % 208.00/208.81 (step @p539 :rule true_elim :premises (@p538)) % 208.00/208.81 (step @p540 :rule eq-refl :args (@t252)) % 208.00/208.81 (step @p541 :rule beta-reduce :args ((= @t285 @t252))) % 208.00/208.81 (step @p542 :rule refl :args (@t252)) % 208.00/208.81 (step @p543 :rule cong :premises (@p542 @p541) :args ((= @t252 @t285))) % 208.00/208.81 (step @p544 :rule trans :premises (@p543 @p540)) % 208.00/208.81 (step @p545 :rule eq-symm :args (@t285 @t252)) % 208.00/208.81 (step @p546 :rule trans :premises (@p545 @p544)) % 208.00/208.81 (step @p547 :rule refl :args (@t242)) % 208.00/208.81 (step @p548 :rule ho_cong :premises (@p219 @p547 @p426)) % 208.00/208.81 (step @p549 :rule cong :premises (@p548 @p542) :args ((= @t286 @t252))) % 208.00/208.81 (step @p550 :rule trans :premises (@p549 @p546)) % 208.00/208.81 (step @p551 :rule true_elim :premises (@p550)) % 208.00/208.81 (step @p552 :rule cong :premises (@p551) :args (@t287)) % 208.00/208.81 (step @p553 :rule eq-refl :args (@t246)) % 208.00/208.81 (step @p554 :rule beta-reduce :args ((= @t288 @t246))) % 208.00/208.81 (step @p555 :rule refl :args (@t246)) % 208.00/208.81 (step @p556 :rule cong :premises (@p555 @p554) :args ((= @t246 @t288))) % 208.00/208.81 (step @p557 :rule trans :premises (@p556 @p553)) % 208.00/208.81 (step @p558 :rule eq-symm :args (@t288 @t246)) % 208.00/208.81 (step @p559 :rule trans :premises (@p558 @p557)) % 208.00/208.81 (step @p560 :rule ho_cong :premises (@p219 @p495 @p547)) % 208.00/208.81 (step @p561 :rule cong :premises (@p560 @p555) :args ((= @t289 @t246))) % 208.00/208.81 (step @p562 :rule trans :premises (@p561 @p559)) % 208.00/208.81 (step @p563 :rule true_elim :premises (@p562)) % 208.00/208.81 (step @p564 :rule cong :premises (@p563) :args (@t290)) % 208.00/208.81 (step @p565 :rule nary_cong :premises (@p564 @p552 @p539) :args (@t291)) % 208.00/208.81 (step @p566 :rule trans :premises (@p565 @p528)) % 208.00/208.81 (step @p567 :rule cong :premises (@p566) :args (@t292)) % 208.00/208.81 (step @p568 :rule cong :premises (@p348 @p567) :args ((=> @t233 @t292))) % 208.00/208.81 (assume-push @p701 @t233) % 208.00/208.81 (step @p570 :rule skolemize :premises (@p701)) % 208.00/208.81 (step-pop @p702 :rule scope :premises (@p570)) % 208.00/208.81 (step @p571 :rule process_scope :premises (@p702) :args (@t292)) % 208.00/208.81 (step @p573 :rule eq_resolve :premises (@p571 @p568)) % 208.00/208.81 (step @p574 :rule implies_elim :premises (@p573)) % 208.00/208.81 (step @p575 :rule eq_resolve :premises (@p574 @p527)) % 208.00/208.81 (step @p576 :rule chain_m_resolution :premises (@p575 @p524) :args (@t232 @t236 (@list @t255))) % 208.00/208.81 (step @p577 :rule cnf_or_pos :args (@t234)) % 208.00/208.81 (step @p578 :rule reordering :premises (@p577) :args ((or @t197 @t196 @t233 @t231 @t229 (not @t234)))) % 208.00/208.81 (step @p579 :rule chain_m_resolution :premises (@p578 @p338 @p302 @p576 @p382 @p358) :args (@t229 (@list true true false false false) (@list @t197 @t196 @t232 @t230 @t234))) % 208.00/208.81 (step @p580 :rule refl :args (@t300)) % 208.00/208.81 (step @p581 :rule bool-double-not-elim :args (@t228)) % 208.00/208.81 (step @p582 :rule nary_cong :premises (@p581 @p580) :args ((or (not @t229) @t300))) % 208.00/208.81 (step @p583 :rule aci_norm :args ((= (or @t298 @t301) @t299))) % 208.00/208.81 (step @p584 :rule eq-refl :args (@t301)) % 208.00/208.81 (step @p585 :rule refl :args (@t301)) % 208.00/208.81 (step @p586 :rule beta-reduce :args (@t302)) % 208.00/208.81 (step @p587 :rule cong :premises (@p586 @p585) :args (@t302)) % 208.00/208.81 (step @p588 :rule trans :premises (@p587 @p584)) % 208.00/208.81 (step @p589 :rule refl :args (@t293)) % 208.00/208.81 (step @p590 :rule refl :args (@t294)) % 208.00/208.81 (step @p591 :rule ho_cong :premises (@p219 @p590 @p589)) % 208.00/208.81 (step @p592 :rule cong :premises (@p591 @p585) :args ((= @t303 @t301))) % 208.00/208.81 (step @p593 :rule trans :premises (@p592 @p588)) % 208.00/208.81 (step @p594 :rule true_elim :premises (@p593)) % 208.00/208.81 (step @p595 :rule refl :args (@t298)) % 208.00/208.81 (step @p596 :rule nary_cong :premises (@p595 @p594) :args (@t304)) % 208.00/208.81 (step @p597 :rule trans :premises (@p596 @p583)) % 208.00/208.81 (step @p598 :rule cong :premises (@p597) :args (@t305)) % 208.00/208.81 (step @p599 :rule cong :premises (@p346 @p598) :args ((=> @t229 @t305))) % 208.00/208.81 (assume-push @p703 @t229) % 208.00/208.81 (step @p601 :rule skolemize :premises (@p703)) % 208.00/208.81 (step-pop @p704 :rule scope :premises (@p601)) % 208.00/208.81 (step @p602 :rule process_scope :premises (@p704) :args (@t305)) % 208.00/208.81 (step @p604 :rule eq_resolve :premises (@p602 @p599)) % 208.00/208.81 (step @p605 :rule implies_elim :premises (@p604)) % 208.00/208.81 (step @p606 :rule eq_resolve :premises (@p605 @p582)) % 208.00/208.81 (step @p607 :rule chain_m_resolution :premises (@p606 @p579) :args (@t300 @t191 (@list @t228))) % 208.00/208.81 (step @p608 :rule cnf_or_neg :args (@t299 2)) % 208.00/208.81 (step @p609 :rule chain_m_resolution :premises (@p608 @p607) :args (@t306 @t191 @t307)) % 208.00/208.81 (step @p610 :rule refl :args (@t313)) % 208.00/208.81 (step @p611 :rule bool-double-not-elim :args (@t295)) % 208.00/208.81 (step @p612 :rule nary_cong :premises (@p611 @p610) :args ((or (not @t306) @t313))) % 208.00/208.81 (assume-push @p705 @t306) % 208.00/208.81 (step @p614 :rule skolemize :premises (@p705)) % 208.00/208.81 (step-pop @p706 :rule scope :premises (@p614)) % 208.00/208.81 (step @p615 :rule process_scope :premises (@p706) :args (@t313)) % 208.00/208.81 (step @p617 :rule implies_elim :premises (@p615)) % 208.00/208.81 (step @p618 :rule eq_resolve :premises (@p617 @p612)) % 208.00/208.81 (step @p619 :rule chain_m_resolution :premises (@p618 @p609) :args (@t313 @t191 (@list @t295))) % 208.00/208.81 (step @p620 :rule bool-double-not-elim :args (@t310)) % 208.00/208.81 (step @p621 :rule refl :args (@t312)) % 208.00/208.81 (step @p622 :rule nary_cong :premises (@p621 @p620) :args ((or @t312 (not @t311)))) % 208.00/208.81 (step @p623 :rule cnf_or_neg :args (@t312 1)) % 208.00/208.81 (step @p624 :rule eq_resolve :premises (@p623 @p622)) % 208.00/208.81 (step @p625 :rule reordering :premises (@p624) :args ((or @t310 @t312))) % 208.00/208.81 (step @p626 :rule chain_m_resolution :premises (@p625 @p619) :args (@t310 @t191 @t314)) % 208.00/208.81 (step @p627 :rule cnf_or_neg :args (@t312 2)) % 208.00/208.81 (step @p628 :rule chain_m_resolution :premises (@p627 @p619) :args ((not @t309) @t191 @t314)) % 208.00/208.81 (step @p629 :rule bool-double-not-elim :args (@t297)) % 208.00/208.81 (step @p630 :rule refl :args (@t299)) % 208.00/208.81 (step @p631 :rule nary_cong :premises (@p630 @p629) :args ((or @t299 (not @t298)))) % 208.00/208.81 (step @p632 :rule cnf_or_neg :args (@t299 0)) % 208.00/208.81 (step @p633 :rule eq_resolve :premises (@p632 @p631)) % 208.00/208.81 (step @p634 :rule reordering :premises (@p633) :args ((or @t297 @t299))) % 208.00/208.81 (step @p635 :rule chain_m_resolution :premises (@p634 @p607) :args (@t297 @t191 @t307)) % 208.00/208.81 (step @p636 :rule cnf_or_pos :args (@t315)) % 208.00/208.81 (step @p637 :rule reordering :premises (@p636) :args ((or @t298 @t309 @t316))) % 208.00/208.81 (step @p638 :rule chain_m_resolution :premises (@p637 @p635 @p628) :args (@t316 (@list false true) (@list @t297 @t309))) % 208.00/208.81 (assume-push @p707 @t310) % 208.00/208.81 (step @p640 :rule instantiate :premises (@p707) :args ((@list @t294 @t293))) % 208.00/208.81 (step-pop @p708 :rule scope :premises (@p640)) % 208.00/208.81 (step @p641 :rule process_scope :premises (@p708) :args (@t315)) % 208.00/208.81 (step @p643 :rule implies_elim :premises (@p641)) % 208.00/208.81 (step @p644 false :rule chain_m_resolution :premises (@p643 @p638 @p626) :args (false (@list true false) (@list @t315 @t310))) % 208.00/208.81 ) % 208.00/208.81 % SZS output end Proof % 208.00/208.82 % cvc5 exiting %------------------------------------------------------------------------------